Nonlinear Force-Free Field Extrapolation of NOAA AR 0696
NASA Astrophysics Data System (ADS)
Thalmann, J. K.; Wiegelmann, T.
2007-12-01
We investigate the 3D coronal magnetic field structure of NOAA AR 0696 in the period of November 09-11, 2004, before and after an X2.5 flare (occurring around 02:13 UT on November 10, 2004). The coronal magnetic field dominates the structure of the solar corona and consequently plays a key role for the understanding of the initiation of flares. The most accurate presently available method to derive the coronal magnetic field is currently the nonlinear force-free field extrapolation from measurements of the photospheric magnetic field vector. These vector-magnetograms were processed from stokes I, Q, U, and V measurements of the Big Bear Solar Observatory and extrapolated into the corona with the nonlinear force-free optimization code developed by Wiegelmann (2004). We analyze the corresponding time series of coronal equilibria regarding topology changes of the 3D coronal magnetic field during the flare. Furthermore, quantities such as the temporal evolution of the magnetic energy and helicity are computed.
Error analysis regarding the calculation of nonlinear force-free field
NASA Astrophysics Data System (ADS)
Liu, S.; Zhang, H. Q.; Su, J. T.
2012-02-01
Magnetic field extrapolation is an alternative method to study chromospheric and coronal magnetic fields. In this paper, two semi-analytical solutions of force-free fields (Low and Lou in Astrophys. J. 352:343, 1990) have been used to study the errors of nonlinear force-free (NLFF) fields based on force-free factor α. Three NLFF fields are extrapolated by approximate vertical integration (AVI) Song et al. (Astrophys. J. 649:1084, 2006), boundary integral equation (BIE) Yan and Sakurai (Sol. Phys. 195:89, 2000) and optimization (Opt.) Wiegelmann (Sol. Phys. 219:87, 2004) methods. Compared with the first semi-analytical field, it is found that the mean values of absolute relative standard deviations (RSD) of α along field lines are about 0.96-1.19, 0.63-1.07 and 0.43-0.72 for AVI, BIE and Opt. fields, respectively. While for the second semi-analytical field, they are about 0.80-1.02, 0.67-1.34 and 0.33-0.55 for AVI, BIE and Opt. fields, respectively. As for the analytical field, the calculation error of <| RSD|> is about 0.1˜0.2. It is also found that RSD does not apparently depend on the length of field line. These provide the basic estimation on the deviation of extrapolated field obtained by proposed methods from the real force-free field.
A nonlinear eigenvalue problem for self-similar spherical force-free magnetic fields
NASA Astrophysics Data System (ADS)
Lerche, I.; Low, B. C.
2014-10-01
An axisymmetric force-free magnetic field B(r, θ) in spherical coordinates is defined by a function r sin θ B φ = Q ( A ) relating its azimuthal component to its poloidal flux-function A. The power law r sin θ B φ = a A | A | 1/ n, n a positive constant, admits separable fields with A = An/(θ)rn, posing a nonlinear boundary-value problem for the constant parameter a as an eigenvalue and An(θ) as its eigenfunction [B. C. Low and Y. Q Lou, Astrophys. J. 352, 343 (1990)]. A complete analysis is presented of the eigenvalue spectrum for a given n, providing a unified understanding of the eigenfunctions and the physical relationship between the field's degree of multi-polarity and rate of radial decay via the parameter n. These force-free fields, self-similar on spheres of constant r, have basic astrophysical applications. As explicit solutions they have, over the years, served as standard benchmarks for testing 3D numerical codes developed to compute general force-free fields in the solar corona. The study presented includes a set of illustrative multipolar field solutions to address the magnetohydrodynamics (MHD) issues underlying the observation that the solar corona has a statistical preference for negative and positive magnetic helicities in its northern and southern hemispheres, respectively; a hemispherical effect, unchanging as the Sun's global field reverses polarity in successive eleven-year cycles. Generalizing these force-free fields to the separable form B = H/(θ ,φ)rn+2 promises field solutions of even richer topological varieties but allowing for φ-dependence greatly complicates the governing equations that have remained intractable. The axisymmetric results obtained are discussed in relation to this generalization and the Parker Magnetostatic Theorem. The axisymmetric solutions are mathematically related to a family of 3D time-dependent ideal MHD solutions for a polytropic fluid of index γ = 4/3 as discussed in the Appendix.
A NEW CODE FOR NONLINEAR FORCE-FREE FIELD EXTRAPOLATION OF THE GLOBAL CORONA
Jiang Chaowei; Feng Xueshang; Xiang Changqing
2012-08-10
Reliable measurements of the solar magnetic field are still restricted to the photosphere, and our present knowledge of the three-dimensional coronal magnetic field is largely based on extrapolations from photospheric magnetograms using physical models, e.g., the nonlinear force-free field (NLFFF) model that is usually adopted. Most of the currently available NLFFF codes have been developed with computational volume such as a Cartesian box or a spherical wedge, while a global full-sphere extrapolation is still under development. A high-performance global extrapolation code is in particular urgently needed considering that the Solar Dynamics Observatory can provide a full-disk magnetogram with resolution up to 4096 Multiplication-Sign 4096. In this work, we present a new parallelized code for global NLFFF extrapolation with the photosphere magnetogram as input. The method is based on the magnetohydrodynamics relaxation approach, the CESE-MHD numerical scheme, and a Yin-Yang spherical grid that is used to overcome the polar problems of the standard spherical grid. The code is validated by two full-sphere force-free solutions from Low and Lou's semi-analytic force-free field model. The code shows high accuracy and fast convergence, and can be ready for future practical application if combined with an adaptive mesh refinement technique.
NASA Technical Reports Server (NTRS)
Tadesse, T.; Wiegelmann, T.; Gosain, S.; MacNeice, P.; Pevtsov, A. A.
2014-01-01
Context. The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently, there are several modelling techniques being used to calculate three-dimensional field lines into the solar atmosphere. Aims. For the first time, synoptic maps of a photospheric-vector magnetic field synthesized from the vector spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model the coronal magnetic field and estimate free magnetic energy in the global scale. The free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. Methods. We solve the nonlinear force-free field equations using an optimization principle in spherical geometry. The resulting threedimensional magnetic fields are used to estimate the magnetic free energy content E(sub free) = E(sub nlfff) - E(sub pot), which is the difference of the magnetic energies between the nonpotential field and the potential field in the global solar corona. For comparison, we overlay the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the atmospheric imaging assembly (AIA) on board the Solar Dynamics Observatory (SDO). Results. For a single Carrington rotation 2121, we find that the global nonlinear force-free field (NLFFF) magnetic energy density is 10.3% higher than the potential one. Most of this free energy is located in active regions.
Study on Two Methods for Nonlinear Force-Free Extrapolation Based on Semi-Analytical Field
NASA Astrophysics Data System (ADS)
Liu, S.; Zhang, H. Q.; Su, J. T.; Song, M. T.
2011-03-01
In this paper, two semi-analytical solutions of force-free fields (Low and Lou, Astrophys. J. 352, 343, 1990) have been used to test two nonlinear force-free extrapolation methods. One is the boundary integral equation (BIE) method developed by Yan and Sakurai ( Solar Phys. 195, 89, 2000), and the other is the approximate vertical integration (AVI) method developed by Song et al. ( Astrophys. J. 649, 1084, 2006). Some improvements have been made to the AVI method to avoid the singular points in the process of calculation. It is found that the correlation coefficients between the first semi-analytical field and extrapolated field using the BIE method, and also that obtained by the improved AVI method, are greater than 90% below a height 10 of the 64×64 lower boundary. For the second semi-analytical field, these correlation coefficients are greater than 80% below the same relative height. Although differences between the semi-analytical solutions and the extrapolated fields exist for both the BIE and AVI methods, these two methods can give reliable results for heights of about 15% of the extent of the lower boundary.
A nonlinear eigenvalue problem for self-similar spherical force-free magnetic fields
Lerche, I.; Low, B. C.
2014-10-15
An axisymmetric force-free magnetic field B(r, θ) in spherical coordinates is defined by a function r sin θB{sub φ}=Q(A) relating its azimuthal component to its poloidal flux-function A. The power law r sin θB{sub φ}=aA|A|{sup 1/n}, n a positive constant, admits separable fields with A=(A{sub n}(θ))/(r{sup n}) , posing a nonlinear boundary-value problem for the constant parameter a as an eigenvalue and A{sub n}(θ) as its eigenfunction [B. C. Low and Y. Q Lou, Astrophys. J. 352, 343 (1990)]. A complete analysis is presented of the eigenvalue spectrum for a given n, providing a unified understanding of the eigenfunctions and the physical relationship between the field's degree of multi-polarity and rate of radial decay via the parameter n. These force-free fields, self-similar on spheres of constant r, have basic astrophysical applications. As explicit solutions they have, over the years, served as standard benchmarks for testing 3D numerical codes developed to compute general force-free fields in the solar corona. The study presented includes a set of illustrative multipolar field solutions to address the magnetohydrodynamics (MHD) issues underlying the observation that the solar corona has a statistical preference for negative and positive magnetic helicities in its northern and southern hemispheres, respectively; a hemispherical effect, unchanging as the Sun's global field reverses polarity in successive eleven-year cycles. Generalizing these force-free fields to the separable form B=(H(θ,φ))/(r{sup n+2}) promises field solutions of even richer topological varieties but allowing for φ-dependence greatly complicates the governing equations that have remained intractable. The axisymmetric results obtained are discussed in relation to this generalization and the Parker Magnetostatic Theorem. The axisymmetric solutions are mathematically related to a family of 3D time-dependent ideal MHD solutions for a polytropic fluid of index γ = 4/3 as
Inoue, S.; Magara, T.; Choe, G. S.; Kim, K. S.; Pandey, V. S.; Shiota, D.; Kusano, K.
2014-01-01
We develop a nonlinear force-free field (NLFFF) extrapolation code based on the magnetohydrodynamic (MHD) relaxation method. We extend the classical MHD relaxation method in two important ways. First, we introduce an algorithm initially proposed by Dedner et al. to effectively clean the numerical errors associated with ∇ · B . Second, the multigrid type method is implemented in our NLFFF to perform direct analysis of the high-resolution magnetogram data. As a result of these two implementations, we successfully extrapolated the high resolution force-free field introduced by Low and Lou with better accuracy in a drastically shorter time. We also applied our extrapolation method to the MHD solution obtained from the flux-emergence simulation by Magara. We found that NLFFF extrapolation may be less effective for reproducing areas higher than a half-domain, where some magnetic loops are found in a state of continuous upward expansion. However, an inverse S-shaped structure consisting of the sheared and twisted loops formed in the lower region can be captured well through our NLFFF extrapolation method. We further discuss how well these sheared and twisted fields are reconstructed by estimating the magnetic topology and twist quantitatively.
NONLINEAR FORCE-FREE MAGNETIC FIELD FITTING TO CORONAL LOOPS WITH AND WITHOUT STEREOSCOPY
Aschwanden, Markus J.
2013-02-15
We developed a new nonlinear force-free magnetic field (NLFFF) forward-fitting algorithm based on an analytical approximation of force-free and divergence-free NLFFF solutions, which requires as input a line-of-sight magnetogram and traced two-dimensional (2D) loop coordinates of coronal loops only, in contrast to stereoscopically triangulated three-dimensional loop coordinates used in previous studies. Test results of simulated magnetic configurations and from four active regions observed with STEREO demonstrate that NLFFF solutions can be fitted with equal accuracy with or without stereoscopy, which relinquishes the necessity of STEREO data for magnetic modeling of active regions (on the solar disk). The 2D loop tracing method achieves a 2D misalignment of {mu}{sub 2} = 2. Degree-Sign 7 {+-} 1. Degree-Sign 3 between the model field lines and observed loops, and an accuracy of Almost-Equal-To 1.0% for the magnetic energy or free magnetic energy ratio. The three times higher spatial resolution of TRACE or SDO/AIA (compared with STEREO) also yields a proportionally smaller misalignment angle between model fit and observations. Visual/manual loop tracings are found to produce more accurate magnetic model fits than automated tracing algorithms. The computation time of the new forward-fitting code amounts to a few minutes per active region.
Nonlinear Force-free Magnetic Field Fitting to Coronal Loops with and without Stereoscopy
NASA Astrophysics Data System (ADS)
Aschwanden, Markus J.
2013-02-01
We developed a new nonlinear force-free magnetic field (NLFFF) forward-fitting algorithm based on an analytical approximation of force-free and divergence-free NLFFF solutions, which requires as input a line-of-sight magnetogram and traced two-dimensional (2D) loop coordinates of coronal loops only, in contrast to stereoscopically triangulated three-dimensional loop coordinates used in previous studies. Test results of simulated magnetic configurations and from four active regions observed with STEREO demonstrate that NLFFF solutions can be fitted with equal accuracy with or without stereoscopy, which relinquishes the necessity of STEREO data for magnetic modeling of active regions (on the solar disk). The 2D loop tracing method achieves a 2D misalignment of μ2 = 2.°7 ± 1.°3 between the model field lines and observed loops, and an accuracy of ≈1.0% for the magnetic energy or free magnetic energy ratio. The three times higher spatial resolution of TRACE or SDO/AIA (compared with STEREO) also yields a proportionally smaller misalignment angle between model fit and observations. Visual/manual loop tracings are found to produce more accurate magnetic model fits than automated tracing algorithms. The computation time of the new forward-fitting code amounts to a few minutes per active region.
Full-disk nonlinear force-free field extrapolation of SDO/HMI and SOLIS/VSM magnetograms
NASA Astrophysics Data System (ADS)
Tadesse, T.; Wiegelmann, T.; Inhester, B.; MacNeice, P.; Pevtsov, A.; Sun, X.
2013-02-01
Context. The magnetic field configuration is essential for understanding solar explosive phenomena, such as flares and coronal mass ejections. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Two complications of this approach are that the measured photospheric magnetic field is not force-free and that one has to apply a preprocessing routine to achieve boundary conditions suitable for the force-free modeling. Furthermore the nonlinear force-free extrapolation code should take uncertainties into account in the photospheric field data. They occur due to noise, incomplete inversions, or azimuth ambiguity-removing techniques. Aims: Extrapolation codes in Cartesian geometry for modeling the magnetic field in the corona do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, e.g., a single active region. Here we apply a method for nonlinear force-free coronal magnetic field modeling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure to full disk vector magnetograms. We compare the analysis of the photospheric magnetic field and subsequent force-free modeling based on full-disk vector maps from Helioseismic and Magnetic Imager (HMI) onboard the solar dynamics observatory (SDO) and Vector Spectromagnetograph (VSM) of the Synoptic Optical Long-term Investigations of the Sun (SOLIS). Methods: We used HMI and VSM photospheric magnetic field measurements to model the force-free coronal field above multiple solar active regions, assuming magnetic forces to dominate. We solved the nonlinear force-free field equations by minimizing a functional in spherical coordinates over a full disk and excluding the poles. After searching for the optimum modeling parameters for the particular data sets, we compared the resulting nonlinear force-free model fields. We compared
Magneto-frictional Modeling of Coronal Nonlinear Force-free Fields. II. Application to Observations
NASA Astrophysics Data System (ADS)
Guo, Y.; Xia, C.; Keppens, R.
2016-09-01
A magneto-frictional module has been implemented and tested in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC) in the first paper of this series. Here, we apply the magneto-frictional method to observations to demonstrate its applicability in both Cartesian and spherical coordinates, and in uniform and block-adaptive octree grids. We first reconstruct a nonlinear force-free field (NLFFF) on a uniform grid of 1803 cells in Cartesian coordinates, with boundary conditions provided by the vector magnetic field observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) at 06:00 UT on 2010 November 11 in active region NOAA 11123. The reconstructed NLFFF successfully reproduces the sheared and twisted field lines and magnetic null points. Next, we adopt a three-level block-adaptive grid to model the same active region with a higher spatial resolution on the bottom boundary and a coarser treatment of regions higher up. The force-free and divergence-free metrics obtained are comparable to the run with a uniform grid, and the reconstructed field topology is also very similar. Finally, a group of active regions, including NOAA 11401, 11402, 11405, and 11407, observed at 03:00 UT on 2012 January 23 by SDO/HMI is modeled with a five-level block-adaptive grid in spherical coordinates, where we reach a local resolution of 0\\buildrel{\\circ}\\over{.} 06 pixel‑1 in an area of 790 Mm × 604 Mm. Local high spatial resolution and a large field of view in NLFFF modeling can be achieved simultaneously in parallel and block-adaptive magneto-frictional relaxations.
Non-linear force-free field modeling: model techniques, boundary conditions, hares, and hounds
NASA Astrophysics Data System (ADS)
Schrijver, C. J.; De Rosa, M. L.; Metcalf, T.
2005-05-01
Understanding the conditions under which solar magnetic fields can destabilize to erupt in flares and coronal mass ejections requires a quantitative understanding of the coronal magnetic field and of the currents that it carries. The increased availability of vector magnetograms, together with EUV and X-ray coronal images, should provide adequate constraints to model the coronal field, and thus to visualize its 3D geometry and to measure the available free energy and helicity. Non-linear force-free fields (NLFFF) are likely a useful model to use when extrapolating the solar surface field upward into the coronal volume. It may even be possible to use the observed trajectories of coronal loops, evident in EUV images of the corona, as a further constraint. We present initial results of a team effort to understand the intricacies of NLFFF modeling: we discuss and evaluate comparisons of NLFFF models computed with different models and applications of boundary conditions, and look ahead to full coronal field modeling for the upcoming Solar-B and SDO missions.
Nonlinear force-free magnetic fields: Calculation and applicatin to astrophysics. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Yang, Wei-Hong
1987-01-01
The problem concerned in this work is that of calculating magnetic field configurations in which the Lorentz force (vector)j x (vector)B is everywhere zero, subject to specified boundary conditions. The magnetic field is represented in terms of Clebsch variables in the form (vector)B = del alpha x del beta. These variables are constant on any field line. The most appropriate choice of boundary conditions is to specify the values of alpha and beta on the bounding surface. It is proposed that the field lines move in the direction of local Lorentz force and relax towards a force-free field configuration. This concept leads to an iteration procedure for modifying the variables alpha and beta that tends asymptotically towards the force-free state. This method is first applied to a simple problem in two rectangular dimensions; the calculation shows that the convergence of magnetic field energy to a minimum state (force-free) is close to exponential. This method is then applied to study some astrophysical force-free magnetic fields, such as the structures and evolution of magnetic fields of rotating sunspots and accretion disks. The implication of the results, as related to the mechanisms of solar flares, extragalactic radio sources and radio jets, are discussed.
Guo, Y.; Ding, M. D.; Liu, Y.; Sun, X. D.; DeRosa, M. L.; Wiegelmann, T.
2012-11-20
We test a nonlinear force-free field (NLFFF) optimization code in spherical geometry using an analytical solution from Low and Lou. Several tests are run, ranging from idealized cases where exact vector field data are provided on all boundaries, to cases where noisy vector data are provided on only the lower boundary (approximating the solar problem). Analytical tests also show that the NLFFF code in the spherical geometry performs better than that in the Cartesian one when the field of view of the bottom boundary is large, say, 20 Degree-Sign Multiplication-Sign 20 Degree-Sign . Additionally, we apply the NLFFF model to an active region observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory (SDO) both before and after an M8.7 flare. For each observation time, we initialize the models using potential field source surface (PFSS) extrapolations based on either a synoptic chart or a flux-dispersal model, and compare the resulting NLFFF models. The results show that NLFFF extrapolations using the flux-dispersal model as the boundary condition have slightly lower, therefore better, force-free, and divergence-free metrics, and contain larger free magnetic energy. By comparing the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly on board SDO, we find that the NLFFF performs better than the PFSS not only for the core field of the flare productive region, but also for large EUV loops higher than 50 Mm.
NASA Astrophysics Data System (ADS)
Guo, Y.; Xia, C.; Keppens, R.; Valori, G.
2016-09-01
We report our implementation of the magneto-frictional method in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC). The method aims at applications where local adaptive mesh refinement (AMR) is essential to make follow-up dynamical modeling affordable. We quantify its performance in both domain-decomposed uniform grids and block-adaptive AMR computations, using all frequently employed force-free, divergence-free, and other vector comparison metrics. As test cases, we revisit the semi-analytic solution of Low and Lou in both Cartesian and spherical geometries, along with the topologically challenging Titov–Démoulin model. We compare different combinations of spatial and temporal discretizations, and find that the fourth-order central difference with a local Lax–Friedrichs dissipation term in a single-step marching scheme is an optimal combination. The initial condition is provided by the potential field, which is the potential field source surface model in spherical geometry. Various boundary conditions are adopted, ranging from fully prescribed cases where all boundaries are assigned with the semi-analytic models, to solar-like cases where only the magnetic field at the bottom is known. Our results demonstrate that all the metrics compare favorably to previous works in both Cartesian and spherical coordinates. Cases with several AMR levels perform in accordance with their effective resolutions. The magneto-frictional method in MPI-AMRVAC allows us to model a region of interest with high spatial resolution and large field of view simultaneously, as required by observation-constrained extrapolations using vector data provided with modern instruments. The applications of the magneto-frictional method to observations are shown in an accompanying paper.
Jiang Chaowei; Feng Xueshang E-mail: fengx@spaceweather.ac.cn
2012-04-20
The magnetic field in the solar corona is usually extrapolated from a photospheric vector magnetogram using a nonlinear force-free field (NLFFF) model. NLFFF extrapolation needs considerable effort to be devoted to its numerical realization. In this paper, we present a new implementation of the magnetohydrodynamics (MHD) relaxation method for NLFFF extrapolation. The magnetofrictional approach, which is introduced for speeding the relaxation of the MHD system, is realized for the first time by the spacetime conservation-element and solution-element scheme. A magnetic field splitting method is used to further improve the computational accuracy. The bottom boundary condition is prescribed by incrementally changing the transverse field to match the magnetogram, and all other artificial boundaries of the computational box are simply fixed. We examine the code using two types of NLFFF benchmark tests, the Low and Lou semi-analytic force-free solutions and a more realistic solar-like case constructed by van Ballegooijen et al. The results show that our implementation is successful and versatile for extrapolations of either the relatively simple cases or the rather complex cases that need significant rebuilding of the magnetic topology, e.g., a flux rope. We also compute a suite of metrics to quantitatively analyze the results and demonstrate that the performance of our code in extrapolation accuracy basically reaches the same level of the present best-performing code, i.e., that developed by Wiegelmann.
NASA Astrophysics Data System (ADS)
He, Han; Wang, Huaning; Yan, Yihua
2011-01-01
The Hinode satellite can obtain high-quality photospheric vector magnetograms of solar active regions and the simultaneous coronal loop images in soft X-ray and extreme ultraviolet (EUV) bands. In this paper, we continue the work of He and Wang (2008) and apply the newly developed upward boundary integration computational scheme for the nonlinear force-free field (NLFFF) extrapolation of the coronal magnetic field to the photospheric vector magnetograms acquired by the Spectro-Polarimeter of the Solar Optical Telescope aboard Hinode. Three time series vector magnetograms of the same solar active region, NOAA 10930, are selected for the NLFFF extrapolations, which were observed within the time interval of 26 h during 10-11 December 2006 when the active region crossed the central area of the Sun's disk. Parallel computation of the NLFFF extrapolation code was realized through OpenMP multithreaded, shared memory parallelism and Fortran 95 programming language for the extrapolation calculations. The comparison between the extrapolated field lines and the coronal loop images obtained by the X-Ray Telescope and the EUV Imaging Spectrometer of Hinode shows that, in the central area of the active region, the field line configurations generally agree with the coronal images, and the orientations of the field lines basically coincide with the coronal loop observations for all three successive magnetograms. This result supports the NLFFF model being used for tracing the time series evolution of the 3-D coronal magnetic structures as the responses of the quasi-equilibrium solar atmosphere to the vector magnetic field changes in the photosphere.
NASA Astrophysics Data System (ADS)
Inoue, S.; Hayashi, K.; Kusano, K.
2016-02-01
We analyze a three-dimensional (3D) magnetic structure and its stability in large solar active region (AR) 12192, using the 3D coronal magnetic field constructed under a nonlinear force-free field (NLFFF) approximation. In particular, we focus on the magnetic structure that produced an X3.1-class flare, which is one of the X-class flares observed in AR 12192. According to our analysis, the AR contains a multiple-flux-tube system, e.g., a large flux tube, with footpoints that are anchored to the large bipole field, under which other tubes exist close to a polarity inversion line (PIL). These various flux tubes of different sizes and shapes coexist there. In particular, the latter are embedded along the PIL, which produces a favorable shape for the tether-cutting reconnection and is related to the X-class solar flare. We further found that most of magnetic twists are not released even after the flare, which is consistent with the fact that no observational evidence for major eruptions was found. On the other hand, the upper part of the flux tube is beyond a critical decay index, essential for the excitation of torus instability before the flare, even though no coronal mass ejections were observed. We discuss the stability of the complicated flux tube system and suggest the reason for the existence of the stable flux tube. In addition, we further point out a possibility for tracing the shape of flare ribbons, on the basis of a detailed structural analysis of the NLFFF before a flare.
NASA Astrophysics Data System (ADS)
Jiang, Chaowei; Wu, S. T.; Feng, Xueshang; Hu, Qiang
2014-01-01
We present a comprehensive study of the formation and eruption of an active region (AR) sigmoid in AR 11283. To follow the quasi-static evolution of the coronal magnetic field, we reconstruct a time sequence of static fields using a recently developed nonlinear force-free field model constrained by vector magnetograms. A detailed analysis of the fields compared with observations suggests the following scenario for the evolution of the region. Initially, a new bipole emerges into the negative polarity of a preexisting bipolar AR, forming a null-point topology between the two flux systems. A weakly twisted flux rope (FR) is then built up slowly in the embedded core region, largely through flux cancellation, forming a bald patch separatrix surface (BPSS). The FR grows gradually until its axis runs into a torus instability (TI) domain, and the BPSS also develops a full S-shape. The combined effects of the TI-driven expansion of the FR and the line tying at the BP tear the FR into two parts with the upper portion freely expelled and the lower portion remaining behind the postflare arcades. This process dynamically perturbs the BPSS and results in the enhanced heating of the sigmoid and the rope. The accelerated expansion of the upper-portion rope strongly pushes its envelope flux near the null point and triggers breakout reconnection at the null, which further drives the eruption. We discuss the important implications of these results for the formation and disruption of the sigmoid region with an FR.
Jing, Ju; Liu, Chang; Lee, Jeongwoo; Wang, Shuo; Xu, Yan; Wang, Haimin; Wiegelmann, Thomas
2014-03-20
Dynamic phenomena indicative of slipping reconnection and magnetic implosion were found in a time series of nonlinear force-free field (NLFFF) extrapolations for the active region 11515, which underwent significant changes in the photospheric fields and produced five C-class flares and one M-class flare over five hours on 2012 July 2. NLFFF extrapolation was performed for the uninterrupted 5 hour period from the 12 minute cadence vector magnetograms of the Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory. According to the time-dependent NLFFF model, there was an elongated, highly sheared magnetic flux rope structure that aligns well with an Hα filament. This long filament splits sideways into two shorter segments, which further separate from each other over time at a speed of 1-4 km s{sup –1}, much faster than that of the footpoint motion of the magnetic field. During the separation, the magnetic arcade arching over the initial flux rope significantly decreases in height from ∼4.5 Mm to less than 0.5 Mm. We discuss the reality of this modeled magnetic restructuring by relating it to the observations of the magnetic cancellation, flares, a filament eruption, a penumbra formation, and magnetic flows around the magnetic polarity inversion line.
NASA Astrophysics Data System (ADS)
Petrie, G. J. D.; Canou, A.; Amari, T.
2011-12-01
Between 24 March 2008 and 2 April 2008, the three active regions (ARs) NOAA 10987, 10988 and 10989 were observed daily by the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) while they traversed the solar disk. We use these measurements and the nonlinear force-free magnetic field code XTRAPOL to reconstruct the coronal magnetic field for each active region and compare model field lines with images from the Solar Terrestrial RElations Observatory (STEREO) and Hinode X-ray Telescope (XRT) telescopes. Synoptic maps made from continuous, round-the-clock Global Oscillations Network Group (GONG) magnetograms provide information on the global photospheric field and potential-field source-surface models based on these maps describe the global coronal field during the Whole Heliosphere Interval (WHI) and its neighboring rotations. Features of the modeled global field, such as the coronal holes and streamer-belt locations, are discussed in comparison with extreme ultra-violet and coronagraph observations from STEREO. The global field is found to be far from a minimum, dipolar state. From the nonlinear models we compute physical quantities for the active regions such as the photospheric magnetic and electric current fluxes, the free magnetic energy and the relative helicity for each region each day where observations permit. The interconnectivity of the three regions is addressed in the context of the potential-field source-surface model. Using local and global quantities derived from the models, we briefly discuss the different observed activity levels of the regions.
NASA Astrophysics Data System (ADS)
Aschwanden, Markus J.
2016-06-01
In this work we provide an updated description of the Vertical-Current Approximation Nonlinear Force-Free Field (VCA-NLFFF) code, which is designed to measure the evolution of the potential, non-potential, free energies, and the dissipated magnetic energies during solar flares. This code provides a complementary and alternative method to existing traditional NLFFF codes. The chief advantages of the VCA-NLFFF code over traditional NLFFF codes are the circumvention of the unrealistic assumption of a force-free photosphere in the magnetic field extrapolation method, the capability to minimize the misalignment angles between observed coronal loops (or chromospheric fibril structures) and theoretical model field lines, as well as computational speed. In performance tests of the VCA-NLFFF code, by comparing with the NLFFF code of Wiegelmann, we find agreement in the potential, non-potential, and free energy within a factor of ≲ 1.3, but the Wiegelmann code yields in the average a factor of 2 lower flare energies. The VCA-NLFFF code is found to detect decreases in flare energies in most X, M, and C-class flares. The successful detection of energy decreases during a variety of flares with the VCA-NLFFF code indicates that current-driven twisting and untwisting of the magnetic field is an adequate model to quantify the storage of magnetic energies in active regions and their dissipation during flares. The VCA-NLFFF code is also publicly available in the Solar SoftWare.
Jiang, Chaowei; Wu, S. T.; Hu, Qiang; Feng, Xueshang E-mail: wus@uah.edu E-mail: fengx@spaceweather.ac.cn
2014-05-10
Solar filaments are commonly thought to be supported in magnetic dips, in particular, in those of magnetic flux ropes (FRs). In this Letter, based on the observed photospheric vector magnetogram, we implement a nonlinear force-free field (NLFFF) extrapolation of a coronal magnetic FR that supports a large-scale intermediate filament between an active region and a weak polarity region. This result is a first, in the sense that current NLFFF extrapolations including the presence of FRs are limited to relatively small-scale filaments that are close to sunspots and along main polarity inversion lines (PILs) with strong transverse field and magnetic shear, and the existence of an FR is usually predictable. In contrast, the present filament lies along the weak-field region (photospheric field strength ≲ 100 G), where the PIL is very fragmented due to small parasitic polarities on both sides of the PIL and the transverse field has a low signal-to-noise ratio. Thus, extrapolating a large-scale FR in such a case represents a far more difficult challenge. We demonstrate that our CESE-MHD-NLFFF code is sufficient for the challenge. The numerically reproduced magnetic dips of the extrapolated FR match observations of the filament and its barbs very well, which strongly supports the FR-dip model for filaments. The filament is stably sustained because the FR is weakly twisted and strongly confined by the overlying closed arcades.
NASA Astrophysics Data System (ADS)
Jiang, Chaowei; Wu, S. T.; Feng, Xueshang; Hu, Qiang
2014-05-01
Solar filaments are commonly thought to be supported in magnetic dips, in particular, in those of magnetic flux ropes (FRs). In this Letter, based on the observed photospheric vector magnetogram, we implement a nonlinear force-free field (NLFFF) extrapolation of a coronal magnetic FR that supports a large-scale intermediate filament between an active region and a weak polarity region. This result is a first, in the sense that current NLFFF extrapolations including the presence of FRs are limited to relatively small-scale filaments that are close to sunspots and along main polarity inversion lines (PILs) with strong transverse field and magnetic shear, and the existence of an FR is usually predictable. In contrast, the present filament lies along the weak-field region (photospheric field strength <~ 100 G), where the PIL is very fragmented due to small parasitic polarities on both sides of the PIL and the transverse field has a low signal-to-noise ratio. Thus, extrapolating a large-scale FR in such a case represents a far more difficult challenge. We demonstrate that our CESE-MHD-NLFFF code is sufficient for the challenge. The numerically reproduced magnetic dips of the extrapolated FR match observations of the filament and its barbs very well, which strongly supports the FR-dip model for filaments. The filament is stably sustained because the FR is weakly twisted and strongly confined by the overlying closed arcades.
Chitta, L. P.; Kariyappa, R.; Van Ballegooijen, A. A.; DeLuca, E. E.; Solanki, S. K.
2014-10-01
In the quiet solar photosphere, the mixed polarity fields form a magnetic carpet that continuously evolves due to dynamical interaction between the convective motions and magnetic field. This interplay is a viable source to heat the solar atmosphere. In this work, we used the line-of-sight (LOS) magnetograms obtained from the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory, and the Imaging Magnetograph eXperiment instrument on the Sunrise balloon-borne observatory, as time-dependent lower boundary conditions, to study the evolution of the coronal magnetic field. We use a magneto-frictional relaxation method, including hyperdiffusion, to produce a time series of three-dimensional nonlinear force-free fields from a sequence of photospheric LOS magnetograms. Vertical flows are added up to a height of 0.7 Mm in the modeling to simulate the non-force-freeness at the photosphere-chromosphere layers. Among the derived quantities, we study the spatial and temporal variations of the energy dissipation rate and energy flux. Our results show that the energy deposited in the solar atmosphere is concentrated within 2 Mm of the photosphere and there is not sufficient energy flux at the base of the corona to cover radiative and conductive losses. Possible reasons and implications are discussed. Better observational constraints of the magnetic field in the chromosphere are crucial to understand the role of the magnetic carpet in coronal heating.
Cosmic Ray Acceleration in Force Free Fields
NASA Astrophysics Data System (ADS)
Colgate, Stirling; Li, Hui; Kronberg, Philipp
2002-11-01
Galactic, extragalactic, and cluster magnetic fields are in apparent pressure equilibrium with the in-fall pressure of matter from the external medium, IGM, onto the Galaxies and clusters, and from the voids onto the galaxy sheets, (walls), implying fields of 5 , 0.5, & 20 μG respectively. Equipartition or minimum energy, implies β_CR=n_CRm_pc^2/(B^2/8π)˜= 1. The total energy in field and CRs is then ˜= 10^55 ergs Galactic and ˜= 4 ot 10^60 ergs per galaxy in the IGM and less within clusters, e.g., radio lobes, synchrotron "glow" in the IGM (Kronberg), and the UHECRs spectrum, Γ =-2.6. CRs escape from the Galaxy to the IGM, τ˜=10^7y, and similarly from the walls to the voids, ˜=10^8y, less than the GZK cut-off time provided B_galaxy>B_IGM>B_voids. The free energy of black hole formation, The Los Alamos model, is just sufficient. The lack of shocks at the boundaries of over pressured radio lobes and the need for high acceleration efficiency suggests eE_allel˜= eη_reconJ_allel, acceleration by reconnection of these force-free fields.
Toroidal linear force-free magnetic fields with axial symmetry
NASA Astrophysics Data System (ADS)
Vandas, M.; Romashets, E.
2016-01-01
Aims: Interplanetary magnetic flux ropes are often described as linear force-free fields. To account for their curvature, toroidal configurations must be used. The aim is to find an analytic description of a linear force-free magnetic field of the toroidal geometry in which the cross section of flux ropes can be controlled. Methods: The solution is found as a superposition of fields given by linear force-free cylinders tangential to a generating toroid. The cylindrical field is expressed in a series of terms that are not all cylindrically symmetric. Results: We found the general form of a toroidal linear force-free magnetic field. The field is azimuthally symmetric with respect to the torus axis. It depends on a set of coefficients that enables controlling the flux rope shape (cross section) to some extent. By varying the coefficients, flux ropes with circular and elliptic cross sections were constructed. Numerical comparison suggests that the simple analytic formula for calculating the helicity in toroidal flux ropes of the circular cross section can be used for flux ropes with elliptic cross sections if the minor radius in the formula is set to the geometric mean of the semi-axes of the elliptic cross section.
Force-free field model of ball lightning
NASA Astrophysics Data System (ADS)
Tsui, K. H.
2001-03-01
Due to the nature that the force-free magnetic field, whose current carried by the conducting plasma is everywhere parallel to the magnetic field it generates, is the minimum energy configuration under the constraint of magnetic helicity conservation, ball lightning is considered as a self-organized phenomenon with a plasma fireball immersed in a spherical force-free magnetic field. Since this field does not exert force on the plasma, the plasma pressure, by itself, is in equilibrium with the surrounding environment, and the force-free magnetic field can take on any value without affecting the plasma. Due to this second feature, singular solutions of the magnetic field that are otherwise excluded are allowed, which enable a large amount of energy to be stored to sustain the ball lightning. The singularity is truncated only by the physical limit of current density that a plasma can carry. Scaling the customary soccer-size fireball to larger dimensions could account for day and night sightings of luminous objects in the sky.
Energy buildup in sheared force-free magnetic fields
NASA Technical Reports Server (NTRS)
Wolfson, Richard; Low, Boon C.
1992-01-01
Photospheric displacement of the footpoints of solar magnetic field lines results in shearing and twisting of the field, and consequently in the buildup of electric currents and magnetic free energy in the corona. The sudden release of this free energy may be the origin of eruptive events like coronal mass ejections, prominence eruptions, and flares. An important question is whether such an energy release may be accompanied by the opening of magnetic field lines that were previously closed, for such open field lines can provide a route for matter frozen into the field to escape the sun altogether. This paper presents the results of numerical calculations showing that opening of the magnetic field is permitted energetically, in that it is possible to build up more free energy in a sheared, closed, force-free magnetic field than is in a related magnetic configuration having both closed and open field lines. Whether or not the closed force-free field attains enough energy to become partially open depends on the form of the shear profile; the results presented compare the energy buildup for different shear profiles. Implications for solar activity are discussed briefly.
Particle energization in a chaotic force-free magnetic field
NASA Astrophysics Data System (ADS)
Li, Xiaocan; Li, Gang; Dasgupta, Brahmananda
2015-04-01
A force-free field (FFF) is believed to be a reasonable description of the solar corona and in general a good approximation for low-beta plasma. The equations describing the magnetic field of FFF is similar to the ABC fluid equations which has been demonstrated to be chaotic. This implies that charged particles will experience chaotic magnetic field in the corona. Here, we study particle energization in a time-dependent FFF using a test particle approach. An inductive electric field is introduced by turbulent motions of plasma parcels. We find efficient particle acceleration with power-law like particle energy spectra. The power-law indices depend on the amplitude of plasma parcel velocity field and the spatial scales of the magnetic field fluctuation. The spectra are similar for different particle species. This model provide a possible mechanism for seed population generation for particle acceleration by, e.g., CME-driven shocks. Generalization of our results to certain non-force-free-field (NFFF) is straightforward as the sum of two or multiple FFFs naturally yield NFFF.
ON THE FORCE-FREE NATURE OF PHOTOSPHERIC SUNSPOT MAGNETIC FIELDS AS OBSERVED FROM HINODE (SOT/SP)
Tiwari, Sanjiv Kumar
2012-01-01
A magnetic field is force-free if there is no interaction between it and the plasma in the surrounding atmosphere, i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. The computation of various magnetic parameters, such as magnetic energy (using the virial theorem), gradient of twist of sunspot magnetic fields (computed from the force-free parameter {alpha}), and any kind of extrapolation, heavily hinges on the force-free approximation of the photospheric sunspot magnetic fields. Thus, it is of vital importance to inspect the force-free behavior of sunspot magnetic fields. The force-free nature of sunspot magnetic fields has been examined earlier by some researchers, ending with incoherent results. Accurate photospheric vector field measurements with high spatial resolution are required to inspect the force-free nature of sunspots. For this purpose, we use several vector magnetograms of high spatial resolution obtained from the Solar Optical Telescope/Spectro-Polarimeter on board Hinode. Both the necessary and sufficient conditions for force-free nature are examined by checking the global and local nature of equilibrium magnetic forces over sunspots. We find that sunspot magnetic fields are not very far from the force-free configuration, although they are not completely force-free on the photosphere. The umbral and inner penumbral fields are more force-free than the middle and outer penumbral fields. During their evolution, sunspot magnetic fields are found to maintain their proximity to force-free field behavior. Although a dependence of net Lorentz force components is seen on the evolutionary stages of the sunspots, we do not find a systematic relationship between the nature of sunspot magnetic fields and the associated flare activity. Further, we examine whether the fields at the photosphere follow linear or nonlinear force-free conditions. After examining this in various complex and simple sunspots, we conclude that
Force-free magnetic fields - Generating functions and footpoint displacements
NASA Technical Reports Server (NTRS)
Wolfson, Richard; Verma, Ritu
1991-01-01
This paper presents analytic and numerical calculations that explore equilibrium sequences of bipolar force-free magnetic fields in relation to displacments of their magnetic footpoints. It is shown that the appearance of magnetic islands - sometimes interpreted as marking the loss of equilibrium in models of the solar atmosphere - is likely associated only with physically unrealistic footpoint displacements such as infinite separation or 'tearing' of the model photosphere. The work suggests that the loss of equilibrium in bipolar configurations, sometimes proposed as a mechanism for eruptive solar events, probably requires either fully three-dimensional field configurations or nonzero plasma pressure. The results apply only to fields that are strictly bipolar, and do not rule out equilibrium loss in more complex structures such as quadrupolar fields.
Force-free magnetic fields - The magneto-frictional method
NASA Technical Reports Server (NTRS)
Yang, W. H.; Sturrock, P. A.; Antiochos, S. K.
1986-01-01
The problem under discussion is that of calculating magnetic field configurations in which the Lorentz force j x B is everywhere zero, subject to specified boundary conditions. We choose to represent the magnetic field in terms of Clebsch variables in the form B = grad alpha x grad beta. These variables are constant on any field line so that each field line is labeled by the corresponding values of alpha and beta. When the field is described in this way, the most appropriate choice of boundary conditions is to specify the values of alpha and beta on the bounding surface. We show that such field configurations may be calculated by a magneto-frictional method. We imagine that the field lines move through a stationary medium, and that each element of magnetic field is subject to a frictional force parallel to and opposing the velocity of the field line. This concept leads to an iteration procedure for modifying the variables alpha and beta, that tends asymptotically towards the force-free state. We apply the method first to a simple problem in two rectangular dimensions, and then to a problem of cylindrical symmetry that was previously discussed by Barnes and Sturrock (1972). In one important respect, our new results differ from the earlier results of Barnes and Sturrock, and we conclude that the earlier article was in error.
Nonlinear Force-free Modeling of a Long-lasting Coronal Sigmoid
NASA Astrophysics Data System (ADS)
Savcheva, Antonia; van Ballegooijen, Adriaan
2009-10-01
A study of the magnetic configuration and evolution of a long-lasting quiescent coronal sigmoid is presented. The sigmoid was observed by Hinode/XRT and Transition Region and Coronal Explorer (TRACE) between 2007 February 6 and 12 when it finally erupted. We construct nonlinear force-free field models for several observations during this period, using the flux-rope insertion method. The high spatial and temporal resolution of the X-Ray Telescope (XRT) allows us to finely select best-fit models that match the observations. The modeling shows that a highly sheared field, consisting of a weakly twisted flux rope embedded in a potential field, very well describes the structure of the X-ray sigmoid. The flux rope reaches a stable equilibrium, but its axial flux is close to the stability limit of about 5 × 1020 Mx. The relative magnetic helicity increases with time from February 8 until just prior to the eruption on February 12. We study the spatial distribution of the torsion parameter α in the vicinity of the flux rope, and find that it has a hollow-core distribution, i.e., electric currents are concentrated in a current layer at the boundary between the flux rope and its surroundings. The current layer is located near the bald patch separatrix surface (BPSS) of the magnetic configuration, and the X-ray emission appears to come from this current layer/BPSS, consistent with the Titov and Démoulin model. We find that the twist angle Φ of the magnetic field increases with time to about 2π just prior to the eruption, but never reaches the value necessary for the kink instability.
Malanushenko, A.; Schrijver, C. J.; DeRosa, M. L.; Wheatland, M. S.; Gilchrist, S. A.
2012-09-10
At present, many models of the coronal magnetic field rely on photospheric vector magnetograms, but these data have been shown to be problematic as the sole boundary information for nonlinear force-free field extrapolations. Magnetic fields in the corona manifest themselves in high-energy images (X-rays and EUV) in the shapes of coronal loops, providing an additional constraint that is not at present used as constraints in the computational domain, directly influencing the evolution of the model. This is in part due to the mathematical complications of incorporating such input into numerical models. Projection effects, confusion due to overlapping loops (the coronal plasma is optically thin), and the limited number of usable loops further complicate the use of information from coronal images. We develop and test a new algorithm to use images of coronal loops in the modeling of the solar coronal magnetic field. We first fit projected field lines with those of constant-{alpha} force-free fields to approximate the three-dimensional distribution of currents in the corona along a sparse set of trajectories. We then apply a Grad-Rubin-like iterative technique, which uses these trajectories as volume constraints on the values of {alpha}, to obtain a volume-filling nonlinear force-free model of the magnetic field, modifying a code and method presented by Wheatland. We thoroughly test the technique on known analytical and solar-like model magnetic fields previously used for comparing different extrapolation techniques and compare the results with those obtained by currently available methods relying only on the photospheric data. We conclude that we have developed a functioning method of modeling the coronal magnetic field by combining the line-of-sight component of the photospheric magnetic field with information from coronal images. Whereas we focus on the use of coronal loop information in combination with line-of-sight magnetograms, the method is readily extended to
Asymptotic analysis of force-free magnetic fields of cylindrical symmetry
NASA Technical Reports Server (NTRS)
Sturrock, P. A.; Antiochos, S. K.; Roumeliotis, G.
1995-01-01
It is known from computer calculations that if a force-free magnetic-field configuration is stressed progressively by footpoint displacements, the configuration expands and approaches the open configuration with the same surface flux distribution, and, in the process, the energy of the field increases progressively. Analysis of a simple model of force-free fields of cylindrical symmetry leads to simple asymptotic expressions for the extent and energy of such a configuration. The analysis is carried through for both spherical and planar source surfaces. According to this model, the field evolves in a well-behaved manner with no indication of instability or loss of equilibrium.
Thalmann, J. K.; Tiwari, S. K.; Wiegelmann, T.
2013-05-20
Photospheric magnetic vector maps from two different instruments are used to model the nonlinear force-free coronal magnetic field above an active region. We use vector maps inferred from polarization measurements of the Solar Dynamics Observatory/Helioseismic and Magnetic Imager (HMI) and the Solar Optical Telescope's Spectropolarimeter (SP) on board Hinode. Besides basing our model calculations on HMI data, we use both SP data of original resolution and scaled down to the resolution of HMI. This allows us to compare the model results based on data from different instruments and to investigate how a binning of high-resolution data affects the model outcome. The resulting three-dimensional magnetic fields are compared in terms of magnetic energy content and magnetic topology. We find stronger magnetic fields in the SP data, translating into a higher total magnetic energy of the SP models. The net Lorentz forces of the HMI and SP lower boundaries verify their force-free compatibility. We find substantial differences in the absolute estimates of the magnetic field energy but similar relative estimates, e.g., the fraction of excess energy and of the flux shared by distinct areas. The location and extension of neighboring connectivity domains differ and the SP model fields tend to be higher and more vertical. Hence, conclusions about the magnetic connectivity based on force-free field models are to be drawn with caution. We find that the deviations of the model solution when based on the lower-resolution SP data are small compared to the differences of the solutions based on data from different instruments.
On some properties of force-free magnetic fields in infinite regions of space
NASA Technical Reports Server (NTRS)
Aly, J. J.
1984-01-01
Techniques for solving boundary value problems (BVP) for a force free magnetic field (FFF) in infinite space are presented. A priori inequalities are defined which must be satisfied by the force-free equations. It is shown that upper bounds may be calculated for the magnetic energy of the region provided the value of the magnetic normal component at the boundary of the region can be shown to decay sufficiently fast at infinity. The results are employed to prove a nonexistence theorem for the BVP for the FFF in the spatial region. The implications of the theory for modeling the origins of solar flares are discussed.
Temporal and Spatial Relationship of Flare Signatures and the Force-free Coronal Magnetic Field
NASA Astrophysics Data System (ADS)
Thalmann, J. K.; Veronig, A.; Su, Y.
2016-08-01
We investigate the plasma and magnetic environment of active region NOAA 11261 on 2011 August 2 around a GOES M1.4 flare/CME (SOL2011-08-02T06:19). We compare coronal emission at the (extreme) ultraviolet and X-ray wavelengths, using SDO AIA and RHESSI images, in order to identify the relative timing and locations of reconnection-related sources. We trace flare ribbon signatures at ultraviolet wavelengths in order to pin down the intersection of previously reconnected flaring loops in the lower solar atmosphere. These locations are used to calculate field lines from three-dimensional (3D) nonlinear force-free magnetic field models, established on the basis of SDO HMI photospheric vector magnetic field maps. Using this procedure, we analyze the quasi-static time evolution of the coronal model magnetic field previously involved in magnetic reconnection. This allows us, for the first time, to estimate the elevation speed of the current sheet’s lower tip during an on-disk observed flare as a few kilometers per second. A comparison to post-flare loops observed later above the limb in STEREO EUVI images supports this velocity estimate. Furthermore, we provide evidence for an implosion of parts of the flaring coronal model magnetic field, and identify the corresponding coronal sub-volumes associated with the loss of magnetic energy. Finally, we spatially relate the build up of magnetic energy in the 3D models to highly sheared fields, established due to the dynamic relative motions of polarity patches within the active region.
A long-lived coronal X-ray arcade. [force-free magnetic field analysis
NASA Technical Reports Server (NTRS)
Mcguire, J. P.; Tandberg-Hanssen, E.; Krall, K. R.; Wu, S. T.; Smith, J. B., Jr.; Speich, D. M.
1977-01-01
A large, long-lived, soft X-ray emitting arch system observed during a Skylab mission is analyzed. The supposition is that these arches owe their stability to the stable coronal magnetic-field configuration. A global constant alpha force-free magnetic field analysis, is used to describe the arches which stayed in the same approximate position for several solar rotations. A marked resemblance is noted between the theoretical magnetic field configuration and the observed X-ray emmitting feature.
Quasi-static evolution of sheared force-free fields and the solar flare problem
NASA Technical Reports Server (NTRS)
Aly, J. J.
1985-01-01
Some new results are given showing the possible evolution of a two-dimensional force-free field in the half-space z greater than 0 toward an open field. This evolution is driven by shearing motions applied to the feet of the field lines on the boundary z = 0. The consequences of these results for a model of the two-ribbon solar flare are discussed.
NASA Technical Reports Server (NTRS)
Sturrock, P. A.; Antiochos, S. K.; Klinchuk, J. A.; Roumeliotis, G.
1994-01-01
It is known from computer calculations that if a force-free magnetic field configuration is stressed progressively by footpoint displacements, the configuration expands and approaches the open configuration with the same surface flux distribution and the energy of the field increases progressively. For configurations of translationalsymmetry, it has been found empirically that the energy tends asymptotically to a certain functional form. It is here shown that analysis of a simple model of the asymptotic form of force-free fields of translational symmetry leads to and therefore justifies this functional form. According to this model, the field evolves in a well-behaved manner with no indication of instability or loss of equilibrium.
Superdiffusion to normal diffusion: particle motion in three-dimensional force-free magnetic fields
NASA Astrophysics Data System (ADS)
Holguin, F.; Ram, A. K.; Krishnamurthy, V.; Dasgupta, B.
2015-11-01
Magnetic fields in regions of low plasma pressure and large currents, such as in interstellar space and gaseous nebulae, are force-free as the Lorentz force vanishes. The Arnold-Beltrami-Childress (ABC) field is an example of a three-dimensional, force-free, helical magnetic field. The field lines form complex and varied structures in space that are a mix of regular and chaotic lines of force. Charged particles moving in the region of chaotic field lines exhibit anomalous superdiffusion. The sine field, or the Archontis field, is a special case of ABC field with the cosine terms left out. The lines of force of a sine field are completely chaotic in space. However, the diffusion of particles in the sine field is normal. The time evolution of an ensemble of particles can be divided into three domains. For short times, the motion is essentially ballistic. For intermediate times, the motion is characterized by a decay of the velocity autocorrelation function. For longer times, the particles undergo diffusion. We present results on the diffusion of field lines, and of particles, in the ABC and sine fields. In particular, the transition from superdiffusion to normal diffusion is discussed.
Mean-field Ohm's law and coaxial helicity injection in force-free plasmas
Weening, R. H.
2011-12-15
A theoretical analysis of steady-state coaxial helicity injection (CHI) in force-free plasmas is presented using a parallel mean-field Ohm's law that includes resistivity {eta} and hyper-resistivity {Lambda} terms. Using Boozer coordinates, a partial differential equation is derived for the time evolution of the mean-field poloidal magnetic flux, or magnetic Hamiltonian function, from the parallel mean-field Ohm's law. A general expression is obtained from the mean-field theory for the efficiency of CHI current drive in force-free plasmas. Inductances of internal energy, magnetic helicity, and poloidal magnetic flux are used to characterize axisymmetric plasma equilibria that have a model current profile. Using the model current profile, a method is suggested to determine the level of magnetohydrodynamic activity at the magnetic axis and the consequent deviation from the completely relaxed Taylor state. The mean-field Ohm's law model suggests that steady-state CHI can be viewed most simply as a boundary layer problem.
A method for embedding circular force-free flux ropes in potential magnetic fields
Titov, V. S.; Török, T.; Mikic, Z.; Linker, J. A.
2014-08-01
We propose a method for constructing approximate force-free equilibria in pre-eruptive configurations in which a thin force-free flux rope is embedded into a locally bipolar-type potential magnetic field. The flux rope is assumed to have a circular-arc axis, a circular cross-section, and electric current that is either concentrated in a thin layer at the boundary of the rope or smoothly distributed across it with a maximum of the current density at the center. The entire solution is described in terms of the magnetic vector potential in order to facilitate the implementation of the method in numerical magnetohydrodynamic (MHD) codes that evolve the vector potential rather than the magnetic field itself. The parameters of the flux rope can be chosen so that its subsequent MHD relaxation under photospheric line-tied boundary conditions leads to nearly exact numerical equilibria. To show the capabilities of our method, we apply it to several cases with different ambient magnetic fields and internal flux-rope structures. These examples demonstrate that the proposed method is a useful tool for initializing data-driven simulations of solar eruptions.
Modeling of Gamma-ray Pulsar Light Curves Using the Force-free Magnetic Field
NASA Astrophysics Data System (ADS)
Bai, Xue-Ning; Spitkovsky, Anatoly
2010-06-01
Gamma-ray emission from pulsars has long been modeled using a vacuum dipole field. This approximation ignores changes in the field structure caused by the magnetospheric plasma and strong plasma currents. We present the first results of gamma-ray pulsar light-curve modeling using the more realistic field taken from three-dimensional force-free (FF) magnetospheric simulations. Having the geometry of the field, we apply several prescriptions for the location of the emission zone, comparing the light curves to observations. We find that when the emission region is chosen according to the conventional slot-gap (or two-pole caustic) prescription, the model fails to produce double-peak pulse profiles, mainly because the size of the polar cap in the FF magnetosphere is larger than the vacuum field polar cap. This suppresses caustic formation in the inner magnetosphere. The conventional outer-gap model is capable of producing only one peak under general conditions because a large fraction of open field lines does not cross the null charge surface. We propose a novel "separatrix layer" model, where the high-energy emission originates from a thin layer on the open field lines just inside of the separatrix that bounds the open flux tube. The emission from this layer generates two strong caustics on the sky map due to the effect we term "Sky Map Stagnation" (SMS). It is related to the fact that the FF field asymptotically approaches the field of a rotating split monopole, and the photons emitted on such field lines in the outer magnetosphere arrive to the observer in phase. The double-peak light curve is a natural consequence of SMS. We show that most features of the currently available gamma-ray pulsar light curves can be reasonably well reproduced and explained with the separatrix layer model using the FF field. Association of the emission region with the current sheet will guide more detailed future studies of the magnetospheric acceleration physics.
Kumar, Dinesh; Bhattacharyya, R.; Smolarkiewicz, P. K.
2013-11-15
In ideal magnetohydrodynamics characterized by an infinite electrical conductivity, the magnetic flux across an arbitrary fluid surface is conserved in time. The magnetofluid then can be partitioned into contiguous subvolumes of fluid, each of which entraps its own subsystem of magnetic flux. During dynamical evolution of the magnetofluid, these subvolumes press into each other; and in the process, two such subvolumes may come into direct contact while ejecting a third interstitial subvolume. Depending on the orientations of magnetic fields of the two interacting subvolumes, the magnetic field at the common surface of interaction may become discontinuous and a current sheet is formed there. This process of current sheet formation and their subsequent decay is believed to be a plausible mechanism for coronal heating and may also be responsible for various eruptive phenomena at the solar corona. In this work, we explore this theoretical concept through numerical simulations of a viscous, incompressible magnetofluid characterized by infinite electrical conductivity. In particular, we show that if the initial magnetic field is prescribed by superposition of two linear force-free fields with different torsion coefficients, then formation of current sheets are numerically realizable in the neighborhood of magnetic nulls.
NASA Astrophysics Data System (ADS)
Farrugia, Charles; Moestl, Christian; Leitner, Martin; Galvin, Antoinette; Lugaz, Noé; Yu, Wenyuan
2016-07-01
This work is about modeling of those small solar wind transients (STs) which have a flux rope geometry. The two models used are: (i) the linear force free solution of Lundquist in terms of Bessel functions, and (ii) the non-linear Gold-Hoyle solution describing a uniformly-twisted flux tube. The first has been used almost exclusively in modeling of both large and small flux ropes in the solar wind. The second was applied to one small transient. In recent work there have been claims that variant (ii) is more appropriate than (i) for large transients, i.e. magnetic clouds. We select by eye six flux rope STs from STEREO and Wind data, chosen purely on the basis of having a large and smooth rotation. We also choose these during solar maximum activity conditions since our current work shows that only then are these models appropriate.
NASA Astrophysics Data System (ADS)
Aschwanden, Markus J.; Wuelser, Jean-Pierre; Nitta, Nariaki V.; Lemen, James R.; DeRosa, Marc L.; Malanushenko, Anna
2012-09-01
The three-dimensional coordinates of stereoscopically triangulated loops provide strong constraints for magnetic field models of active regions in the solar corona. Here, we use STEREO/A and B data from some 500 stereoscopically triangulated loops observed in four active regions (2007 April 30, May 9, May 19, and December 11), together with SOHO/MDI line-of-sight magnetograms. We measure the average misalignment angle between the stereoscopic loops and theoretical magnetic field models, finding a mismatch of μ = 19°-46° for a potential field model, which is reduced to μ = 14°-19° for a non-potential field model parameterized by twist parameters. The residual error is commensurable with stereoscopic measurement errors (μSE ≈ 8°-12°). We developed a potential field code that deconvolves a line-of-sight magnetogram into three magnetic field components (Bx , By , Bz ), as well as a non-potential field forward-fitting code that determines the full length of twisted loops (L ≈ 50-300 Mm), the number of twist turns (median N twist = 0.06), the nonlinear force-free α-parameter (median α ≈ 4 × 10-11 cm-1), and the current density (median jz ≈ 1500 Mx cm-2 s-1). All twisted loops are found to be far below the critical value for kink instability, and Joule dissipation of their currents is found to be far below the coronal heating requirement. The algorithm developed here, based on an analytical solution of nonlinear force-free fields that is accurate to second order (in the force-free parameter α), represents the first code that enables fast forward fitting to photospheric magnetograms and stereoscopically triangulated loops in the solar corona.
NASA Astrophysics Data System (ADS)
Ram, Abhay K.; Dasgupta, Brahmananda; Krishnamurthy, V.; Mitra, Dhrubaditya
2014-07-01
The cosmic magnetic fields in regions of low plasma pressure and large currents, such as in interstellar space and gaseous nebulae, are force-free in the sense that the Lorentz force vanishes. The three-dimensional Arnold-Beltrami-Childress (ABC) field is an example of a force-free, helical magnetic field. In fluid dynamics, ABC flows are steady state solutions of the Euler equation. The ABC magnetic field lines exhibit a complex and varied structure that is a mix of regular and chaotic trajectories in phase space. The characteristic features of field line trajectories are illustrated through the phase space distribution of finite-distance and asymptotic-distance Lyapunov exponents. In regions of chaotic trajectories, an ensemble-averaged variance of the distance between field lines reveals anomalous diffusion—in fact, superdiffusion—of the field lines. The motion of charged particles in the force-free ABC magnetic fields is different from the flow of passive scalars in ABC flows. The particles do not necessarily follow the field lines and display a variety of dynamical behavior depending on their energy, and their initial pitch-angle. There is an overlap, in space, of the regions in which the field lines and the particle orbits are chaotic. The time evolution of an ensemble of particles, in such regions, can be divided into three categories. For short times, the motion of the particles is essentially ballistic; the ensemble-averaged, mean square displacement is approximately proportional to t2, where t is the time of evolution. The intermediate time region is defined by a decay of the velocity autocorrelation function—this being a measure of the time after which the collective dynamics is independent of the initial conditions. For longer times, the particles undergo superdiffusion—the mean square displacement is proportional to tα, where α > 1, and is weakly dependent on the energy of the particles. These super-diffusive characteristics, both of magnetic
Ram, Abhay K.; Dasgupta, Brahmananda; Krishnamurthy, V.; Mitra, Dhrubaditya
2014-07-15
The cosmic magnetic fields in regions of low plasma pressure and large currents, such as in interstellar space and gaseous nebulae, are force-free in the sense that the Lorentz force vanishes. The three-dimensional Arnold-Beltrami-Childress (ABC) field is an example of a force-free, helical magnetic field. In fluid dynamics, ABC flows are steady state solutions of the Euler equation. The ABC magnetic field lines exhibit a complex and varied structure that is a mix of regular and chaotic trajectories in phase space. The characteristic features of field line trajectories are illustrated through the phase space distribution of finite-distance and asymptotic-distance Lyapunov exponents. In regions of chaotic trajectories, an ensemble-averaged variance of the distance between field lines reveals anomalous diffusion—in fact, superdiffusion—of the field lines. The motion of charged particles in the force-free ABC magnetic fields is different from the flow of passive scalars in ABC flows. The particles do not necessarily follow the field lines and display a variety of dynamical behavior depending on their energy, and their initial pitch-angle. There is an overlap, in space, of the regions in which the field lines and the particle orbits are chaotic. The time evolution of an ensemble of particles, in such regions, can be divided into three categories. For short times, the motion of the particles is essentially ballistic; the ensemble-averaged, mean square displacement is approximately proportional to t{sup 2}, where t is the time of evolution. The intermediate time region is defined by a decay of the velocity autocorrelation function—this being a measure of the time after which the collective dynamics is independent of the initial conditions. For longer times, the particles undergo superdiffusion—the mean square displacement is proportional to t{sup α}, where α > 1, and is weakly dependent on the energy of the particles. These super-diffusive characteristics
NASA Astrophysics Data System (ADS)
Rudenko, George; Myshyakov, Ivan; Anfinogentov, Sergey
A possibility for satisfactory removing of azimuthal ambiguity in the transverse field of vector magnetograms and the extrapolation of magnetic fields independently of the region position on the solar disk is shown. It is demonstrated an exact correspondence between the calculated field and the nonpotential loop structure in a near-limb region. The new technique of azimuthal ambiguity removing consists of the following parts: -translation of data in the form of artificial Stokes parameters into the working "quasi-spherical" coordinate system with subsequent smoothing to reduce noise component of the transverse field and with the inverse transformation to the vector form; -FFT extrapolation of the boundary potential field with constant direction of the oblique derivative corresponding to the observed line-of-sight component in the "quasi-spherical" coordinate system; -modification of the Metropolis's minimum energy method to spherical geometry with no need for data grid uniformity. Based on a version of the optimization method from Rudenko and Myshyakov (2009, Solar Phys. V. 257, 28), we use magnetograms corrected with modification of the Metropolis's method as boundary conditions for magnetic field extrapolation in the nonlinear force-free approximation.
EFFECT OF POLARIMETRIC NOISE ON THE ESTIMATION OF TWIST AND MAGNETIC ENERGY OF FORCE-FREE FIELDS
Tiwari, Sanjiv Kumar; Venkatakrishnan, P.; Gosain, Sanjay; Joshi, Jayant E-mail: pvk@prl.res.in E-mail: jayant@prl.res.in
2009-07-20
The force-free parameter {alpha}, also known as helicity parameter or twist parameter, bears the same sign as the magnetic helicity under some restrictive conditions. The single global value of {alpha} for a whole active region gives the degree of twist per unit axial length. We investigate the effect of polarimetric noise on the calculation of global {alpha} value and magnetic energy of an analytical bipole. The analytical bipole has been generated using the force-free field approximation with a known value of constant {alpha} and magnetic energy. The magnetic parameters obtained from the analytical bipole are used to generate Stokes profiles from the Unno-Rachkovsky solutions for polarized radiative transfer equations. Then we add random noise of the order of 10{sup -3} of the continuum intensity (I {sub c}) in these profiles to simulate the real profiles obtained by modern spectropolarimeters such as Hinode (SOT/SP), SVM (USO), ASP, DLSP, POLIS, and SOLIS etc. These noisy profiles are then inverted using a Milne-Eddington inversion code to retrieve the magnetic parameters. Hundred realizations of this process of adding random noise and polarimetric inversion is repeated to study the distribution of error in global {alpha} and magnetic energy values. The results show that (1) the sign of {alpha} is not influenced by polarimetric noise and very accurate values of global twist can be calculated, and (2) accurate estimation of magnetic energy with uncertainty as low as 0.5% is possible under the force-free condition.
Comparative study of a constant-alpha force-free field and its approximations in an ideal toroid
NASA Astrophysics Data System (ADS)
Vandas, M.; Romashets, E.
2015-08-01
Aims: Magnetic clouds in the solar wind are large, loop-like interplanetary flux ropes and may be locally approximated by a toroidal flux rope. We compare approximate constant-alpha force-free fields in an ideal toroid, used in magnetic cloud analysis, with the exact solution, and examine their validity for low aspect ratios, which can be found in magnetic clouds. The approximate toroidal solutions were originally derived under the assumption of large aspect ratios. Methods: Three analytic simple approximate constant-alpha force-free solutions and the exact analytic solution are compared with respect to magnetic field profiles, magnetic field magnitude distributions, and magnetic helicity, with moderate (2-3) and very low (<2) aspect ratios. Results: The Miller & Turner (1981, Phys. Fluids, 24, 363) field and its modification (to satisfy exact solenoidality) match the position of the magnetic axis in the toroidal flux rope well even for very low aspect ratios. The same can be said for the modified field and the position of the magnetic field maximum. When calculating helicity of the toroidal flux rope, the Miller & Turner field yields better results. A simple formula for magnetic helicity derived from the Miller & Turner solution is valid with a good accuracy even for very low aspect ratios. Conclusions: The Miller & Turner solution is a reasonable substitute for the exact solution even for low aspect ratios (≈2).
Aschwanden, Markus J.; Wuelser, Jean-Pierre; Nitta, Nariaki V.; Lemen, James R.; DeRosa, Marc L.; Malanushenko, Anna
2012-09-10
The three-dimensional coordinates of stereoscopically triangulated loops provide strong constraints for magnetic field models of active regions in the solar corona. Here, we use STEREO/A and B data from some 500 stereoscopically triangulated loops observed in four active regions (2007 April 30, May 9, May 19, and December 11), together with SOHO/MDI line-of-sight magnetograms. We measure the average misalignment angle between the stereoscopic loops and theoretical magnetic field models, finding a mismatch of {mu} = 19 Degree-Sign -46 Degree-Sign for a potential field model, which is reduced to {mu} 14 Degree-Sign -19 Degree-Sign for a non-potential field model parameterized by twist parameters. The residual error is commensurable with stereoscopic measurement errors ({mu}{sub SE} Almost-Equal-To 8 Degree-Sign -12 Degree-Sign ). We developed a potential field code that deconvolves a line-of-sight magnetogram into three magnetic field components (B{sub x} , B{sub y} , B{sub z} ), as well as a non-potential field forward-fitting code that determines the full length of twisted loops (L Almost-Equal-To 50-300 Mm), the number of twist turns (median N{sub twist} = 0.06), the nonlinear force-free {alpha}-parameter (median {alpha} Almost-Equal-To 4 Multiplication-Sign 10{sup -11} cm{sup -1}), and the current density (median j{sub z} Almost-Equal-To 1500 Mx cm{sup -2} s{sup -1}). All twisted loops are found to be far below the critical value for kink instability, and Joule dissipation of their currents is found to be far below the coronal heating requirement. The algorithm developed here, based on an analytical solution of nonlinear force-free fields that is accurate to second order (in the force-free parameter {alpha}), represents the first code that enables fast forward fitting to photospheric magnetograms and stereoscopically triangulated loops in the solar corona.
The galactic dynamo, the helical force free field and the emissions of AGN
Colgate, S.; Li, Hui
1997-05-01
We present a theory relating the central galactic black hole (BH) formation to the galactic dynamo through an accretion disk. The associated AGN emissions and the collimated radio sources are then a result of the dynamo process. A unified theory of quasar and BL-Lac formation (hereafter AGN) starts with the collapse of damped Lyman-alpha clouds, presumably proto-galaxies, which then evolve to a central disk and black hole, (BH). An alpha - omega dynamo forms in this accretion disk where the augmentation of the poloidal field from the toroidal field depends upon star disk collisions. The winding number of the inner most orbit of the disk is so large, tilde 10 to the 11th power that the total gain of the dynamo is semi-infinite, and the original seed field of no consequence. The total magnetic flux produced is tilde 10000 times that of the galaxy, sufficient to explain the much larger flux of clusters. The semi-infinite gain of the dynamo implies that the field saturates at the dynamic stress so that most of the free energy of formation of the BH is carried off as magnetic energy in the form of a magnetic helix. The dissipation of this magnetic energy leads to the unique emission spectrum of AGN as well as the equally startling collimated radio and optical sources.
NASA Technical Reports Server (NTRS)
Low, B. C.
1974-01-01
A one-dimensional model is considered in which an increasingly large electric field is induced by a rapidly evolving magnetic field. In the case of solar flares, energies are estimated to which protons and electrons may be directly accelerated by such an induced electric field.
An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta
Allanson, O. Neukirch, T. Wilson, F. Troscheit, S.
2015-10-15
We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.
Covariant hyperbolization of force-free electrodynamics
NASA Astrophysics Data System (ADS)
Carrasco, F. L.; Reula, O. A.
2016-04-01
Force-free electrodynamics (FFE) is a nonlinear system of equations modeling the evolution of the electromagnetic field, in the presence of a magnetically dominated relativistic plasma. This configuration arises on several astrophysical scenarios which represent exciting laboratories to understand physics in extreme regimes. We show that this system, when restricted to the correct constraint submanifold, is symmetric hyperbolic. In numerical applications, it is not feasible to keep the system in that submanifold, and so it is necessary to analyze its structure first in the tangent space of that submanifold and then in a whole neighborhood of it. As has been shown [1], a direct (or naive) formulation of this system (in the whole tangent space) results in a weakly hyperbolic system of evolution equations for which well-posedness for the initial value formulation does not follow. Using the generalized symmetric hyperbolic formalism of Geroch [2], we introduce here a covariant hyperbolization for the FFE system. In fact, in analogy to the usual Maxwell case, a complete family of hyperbolizers is found, both for the restricted system on the constraint submanifold as well as for a suitably extended system defined in a whole neighborhood of it. A particular symmetrizer among the family is then used to write down the pertaining evolution equations, in a generic (3 +1 ) decomposition on a background spacetime. Interestingly, it turns out that for a particular choice of the lapse and shift functions of the foliation, our symmetrized system reduces to the one found in [1]. Finally, we analyze the characteristic structure of the resulting evolution system.
Splitting of force-free EMHD current rings
NASA Astrophysics Data System (ADS)
Stenzel, R. L.
2005-10-01
Tilting of boundary-free field-reversed configurations has been observed in a laboratory plasma in the regime of electron magnetohydrodynamics (EMHD) [R. L. Stenzel, J. M. Urrutia, K. D. Strohmaier, and M. C. Griskey, Experiments on nonlinear EMHD fields, Physica Scripta T107, 163 (2004)]. Further investigations have revealed that the tilting is not due to magnetic forces, i.e., the torque on a magnetic dipole in an external field, because the magnetic force is balanced by the electric force in EMHD. The force-free current ring splits and moves slowly apart. Transverse gradients cause differences in propagation speed leading to an apparent tilt of the expanding current layer. The gradients are created in the early phase of the FRC creation. The propagation of EMHD fields depends primarily on magnetic field and density both of which are nonlinearly modified. The initially symmetric FRC relaxes into a spatially highly nonuniform field with multiple 3-D null points. Similar phenomena are seen during the interaction of two FRCs and also may occur in strong EMHD turbulence.
STABILITY OF RELATIVISTIC FORCE-FREE JETS
Narayan, Ramesh; Tchekhovskoy, Alexander; Li, Jason
2009-06-01
We consider a two-parameter family of cylindrical force-free equilibria, modeled to match numerical simulations of relativistic force-free jets. We study the linear stability of these equilibria, assuming a rigid impenetrable wall at the outer cylindrical radius R{sub j}. Equilibria in which the Lorentz factor {gamma}(R) increases monotonically with increasing radius R are found to be stable. On the other hand, equilibria in which {gamma}(R) reaches a maximum value at an intermediate radius and then declines to a smaller value {gamma}{sub j} at R{sub j} are unstable. A feature of these unstable equilibria is that poloidal field line curvature plays a prominent role in maintaining transverse force balance. The most rapidly growing mode is an m = 1 kink instability which has a growth rate {approx}(0.4/{gamma} {sub j})(c/R{sub j}). The e-folding length of the equivalent convected instability is {approx}2.5{gamma} {sub j} R{sub j}. For a typical jet with an opening angle {theta}{sub j} {approx} few/{gamma}{sub j}, the mode amplitude grows only weakly with increasing distance from the base of the jet. The growth is much slower than one might expect from a naive application of the Kruskal-Shafranov stability criterion.
Separable solutions of force-free spheres and applications to solar active regions
Prasad, A.; Mangalam, A.; Ravindra, B. E-mail: mangalam@iiap.res.in
2014-05-10
We present a systematic study of the force-free field equation for simple axisymmetric configurations in spherical geometry and apply it to the solar active regions. The condition of separability of solutions in the radial and angular variables leads to two classes of solutions: linear and nonlinear force-free fields (NLFF). We have studied these linear solutions and extended the nonlinear solutions for the radial power law index to the irreducible rational form n = p/q, which is allowed for all cases of odd p and cases of q > p for even p, where the poloidal flux ψ∝1/r{sup n} and the field B∝1/r {sup n+2}. We apply these solutions to simulate photospheric vector magnetograms obtained using the spectropolarimeter on board Hinode. The effectiveness of our search strategy is first demonstrated on test inputs of dipolar, axisymmetric, and nonaxisymmetric linear force-free fields. Using the best fit, we build three-dimensional axisymmetric field configurations and calculate the energy and relative helicity with two independent methods, which are in agreement. We have analyzed five magnetograms for AR 10930 spanning a period of three days during which two X-class flares occurred and found the free energy and relative helicity of the active region before and after the flare; our analysis indicates a peak in these quantities before the flare events, which is consistent with the other results. We also analyzed single-polarity regions AR 10923 and 10933, which showed very good fits to potential fields. This method provides useful reconstruction of NLFF and input fields for other numerical techniques.
Separable Solutions of Force-Free Spheres and Applications to Solar Active Regions
NASA Astrophysics Data System (ADS)
Prasad, A.; Mangalam, A.; Ravindra, B.
2014-05-01
We present a systematic study of the force-free field equation for simple axisymmetric configurations in spherical geometry and apply it to the solar active regions. The condition of separability of solutions in the radial and angular variables leads to two classes of solutions: linear and nonlinear force-free fields (NLFF). We have studied these linear solutions and extended the nonlinear solutions for the radial power law index to the irreducible rational form n = p/q, which is allowed for all cases of odd p and cases of q > p for even p, where the poloidal flux ψvprop1/rn and the field Bvprop1/r n + 2. We apply these solutions to simulate photospheric vector magnetograms obtained using the spectropolarimeter on board Hinode. The effectiveness of our search strategy is first demonstrated on test inputs of dipolar, axisymmetric, and nonaxisymmetric linear force-free fields. Using the best fit, we build three-dimensional axisymmetric field configurations and calculate the energy and relative helicity with two independent methods, which are in agreement. We have analyzed five magnetograms for AR 10930 spanning a period of three days during which two X-class flares occurred and found the free energy and relative helicity of the active region before and after the flare; our analysis indicates a peak in these quantities before the flare events, which is consistent with the other results. We also analyzed single-polarity regions AR 10923 and 10933, which showed very good fits to potential fields. This method provides useful reconstruction of NLFF and input fields for other numerical techniques.
Magnetospheres of black hole systems in force-free plasma
Palenzuela, Carlos; Garrett, Travis; Lehner, Luis; Liebling, Steven L.
2010-08-15
The interaction of black holes with ambient magnetic fields is important for a variety of highly energetic astrophysical phenomena. We study this interaction within the force-free approximation in which a tenuous plasma is assumed to have zero inertia. Blandford and Znajek used this approach to demonstrate the conversion of some of the black hole's energy into electromagnetic Poynting flux in stationary and axisymmetric single black hole systems. We adopt this approach and extend it to examine asymmetric and, most importantly, dynamical systems by implementing the fully nonlinear field equations of general relativity coupled to Maxwell's equations. For single black holes, we study, in particular, the dependence of the Poynting flux and show that, even for misalignments between the black hole spin and the direction of the asymptotic magnetic field, a Poynting flux is generated with a luminosity dependent on such misalignment. For binary black hole systems, we show both in the head-on and orbiting cases that the moving black holes generate a Poynting flux.
Gauge fields, nonlinear realizations, supersymmetry
NASA Astrophysics Data System (ADS)
Ivanov, E. A.
2016-07-01
This is a brief survey of the all-years research activity in the Sector "Supersymmetry" (the former Markov Group) at the Bogoliubov Laboratory of Theoretical Physics. The focus is on the issues related to gauge fields, spontaneously broken symmetries in the nonlinear realizations approach, and diverse aspects of supersymmetry.
The Nonlinear Field Space Theory
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
Shaping the nonlinear near field.
Wolf, Daniela; Schumacher, Thorsten; Lippitz, Markus
2016-01-01
Light scattering at plasmonic nanoparticles and their assemblies has led to a wealth of applications in metamaterials and nano-optics. Although shaping of fields around nanostructures is widely studied, the influence of the field inside the nanostructures is often overlooked. The linear field distribution inside the structure taken to the third power causes third-harmonic generation, a nonlinear optical response of matter. Here we demonstrate by a far field Fourier imaging method how this simple fact can be used to shape complex fields around a single particle alone. We employ this scheme to switch the third-harmonic emission from a single point source to two spatially separated but coherent sources, as in Young's double-slit assembly. We envision applications as diverse as coherently feeding antenna arrays and optical spectroscopy of spatially extended electronic states. PMID:26762487
Shaping the nonlinear near field
Wolf, Daniela; Schumacher, Thorsten; Lippitz, Markus
2016-01-01
Light scattering at plasmonic nanoparticles and their assemblies has led to a wealth of applications in metamaterials and nano-optics. Although shaping of fields around nanostructures is widely studied, the influence of the field inside the nanostructures is often overlooked. The linear field distribution inside the structure taken to the third power causes third-harmonic generation, a nonlinear optical response of matter. Here we demonstrate by a far field Fourier imaging method how this simple fact can be used to shape complex fields around a single particle alone. We employ this scheme to switch the third-harmonic emission from a single point source to two spatially separated but coherent sources, as in Young's double-slit assembly. We envision applications as diverse as coherently feeding antenna arrays and optical spectroscopy of spatially extended electronic states. PMID:26762487
Force-free electrodynamics in dynamical curved spacetimes
NASA Astrophysics Data System (ADS)
McWilliams, Sean
2015-04-01
We present results on our study of force-free electrodynamics in curved spacetimes. Specifically, we present several improvements to what has become the established set of evolution equations, and we apply these to study the nonlinear stability of analytically known force-free solutions for the first time. We implement our method in a new pseudo-spectral code built on top of the SpEC code for evolving dynamic spacetimes. Finally, we revisit these known solutions and attempt to clarify some interesting properties that render them analytically tractable. Finally, we preview some new work that similarly revisits the established approach to solving another problem in numerical relativity: the post-merger recoil from asymmetric gravitational-wave emission. These new results may have significant implications for the parameter dependence of recoils, and consequently on the statistical expectations for recoil velocities of merged systems.
Freely Decaying Turbulence in Force-free Electrodynamics
NASA Astrophysics Data System (ADS)
Zrake, Jonathan; East, William E.
2016-02-01
Freely decaying, relativistic force-free turbulence is studied for the first time. We initiate the magnetic field at a short wavelength and simulate its relaxation toward equilibrium on two- and three-dimensional periodic domains in both helical and nonhelical settings. Force-free turbulent relaxation is found to exhibit an inverse cascade in all settings and in three dimensions to have a magnetic energy spectrum consistent with the Kolmogorov 5/3 power law. Three-dimensional relaxations also obey the Taylor hypothesis; they settle promptly into the lowest-energy configuration allowed by conservation of the total magnetic helicity. However, in two dimensions, the relaxed state is a force-free equilibrium whose energy greatly exceeds the Taylor minimum and that contains persistent force-free current layers and isolated flux tubes. We explain this behavior in terms of additional topological invariants that exist only in two dimensions, namely the helicity enclosed within each level surface of the magnetic potential function. The speed and completeness of turbulent magnetic free-energy discharge could help account for rapidly variable gamma-ray emission from the Crab Nebula, gamma-ray bursts, blazars, and radio galaxies.
Force-free electromagnetic pulses in a laboratory plasma
NASA Technical Reports Server (NTRS)
Stenzel, R. L.; Urrutia, J. M.
1990-01-01
A short, intense current pulse is drawn from an electrode immersed in a magnetized afterglow plasma. The induced magnetic field B(r,t) assumes the shape of a helical double vortex which propagates along B(0) through the uniform plasma as a whistler mode. The observations support a prediction of force-free (J x B + neE = 0) electromagnetic fields and solitary waves. Energy and helicity are approximately conserved.
Ball lightning as a force-free magnetic knot
Ranada; Soler; Trueba
2000-11-01
The stability of fireballs in a recent model of ball lightning is studied. It is shown that the balls shine while relaxing in an almost quiescent expansion, and that three effects contribute to their stability: (i) the formation in each one during a process of Taylor relaxation of a force-free magnetic field, a concept introduced in 1954 in order to explain the existence of large magnetic fields and currents in stable configurations of astrophysical plasmas; (ii) the so called Alfven conditions in magnetohydrodynamics; and (iii) the approximate conservation of the helicity integral. The force-free fields that appear are termed "knots" because their magnetic lines are closed and linked. PMID:11102074
Spectral simulations of an axisymmetric force-free pulsar magnetosphere
NASA Astrophysics Data System (ADS)
Cao, Gang; Zhang, Li; Sun, Sineng
2016-02-01
A pseudo-spectral method with an absorbing outer boundary is used to solve a set of time-dependent force-free equations. In this method, both electric and magnetic fields are expanded in terms of the vector spherical harmonic (VSH) functions in spherical geometry and the divergence-free state of the magnetic field is enforced analytically by a projection method. Our simulations show that the Deutsch vacuum solution and the Michel monopole solution can be reproduced well by our pseudo-spectral code. Further, the method is used to present a time-dependent simulation of the force-free pulsar magnetosphere for an aligned rotator. The simulations show that the current sheet in the equatorial plane can be resolved well and the spin-down luminosity obtained in the steady state is in good agreement with the value given by Spitkovsky.
ON THE GLOBAL STRUCTURE OF PULSAR FORCE-FREE MAGNETOSPHERE
Petrova, S. A.
2013-02-20
The dipolar magnetic field structure of a neutron star is modified by the plasma originating in the pulsar magnetosphere. In the simplest case of a stationary axisymmetric force-free magnetosphere, a self-consistent description of the fields and currents is given by the well-known pulsar equation. Here we revise the commonly used boundary conditions of the problem in order to incorporate the plasma-producing gaps and to provide a framework for a truly self-consistent treatment of the pulsar magnetosphere. A generalized multipolar solution of the pulsar equation is found, which, as compared to the customary split monopole solution, is suggested to better represent the character of the dipolar force-free field at large distances. In particular, the outer gap location entirely inside the light cylinder implies that beyond the light cylinder the null and critical lines should be aligned and become parallel to the equator at a certain altitude. Our scheme of the pulsar force-free magnetosphere, which will hopefully be followed by extensive analytic and numerical studies, may have numerous implications for different fields of pulsar research.
THE FORCE-FREE MAGNETOSPHERE OF A ROTATING BLACK HOLE
Contopoulos, Ioannis; Kazanas, Demosthenes
2013-03-10
We revisit the Blandford-Znajek process and solve the fundamental equation that governs the structure of the steady-state force-free magnetosphere around a Kerr black hole. The solution depends on the distributions of the magnetic field angular velocity {omega} and the poloidal electric current I. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem: the inner ''light surface'' located inside the ergosphere and the outer ''light surface'' which is the generalization of the pulsar light cylinder. We find the solution for the simplest possible magnetic field configuration, the split monopole, through a numerical iterative relaxation method analogous to the one that yields the structure of the steady-state axisymmetric force-free pulsar magnetosphere. We obtain the rate of electromagnetic extraction of energy and confirm the results of Blandford and Znajek and of previous time-dependent simulations. Furthermore, we discuss the physical applicability of magnetic field configurations that do not cross both ''light surfaces''.
The Force-Free Magnetosphere of a Rotating Black Hole
NASA Technical Reports Server (NTRS)
Contopoulos, Ioannis; Kazanas, Demosthenes; Papadopoulos, Demetrios B.
2013-01-01
We revisit the Blandford-Znajek process and solve the fundamental equation that governs the structure of the steady-state force-free magnetosphere around a Kerr black hole. The solution depends on the distributions of the magnetic field angular velocity and the poloidal electric current. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem: the inner "light surface" located inside the ergosphere and the outer "light surface" which is the generalization of the pulsar light cylinder.We find the solution for the simplest possible magnetic field configuration, the split monopole, through a numerical iterative relaxation method analogous to the one that yields the structure of the steady-state axisymmetric force-free pulsar magnetosphere. We obtain the rate of electromagnetic extraction of energy and confirm the results of Blandford and Znajek and of previous time-dependent simulations. Furthermore, we discuss the physical applicability of magnetic field configurations that do not cross both "light surfaces."
Nonlinear diffusion waves in high magnetic fields
NASA Astrophysics Data System (ADS)
Oreshkin, V. I.; Chaikovsky, S. A.; Labetskaya, N. A.; Datsko, I. M.; Rybka, D. V.; Ratakhin, N. A.; Khishchenko, K. V.
2015-11-01
The nonlinear diffusion of a magnetic field and the large-scale instabilities arising upon an electrical explosion of conductors in a superstrong (2-3 MG) magnetic field were investigated experimentally on the MIG high-current generator (up to 2.5 peak current, 100 ns current rise time). It was observed that in the nonlinear stage of the process, the wavelength of thermal instabilities (striations) increased with a rate of 1.5-3 km/s.
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Primordial magnetic fields and nonlinear electrodynamics
Kunze, Kerstin E.
2008-01-15
The creation of large scale magnetic fields is studied in an inflationary universe where electrodynamics is assumed to be nonlinear. After inflation ends electrodynamics becomes linear and thus the description of reheating and the subsequent radiation dominated stage are unaltered. The nonlinear regime of electrodynamics is described by Lagrangians having a power-law dependence on one of the invariants of the electromagnetic field. It is found that there is a range of parameters for which primordial magnetic fields of cosmologically interesting strengths can be created.
Three-dimensional force-free looplike magnetohydrodynamic equilibria
NASA Technical Reports Server (NTRS)
Finn, John M.; Guzdar, Parvez N.; Usikov, Daniel
1994-01-01
Computations of three-dimensional force-free magnetohydrodynamic (MHD) equilibria, del x B = lambdaB with lambda = lambda(sub 0), a constant are presented. These equilibria are determined by boundary conditions on a surface corresponding to the solar photosphere. The specific boundary conditions used correspond to looplike magnetic fields in the corona. It is found that as lambda(sub 0) is increased, the loops of flux become kinked, and for sufficiently large lambda(sub 0), develop knots. The relationship between the kinking and knotting properties of these equilibria and the presence of a kink instability and related loss of equilibrium is explored. Clearly, magnetic reconnection must be involved for an unknotted loop equilibrium to become knotted, and speculations are made about the creation of a closed hyperbolic field line (X-line) about which this reconnection creating knotted field lines is centered.
Induced gravitation in nonlinear field models
NASA Astrophysics Data System (ADS)
Chernitskii, Alexander A.
2016-03-01
The description of gravitation in the framework of soliton interaction is considered for two nonlinear field models. These models are Born — Infeld nonlinear electrodynamics and so-called Born — Infeld type scalar field model. The last model can also be called the extremal space-time film one because of the specific form of the appropriate variational principle. Gravitational interaction is considered in the context of unification for all interactions of material particles. It is shown that long-range interaction of solitons of the models appears as force one and metrical one. The force interaction can be interpreted as electromagnetic one. The metrical interaction can be interpreted as gravitational one.
General-relativistic force-free pulsar magnetospheres
NASA Astrophysics Data System (ADS)
Pétri, J.
2016-02-01
Pulsar magnetospheres are shaped by ultrarelativistic electron/positron plasmas flowing in a strong magnetic field and subject to strong gravitational fields. The former induces magnetospheric currents and space charges responsible for the distortion of the electromagnetic field based on pure electrodynamics. The latter induces other perturbations in these fields based on space-time curvature. The force-free approximation describes the response of this magnetosphere to the presence of currents and charges and has been investigated by many authors. In this context, general relativity has been less discussed to quantify its influence on the neutron star electrodynamics. It is the purpose of this paper to compute general-relativistic force-free pulsar magnetospheres for realistic magnetic field configurations such as the inclined dipole. We performed time-dependent simulations of Maxwell equations in the 3+1 formalism of a stationary background metric in the slow-rotation approximation. We computed the resulting Poynting flux depending on the ratio R/rL and on frame-dragging through the spin parameter as, R is the neutron star radius and rL the light-cylinder radius. Both effects act together to increase the total Poynting flux seen by a distant observer by a factor up to 2 depending on the rotation rate. Moreover we retrieve the sin 2χ dependence of this luminosity, χ being the obliquity of the pulsar, as well as a braking index close to n = 3. We also show that the angular dependence of the Poynting flux scales like sin 2ϑ for the aligned rotator but like sin 4ϑ for the orthogonal rotator, ϑ being the colatitude.
Nonlinear cell response to strong electric fields
NASA Astrophysics Data System (ADS)
Bardos, D. C.; Thompson, C. J.; Yang, Y. S.; Joyner, K. H.
2000-07-01
The response of living cells to externally applied electric fields is of widespread interest. In particular, the intensification of electric fields across cell membranes is believed to be responsible, through membrane rupture and reversible membrane breakdown processes, for certain types of tissue damage in electrical trauma cases which cannot be attributed to Joule heating. Large elongated cells such as skeletal muscle fibres are particularly vulnerable to such damage. Previous theoretical studies of field intensification across cell membranes in such cells have assumed the membrane current to be linear in the applied field (Ohmic membrane conductivity) and were limited to sinusoidal applied fields. In this paper, we investigate a simple model of a long cylindrical cell, corresponding to nerve or skeletal muscle cells. Employing the electroquasistatic approximation, a system of coupled first-order differential equations for the membrane electric field is derived which incorporates arbitrary time dependence in the external field and nonlinear membrane response (non-Ohmic conductivity). The behaviour of this model is investigated for a variety of applied fields in both the linear and highly nonlinear regimes. We find that peak membrane fields predicted by the nonlinear model are approximately twice as intense, for low-frequency electrical trauma conditions, as those of the linear theory.
Imbalanced relativistic force-free magnetohydrodynamic turbulence
Cho, Jungyeon; Lazarian, A.
2014-01-01
When magnetic energy density is much larger than that of matter, as in pulsar/black hole magnetospheres, the medium becomes force-free and we need relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD), Alfvénic MHD turbulence in the relativistic limit can be described by interactions of counter-traveling wave packets. In this paper, we numerically study strong imbalanced MHD turbulence in such environments. Here, imbalanced turbulence means the waves traveling in one direction (dominant waves) have higher amplitudes than the opposite-traveling waves (sub-dominant waves). We find that (1) spectrum of the dominant waves is steeper than that of sub-dominant waves, (2) the anisotropy of the dominant waves is weaker than that of sub-dominant waves, and (3) the dependence of the ratio of magnetic energy densities of dominant and sub-dominant waves on the ratio of energy injection rates is steeper than quadratic (i.e., b{sub +}{sup 2}/b{sub −}{sup 2}∝(ϵ{sub +}/ϵ{sub −}){sup n} with n > 2). These results are consistent with those obtained for imbalanced non-relativistic Alfvénic turbulence. This corresponds well to the earlier reported similarity of the relativistic and non-relativistic balanced magnetic turbulence.
Force-free electromagnetic pulses in a laboratory plasma
Stenzel, R.L.; Urrutia, J.M. )
1990-10-15
A short, intense current pulse ({ital I}=150 A, {Delta}{ital t}{congruent}0.2 {mu}s, {ital N}{congruent}2{times}10{sup 14} electrons) is drawn from an electrode immersed in a magnetized afterglow plasma ({ital n}{congruent}2{times}10{sup 11} cm{sup {minus}3}, {ital kT}{sub {ital e}}{congruent}1.3 eV, {ital B}{sub 0}=10 G). The induced magnetic field {bold B}({bold r},{ital t}) assumes the shape of a helical double vortex which propagates along {bold B}{sub 0} through the uniform plasma as a whistler mode. The observations support a prediction of force-free ({bold J}{times}{bold B}+{ital ne}{bold E}=0) electromagnetic fields and solitary waves. Energy and helicity are approximately conserved.
New approaches to nonlinear diffractive field propagation.
Christopher, P T; Parker, K J
1991-07-01
In many domains of acoustic field propagation, such as medical ultrasound imaging, lithotripsy shock treatment, and underwater sonar, a realistic calculation of beam patterns requires treatment of the effects of diffraction from finite sources. Also, the mechanisms of loss and nonlinear effects within the medium are typically nonnegligible. The combination of diffraction, attenuation, and nonlinear effects has been treated by a number of formulations and numerical techniques. A novel model that incrementally propagates the field of baffled planar sources with substeps that account for the physics of diffraction, attenuation, and nonlinearity is presented. The model accounts for the effect of refraction and reflection (but not multiple reflections) in the case of propagation through multiple, parallel layers of fluid medium. An implementation of the model for axis symmetric sources has been developed. In one substep of the implementation, a new discrete Hankel transform is used with spatial transform techniques to propagate the field over a short distance with diffraction and attenuation. In the other substep, the temporal frequency domain solution to Burgers' equation is implemented to account for the nonlinear accretion and depletion of harmonics. This approach yields a computationally efficient procedure for calculating beam patterns from a baffled planar, axially symmetric source under conditions ranging from quasilinear through shock. The model is not restricted by the usual parabolic wave approximation and the field's directionality is explicitly accounted for at each point. Useage of a harmonic-limiting scheme allows the model to propagate some previously intractable high-intensity nonlinear fields. Results of the model are shown to be in excellent agreement with measurements performed on the nonlinear field of an unfocused 2.25-MHz piston source, even in the near field where the established parabolic wave approximation model fails. Next, the model is used to
High field optical nonlinearities in gases
NASA Astrophysics Data System (ADS)
Cheng, Yu-Hsiang
Optical femtosecond self-channeling in gases, also called femtosecond filamentation, has become an important area of research in high field nonlinear optics. Filamentation occurs when laser light self-focuses in a gas owing to self-induced nonlinearity, and then defocuses in the plasma generated by the self-focused beam. The result of this process repeating itself multiple times is an extended region of plasma formation. Filamentation studies have been motivated by the extremely broad range of applications, especially in air, including pulse compression, supercontinuum generation, broadband high power terahertz pulse generation, discharge triggering and guiding, and remote sensing. Despite the worldwide work in filamentation, the fundamental gas nonlinearities governing self-focusing had never been directly measured in the range of laser intensity up to and including the ionization threshold. This dissertation presents the first such measurements. We absolutely measured the temporal refractive index change of O2, N2, Ar, H2, D2 and N2O caused by highfield ultrashort optical pulses with single-shot supercontinuum spectral interferometry, cleanly separating for the first time the instantaneous electronic and delayed rotational nonlinear response in diatomic gases. We conclusively showed that a recent claim by several European groups that the optical bound electron nonlinearity saturates and goes negative is not correct. Such a phenomenon would preclude the need for plasma to provide the defocusing contribution for filamentation. Our results show that the 'standard model of filamentation', where the defocusing is provided by plasma, is correct. Finally, we demonstrated that high repetition rate femtosecond laser pulses filamenting in gases can generate long-lived gas density `holes' which persist on millisecond timescales, long after the plasma has recombined. Gas density decrements up to ~20% have been measured. The density hole refilling is dominated by thermal
A short model excitation of an asymmetric force free superconducting transmission line magnet
Wake, M.; Sato, H.; Carcagno, R.; Foster, W.; Hays, S.; Kashikhin, V.; Oleck, A.; Piekarz, H.; Rabehl, R,; /Fermilab
2005-09-01
A short model of asymmetric force free magnet with single beam aperture was tested at Fermilab together with the excitation test of VLHC transmission line magnet. The design concept of asymmetric force free superconducting magnet was verified by the test. The testing reached up to 104 kA current and no indication of force imbalance was observed. Since the model magnet length was only 10cm, A 0.75m model was constructed and tested at KEK with low current to ensure the validity of the design. The cool down and the excitation at KEK were also successful finding very small thermal contraction of the conductor and reasonable field homogeneity.
NASA Astrophysics Data System (ADS)
He, Xiaokai; Cao, Zhoujian
2016-01-01
The Hertz potential is a powerful tool for the source-free electrodynamics. Especially for the algebraically special spacetime background, the Hertz potential formalism simplifies the Maxwell equations quite much. In astrophysics, strong electric-magnetic field is very common. Force-free electrodynamics is a good approximation for strong enough electric-magnetic field compared to the inertial energy of the involved plasma. For example, the force-free model has been extensively used to describe the magnetosphere of stars in the universe. In this paper, we extend the Hertz potential formalism to the force-free electrodynamics. The Hertz potential formalism simplifies the force-free dynamical equations as much as that in the source-free case. As an application, we use the Hertz potential formalism to the Schwarzschild background. And the Brennan-Gralla-Jacobson solutions are recovered straightforwardly.
Towards an understanding of the force-free magnetosphere of rapidly spinning black holes
NASA Astrophysics Data System (ADS)
Zhang, Fan; Yang, Huan; Lehner, Luis
2014-12-01
The ability of a plasma surrounding spinning black holes to extract rotational energy and power energetic emissions has been recognized as a key astrophysical phenomenon. Important insights into the nature of this process are obtained through the analysis of the interplay between a force-free magnetosphere and the black hole. This task involves solving a complicated system of equations, often requiring complex numerical simulations. Recent analytical attempts at tackling this problem have exploited the fact that the near-horizon region of extreme Kerr (NHEK) is endowed with an enhanced symmetry group. We continue in this direction and show that for some conformally self-similar solutions, the NHEK force-free equations reduce to a single nonlinear ordinary differential equation which is difficult to solve with straightforward integration. We here introduce a new approach specifically tailored to this problem and describe how one can obtain physically meaningful solutions.
Time Evolution of Force-Free Parameter and Free Magnetic Energy in Active Region NOAA 10365
NASA Astrophysics Data System (ADS)
Valori, G.; Romano, P.; Malanushenko, A.; Ermolli, I.; Giorgi, F.; Steed, K.; van Driel-Gesztelyi, L.; Zuccarello, F.; Malherbe, J.-M.
2015-02-01
We describe the variation of the accumulated coronal helicity derived from the magnetic helicity flux through the photosphere in active region (AR) NOAA 10365, where several large flares and coronal mass ejections (CMEs) occurred. We used SOHO/MDI full-disk line-of-sight magnetograms to measure the helicity flux, and the integral of GOES X-ray flux as a proxy of the coronal energy variations due to flares or CMEs. Using the linear force-free field model, we transformed the accumulated helicity flux into a time sequence of the force-free parameter α accounting for flares or CMEs via the proxy derived from GOES observations. This method can be used to derive the value of α at different times during the AR evolution, and is a partial alternative to the commonly used match of field lines with EUV loops. By combining the accumulated helicity obtained from the observations with the linear force-free theory, we describe the main phases of the emergence process of the AR, and relate them temporally with the occurrence of flares or CMEs. Additionally, a comparison with the loop-matching method of fixing alpha at each time independently shows that the proposed method may be helpful in avoiding unrealistic or undetermined values of alpha that may originate from an insufficient quality of the image used to identify coronal loops at a given time. For the relative intensity of the considered events, the linear force-free field theory implies that there is a direct correlation between the released energy on the one hand and the product of the coronal helicity with the variation of α due to the event on the other. Therefore, the higher the value of the accumulated coronal helicity, the smaller the force-free parameter variation required to produce the same decrease in the free energy during the CMEs.
Forced free-shear layer measurements
NASA Technical Reports Server (NTRS)
Leboeuf, Richard L.
1994-01-01
Detailed three-dimensional three-component phase averaged measurements of the spanwise and streamwise vorticity formation and evolution in acoustically forced plane free-shear flows have been obtained. For the first time, phase-averaged measurements of all three velocity components have been obtained in both a mixing layer and a wake on three-dimensional grids, yielding the spanwise and streamwise vorticity distributions without invoking Taylor's hypothesis. Initially, two-frequency forcing was used to phase-lock the roll-up and first pairing of the spanwise vortical structures in a plane mixing layer. The objective of this study was to measure the near-field vortical structure morphology in a mixing layer with 'natural' laminar initial boundary layers. For the second experiment the second and third subharmonics of the fundamental roll-up frequency were added to the previous two-frequency forcing in order to phase-lock the roll-up and first three pairings of the spanwise rollers in the mixing layer. The objective of this study was to determine the details of spanwise scale changes observed in previous time-averaged measurements and flow visualization of unforced mixing layers. For the final experiment, single-frequency forcing was used to phase-lock the Karman vortex street in a plane wake developing from nominally two-dimensional laminar initial boundary layers. The objective of this study was to compare measurements of the three-dimensional structure in a wake developing from 'natural' initial boundary layers to existing models of wake vortical structure.
EFFECT OF SOLAR CHROMOSPHERIC NEUTRALS ON EQUILIBRIUM FIELD STRUCTURES
Arber, T. D.; Botha, G. J. J.; Brady, C. S. E-mail: G.J.J.Botha@warwick.ac.u
2009-11-10
Solar coronal equilibrium fields are often constructed by nonlinear force-free field (NLFFF) extrapolation from photospheric magnetograms. It is well known that the photospheric field is not force-free and the correct lower boundary for NLFFF construction ought to be the top of the chromosphere. To compensate for this, pre-filtering algorithms are often applied to the photospheric data to remove the non-force-free components. Such pre-filtering models, while physically constrained, do not address the mechanisms that may be responsible for the field becoming force-free. The chromospheric field can change through, for example, field expansion due to gravitational stratification, reconnection, or flux emergence. In this paper, we study and quantify the effect of the chromospheric neutrals on equilibrium field structures. It is shown that, depending on the degree to which the photospheric field is not force-free, the chromosphere will change the structure of the equilibrium field. This is quantified to give an estimate of the change in alpha profiles one might expect due to neutrals in the chromosphere. Simple scaling of the decay time of non-force-free components of the magnetic field due to chromospheric neutrals is also derived. This is used to quantify the rate at which, or equivalent at which height, the chromosphere is expected to become force-free.
NASA Astrophysics Data System (ADS)
Rapoport, Yu G.; Boardman, A. D.; Grimalsky, V. V.; Ivchenko, V. M.; Kalinich, N.
2014-05-01
The idea of nonlinear ‘transformation optics-inspired’ [1-6] electromagnetic cylindrical field concentrators has been taken up in a preliminary manner in a number of conference reports [7-9]. Such a concentrator includes both external linear region with a dielectric constant increased towards the centre and internal region with nonlinearity characterized by constant coefficients. Then, in the process of farther investigations we realized the following factors considered neither in [7-9] nor in the recent paper [10]: saturation of nonlinearity, nonlinear losses, linear gain, numerical convergence, when nonlinear effect becomes very strong and formation of ‘hotspots’ starts. It is clearly demonstrated here that such a strongly nonlinear process starts when the nonlinear amplitude of any incident beam(s) exceeds some ‘threshold’ value. Moreover, it is shown that the formation of hotspots may start as the result of any of the following processes: an increase of the input amplitude, increasing the linear amplification in the central nonlinear region, decreasing the nonlinear losses, a decrease in the saturation of the nonlinearity. Therefore, a tendency to a formation of ‘hotspots’ is a rather universal feature of the strongly nonlinear behaviour of the ‘nonlinear resonator’ system, while at the same time the system is not sensitive to the ‘prehistory’ of approaching nonlinear threshold intensity (amplitude). The new proposed method includes a full-wave nonlinear solution analysis (in the nonlinear region), a new form of complex geometric optics (in the linear inhomogeneous external cylinder), and new boundary conditions, matching both solutions. The observed nonlinear phenomena will have a positive impact upon socially and environmentally important devices of the future. Although a graded-index concentrator is used here, it is a direct outcome of transformation optics. Numerical evaluations show that for known materials these nonlinear effects
Field Measurement of the Acoustic Nonlinearity Parameter in Turbine Blades
NASA Technical Reports Server (NTRS)
Hinton, Yolanda L.; Na, Jeong K.; Yost, William T.; Kessel, Gregory L.
2000-01-01
Nonlinear acoustics techniques were used to measure fatigue in turbine blades in a power generation plant. The measurements were made in the field using a reference based measurement technique, and a reference sample previously measured in the laboratory. The acoustic nonlinearity parameter showed significant increase with fatigue in the blades, as indicated by service age and areas of increased stress. The technique shows promise for effectively measuring fatigue in field applications and predicting subsequent failures.
NASA Astrophysics Data System (ADS)
Yu, Cong
2011-03-01
The force-free (or low inertia) limit of magnetohydrodynamics (MHD) can be applied to many astrophysical objects, including black holes, neutron stars and accretion discs, where the electromagnetic field is so strong that the inertia and pressure of the plasma can be ignored. This is difficult to achieve with the standard MHD numerical methods because they still have to deal with plasma inertial terms even when these terms are much smaller than the electromagnetic terms. Under the force-free approximation, the plasma dynamics is entirely determined by the magnetic field. The plasma provides the currents and charge densities required by the dynamics of electromagnetic fields, but these currents carry no inertia. We present a high-order Godunov scheme to study such force-free electrodynamics. We have implemented weighted essentially non-oscillatory (WENO) spatial interpolations in our scheme. An exact Riemann solver is implemented, which requires spectral decomposition into characteristic waves. We advance the magnetic field with the constrained transport (CT) scheme to preserve the divergence-free condition to machine round-off error. We apply the third-order total variation diminishing (TVD) Runge-Kutta scheme for the temporal integration. The mapping from face-centred variables to volume-centred variables is carefully considered. Extensive testing are performed to demonstrate the ability of our scheme to address force-free electrodynamics correctly. We finally apply the scheme to study relativistic magnetically dominated tearing instabilities and neutron star magnetospheres.
Exact force-free electrodynamic solutions and their perturbations
NASA Astrophysics Data System (ADS)
Zhang, Fan; Lehner, Luis; McWilliams, Sean; Pfeiffer, Harald; Yang, Huan
2015-04-01
This talk is an amalgamation of several works relating to finding exact force-free electrodynamic (FFE) solutions and examining their behaviour under perturbations, both analytically and numerically. The talk will briefly discuss technical points such as the choice of numerical FFE evolution systems and challenges posed by light surfaces when seeking analytical FFE solutions, presenting along the way a couple of new solutions in the near horizon extreme Kerr spacetime. It will then move on to present the mode structure of the perturbed Blandford-Znajek solution and some results concerning the stability of a family of exact propagating FFE solutions. Supported in part by NSFC Grant No. 11443008.
Nonlinear spin-wave excitations at low magnetic bias fields
Bauer, Hans G.; Majchrak, Peter; Kachel, Torsten; Back, Christian H.; Woltersdorf, Georg
2015-01-01
Nonlinear magnetization dynamics is essential for the operation of numerous spintronic devices ranging from magnetic memory to spin torque microwave generators. Examples are microwave-assisted switching of magnetic structures and the generation of spin currents at low bias fields by high-amplitude ferromagnetic resonance. Here we use X-ray magnetic circular dichroism to determine the number density of excited magnons in magnetically soft Ni80Fe20 thin films. Our data show that the common model of nonlinear ferromagnetic resonance is not adequate for the description of the nonlinear behaviour in the low magnetic field limit. Here we derive a model of parametric spin-wave excitation, which correctly predicts nonlinear threshold amplitudes and decay rates at high and at low magnetic bias fields. In fact, a series of critical spin-wave modes with fast oscillations of the amplitude and phase is found, generalizing the theory of parametric spin-wave excitation to large modulation amplitudes. PMID:26374256
Nonlinear spin-wave excitations at low magnetic bias fields
NASA Astrophysics Data System (ADS)
Woltersdorf, Georg
We investigate experimentally and theoretically the nonlinear magnetization dynamics in magnetic films at low magnetic bias fields. Nonlinear magnetization dynamics is essential for the operation of numerous spintronic devices ranging from magnetic memory to spin torque microwave generators. Examples are microwave-assisted switching of magnetic structures and the generation of spin currents at low bias fields by high-amplitude ferromagnetic resonance. In the experiments we use X-ray magnetic circular dichroism to determine the number density of excited magnons in magnetically soft Ni80Fe20 thin films. Our data show that the common Suhl instability model of nonlinear ferromagnetic resonance is not adequate for the description of the nonlinear behavior in the low magnetic field limit. Here we derive a model of parametric spin-wave excitation, which correctly predicts nonlinear threshold amplitudes and decay rates at high and at low magnetic bias fields. In fact, a series of critical spin-wave modes with fast oscillations of the amplitude and phase is found, generalizing the theory of parametric spin-wave excitation to large modulation amplitudes. For these modes, we also find pronounced frequency locking effects that may be used for synchronization purposes in magnonic devices. By using this effect, effective spin-wave sources based on parametric spin-wave excitation may be realized. Our results also show that it is not required to invoke a wave vector-dependent damping parameter in the interpretation of nonlinear magnetic resonance experiments performed at low bias fields.
Gamma-Ray Pulsar Light Curves in Vacuum and Force-Free Geometry
NASA Technical Reports Server (NTRS)
Harding, Alice K.; DeCesar, Megan E.; Miller, M. Coleman; Kalapotharakos, Constantinos; Contopoulos, Ioannis
2011-01-01
Recent studies have shown that gamma-ray pulsar light curves are very sensitive to the geometry of the pulsar magnetic field. Pulsar magnetic field geometries, such as the retarded vacuum dipole and force-free magnetospheres have distorted polar caps that are offset from the magnetic axis in the direction opposite to rotation. Since this effect is due to the sweepback of field lines near the light cylinder, offset polar caps are a generic property of pulsar magnetospheres and their effects should be included in gamma-ray pulsar light curve modeling. In slot gap models (having two-pole caustic geometry), the offset polar caps cause a strong azimuthal asymmetry of the particle acceleration around the magnetic axis. We have studied the effect of the offset polar caps in both retarded vacuum dipole and force-free geometry on the model high-energy pulse profiles. We find that, compared to the profiles derived from symmetric caps, the flux in the pulse peaks, which are caustics formed along the trailing magnetic field lines, increases significantly relative to the off-peak emission, formed along leading field lines. The enhanced contrast produces improved slot gap model fits to Fermi pulsar light curves like Vela, with vacuum dipole fits being more favorable.
A nonlinear field theory of deformable dielectrics
NASA Astrophysics Data System (ADS)
Suo, Zhigang; Zhao, Xuanhe; Greene, William H.
Two difficulties have long troubled the field theory of dielectric solids. First, when two electric charges are placed inside a dielectric solid, the force between them is not a measurable quantity. Second, when a dielectric solid deforms, the true electric field and true electric displacement are not work conjugates. These difficulties are circumvented in a new formulation of the theory in this paper. Imagine that each material particle in a dielectric is attached with a weight and a battery, and prescribe a field of virtual displacement and a field of virtual voltage. Associated with the virtual work done by the weights and inertia, define the nominal stress as the conjugate to the gradient of the virtual displacement. Associated with the virtual work done by the batteries, define the nominal electric displacement as the conjugate to the gradient of virtual voltage. The approach does not start with Newton's laws of mechanics and Maxwell-Faraday theory of electrostatics, but produces them as consequences. The definitions lead to familiar and decoupled field equations. Electromechanical coupling enters the theory through material laws. In the limiting case of a fluid dielectric, the theory recovers the Maxwell stress. The approach is developed for finite deformation, and is applicable to both elastic and inelastic dielectrics. As applications of the theory, we discuss material laws for elastic dielectrics, and study infinitesimal fields superimposed upon a given field, including phenomena such as vibration, wave propagation, and bifurcation.
Analytic Properties of Force-free Jets in the Kerr Spacetime—II
NASA Astrophysics Data System (ADS)
Pan, Zhen; Yu, Cong
2016-01-01
We reinvestigate the structure of a steady axisymmetric force-free magnetosphere around a Kerr black hole (BH). The BH magnetosphere structure is governed by a second-order differential equation of Aϕ depending on two “free” functions Ω and I, where Aϕ is the ϕ component of the vector potential of the electromagnetic field, Ω is the angular velocity of the magnetic field lines, and I is the poloidal electric current. While the two functions Ω and I are not arbitrarily given, they do need to be self-consistently determined along with the differential equation. Based on the perturbation approach we proposed in paper I, in this paper, we self-consistently sort out two boundary conditions governing Ω and I, and interpret these conditions mathematically and physically. Making use of the boundary conditions, we prove that all magnetic field lines crossing the infinite-redshift surface also penetrate the event horizon. Furthermore, we argue that the BH Meissner effect does not work in a force-free magnetosphere due to the perfect conductivity.
Seismological Field Observation of Mesoscopic Nonlinearity
NASA Astrophysics Data System (ADS)
Sens-Schönfelder, Christoph; Gassenmeier, Martina; Eulenfeld, Tom; Tilmann, Frederik; Korn, Michael; Niederleithinger, Ernst
2016-04-01
of events associated with separately inverted parameters. As the local ground acceleration is not correlated to static stress changes we can exclude static stress changes as causative process. The shaking sensitivity and healing process is well known from laboratory experiments in composite materials as mesoscopic nonlinearity. The sensitive behavior at this station is related to the particular near surface material that is a conglomerate cemented with gypsum - so called gypcrete. However, mesoscopic nonlinearity with different parameters might be a key to understand velocity changes also at other sites.
Equilibrium thermodynamics and stochastic nonlinear acoustic fields. [in crystalline lattices
NASA Technical Reports Server (NTRS)
Cantrell, J. H.
1985-01-01
A crystalline solid is considered to consist of a large number of incoherent nonlinear acoustic radiation sources identified with the vibrating particles of the crystalline lattice. Randomization of the field, together with the assumption of a stochastically independent, fluctuating, radiation field at the absolue zero of temperature, leads to an expression of the temperature-dependent radiation field in terms of the zero-point field. The equation is identified with the Planck distribution formula of quantum mechanics in the linear field limit. The thermodynamic state functions are also obtained in terms of the nonlinear acoustic modal energies per unit mass and reduce to the results of the Debye-Einstein stochastic quantum oscillator model in the linear field limit.
Modulation of Radio Frequency Signals by Nonlinearly Generated Acoustic Fields
NASA Astrophysics Data System (ADS)
Johnson, Spencer Joseph
Acousto-electromagnetic scattering is a process in which an acoustic excitation is utilized to induce modulation on an electromagnetic (EM) wave. This phenomenon can be exploited in remote sensing and detection schemes whereby target objects are mechanically excited by high powered acoustic waves resulting in unique object characterizations when interrogated with EM signals. Implementation of acousto-EM sensing schemes, however, are limited by a lack of fundamental understanding of the nonlinear interaction between acoustic and EM waves and inefficient simulation methods in the determination of the radiation patterns of higher order scattered acoustic fields. To address the insufficient simulation issue, a computationally efficient mathematical model describing higher order scattered sound fields, particularly of third-order in which a 40x increase in computation speed is achieved, is derived using a multi-Gaussian beam (MGB) expansion that expresses the sound field of any arbitrary axially symmetric beam as a series of Gaussian base functions. The third-order intermodulation (IM3) frequency components are produced by considering the cascaded nonlinear second-order effects when analyzing the interaction between the first- and second-order frequency components during the nonlinear scattering of sound by sound from two noncollinear ultrasonic baffled piston sources. The theory is extended to the modeling of the sound beams generated by parametric transducer arrays, showing that the MGB model can be efficiently used to calculate both the second- and third-order sound fields of the array. Additionally, a near-to-far-field (NTFF) transformation method is developed to model the far-field characteristics of scattered sound fields, extending Kirchhoff's theorem, typically applied to EM waves, determining the far-field patterns of an acoustic source from amplitude and phase measurements made in the near-field by including the higher order sound fields generated by the
Nonlinear plasma and beam physics in plasma wake-fields
Rosenzweig, J.B.
1990-02-12
In experimental studies of the Plasma Wake-field Accelerator performed to date at the Argonne Advanced Accelerator Test Facility, significant nonlinearities in both plasma and beam behavior have been observed. The plasma waves driven in the wake of the intense driving beam in these experiments exhibit three-dimensional nonlinear behavior which has as yet no quantitative theoretical explanation. This nonlinearity is due in part to the self-pinching of the driving beam in the plasma, as the denser self-focused beam can excite larger amplitude plasma waves. The self-pinching is a process with interesting nonlinear aspects: the initial evolution of the beam envelope and the subsequent approach to Bennett equilibrium through phase mixing. 35 refs., 10 figs.
Nonlinear Bubble Interactions in Acoustic Pressure Fields
NASA Technical Reports Server (NTRS)
Barbat, Tiberiu; Ashgriz, Nasser; Liu, Ching-Shi
1996-01-01
The systems consisting of a two-phase mixture, as clouds of bubbles or drops, have shown many common features in their responses to different external force fields. One of particular interest is the effect of an unsteady pressure field applied to these systems, case in which the coupling of the vibrations induced in two neighboring components (two drops or two bubbles) may result in an interaction force between them. This behavior was explained by Bjerknes by postulating that every body that is moving in an accelerating fluid is subjected to a 'kinetic buoyancy' equal with the product of the acceleration of the fluid multiplied by the mass of the fluid displaced by the body. The external sound wave applied to a system of drops/bubbles triggers secondary sound waves from each component of the system. These secondary pressure fields integrated over the surface of the neighboring drop/bubble may result in a force additional to the effect of the primary sound wave on each component of the system. In certain conditions, the magnitude of these secondary forces may result in significant changes in the dynamics of each component, thus in the behavior of the entire system. In a system containing bubbles, the sound wave radiated by one bubble at the location of a neighboring one is dominated by the volume oscillation mode and its effects can be important for a large range of frequencies. The interaction forces in a system consisting of drops are much smaller than those consisting of bubbles. Therefore, as a first step towards the understanding of the drop-drop interaction subject to external pressure fluctuations, it is more convenient to study the bubble interactions. This paper presents experimental results and theoretical predictions concerning the interaction and the motion of two levitated air bubbles in water in the presence of an acoustic field at high frequencies (22-23 KHz).
Nonlinear electromagnetic fields as a source of universe acceleration
NASA Astrophysics Data System (ADS)
Kruglov, S. I.
2016-04-01
A model of nonlinear electromagnetic fields with a dimensional parameter β is proposed. From PVLAS experiment the bound on the parameter β was obtained. Electromagnetic fields are coupled with the gravitation field and we show that the universe accelerates due to nonlinear electromagnetic fields. The magnetic universe is considered and the stochastic magnetic field is a background. After inflation the universe decelerates and approaches to the radiation era. The range of the scale factor, when the causality of the model and a classical stability take place, was obtained. The spectral index, the tensor-to-scalar ratio, and the running of the spectral index were estimated which are in approximate agreement with the Planck, WMAP, and BICEP2 data.
Nonlinear electron acoustic waves in presence of shear magnetic field
Dutta, Manjistha; Khan, Manoranjan; Ghosh, Samiran; Chakrabarti, Nikhil
2013-12-15
Nonlinear electron acoustic waves are studied in a quasineutral plasma in the presence of a variable magnetic field. The fluid model is used to describe the dynamics of two temperature electron species in a stationary positively charged ion background. Linear analysis of the governing equations manifests dispersion relation of electron magneto sonic wave. Whereas, nonlinear wave dynamics is being investigated by introducing Lagrangian variable method in long wavelength limit. It is shown from finite amplitude analysis that the nonlinear wave characteristics are well depicted by KdV equation. The wave dispersion arising in quasineutral plasma is induced by transverse magnetic field component. The results are discussed in the context of plasma of Earth's magnetosphere.
Nonlinear propagation in ultrasonic fields: measurements, modelling and harmonic imaging.
Humphrey, V F
2000-03-01
In high amplitude ultrasonic fields, such as those used in medical ultrasound, nonlinear propagation can result in waveform distortion and the generation of harmonics of the initial frequency. In the nearfield of a transducer this process is complicated by diffraction effects associated with the source. The results of a programme to study the nonlinear propagation in the fields of circular, focused and rectangular transducers are described, and comparisons made with numerical predictions obtained using a finite difference solution to the Khokhlov-Zabolotskaya-Kuznetsov (or KZK) equation. These results are extended to consider nonlinear propagation in tissue-like media and the implications for ultrasonic measurements and ultrasonic heating are discussed. The narrower beamwidths and reduced side-lobe levels of the harmonic beams are illustrated and the use of harmonics to form diagnostic images with improved resolution is described. PMID:10829672
Formation of sub-ion scale filamentary force-free structures in the vicinity of reconnection region
NASA Astrophysics Data System (ADS)
Zelenyi, L. M.; Frank, A. G.; Artemyev, A. V.; Petrukovich, A. A.; Nakamura, R.
2016-05-01
In this paper we review the results of spacecraft observations of current sheets (CSs) of sub-ion spatial scales in the Earth’s magnetotail as well as experiments with these structures in laboratory devices. We demonstrate that such sub-ion CSs having a thickness less than the ion gyroradius are usually formed in the vicinity of the magnetic reconnection region and are supported by strong electron currents flowing along magnetic field lines. The magnetic field configuration of sub-ion CSs is close to the force-free configuration, with a strong shear magnetic field component in the CS central region. Spacecraft observations suggest that parallel electron currents are generated by electron beams (pronounced enhancement of the phase space density for electrons with small pitch angles and energies ∼1–3 keV). We discuss several models describing such force-free sub-ion CSs.
NASA Astrophysics Data System (ADS)
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu
2016-02-01
The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu
2016-02-01
The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition. PMID:26497312
Active-Region Twist Derived from Magnetic Tongues and Linear Force-Free Extrapolations
NASA Astrophysics Data System (ADS)
Poisson, Mariano; López Fuentes, Marcelo; Mandrini, Cristina H.; Démoulin, Pascal
2015-11-01
The main aim of this study is to compare the amount of twist present in emerging active regions (ARs) from photospheric and coronal data. We use linear force-free field models of the observed coronal structure of ARs to determine the global twist. The coronal twist is derived, on one hand, from the force-free parameter [α] of the model and, on the other, from the computed coronal magnetic helicity normalized by the magnetic flux squared. We compare our results, for the same set of ARs, with those of Poisson et al. ( Solar Phys. 290, 727, 2015), in which the twist was estimated using the so-called magnetic tongues observed in line-of-sight magnetograms during AR emergence. We corroborate the agreement between the photospheric and coronal twist-sign and the presence of magnetic tongues as an early proxy of the AR non-potentiality. We find a globally linear relationship between the coronal twist and the one previously deduced for the emerging AR flux rope at the photospheric level. The coronal-twist value is typically lower by a factor of six than the one deduced for the emerging flux rope. We interpret this result as due to the partial emergence of the flux rope that forms the region.
Spectral investigation of nonlinear local field effects in Ag nanoparticles
Sato, Rodrigo Takeda, Yoshihiko; Ohnuma, Masato; Oyoshi, Keiji
2015-03-21
The capability of Ag nanoparticles to modulate their optical resonance condition, by optical nonlinearity, without an external feedback system was experimentally demonstrated. These optical nonlinearities were studied in the vicinity of the localized surface plasmon resonance (LSPR), using femtosecond pump-and-probe spectroscopy with a white-light continuum probe. Transient transmission changes ΔT/T exhibited strong photon energy and particle size dependence and showed a complex and non-monotonic change with increasing pump light intensity. Peak position and change of sign redshift with increasing pump light intensity demonstrate the modulation of the LSPR. These features are discussed in terms of the intrinsic feedback via local field enhancement.
Relativistic nonlinear plasma waves in a magnetic field
NASA Technical Reports Server (NTRS)
Kennel, C. F.; Pellat, R.
1975-01-01
Five relativistic plane nonlinear waves were investigated: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. When the ions are driven relativistic, they behave like electrons, and the assumption of an 'electron-positron' plasma leads to equations which have the form of a one-dimensional potential well. The solutions indicate that a large-amplitude superluminous wave determines the average plasma properties.
Nonlinear electric field structures in the inner magnetosphere
Malaspina, D. M.; Andersson, L.; Ergun, R. E.; Wygant, J. R.; Bonnell, J. W.; Kletzing, C.; Reeves, G. D.; Skoug, R. M.; Larsen, B. A.
2014-08-28
Recent observations by the Van Allen Probes spacecraft have demonstrated that a variety of electric field structures and nonlinear waves frequently occur in the inner terrestrial magnetosphere, including phase space holes, kinetic field-line resonances, nonlinear whistler-mode waves, and several types of double layer. However, it is nuclear whether such structures and waves have a significant impact on the dynamics of the inner magnetosphere, including the radiation belts and ring current. To make progress toward quantifying their importance, this study statistically evaluates the correlation of such structures and waves with plasma boundaries. A strong correlation is found. These statistical results, combinedmore » with observations of electric field activity at propagating plasma boundaries, are consistent with the identification of these boundaries as the source of free energy responsible for generating the electric field structures and nonlinear waves of interest. Therefore, the ability of these structures and waves to influence plasma in the inner magnetosphere is governed by the spatial extent and dynamics of macroscopic plasma boundaries in that region.« less
Nonlinear electric field structures in the inner magnetosphere
Malaspina, D. M.; Andersson, L.; Ergun, R. E.; Wygant, J. R.; Bonnell, J. W.; Kletzing, C.; Reeves, G. D.; Skoug, R. M.; Larsen, B. A.
2014-08-28
Recent observations by the Van Allen Probes spacecraft have demonstrated that a variety of electric field structures and nonlinear waves frequently occur in the inner terrestrial magnetosphere, including phase space holes, kinetic field-line resonances, nonlinear whistler-mode waves, and several types of double layer. However, it is nuclear whether such structures and waves have a significant impact on the dynamics of the inner magnetosphere, including the radiation belts and ring current. To make progress toward quantifying their importance, this study statistically evaluates the correlation of such structures and waves with plasma boundaries. A strong correlation is found. These statistical results, combined with observations of electric field activity at propagating plasma boundaries, are consistent with the identification of these boundaries as the source of free energy responsible for generating the electric field structures and nonlinear waves of interest. Therefore, the ability of these structures and waves to influence plasma in the inner magnetosphere is governed by the spatial extent and dynamics of macroscopic plasma boundaries in that region.
Malanushenko, A.; Longcope, D. W.; McKenzie, D. E.
2009-12-20
Nonlinear force-free fields are the most general case of force-free fields, but the hardest to model as well. There are numerous methods of computing such fields by extrapolating vector magnetograms from the photosphere, but very few attempts have so far made quantitative use of coronal morphology. We present a method to make such quantitative use of X-ray and EUV images of coronal loops. Each individual loop is fit to a field line of a linear force-free field, allowing the estimation of the field line's twist, three-dimensional geometry, and the field strength along it. We assess the validity of such a reconstruction since the actual corona is probably not a linear force-free field, and that the superposition of linear force-free fields is generally not itself a force-free field. To do so, we perform a series of tests on nonlinear force-free fields, described in Low and Lou. For model loops we project field lines onto the photosphere. We compare several results of the method with the original field, in particular the three-dimensional loop shapes, local twist (coronal alpha), distribution of twist in the model photosphere, and strength of the magnetic field. We find that (1) for these trial fields, the method reconstructs twist with a mean absolute deviation of at most 15% of the range of photospheric twist, (2) heights of the loops are reconstructed with a mean absolute deviation of at most 5% of the range of trial heights, and (3) the magnitude of non-potential contribution to a photospheric field is reconstructed with a mean absolute deviation of at most 10% of the maximal value.
Nonlinear response of electric fields at a neutral point
NASA Astrophysics Data System (ADS)
Berkovsky, Mikhail; Dufty, James W.; Calisti, Annette; Stamm, Roland; Talin, Bernard
1995-05-01
The complex dynamics of electric fields at a neutral point in a plasma is studied via a model of noninteracting ``quasiparticles.'' The simplicity of the model allows the reduction of the many-body problem to an effective single-particle analysis-all properties of interest can be reduced to quadratures. Still, the final calculations to extract a quantitative or even qualitative understanding of the field dynamics can be difficult. Attention here is focused on the dynamics of the conditional electric field: the field value at time t for a given initial value of the field. In addition to the relevant linear response function (electric field time correlation function), this property provides the complete nonlinear response of the electric field to arbitrary initial field perturbations. The static properties (distribution of electric fields and field time derivatives) and the electric field time correlation function have been known for some time for this model. We compare these results and the present result for the conditional electric field with molecular dynamics simulations including interactions. The comparisons suggest that the model provides a quantitative representation of electric field dynamics in real plasmas, except at strong coupling. The exact theoretical results are compared also with those obtained by modeling the electric field as a stochastic variable obeying a kangaroo process. The latter can be constructed to yield both the exact stationary distribution and the exact electric field time correlation function. However, we find that the conditional field is never well approximated by this process. An alternative representation of the joint distribution for electric fields, consistent with the exact stationary distribution, field correlation function, and conditional electric field, is suggested.
Acoustic field distribution of sawtooth wave with nonlinear SBE model
Liu, Xiaozhou Zhang, Lue; Wang, Xiangda; Gong, Xiufen
2015-10-28
For precise prediction of the acoustic field distribution of extracorporeal shock wave lithotripsy with an ellipsoid transducer, the nonlinear spheroidal beam equations (SBE) are employed to model acoustic wave propagation in medium. To solve the SBE model with frequency domain algorithm, boundary conditions are obtained for monochromatic and sawtooth waves based on the phase compensation. In numerical analysis, the influence of sinusoidal wave and sawtooth wave on axial pressure distributions are investigated.
Nonlinear magnetic field transport in opening switch plasmas
Mason, R.J. ); Auer, P.L.; Sudan, R.N.; Oliver, B.V.; Seyler, C.E.; Greenly, J.B. )
1993-04-01
The nonlinear transport of magnetic field in collisionless plasmas, as present in the plasma opening switch (POS), using the implicit multifluid simulation code ANTHEM [J. Comput. Phys. [bold 71], 429 (1987)] is studied. The focus is on early time behavior in the electron--magnetohydrodynamic (EMHD) limit, with the ions fixed, and the electrons streaming as a fluid under the influence of [bold v][sub [ital e
DC Magnetic Field Generation by Nonlinear Whis-tlers
NASA Astrophysics Data System (ADS)
Stenzel, R. L.; Urrutia, J. M.; Griskey, M. C.
1998-11-01
A magnetic loop antenna is immersed into a large laboratory plasma (1 m diam, 2.5 m length, 10^12 cm-3, 3 eV, 5 G). It excites whistlers whose wave magnetic field exceeds the ambient dc field.(R. L. Stenzel and J. M. Urrutia, Phys. Rev. Lett. (1998).) The periodic reversal of both the electric and magnetic field produces a time-average electron Hall currents which results in the generation of a dc magnetic field. Copious harmonics of the fundamental frequency are produced. The propagation of nonlinear whistlers depends on amplitude and field direction. These phenomena are important for the excitation of large amplitude whistler with antennas in space.
Nonlinear spinor fields in Bianchi type-VI0 spacetime
NASA Astrophysics Data System (ADS)
Saha, Bijan
2015-10-01
Within the scope of Bianchi type- V I 0 spacetime we study the role of spinor field on the evolution of the Universe. It is found that the presence of the non-trivial non-diagonal components of the energy-momentum tensor of the spinor field plays a vital role on the evolution of the Universe. As a result of their mutual influence, there occur two different scenarios. In one case the invariants constructed from the bilinear forms of the spinor field become trivial, thus giving rise to a massless and linear spinor field Lagrangian. According to the second scenario massive and nonlinear terms do not vanish and depending on the sign of the coupling constants we have either an expanding mode of expansion or the one that, after obtaining some maximum value, contracts and ends in a big crunch generating spacetime singularity. This result shows that the spinor field is highly sensitive to the gravitational one.
Nonlinear nanoprobes for characterizing ultrafast optical near field
NASA Astrophysics Data System (ADS)
Li, Haifeng
With the rapid development of ultrafast optics and nanophotonics, it is crucial to measure the spatiotemporal evolution of an ultrafast optical near field in nanometer spatial and femtosecond temporal resolution with minimal perturbation. Although near-field scanning optical microscopy (NSOM) can achieve nanoscale spatial resolution and various ultrashort pulse diagnostic tools can characterize femtosecond laser pulses, yet such capability to noninvasively characterize the nanoscale characteristics of femtosecond pulses in all three spatial dimensions remains elusive. In this dissertation, we developed different types of nonlinear optical probes to characterize ultrashort optical pulses. The nonlinear optical probe is composed of three parts, a silica fiber taper, a single nanowire bonded to the end of the fiber and nonlinear nanoparticles attached on the tip of the nanowire. The optical fiber taper can be readily mounted on a mechanical stage and served as a macroscopic interface for handling and positioning control. The single nanowire bridges the dimension gap between the nanocrystals and the fiber taper, and is critical for achieving large aspect ratio and hence minimizing optical scattering and perturbation. The nonlinear nanoparticles give rise to its capability to characterize ultrashort optical pulses. The unique fusion of nanoscale and nonlinear features in developed nonlinear optical probes provides the ability of probing ultrafast optical field in complex 3D microand nano- structures. The demonstration of such ability is crucial for understanding the interaction of ultrafast optical fields and nanoscale systems. The fabrication processes of the nonlinear optical probes are illustrated in detail and the optical properties of the probes are investigated. Two different types of nonlinear optical probes, two-photon fluorescent nanoprobes and Second HARmonic nanoProbes (SHARP), are fabricated. Interferometric autocorrelation measurements near the focal point
Comparison of recent non-linear filters from graphics field
NASA Astrophysics Data System (ADS)
Wang, Yang; Fu, Kun; Xu, Guangluan
2015-12-01
Image filtering is an important and fundamental issue in image processing pipelines and find itself a lot of applications in segmentation, salient features detection, colorization, stylization and so on. In recent years, several nonlinear filters aiming at edge-preserving smoothing has been proposed from different fields. However, none of these filters is perfect for all applications due to their own model assumption and solving strategy. In this paper, we give a brief introduction to several of them particularly from graphics field and comparison about their advantages and limitations through experiments. We look forward to offer an helpful starting point for researchers to select or improve them.
Non-linear dielectric response of ferrofluids under magnetic field
NASA Astrophysics Data System (ADS)
Licinio, Pedro; Teixeira, Alvaro V.; Figueiredo, José Marcos A.
2005-03-01
The dielectric response of a water-based magnetic fluid is investigated at room temperature and in the frequency range of 100-10 7 rad/s. The response is linear in the electric fields used. Upon application of a constant magnetic field of 40 mT, which is well below the sample saturation, the response becomes non-linear. Magnetic field effects are isolated by performing a differential analysis of the inverse dielectric permittivity with and without applied field in both perpendicular and parallel configurations. The imaginary part of the differential inverse permittivity displays two peaks. The low-frequency peak is seen to correspond to the orientation relaxation of aggregates also detected in SAXS, photon correlation and atomic force microscopy measurements. The high-frequency peak corresponds to single magnetic particle reorientation.
Stability of exact force-free electrodynamic solutions and scattering from spacetime curvature
NASA Astrophysics Data System (ADS)
Zhang, Fan; McWilliams, Sean T.; Pfeiffer, Harald P.
2015-07-01
Recently, a family of exact force-free electrodynamic (FFE) solutions was given by Brennan, Gralla and Jacobson, which generalizes earlier solutions by Michel, Menon and Dermer, and other authors. These solutions have been proposed as useful models for describing the outer magnetosphere of conducting stars. As with any exact analytical solution that aspires to describe actual physical systems, it is vitally important that the solution possess the necessary stability. In this paper, we show via fully nonlinear numerical simulations that the aforementioned FFE solutions, despite being highly special in their properties, are nonetheless stable under small perturbations. Through this study, we also introduce a three-dimensional pseudospectral relativistic FFE code that achieves exponential convergence for smooth test cases, as well as two additional well-posed FFE evolution systems in the appendix that have desirable mathematical properties. Furthermore, we provide an explicit analysis that demonstrates how propagation along degenerate principal null directions of the spacetime curvature tensor simplifies scattering, thereby providing an intuitive understanding of why these exact solutions are tractable, i.e. why they are not backscattered by spacetime curvature.
Analytic Properties of Force-free Jets in the Kerr Spacetime - I
NASA Astrophysics Data System (ADS)
Pan, Zhen; Yu, Cong
2015-10-01
The Blandford-Znajek (BZ) mechanism describes a process for extracting the rotation energy from a spinning black hole (BH) via magnetic field lines penetrating the event horizon of the central BH. In this paper, we present a perturbation approach to study force-free jets launched by the BZ mechanism, and then discuss its two immediate applications: (1) we present a high-order split-monopole perturbation solution to the BZ mechanism which accurately pins down the energy extraction rate \\dot{E} and well describes the structure of the BH magnetosphere for the entire range of BH spins (0 ≤ a ≤ 1); (2) the approach yields an exact constraint for the monopole field configuration in Kerr spacetime, I={{Ω }}(1-{A}φ 2), where Aϕ is the ϕ component of the vector potential of electromagnetic field, Ω is the angular velocity of the magnetic field lines, and I is the poloidal electric current. The constraint is of particular importance to benchmark the accuracy of numerical simulations.
The spatial structure of a nonlinear receptive field
Schwartz, Gregory W.; Okawa, Haruhisa; Dunn, Felice A.; Morgan, Josh L.; Kerschensteiner, Daniel; Wong, Rachel O.; Rieke, Fred
2012-01-01
Understanding a sensory system implies the ability to predict responses to a variety of inputs from a common model. In the retina, this includes predicting how the integration of signals across visual space shapes the outputs of retinal ganglion cells. Existing models of this process generalize poorly to predict responses to novel stimuli. This failure arises in part from properties of the ganglion cell response that are not well captured by standard receptive field mapping techniques: nonlinear spatial integration and fine-scale heterogeneities in spatial sampling. Here, we characterize a ganglion cell’s spatial receptive field using a mechanistic model based on measurements of the physiological properties and connectivity of only the primary excitatory circuitry of the retina. The resulting simplified circuit model successfully predicts ganglion cell responses to a variety of spatial patterns and thus provides a direct correspondence between circuit connectivity and retinal output. PMID:23001060
A two-fluid study of oblique tearing modes in a force-free current sheet
NASA Astrophysics Data System (ADS)
Akçay, Cihan; Daughton, William; Lukin, Vyacheslav S.; Liu, Yi-Hsin
2016-01-01
Kinetic simulations have demonstrated that three-dimensional reconnection in collisionless regimes proceeds through the formation and interaction of magnetic flux ropes, which are generated due to the growth of tearing instabilities at multiple resonance surfaces. Since kinetic simulations are intrinsically expensive, it is desirable to explore the feasibility of reduced two-fluid models to capture this complex evolution, particularly, in the strong guide field regime, where two-fluid models are better justified. With this goal in mind, this paper compares the evolution of the collisionless tearing instability in a force-free current sheet with a two-fluid model and fully kinetic simulations. Our results indicate that the most unstable modes are oblique for guide fields larger than the reconnecting field, in agreement with the kinetic results. The standard two-fluid tearing theory is extended to address the tearing instability at oblique angles. The resulting theory yields a flat oblique spectrum and underestimates the growth of oblique modes in a similar manner to kinetic theory relative to kinetic simulations.
A two-fluid study of oblique tearing modes in a force-free current sheet
Akçay, Cihan; Daughton, William; Lukin, Vyacheslav S.; Liu, Yi-Hsin
2016-01-01
Kinetic simulations have demonstrated that three-dimensional reconnection in collisionless regimes proceeds through the formation and interaction of magnetic flux ropes, which are generated due to the growth of tearing instabilities at multiple resonance surfaces. Because kinetic simulations are intrinsically expensive, it is desirable to explore the feasibility of reduced two-fluid models to capture this complex evolution, particularly, in the strong guide field regime, where two-fluid models are better justified. With this goal in mind, this paper compares the evolution of the collisionless tearing instability in a force-free current sheet with a two-fluid model and fully kinetic simulations. Our results indicatemore » that the most unstable modes are oblique for guide fields larger than the reconnecting field, in agreement with the kinetic results. The standard two-fluid tearing theory is extended to address the tearing instability at oblique angles. As a results this theory yields a flat oblique spectrum and underestimates the growth of oblique modes in a similar manner to kinetic theory relative to kinetic simulations.« less
A two-fluid study of oblique tearing modes in a force-free current sheet
Akçay, Cihan; Daughton, William; Lukin, Vyacheslav S.; Liu, Yi-Hsin
2016-01-01
Kinetic simulations have demonstrated that three-dimensional reconnection in collisionless regimes proceeds through the formation and interaction of magnetic flux ropes, which are generated due to the growth of tearing instabilities at multiple resonance surfaces. Because kinetic simulations are intrinsically expensive, it is desirable to explore the feasibility of reduced two-fluid models to capture this complex evolution, particularly, in the strong guide field regime, where two-fluid models are better justified. With this goal in mind, this paper compares the evolution of the collisionless tearing instability in a force-free current sheet with a two-fluid model and fully kinetic simulations. Our results indicate that the most unstable modes are oblique for guide fields larger than the reconnecting field, in agreement with the kinetic results. The standard two-fluid tearing theory is extended to address the tearing instability at oblique angles. As a results this theory yields a flat oblique spectrum and underestimates the growth of oblique modes in a similar manner to kinetic theory relative to kinetic simulations.
NONLINEAR SIMULATION OF TURBULENT FIELD LINES: DISPERSAL STATISTICS
Ragot, B. R.
2010-11-10
A new method for the full nonlinear computation of sets of turbulent field lines is introduced that extends the sums of random numbers distribution method previously applied to the computation of individual field lines. With a multiscale variation of the phases consistent with in situ observations of intermittent solar wind (SW) turbulence, the new method allows inclusion of the equivalent of more than four decades of turbulent scales with a fully three-dimensional distribution of wavevectors. As a first application, pairs of magnetic field lines are computed in independent realizations of the turbulence, for spectra typical of the quiet slow SW near 1 AU. The statistics of field-line dispersal are then studied from the simulated pairs of magnetic field lines and compared to earlier theoretical predictions. It appears that while the earlier theoretical picture remains relatively accurate as long as the mean variation of separation logarithm {Lambda} is less than one, the qualitative picture is quickly altered as {Lambda} grows past one.
Thermally relativistic flows induced by gravitational-force-free particle motion in curved spacetime
Yano, Ryosuke; Suzuki, Kojiro; Kuroda, Hisayasu
2009-12-15
Thermally relativistic flows in the early Universe can be characterized by the emergence of flows induced by gravitational-force-free particle motion in curved spacetime as well as induced by the gravitational force. In this paper, thermally relativistic flows induced by gravitational-force-free particle motion in curved spacetime are discussed on the basis of the general relativistic Boltzmann equation. As an object of analysis, we consider the flow from the static state inside the Schwarzschild radius of a thermally relativistic stuffed black hole induced by such motion. Analytical results obtained using the collisionless, nongravitational general relativistic Boltzmann equation reveal that the initial cluster is induced by gravitational-force-free particle motion. Numerical results obtained using the nongravitational general relativistic Anderson-Witting model confirm the presence of an initial cluster inside the thermally relativistic stuffed black hole, which is induced by gravitational-force-free particle motion.
Time-asymptotic field amplitudes in nonlinear Landau damping
Buchanan, M.; Kirkitelos, P.; Dorning, J.J. )
1993-01-01
The behavior of an electrostatic plasma wave of initial amplitude Ei in a collisionless electron plasma depends crucially on the ratio [delta] = [gamma]L/[omega]B, where [gamma]L is the damping coefficient calculated from linear plasma kinetic theory and [omega]B = (ekEi/m)[sup 1/2] is the [open quotes]bounce[close quotes] frequency for trapped electrons. For sufficiently small E[sub i], i.e., [delta] [much gt] 1, the wave damps away completely; conversely, a wave of large initial amplitude, for which [delta] [much lt] 1, saturates at a finite final amplitude due to the nonlinear effects of particle trapping. In this paper, we report results concerning the transition region [delta] [approximately] 0(1), which separates these two regimes. For the case of weak damping, i.e., [vert bar][gamma]L/[omega]p[vert bar][much lt]1, where [omega]p is the plasma frequency, we calculate analytically the critical value [delta][sub i,e] below which complete damping occurs and derive the first explicit analytic relationship between E[sub i] and E[sub f], the time-asymptotic amplitude, for E[sub i] above the critical value E[sub i,c] = (m,ek)([gamma]L/[delta][sub i,c]). The results predict an interesting phenomenon - a finite jump [delta]E in the final field amplitude as E[sub i] is increased through E[sub i,c]. We have corroborated the reality of this phenomenon through large-scale numerical simulations of the Vlasov-Poisson system, carried out using the spectral splitting code of Klimas. These important new results establish a detailed picture of the fundamental transition between linear and nonlinear Landau damping and, in particular, show that the onset of essentially nonlinear behavior occurs very abruptly as the initial wave amplitude increases through its critical value.
Magnetic energy dissipation in force-free jets
NASA Technical Reports Server (NTRS)
Choudhuri, Arnab Rai; Konigl, Arieh
1986-01-01
It is shown that a magnetic pressure-dominated, supersonic jet which expands or contracts in response to variations in the confining external pressure can dissipate magnetic energy through field-line reconnection as it relaxes to a minimum-energy configuration. In order for a continuous dissipation to occur, the effective reconnection time must be a fraction of the expansion time. The dissipation rate for the axisymmetric minimum-energy field configuration is analytically derived. The results indicate that the field relaxation process could be a viable mechanism for powering the synchrotron emission in extragalactic jets if the reconnection time is substantially shorter than the nominal resistive tearing time in the jet.
Force-free equilibria of magnetized jets. [pressure confined extragalactic radio hydromagnetics
NASA Technical Reports Server (NTRS)
Koenigl, A.; Choudhuri, A. R.
1985-01-01
Force-free equilibrium configurations of magnetic-pressure-dominated magnetized supersonic jets confined by slowly varying external pressure are investigated analytically. For the case where internal dissipation mechanisms are active, the lowest-energy field configuration is found to be the superposition of an axisymmetric mode and a helical mode with a wavelength equal to 5 times the jet radius, and the pressure below which the nonaxisymmetric mode becomes energetically favorable is given as 2700 times the product of the 4th power of the magnetic helicity per unit length and the -6th power of the magnetic flux. A model of the total and polarized emission of such a configuration is developed and applied to the extended well-collimated astronomically resolved jet NGC 6251. The model is shown to reproduce significant features such as transverse oscillations of the ridge line, width oscillations and emission knots, the projected magnetic-field configuration, oscillations of the degree of polarization, and the distribution of the Faraday rotation measure.
PREPROCESSING MAGNETIC FIELDS WITH CHROMOSPHERIC LONGITUDINAL FIELDS
Yamamoto, Tetsuya T.; Kusano, K.
2012-06-20
Nonlinear force-free field (NLFFF) extrapolation is a powerful tool for the modeling of the magnetic field in the solar corona. However, since the photospheric magnetic field does not in general satisfy the force-free condition, some kind of processing is required to assimilate data into the model. In this paper, we report the results of new preprocessing for the NLFFF extrapolation. Through this preprocessing, we expect to obtain magnetic field data similar to those in the chromosphere. In our preprocessing, we add a new term concerning chromospheric longitudinal fields into the optimization function proposed by Wiegelmann et al. We perform a parameter survey of six free parameters to find minimum force- and torque-freeness with the simulated-annealing method. Analyzed data are a photospheric vector magnetogram of AR 10953 observed with the Hinode spectropolarimeter and a chromospheric longitudinal magnetogram observed with SOLIS spectropolarimeter. It is found that some preprocessed fields show the smallest force- and torque-freeness and are very similar to the chromospheric longitudinal fields. On the other hand, other preprocessed fields show noisy maps, although the force- and torque-freeness are of the same order. By analyzing preprocessed noisy maps in the wave number space, we found that small and large wave number components balance out on the force-free index. We also discuss our iteration limit of the simulated-annealing method and magnetic structure broadening in the chromosphere.
Nonlinear Transport of Cosmic Rays in Turbulent Magnetic Field
NASA Astrophysics Data System (ADS)
Yan, H.; Xu, S.
2014-09-01
Recent advances in both the MHD turbulence theory and cosmic ray observations call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulations, in which turbulence is injected at large scale and cascades to small scales. We shall present the nonlinear results for cosmic ray transport, in particular, the cross field transport of CRs. We demonstrate that the concept of cosmic ray subdiffusion in general does not apply and the perpendicular motion is well described by normal diffusion with M A4 dependence. Moreover, on scales less than the injection scale of turbulence, CRs' transport becomes super-diffusive. Quantitative predictions for both the normal diffusion on large scale and super diffusion on small scale are confirmed with recent numerical simulations. Implication for shock acceleration is briefly discussed.
Nonlinear Dirac equation solitary waves in external fields.
Mertens, Franz G; Quintero, Niurka R; Cooper, Fred; Khare, Avinash; Saxena, Avadh
2012-10-01
We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2/κ+1(Ψ[over ¯]Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP(t)/dq[over ̇](t)<0. Here P(t) is the momentum of the solitary wave, and q[over ̇] is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials that we always have dP(t)/dq[over ̇](t)>0, so, when instabilities do occur, they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that, when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations. We found that the time evolution of the collective coordinates of the solitary wave in our numerical simulations, namely the position of the average charge density and the momentum of the solitary wave, provide good indicators for when the solitary wave first becomes unstable. When these variables stop being smooth functions of time (t), then the solitary wave starts to distort
Nonlinear density fluctuation field theory for large scale structure
NASA Astrophysics Data System (ADS)
Zhang, Yang; Miao, Hai-Xing
2009-05-01
We develop an effective field theory of density fluctuations for a Newtonian self-gravitating N-body system in quasi-equilibrium and apply it to a homogeneous universe with small density fluctuations. Keeping the density fluctuations up to second order, we obtain the nonlinear field equation of 2-pt correlation ξ(r), which contains 3-pt correlation and formal ultra-violet divergences. By the Groth-Peebles hierarchical ansatz and mass renormalization, the equation becomes closed with two new terms beyond the Gaussian approximation, and their coefficients are taken as parameters. The analytic solution is obtained in terms of the hypergeometric functions, which is checked numerically. With one single set of two fixed parameters, the correlation ξ(r) and the corresponding power spectrum P(κ) simultaneously match the results from all the major surveys, such as APM, SDSS, 2dfGRS, and REFLEX. The model gives a unifying understanding of several seemingly unrelated features of large scale structure from a field-theoretical perspective. The theory is worth extending to study the evolution effects in an expanding universe.
Nonlinear gravitational self-force: Field outside a small body
NASA Astrophysics Data System (ADS)
Pound, Adam
2012-10-01
A small extended body moving through an external spacetime gαβ creates a metric perturbation hαβ, which forces the body away from geodesic motion in gαβ. The foundations of this effect, called the gravitational self-force, are now well established, but concrete results have mostly been limited to linear order. Accurately modeling the dynamics of compact binaries requires proceeding to nonlinear orders. To that end, I show how to obtain the metric perturbation outside the body at all orders in a class of generalized wave gauges. In a small buffer region surrounding the body, the form of the perturbation can be found analytically as an expansion for small distances r from a representative worldline. Given only a specification of the body’s multipole moments, the field obtained in the buffer region suffices to find the metric everywhere outside the body via a numerical puncture scheme. Following this procedure at first and second order, I calculate the field in the buffer region around an arbitrarily structured compact body at sufficiently high order in r to numerically implement a second-order puncture scheme, including effects of the body’s spin. I also define nth-order (local) generalizations of the Detweiler-Whiting singular and regular fields and show that in a certain sense, the body can be viewed as a skeleton of multipole moments.
Forced Field Extrapolation of the Magnetic Structure of the Hα fibrils in the Solar Chromosphere
NASA Astrophysics Data System (ADS)
Xiaoshuai, Zhu; Huaning, Wang; Zhanle, Du; Han, He
2016-07-01
We present a careful assessment of forced field extrapolation using the Solar Dynamics Observatory/Helioseismic and Magnetic Imager magnetogram. We use several metrics to check the convergence property. The extrapolated field lines below 3600 km appear to be aligned with most of the Hα fibrils observed by the New Vacuum Solar Telescope. In the region where magnetic energy is far larger than potential energy, the field lines computed by forced field extrapolation are still consistent with the patterns of Hα fibrils while the nonlinear force-free field results show a large misalignment. The horizontal average of the lorentz force ratio shows that the forced region where the force-free assumption fails can reach heights of 1400–1800 km. The non-force-free state of the chromosphere is also confirmed based on recent radiation magnetohydrodynamics simulations.
Chaotic structures of nonlinear magnetic fields. I - Theory. II - Numerical results
NASA Technical Reports Server (NTRS)
Lee, Nam C.; Parks, George K.
1992-01-01
A study of the evolutionary properties of nonlinear magnetic fields in flowing MHD plasmas is presented to illustrate that nonlinear magnetic fields may involve chaotic dynamics. It is shown how a suitable transformation of the coupled equations leads to Duffing's form, suggesting that the behavior of the general solution can also be chaotic. Numerical solutions of the nonlinear magnetic field equations that have been cast in the form of Duffing's equation are presented.
NASA Astrophysics Data System (ADS)
Fu, Yiming; Chen, Yang; Zhong, Jun
2014-10-01
The nonlinear dynamic response problems of fiber-metal laminated beams with delamination are studied in this paper. Basing on the Timoshenko beam theory, and considering geometric nonlinearity, transverse shear deformation, temperature effect and contact effect, the nonlinear governing equations of motion for fiber-metal laminated beams under unsteady temperature field are established, which are solved by the differential quadrature method, Nermark-β method and iterative method. In numerical examples, the effects of delamination length, delamination depth, temperature field, geometric nonlinearity and transverse shear deformation on the nonlinear dynamic response of the glass reinforced aluminum laminated beam with delamination are discussed in details.
Nonlinear phase field model for electrodeposition in electrochemical systems
Liang, Linyun; Chen, Long-Qing
2014-12-29
A nonlinear phase-field model has been developed for describing the electrodeposition process in electrochemical systems that are highly out of equilibrium. Main thermodynamic driving forces for the electrode-electrolyte interface (EEI) evolution are limited to local variations of overpotential and ion concentration. Application of the model to Li-ion batteries describes the electrode interface motion and morphology change caused by charge mass transfer in the electrolyte, an electrochemical reaction at the EEI and cation deposition on the electrode surface during the charging operation. The Li electrodeposition rate follows the classical Butler-Volmer kinetics with exponentially and linearly depending on local overpotential and cation concentration at the electrode surface, respectively. Simulation results show that the Li deposit forms a fiber-like shape and grows parallel to the electric field direction. The longer and thicker deposits are observed both for higher current density and larger rate constant where the surface reaction rate is expected to be high. The proposed diffuse interface model well captures the metal electrodeposition phenomena in plenty of non-equilibrium electrochemical systems.
Nonlinear stability of field-reversed configurations with self-generated toroidal field
Omelchenko, Y. A.; Schaffer, M. J.; Parks, P. B.
2001-10-01
The field-reversed configuration (FRC) is a high-beta compact toroidal plasma confinement scheme in which the external poloidal field is reversed on the geometric axis by azimuthal (toroidal) plasma current. A quasineutral, hybrid, particle-in-cell (PIC) approach [Y. A. Omelchenko and R. N. Sudan, Phys. Plasmas 2, 2773 (1995)] is applied to study long-term nonlinear stability of computational FRC equilibria to a number of toroidal modes, including the most disruptive tilt mode. In particular, a self-generated toroidal magnetic field is found to be an important factor in mitigating the instability and preventing the confinement disruption. This is shown to be a unique FRC property resulting from the Hall effect in the regions of vanishing poloidal magnetic field. The instability-driven toroidal field stabilizes kink formation by increasing the magnetic field energy without destabilizing curvature-driven plasma motion. Finally, the tilt instability saturates due to nonlinear, finite Larmor radius (FLR) effects and plasma relaxation to a quasisteady kinetic state. During this transition the FRC is shown to dissipate a substantial amount of initially trapped flux and plasma energy. These effects are demonstrated for kinetic and fluid-like, spherical and prolate FRCs.
Role of nonlinear refraction in the generation of terahertz field pulses by light fields
Zabolotskii, A. A.
2013-07-15
The generation of microwave (terahertz) pulses without any envelope in a four-level quasi-resonant medium is considered. Two intense quasi-monochromatic laser fields lead to a partial upper-level population. Microwave field pulses cause the transition between these levels. For appropriately chosen scales, the evolution of the fields is shown to be described by the pseudo-spin evolution equations in a microwave field with the inclusion of nonlinear refraction caused by an adiabatic upper-level population. The evolution of terahertz field pulses is described outside the scope of the slow-envelope approximation. When a number of standard approximations are taken into account, this system of equations is shown to be equivalent to an integrable version of the generalized reduced Maxwell-Bloch equations or to the generalized three-wave mixing equations. The soliton solution found by the inverse scattering transform method is used as an example to show that nonlinear refraction leads to a strong compression of the microwave (terahertz) field soliton.
Role of nonlinear refraction in the generation of terahertz field pulses by light fields
NASA Astrophysics Data System (ADS)
Zabolotskii, A. A.
2013-07-01
The generation of microwave (terahertz) pulses without any envelope in a four-level quasi-resonant medium is considered. Two intense quasi-monochromatic laser fields lead to a partial upper-level population. Microwave field pulses cause the transition between these levels. For appropriately chosen scales, the evolution of the fields is shown to be described by the pseudo-spin evolution equations in a microwave field with the inclusion of nonlinear refraction caused by an adiabatic upper-level population. The evolution of terahertz field pulses is described outside the scope of the slow-envelope approximation. When a number of standard approximations are taken into account, this system of equations is shown to be equivalent to an integrable version of the generalized reduced Maxwell-Bloch equations or to the generalized three-wave mixing equations. The soliton solution found by the inverse scattering transform method is used as an example to show that nonlinear refraction leads to a strong compression of the microwave (terahertz) field soliton.
Zhou, Fushun; Huang, Can Lu, Quanming; Wang, Shui; Xie, Jinlin
2015-09-15
Two-dimensional particle-in-cell simulation is performed to investigate magnetic reconnection in a force-free current sheet. The results show that the evolution of the ion diffusion region has two different phases. In the first phase, the electrons flow toward the X line along one pair of separatrices and away from the X line along the other pair of separatrices. Therefore, in the ion diffusion region, a distorted quadrupole structure of the out-of-plane magnetic field is formed, which is similar to that of a typical guide field reconnection in the Harris current sheet. In the second phase, the electrons move toward the X line along the separatrices and then flow away from the X line at the inner side of the separatrices. In the ion diffusion region, the out-of-plane magnetic field exhibits a characteristic quadrupole pattern with a good symmetry, which is similar to that of antiparallel reconnection in the Harris current sheet.
Nonlinear response of superconductors to alternating fields and currents
McDonald, J.
1997-10-08
This report discusses the following topics on superconductivity: nonlinearities in hard superconductors such as surface impedance of a type II superconductimg half space and harmonic generation and intermodulation due to alternating transport currents; and nonlinearities in superconducting weak links such as harmonic generation by a long Josephson Junction in a superconducting slab.
RECONSTRUCTION OF THE CORONAL MAGNETIC FIELD USING THE CESE-MHD METHOD
Jiang Chaowei; Feng, Xueshang; Xiang, Changqing; Fan, Yuliang E-mail: fengx@spaceweather.ac.cn E-mail: fanyuliang@bao.ac.cn
2011-02-01
We present a new implementation of the MHD relaxation method for reconstruction of the nearly force-free coronal magnetic field from a photospheric vector magnetogram. A new numerical MHD scheme is proposed to solve the full MHD equations by using the spacetime conservation-element and solution-element method. The bottom boundary condition is prescribed in a similar way as in the stress-and-relax method, by changing the transverse field incrementally to match the magnetogram, and other boundaries of the computational box are set by the nonreflecting boundary conditions. Applications to the well-known benchmarks for nonlinear force-free-field reconstruction, the Low and Lou force-free equilibria, validate the method and confirm its capability for future practical application, with observed magnetograms as inputs.
Aerodynamic characteristics of missile control fins in nonlinear flow fields
NASA Technical Reports Server (NTRS)
Hemsch, M. J.; Nielsen, J. N.
1983-01-01
Recent experimental results show that the control effectiveness of a missile fin in supersonic flow at moderate-to-high angles of attack is a strong nonlinear function of free-stream Mach number, body incidence angle, fin bank angle and fin deflection angle. Analysis of the experimental results using an Euler finite-difference computer code with flow separation together with the equivalent angle-of-attack concept indicates that the observed nonlinearities are due to the variation of local dynamic pressure and local Mach number around the missile body alone. The nonlinearities are shown to be a strong source of control cross-coupling for high Mach number, high angle-of-attack combinations. The analysis suggests a relatively simple yet comprehensive approach for accurately accounting for these nonlinear effects.
Neural field theory of nonlinear wave-wave and wave-neuron processes
NASA Astrophysics Data System (ADS)
Robinson, P. A.; Roy, N.
2015-06-01
Systematic expansion of neural field theory equations in terms of nonlinear response functions is carried out to enable a wide variety of nonlinear wave-wave and wave-neuron processes to be treated systematically in systems involving multiple neural populations. The results are illustrated by analyzing second-harmonic generation, and they can also be applied to wave-wave coalescence, multiharmonic generation, facilitation, depression, refractoriness, and other nonlinear processes.
Coronal magnetic field modeling using stereoscopy constraints
NASA Astrophysics Data System (ADS)
Chifu, I.; Inhester, B.; Wiegelmann, T.
2015-05-01
Aims: Nonlinear force-free field (NLFFF) extrapolation has been used extensively in the past to extrapolate solar surface magnetograms to stationary coronal field models. In theoretical tests with known boundary conditions, the nonlinear boundary value problem can be solved reliably. However, if the magnetogram is measured with errors, the extrapolation often yields field lines that disagree with the shapes of simultaneously observed and stereoscopically reconstructed coronal loops. We here propose an extension to an NLFFF extrapolation scheme that remedies this deficiency in that it incorporates the loop information in the extrapolation procedure. Methods: We extended the variational formulation of the NLFFF optimization code by an additional term that monitors and minimizes the difference of the local magnetic field direction and the orientation of 3D plasma loops. We tested the performance of the new code with a previously reported semi-analytical force-free solution. Results: We demonstrate that there is a range of force-free and divergence-free solutions that comply with the boundary measurements within some error bound. With our new approach we can obtain the solution out of this set the coronal fields which is well aligned with given loops. Conclusions: We conclude that the shape of coronal loops reconstructed by stereoscopy may lead to an important stabilization of coronal NLFFF field solutions when, as is typically the case, magnetic surface measurements with limited precision do not allow determining the solution solely from photospheric field measurements.
Christodoulides, D N; Joseph, R L
1984-06-01
The propagation of nonlinear optical pulses in fibers is discussed, taking into account physical effects arising from nonlinearity, dispersion, and transverse confinement. The wave equation is solved by treating the radial dependence of the field in an exact way. The conditions supporting bright solitary waves are presented and compared with previous results. PMID:19721553
NASA Astrophysics Data System (ADS)
Gong, Xiao-Bo; Liao, Yi; Xu, Zhao-Yi
2016-09-01
Based on the Lagrangian of the steady axisymmetric force-free magnetosphere (FFM) equation around Kerr black holes (KBHs), we find that the FFM equation can be rewritten in a new form as f,rr / (1 -μ2) +f,μμ / Δ + K (f (r , μ) , r , μ) = 0, where μ = - cos θ. With coordinate transformation, the above equation can be given as s,yy +s,zz + D (s (y , z) , y , z) = 0. Using this form, we prove that the Meissner effect is not possessed by a KBH-FFM with the condition dω / dAϕ ⩽ 0 and Hϕ (dHϕ / dAϕ) ⩾ 0, here Aϕ is the ϕ component of the vector potential A → , ω is the angular velocity of magnetic fields and Hϕ corresponds to twice the poloidal electric current.
Weakly nonlinear study of normal-field instability in confined ferrofluids.
Lira, Sérgio A; Miranda, José A
2011-07-01
Similar to the classic three-dimensional Rosensweig instability, a ferrofluid confined in a vertical Hele-Shaw cell subjected to an in-plane normal magnetic field develops a periodic array of peaked interfacial structures. We perform a weakly nonlinear analysis that is able to reproduce the morphology of such pattern formation phenomenon at lowest nonlinear order. A mode-coupling theory is applied to compare the early nonlinear evolution of the interface with static shapes obtained when relevant forces equilibrate. Our nonlinear results indicate that the time-evolving shapes tend to approach stable stationary solutions. PMID:21867300
Nonlinear Generation of shear flows and large scale magnetic fields by small scale
NASA Astrophysics Data System (ADS)
Aburjania, G.
2009-04-01
EGU2009-233 Nonlinear Generation of shear flows and large scale magnetic fields by small scale turbulence in the ionosphere by G. Aburjania Contact: George Aburjania, g.aburjania@gmail.com,aburj@mymail.ge
NASA Astrophysics Data System (ADS)
Mukai, Y.; Hirori, H.; Yamamoto, T.; Kageyama, H.; Tanaka, K.
2016-01-01
We report on the nonlinear magnetization dynamics of a HoFeO3 crystal induced by a strong terahertz magnetic field resonantly enhanced with a split ring resonator and measured with magneto-optical Kerr effect microscopy. The terahertz magnetic field induces a large change (˜40%) in the spontaneous magnetization. The frequency of the antiferromagnetic resonance decreases in proportion to the square of the magnetization change. A modified Landau-Lifshitz-Gilbert equation with a phenomenological nonlinear damping term quantitatively reproduced the nonlinear dynamics.
Nonlinear waves on the free surface of a dielectric liquid in an oblique electric field
Gashkov, M. A.; Zubarev, N. M. Kochurin, E. A.
2015-09-15
The nonlinear dynamics of the free surface of an ideal dielectric liquid that is exposed to an external oblique electric field has been studied theoretically. In the framework of the Hamiltonian formalism, a system of nonlinear integro-differential equations has been derived that describes the dynamics of nonlinear waves in the small-angle approximation. It is established that for a liquid with high dielectric permittivity, these equations have a solution in the form of plane waves of arbitrary shape that propagate without distortion in the direction of the horizontal component of the external field.
NASA Astrophysics Data System (ADS)
Wang, Y.; Shen, C.; Liu, R.; Zhou, Z.
2014-12-01
Magnetic clouds (MCs) are the interplanetary counterparts of coronal mass ejections (CMEs). Due to the very low value of Can't connect to bucket.int.confex.com:4201 (Connection refused) LWP::Protocol::http::Socket: connect: Connection refused at /usr/local/lib/perl5/site_perl/5.8.8/LWP/Protocol/http.pm line 51. in MCs, they are believed to be in a nearly force-free state and therefore are able to be modeled by a cylindrical force-free flux rope. However, the force-free state only describes the magnetic field topology but not the plasma motion of a MC. For a MC propagating in interplanetary space, the global plasma motion has three possible components: linear propagating motion of a MC away from the Sun, expanding motion and circular motion with respect to the axis of the MC. By assuming the quasi-steady evolution and self-similar expansion, we introduced the three-component motion into the cylindrical force-free flux rope model, and developed a velocity-modified model. Then we applied the model to 73 MCs observed by Wind spacecraft to investigate the properties of the plasma motion of MCs. It is found that (1) some MCs did not propagate along the Sun-Earth line, suggesting the direct evidence of the CME's deflected propagation and/or rotation in interplanetary space, (2) the expansion speed is correlated with the radial propagation speed and 62%/17% of MCs underwent a under/over-expansion at 1 AU, and (3) the circular motion does exists though it is only on the order of 10 km s-1. These findings advance our understanding of the MC's properties at 1 AU as well as the dynamic evolution of CMEs from the Sun to interplanetary space.
Effect of nonlinear chirped Gaussian laser pulse on plasma wake field generation
Afhami, Saeedeh; Eslami, Esmaeil
2014-08-15
An ultrashort laser pulse propagating in plasma can excite a nonlinear plasma wake field which can accelerate charged particles up to GeV energies within a compact space compared to the conventional accelerator devices. In this paper, the effect of different kinds of nonlinear chirped Gaussian laser pulse on wake field generation is investigated. The numerical analysis of our results depicts that the excitation of plasma wave with large and highly amplitude can be accomplished by nonlinear chirped pulses. The maximum amplitude of excited wake in nonlinear chirped pulse is approximately three times more than that of linear chirped pulse. In order to achieve high wake field generation, chirp parameters and functions should be set to optimal values.
Effects of non-linearities on magnetic field generation
Nalson, Ellie; Malik, Karim A.; Christopherson, Adam J. E-mail: achristopherson@gmail.com
2014-09-01
Magnetic fields are present on all scales in the Universe. While we understand the processes which amplify the fields fairly well, we do not have a ''natural'' mechanism to generate the small initial seed fields. By using fully relativistic cosmological perturbation theory and going beyond the usual confines of linear theory we show analytically how magnetic fields are generated. This is the first analytical calculation of the magnetic field at second order, using gauge-invariant cosmological perturbation theory, and including all the source terms. To this end, we have rederived the full set of governing equations independently. Our results suggest that magnetic fields of the order of 10{sup -30}- 10{sup -27} G can be generated (although this depends on the small scale cut-off of the integral), which is largely in agreement with previous results that relied upon numerical calculations. These fields are likely too small to act as the primordial seed fields for dynamo mechanisms.
Second-order theory for nonlinear dielectric composites incorporating field fluctuations
NASA Astrophysics Data System (ADS)
Ponte Castañeda, P.
2001-12-01
This paper deals with the development of an improved second-order theory for estimating the effective behavior of nonlinear composite dielectrics. The theory makes use of the field fluctuations in the phases of the relevant ``linear comparison composite'' to generate improved Maxwell-Garnett (MGA) and effective-medium (EMA) types of approximations for nonlinear media. Similar to the earlier version of the theory, the resulting MGA and EMA predictions are exact to second-order in the contrast, but-unlike the earlier version-the estimates satisfy all known bounds. In particular, the EMA estimates exhibit a nonlinearity-independent percolation threshold, and critical exponents that are consistent with recently developed bounds on these exponents. In addition, the MGA and EMA estimates are shown to yield reasonable predictions for strongly nonlinear composites with ``threshold-type'' nonlinearities, which are extreme cases where earlier methods have been known to sometimes fail.
Nonlinear interactions between black holes and Proca fields
NASA Astrophysics Data System (ADS)
Zilhão, Miguel; Witek, Helvi; Cardoso, Vitor
2015-12-01
Physics beyond the standard model is an important candidate for dark matter, and an interesting testing ground for strong-field gravity: the equivalence principle ‘forces’ all forms of matter to fall in the same way, and it is therefore natural to look for imprints of these fields in regions with strong gravitational fields, such as compact stars or black holes (BHs). Here we study general relativity minimally coupled to a massive vector field, and how BHs in this theory lose ‘hair’. Our results indicate that BHs can sustain Proca field condensates for extremely long time-scales.
Nonlinear Structure Formation, Backreaction and Weak Gravitational Fields
NASA Astrophysics Data System (ADS)
Paranjape, A.
There is an ongoing debate in the literature concerning the effects of averaging out inhomogeneities (“backreaction”) in cosmology. In particular, some simple models of structure formation studied in the literature seem to indicate that the backreaction can play a significant role at late times, and it has also been suggested that the standard perturbed FLRW framework is no longer a good approximation during structure formation, when the density contrast becomes nonlinear. In this work we use Zalaletdinov's covariant averaging scheme (macroscopic gravity or MG) to show that as long as the metric of the Universe can be described by the perturbed FLRW form, the corrections due to averaging remain negligibly small. Further, using a fully relativistic and reasonably generic model of pressureless spherical collapse, we show that as long as matter velocities remain small (which is true in our model), the perturbed FLRW form of the metric can be explicitly recovered. Together, these results imply that the backreaction remains small even during nonlinear structure formation, and we confirm this within the toy model with a numerical calculation.
Stages: sub-Fourier dynamic shim updating using nonlinear magnetic field phase preparation.
Witschey, Walter R T; Littin, Sebastian; Cocosco, Chris A; Gallichan, Daniel; Schultz, Gerrit; Weber, Hans; Welz, Anna; Hennig, Jürgen; Zaitsev, Maxim
2014-01-01
Heterogeneity of the static magnetic field in magnetic resonance imaging may cause image artifacts and degradation in image quality. The field heterogeneity can be reduced by dynamically adjusting shim fields or dynamic shim updating, in which magnetic field homogeneity is optimized for each tomographic slice to improve image quality. A limitation of this approach is that a new magnetic field can be applied only once for each slice, otherwise image quality would improve somewhere to its detriment elsewhere in the slice. The motivation of this work is to overcome this limitation and develop a technique using nonlinear magnetic fields to dynamically shim the static magnetic field within a single Fourier-encoded volume or slice, called sub-Fourier dynamic shim updating. However, the nonlinear magnetic fields are not used as shim fields; instead, they impart a strong spatial dependence to the acquired MR signal by nonlinear phase preparation, which may be exploited to locally improve magnetic field homogeneity during acquisition. A theoretical description of the method is detailed, simulations and a proof-of-principle experiment are performed using a magnet coil with a known field geometry. The method is shown to remove artifacts associated with magnetic field homogeneity in balanced steady-state free-precession pulse sequences. We anticipate that this method will be useful to improve the quality of magnetic resonance images by removing deleterious artifacts associated with a heterogeneous static magnetic field. PMID:23440677
SIMULATION OF THREE-DIMENSIONAL NONLINEAR FIELDS OF ULTRASOUND THERAPEUTIC ARRAYS
Yuldashev, P. V.; Khokhlova, V. A.
2011-01-01
A novel numerical model was developed to simulate three-dimensional nonlinear fields generated by high intensity focused ultrasound (HIFU) arrays. The model is based on the solution to the Westervelt equation; the developed algorithm makes it possible to model nonlinear pressure fields of periodic waves in the presence of shock fronts localized near the focus. The role of nonlinear effects in a focused beam of a two-dimensional array was investigated in a numerical experiment in water. The array consisting of 256 elements and intensity range on the array elements of up to 10 W/cm2 was considered. The results of simulations have shown that for characteristic intensity outputs of modern HIFU arrays, nonlinear effects play an important role and shock fronts develop in the pressure waveforms at the focus. PMID:21804751
Aspects of Magnetic Field Configurations in Planar Nonlinear Electrodynamics
NASA Astrophysics Data System (ADS)
de Assis, L. P. G.; Gaete, Patricio; Helaÿel-Neto, José A.; Vellozo, S. O.
2012-02-01
In the framework of three-dimensional Born-Infeld Electrodynamics, we pursue an investigation of the consequences of the space-time dimensionality on the existence of magnetostatic fields generated by electric charges at rest in an inertial frame, which are present in its four-dimensional version. Our analysis reveals interesting features of the model. In fact, a magnetostatic field associated with an electric charge at rest does not appear in this case. Interestingly, the addition of the topological term (Chern-Simons) to Born-Infeld Electrodynamics yields the appearance of the magnetostatic field. We also contemplate the fields associated to the would-be-magnetic monopole in three dimensions.
Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity.
Polesana, P; Dubietis, A; Porras, M A; Kucinskas, E; Faccio, D; Couairon, A; Di Trapani, P
2006-05-01
The near-field dynamics of a femtosecond Bessel beam propagating in a Kerr nonlinear medium (fused silica) is investigated both numerically and experimentally. We demonstrate that the input Bessel beam experiences strong nonlinear reshaping. Due to the combined action of self-focusing and nonlinear losses the reshaped beam exhibits a radial compression and reduced visibility of the Bessel oscillations. Moreover, we show that the reshaping process starts from the intense central core and gradually replaces the Bessel beam profile during propagation, highlighting the conical geometry of the energy flow. PMID:16803062
Parametrically driven field emission in strongly nonlinear coupled electron-shuttles
NASA Astrophysics Data System (ADS)
Kim, Chulki; Prada, Marta; Platero, Gloria; Seo, Minah; Lee, Taikjin; Kim, Jae Hun; Lee, Seok; Blick, Robert
2014-03-01
The transition of coupled electron shuttles from a stable to a strongly nonlinear response is demonstrated at room temperature. The electron transport is Coulomb-controlled at low voltages but changes to the conventional field emission in this transition. This reversible process forms a well-defined band within a broad frequency range in the parameter space. Both the experimental data and numerical calculations indicate that the source of the nonlinearity is provided by the electromechanical coupling. The increased current in the nonlinear regime has the potential to form the basis for energy harvesting via nanomechanical shuttles.
Nonlinear decay of magnetic helicity in magnetohydrodynamic turbulence with a mean magnetic field
NASA Technical Reports Server (NTRS)
Stribling, Troy; Matthaeus, William H.; Ghosh, Sanjoy
1994-01-01
We show that the magnetic helicity associated with fluctuations in homogeneous incompressible magnetohydrodynamic (MHD) turbulence with a mean magnetic field decays in time because of nonlinear processes. Evidence is obtained numerically, by use of both dissipative and nondissipative spectral method simulations. The described effect stands in contrast to expectations based on studies of MHD turbulence without an applied mean field, in which magnetic helicity is transferred nonlinearly to long wavelengths and is preserved in time because of selective decay when dissipation is present. The process of nonlinear decay is described in terms of a generalized ideal helicity invariant and is characterized by the transient production of a mean induced electric field aligned with the applied magnetic field, an effect reminiscent of the alpha effect in dynamo theory. A simple phenomenological model for the decay process is proposed.
NASA Astrophysics Data System (ADS)
El-Dib, Yusry O.
1993-04-01
Nonlinear wave propagation on the surface between two superposed magnetic fluids stressed by a tangential periodic magnetic field is investigated using the method of multiple scales. A stability analysis reveals the existence of both nonresonant and resonant cases. From the solvability conditions, three types of nonlinear Schrodinger equation are obtained. The necessary and sufficient conditions for stability are obtained in each case. Formulae for the surface elevation are also obtained in both the non-resonant and the resonant cases. It is found from the numerical calculation that the tangential periodic magnetic field plays a dual role in the stability criterion, while the field frequency has a destabilizing influence.
Magnetic-field generation by the ablative nonlinear Rayleigh–Taylor instability
Nilson, P. M.; Gao, L.; Igumenshchev, I. V.; Fiksel, G.; Yan, R.; Davies, J. R.; Martinez, D.; Smalyuk, V. A.; Haines, M. G.; Blackman, E. G.; Froula, D. H.; Betti, R.; Meyerhofer, D. D.
2015-04-01
Experiments reporting magnetic-field generation by the ablative nonlinear Rayleigh–Taylor (RT) instability are reviewed. The experiments show how large-scale magnetic fields can, under certain circumstances, emerge and persist in strongly driven laboratory and astrophysical flows at drive pressures exceeding one million times atmospheric pressure.
Force-free swimming of a model helical flagellum in viscoelastic fluids
Liu, Bin; Powers, Thomas R.; Breuer, Kenneth S.
2011-01-01
We precisely measure the force-free swimming speed of a rotating helix in viscous and viscoelastic fluids. The fluids are highly viscous to replicate the low Reynolds number environment of microorganisms. The helix, a macroscopic scale model for the bacterial flagellar filament, is rigid and rotated at a constant rate while simultaneously translated along its axis. By adjusting the translation speed to make the net hydrodynamic force vanish, we measure the force-free swimming speed as a function of helix rotation rate, helix geometry, and fluid properties. We compare our measurements of the force-free swimming speed of a helix in a high-molecular weight silicone oil with predictions for the swimming speed in a Newtonian fluid, calculated using slender-body theories and a boundary-element method. The excellent agreement between theory and experiment in the Newtonian case verifies the high accuracy of our experiments. For the viscoelastic fluid, we use a polymer solution of polyisobutylene dissolved in polybutene. This solution is a Boger fluid, a viscoselastic fluid with a shear-rate-independent viscosity. The elasticity is dominated by a single relaxation time. When the relaxation time is short compared to the rotation period, the viscoelastic swimming speed is close to the viscous swimming speed. As the relaxation time increases, the viscoelastic swimming speed increases relative to the viscous speed, reaching a peak when the relaxation time is comparable to the rotation period. As the relaxation time is further increased, the viscoelastic swimming speed decreases and eventually falls below the viscous swimming speed. PMID:22106263
Varying self-inductance and energy storage in a sheared force-free arcade. [of coronal loops
NASA Technical Reports Server (NTRS)
Zuccarello, F.; Burm, H.; Kuperus, M.; Raadu, M.; Spicer, D. S.
1987-01-01
An electric circuit analogy is used to model the build-up and storage of magnetic energy in the coronal loops known to exist in the atmosphere of the sun. The present parameterization of magnetic energy storage in an electric circuit analog uses a bulk current I flowing in the circuit and a self-inductance L. Because the self-inductance is determined by the geometry of the magnetic configuration any change in its dimensions will change L. If L is increased, the amount of magnetic energy stored and the rate at which magnetic energy is stored are both increased. One way of increasing L is to shear the magnetic field lines and increase their effective geometrical length. Using the force-free field approximation for a magnetic arcade whose field lines are sheared by photospheric motions, it is demonstrated that the increase of magnetic energy is initially due to the increase of the current intensity I and later mainly due to the increase of the self-inductance.
Effect of the mass center shift for force-free flexible spacecraft
NASA Technical Reports Server (NTRS)
Meirovitch, L.; Juang, J.-N.
1975-01-01
For a spinning flexible spacecraft the mass center generally shifts relative to the nominal undeformed position. It is thought that this shift of center complicates spacecraft stability analysis. It is proved, on the basis of results achieved by Meirovitch and Calico (1972), that for the general class of force-free single-spin flexible spacecraft it is possible to ignore this shift of center without affecting the stability criteria in any significant way. A new theorem on inequalities for quadratic forms is proved to demonstrate the validity of the stability analysis.
Nonlinear energy dissipation of magnetic nanoparticles in oscillating magnetic fields
NASA Astrophysics Data System (ADS)
Soto-Aquino, D.; Rinaldi, C.
2015-11-01
The heating of magnetic nanoparticle suspensions subjected to alternating magnetic fields enables a variety of emerging applications such as magnetic fluid hyperthermia and triggered drug release. Rosensweig (2002) [25] obtained a model for the heat dissipation rate of a collection of non-interacting particles. However, the assumptions made in this analysis make it rigorously valid only in the limit of small applied magnetic field amplitude and frequency (i.e., values of the Langevin parameter that are much less than unity and frequencies below the inverse relaxation time). In this contribution we approach the problem from an alternative point of view by solving the phenomenological magnetization relaxation equation exactly for the case of arbitrary magnetic field amplitude and frequency and by solving a more accurate magnetization relaxation equation numerically. We also use rotational Brownian dynamics simulations of non-interacting magnetic nanoparticles subjected to an alternating magnetic field to estimate the rate of energy dissipation and compare the results of the phenomenological theories to the particle-scale simulations. The results are summarized in terms of a normalized energy dissipation rate and show that Rosensweig's expression provides an upper bound on the energy dissipation rate achieved at high field frequency and amplitude. Estimates of the predicted dependence of energy dissipation rate, quantified as specific absorption rate (SAR), on magnetic field amplitude and frequency, and particle core and hydrodynamic diameter, are also given.
NASA Astrophysics Data System (ADS)
Williams, Timothy C.; Shaddix, Christopher R.
2007-12-01
Intensified charge-coupled devices (ICCDs) are used extensively in many scientific and engineering environments to image weak or temporally short optical events. Care has to be taken in interpreting the images from ICCDs if quantitative results are required. In particular, nonuniform gain (flat field) and nonlinear response effects must be properly accounted for. Traditional flat-field corrections can only be applied in the linear regime of the ICCD camera, which limits the usable dynamic range. This paper reports a more general approach to image correction whereby the nonlinear gain response of each pixel of the ICCD is characterized over the full dynamic range of the camera. Image data can then be corrected for the combined effects of nonuniform gain and nonlinearity. The results from a two-color pyrometry measurement of soot field temperature are used to illustrate the capabilities of the new correction approach.
Elena V. Belova; Ronald C. Davidson; Hantao Ji; Masaaki Yamada
2003-11-25
Results of three-dimensional hybrid simulations of the field-reversed configuration (FRC) are presented. Emphasis of this work is on the nonlinear evolution of magnetohydrodynamic (MHD) instabilities in kinetic FRCs. A wide range of ''bar s'' values is considered, where the ''bar s'' is the FRC kinetic parameter, which measures the number of ion gyroradii in the configuration. The linear and nonlinear stability of MHD modes with toroidal mode numbers n greater than or equal to 1 is investigated, including the effects of ion rotation, finite electron pressure, and weak toroidal field. Low-''bar s'' simulations show nonlinear saturation of the n = 1 tilt mode. The n greater than or equal to 2 rotational modes are observed to grow during the nonlinear phase of the tilt instability due to ion spin-up in the toroidal direction. Large-''bar s'' simulations show no saturation of the tilt mode, and there is a slow nonlinear evolution of the instability after the initial fast linear growth. Overall, the hybrid simulations demonstrate the importance of nonlinear effects, which are responsible for the saturation of instabilities in low-''bar s'' configurations, and also for the increase in FRC life-time compared to MHD models in high-''bar s'' configurations.
Kinetic model of force-free current sheets with non-uniform temperature
Kolotkov, D. Y.; Nakariakov, V. M.; Vasko, I. Y.
2015-11-15
The kinetic model of a one-dimensional force-free current sheet (CS) developed recently by Harrison and Neukirch [Phys. Rev. Lett. 102(13), 135003 (2009)] predicts uniform distributions of the plasma temperature and density across the CS. However, in realistic physical systems, inhomogeneities of these plasma parameters may arise quite naturally due to the boundary conditions or local plasma heating. Moreover, as the CS spatial scale becomes larger than the characteristic kinetic scales (the regime often referred to as the MHD limit), it should be possible to set arbitrary density and temperature profiles. Thus, an advanced model has to allow for inhomogeneities of the macroscopic plasma parameters across the CS, to be consistent with the MHD limit. In this paper, we generalise the kinetic model of a force-free current sheet, taking into account the inhomogeneity of the density and temperature across the CS. In the developed model, the density may either be enhanced or depleted in the CS central region. The temperature profile is prescribed by the density profile, keeping the plasma pressure uniform across the CS. All macroscopic parameters, as well as the distribution functions for the protons and electrons, are determined analytically. Applications of the developed model to current sheets observed in space plasmas are discussed.
Time-dependent Force-free Pulsar Magnetospheres: Axisymmetric and Oblique Rotators
Spitkovsky, Anatoly; /KIPAC, Menlo Park
2006-04-10
Magnetospheres of many astrophysical objects can be accurately described by the low-inertia (or ''force-free'') limit of MHD. We present a new numerical method for solution of equations of force-free relativistic MHD based on the finite-difference time-domain (FDTD) approach with a prescription for handling spontaneous formation of current sheets. We use this method to study the time-dependent evolution of pulsar magnetospheres in both aligned and oblique magnetic geometries. For the aligned rotator we confirm the general properties of the time-independent solution of Contopoulos et al. (1999). For the oblique rotator we present the 3D structure of the magnetosphere and compute, for the first time, the spindown power of pulsars as a function of inclination of the magnetic axis. We find the pulsar spindown luminosity to be L {approx} ({mu}{sup 2}{Omega}{sub *}{sup 4}/c{sup 3})(1 + sin{sup 2}{alpha}) for a star with the dipole moment {mu}, rotation frequency {Omega}{sub *}, and magnetic inclination angle {alpha}. We also discuss the effects of current sheet resistivity and reconnection on the structure and evolution of the magnetosphere.
Non-linear vacuum polarization in strong fields
Gyulassy, M.
1981-07-01
The Wichmann-Kroll formalism for calculating the vacuum polarization density to first order in ..cap alpha.. but to all orders in Z..cap alpha.. is derived. The most essential quantity is shown to be the electrons Green's function in these calculations. The method of constructing that Green's function in the field of finite radius nuclei is then presented.
Blumenfeld, I.; Clayton, C.E.; Decker, F.J.; Hogan, M.J.; Huang, C.; Ischebeck, R.; Iverson, R.H.; Joshi, C.; Katsouleas, T.; Kirby, N.; Lu, W.; Marsh, K.A.; Mori, W.B.; Muggli, P.; Oz, E.; Siemann, R.H.; Walz, D.R.; Zhou, M.; /UCLA
2012-06-12
The scaling of the two important figures of merit, the transformer ratio T and the longitudinal electric field E{sub z}, with the peak drive-bunch current I{sub p}, in a nonlinear plasma wakefield accelerator is presented for the first time. The longitudinal field scales as I{sub P}{sup 0.623{+-}0.007}, in good agreement with nonlinear wakefield theory ({approx}I{sub P}{sup 0.5}), while the unloaded transformer ratio is shown to be greater than unity and scales weakly with the bunch current. The effect of bunch head erosion on both parameters is also discussed.
Nonlocality in quantum theory understood in terms of Einstein's nonlinear field approach
NASA Astrophysics Data System (ADS)
Bohm, D.; Hiley, B. J.
1981-08-01
We discuss Einstein's ideas on the need for a theory that is both objective and local and also his suggestion for realizing such a theory through nonlinear field equations. We go on to analyze the nonlocality implied by the quantum theory, especially in terms of the experiment of Einstein, Podolsky, and Rosen. We then suggest an objective local field model along Einstein's lines, which might explain quantum nonlocality as a coordination of the properties of pulse-like solutions of the nonlinear equations that would represent particles. Finally, we discuss the implications of our model for Bell's inequality.
Stenzel, R. L.; Urrutia, J. M.; Strohmaier, K. D.
2008-04-15
The nonlinear interactions of time-varying magnetic fields with plasmas is investigated in the regime of electron magnetohydrodynamics. Simple magnetic field geometries are excited in a large laboratory plasma with a loop antenna driven with large oscillatory currents. When the axial loop field opposes the ambient field, the net field can be reversed to create a field-reversed configuration (FRC). In the opposite polarity, a strong field enhancement is produced. The time-varying antenna field excites whistler modes with wave magnetic fields exceeding the ambient magnetic field. The resulting magnetic field topologies have been measured. As the magnetic topology is changed from FRC to strong enhancement, two propagating field configurations resembling spheromaks are excited, one with positive and the other with negative helicity. Such 'whistler spheromaks' propagate with their null points along the weaker ambient magnetic field, with the current density localized around its O-line. In contrast, 'whistler mirrors' which have topologies similar to linear whistlers, except with B{sub wave}>B{sub 0}, have no null regions and, therefore, broad current layers. This paper describes the basic field topologies of whistler spheromaks and mirrors, while companion papers discuss the associated nonlinear phenomena as well as the interaction between them.
Nonlinear dependence of complex plasma parameters on applied electric field
Sodha, M. S.; Mishra, S. K.; Misra, Shikha
2011-02-15
This paper presents an analysis of the effect of an applied static or alternating electric field on the electron density and temperature, charge on the particles, the electron collision frequency, the electronic conductivity, and the coefficient of electron diffusion in a complex plasma (i) when not illuminated by light, which can cause photoelectric emission from the particles, and (ii) when so illuminated. A parametric analysis based on computations for some typical sets of parameters has also been made. The significance of this work to (i) the disappearance of a polar mesospheric summer echoes structure by radio wave and (ii) magneto-hydrodynamic (MHD) power generation has also been indicated. The time dependence of the various parameters after the application of the electric field has also been discussed.
HELICITY CONSERVATION IN NONLINEAR MEAN-FIELD SOLAR DYNAMO
Pipin, V. V.; Sokoloff, D. D.; Zhang, H.; Kuzanyan, K. M.
2013-05-01
It is believed that magnetic helicity conservation is an important constraint on large-scale astrophysical dynamos. In this paper, we study a mean-field solar dynamo model that employs two different formulations of the magnetic helicity conservation. In the first approach, the evolution of the averaged small-scale magnetic helicity is largely determined by the local induction effects due to the large-scale magnetic field, turbulent motions, and the turbulent diffusive loss of helicity. In this case, the dynamo model shows that the typical strength of the large-scale magnetic field generated by the dynamo is much smaller than the equipartition value for the magnetic Reynolds number 10{sup 6}. This is the so-called catastrophic quenching (CQ) phenomenon. In the literature, this is considered to be typical for various kinds of solar dynamo models, including the distributed-type and the Babcock-Leighton-type dynamos. The problem can be resolved by the second formulation, which is derived from the integral conservation of the total magnetic helicity. In this case, the dynamo model shows that magnetic helicity propagates with the dynamo wave from the bottom of the convection zone to the surface. This prevents CQ because of the local balance between the large-scale and small-scale magnetic helicities. Thus, the solar dynamo can operate in a wide range of magnetic Reynolds numbers up to 10{sup 6}.
High-order optical processes in intense laser field: Towards nonperturbative nonlinear optics
NASA Astrophysics Data System (ADS)
Strelkov, V. V.
2016-05-01
We develop an approach describing nonlinear-optical processes in the strong-field domain characterized by the nonperturbative field-with-matter interaction. The polarization of an isolated atom in the external field calculated via the numerical solution of the time-dependent Schrödinger equation agrees with our analytical findings. For the practically important case of one strong laser field and several weaker fields, we derive and analytically solve propagation equations describing high-order (HO) wave mixing, HO parametric amplification, and HO stimulated scattering. These processes provide a way of efficient coherent xuv generation. Some properties of HO processes are new in nonlinear optics: essentially complex values of the coefficients in the propagation equations, the superexponential (hyperbolic) growing solutions, etc. Finally, we suggest conditions for the practical realization of these processes and discuss published numerical and experimental results where such processes could have been observed.
Nonlinear deformation of a ferrofluid droplet in a uniform magnetic field.
Zhu, Gui-Ping; Nguyen, Nam-Trung; Ramanujan, R V; Huang, Xiao-Yang
2011-12-20
This paper reports experimental and numerical results of the deformation of a ferrofluid droplet on a superhydrophobic surface under the effect of a uniform magnetic field. A water-based ferrofluid droplet surrounded by immiscible mineral oil was stretched by a magnetic field parallel to the substrate surface. The results show that an increasing flux density increases the droplet width and decreases the droplet height. A numerical model was established to study the equilibrium shape of the ferrofluid droplet. The governing equations for physical fields, including the magnetic field, are solved by the finite volume method. The interface between the two immiscible liquids was tracked by the level-set method. Nonlinear magnetization was implemented in the model. Comparison between experimental and numerical results shows that the numerical model can predict well the nonlinear deformation of a ferrofluid droplet in a uniform magnetic field. PMID:22044246
Nonlinear perturbations of cosmological scalar fields with non-standard kinetic terms
NASA Astrophysics Data System (ADS)
Renaux-Petel, Sébastien; Tasinato, Gianmassimo
2009-01-01
We adopt a covariant formalism to derive exact evolution equations for nonlinear perturbations, in a universe dominated by two scalar fields. These scalar fields are characterized by non-canonical kinetic terms and an arbitrary field space metric, a situation typically encountered in inflationary models inspired by string theory. We decompose the nonlinear scalar perturbations into adiabatic and entropy modes, generalizing the definition adopted in the linear theory, and we derive the corresponding exact evolution equations. We also obtain a nonlinear generalization of the curvature perturbation on uniform density hypersurfaces, showing that on large scales it is sourced only by the nonlinear version of the entropy perturbation. We then expand these equations to second order in the perturbations, using a coordinate based formalism. Our results are relatively compact and elegant and enable one to identify the new effects coming from the non-canonical structure of the scalar fields Lagrangian. We also explain how to analyze, in our formalism, the interesting scenario of multi-field Dirac-Born-Infeld inflation.
But, D. B.; Drexler, C.; Ganichev, S. D.; Sakhno, M. V.; Sizov, F. F.; Dyakonova, N.; Drachenko, O.; Gutin, A.; Knap, W.
2014-04-28
Terahertz power dependence of the photoresponse of field effect transistors, operating at frequencies from 0.1 to 3 THz for incident radiation power density up to 100 kW/cm{sup 2} was studied for Si metal–oxide–semiconductor field-effect transistors and InGaAs high electron mobility transistors. The photoresponse increased linearly with increasing radiation intensity up to the kW/cm{sup 2} range. Nonlinearity followed by saturation of the photoresponse was observed for all investigated field effect transistors for intensities above several kW/cm{sup 2}. The observed photoresponse nonlinearity is explained by nonlinearity and saturation of the transistor channel current. A theoretical model of terahertz field effect transistor photoresponse at high intensity was developed. The model explains quantitative experimental data both in linear and nonlinear regions. Our results show that dynamic range of field effect transistors is very high and can extend over more than six orders of magnitudes of power densities (from ∼0.5 mW/cm{sup 2} to ∼5 kW/cm{sup 2})
NASA Astrophysics Data System (ADS)
Elhefnawy, Abdel R. F.
1993-05-01
A weakly nonlinear evolution of two dimensional wave packets on the surface of a magnetic fluid in the presence of an uniform magnetic field is presented, taking into account the surface tension. The method used is that of multiple scales to derive two partial differential equations. These differential equations can be combined to yield two alternate nonlinear Schroedinger equations. The first equation is valid near the cutoff wavenumber while the second equation is used to show that stability of uniform wave trains depends on the wavenumber, the density, the surface tension and the magnetic field. At the critical point, a generalized formulation of the evolution equation governing the amplitude is developed which leads to the nonlinear Klein-Gordon equation. From the latter equation, the various stability criteria are obtained.
Nonlinear analysis of generalized cross-field current instability
NASA Technical Reports Server (NTRS)
Yoon, Peter H.; Lui, Anthony T. Y.
1993-01-01
Analysis of the generalized cross-field current instability is carried out in which cross-field drift of both the ions and electrons and their temperatures are permitted to vary in time. The unstable mode under consideration is the electromagnetic generalization of the classical modified-two-stream instability. The generalized instability is made of the modified-two-stream and ion-Weibel modes. The relative importance of the features associated with the ion-Weibel mode and those of the modified-two-stream mode is assessed. Specific applications are made to the Earth's neutral sheet prior to substorm onset and to the Earth's bow shock. The numerical solution indicates that the ion-Weibel mode dominates in the Earth's neutral sheet environment. In contrast, the situation for the bow shock is dominated by the modified-two-stream mode. Notable differences are found between the present calculation and previous results on ion-Weibel mode which restrict the analysis to only parallel propagating waves. However, in the case of Earth's bow shock for which the ion-Weibel mode plays no important role, the inclusion of the electromagnetic ion response is found to differ little from the previous results which treats ions responding only to the electrostatic component of the excited waves.
The nonlinear evolution of magnetized solar filaments
NASA Technical Reports Server (NTRS)
Sparks, L.; Van Hoven, G.; Schnack, D. D.
1990-01-01
Thermal instability driven by optically thin radiation is believed to initiate the formation of plasma filaments in the solar corona. The fact that filaments are observed generally to separate regions of opposite, line-of-sight, magnetic polarity in the underlying photosphere suggests that filament formation requires the presence of a highly sheared, local magnetic field. Two-dimensional, nonlinear, magnetohydrodynamic simulations of the local genesis and growth of solar filaments in a force-free, sheared, magnetic field were performed, and the evolution of generic perturbations possessing broad spatial profiles was traced. It was found that simulations of the evolution of initial random-noise perturbations produce filamentary plasma structures that exhibit densities and temperatures characteristic of observed solar filaments. Furthermore, in each of these simulations, the filament axis lies at a finite angle with respect to the local magnetic field, consistent with solar observations.
Nonlinear response of the benzene molecule to strong magnetic fields
NASA Astrophysics Data System (ADS)
Pagola, G. I.; Caputo, M. C.; Ferraro, M. B.; Lazzeretti, P.
2005-02-01
The fourth-rank hypermagnetizability tensor of the benzene molecule has been evaluated at the coupled Hartree-Fock level of accuracy within the conventional common-origin approach, adopting gaugeless basis sets of increasing size and flexibility. The degree of convergence of theoretical tensor components has been estimated allowing for two different coordinate systems. It is shown that a strong magnetic field perpendicular to the plane of the molecule causes a distortion of the electron charge density, which tends to concentrate in the region of the C-C bonds. This charge contraction has a dynamical origin, and can be interpreted as a feedback effect in terms of the classical Lorentz force acting on the electron current density.
Nonlinear response of the benzene molecule to strong magnetic fields.
Pagola, G I; Caputo, M C; Ferraro, M B; Lazzeretti, P
2005-02-15
The fourth-rank hypermagnetizability tensor of the benzene molecule has been evaluated at the coupled Hartree-Fock level of accuracy within the conventional common-origin approach, adopting gaugeless basis sets of increasing size and flexibility. The degree of convergence of theoretical tensor components has been estimated allowing for two different coordinate systems. It is shown that a strong magnetic field perpendicular to the plane of the molecule causes a distortion of the electron charge density, which tends to concentrate in the region of the C-C bonds. This charge contraction has a dynamical origin, and can be interpreted as a feedback effect in terms of the classical Lorentz force acting on the electron current density. PMID:15743243
Detecting non-linearities in neuro-electrical signals: A study of synchronous local field potentials
NASA Astrophysics Data System (ADS)
Müller-Gerking, Johannes; Martinerie, Jacques; Neuenschwander, Sergio; Pezard, Laurent; Renault, Bernard; Varela, Francisco J.
The question of the presence and detection of non-linear dynamics and possibly low-dimensional chaos in the brain is still an open question, with recent results indicating that initial claims for low dimensionality were faulted by incomplete statistical testing. To make some progress on this question, our approach was to use stringent data analysis of precisely controlled and behaviorally significant neuroelectric data. There are strong indications that functional brain activity is correlated with synchronous local field potentials. We examine here such synchronous episodes in data recorded from the visual system of behaving cats and pigeons. Our purpose was to examine under these ideal conditions whether the time series showed any evidence of non-linearity concommitantly with the arising of synchrony. To test for non-linearity we have used surrogate sets for non-linear forecasting, the false nearest strands method, and an examination of deterministic vs stochastic modeling. Our results indicate that the time series under examination do show evidence for traces of non-linear dynamics but weakly, since they are not robust under changes of parameters. We conclude that low-dimensional chaos is unlikely to be found in the brain, and that a robust detection and characterization of higher-dimensional non-linear dynamics is beyond the reach of current analytical tools.
Photorefractive nonlinearities caused by the Dember space-charge field in undoped CdTe.
Schroeder, W A; Stark, T S; Boggess, T F; Smirl, A L; Valley, G C
1991-06-01
The photorefractive nonlinearity associated with the Dember space-charge field between electrons and holes produced by two-photon absorption is unambiguously isolated and studied in undoped CdTe by using a nondegenerate, forward-probing, polarization-sensitive, transient-grating technique with a temporal resolution of <5 ps. PMID:19776789
Information field theory for cosmological perturbation reconstruction and nonlinear signal analysis
NASA Astrophysics Data System (ADS)
Enßlin, Torsten A.; Frommert, Mona; Kitaura, Francisco S.
2009-11-01
We develop information field theory (IFT) as a means of Bayesian inference on spatially distributed signals, the information fields. A didactical approach is attempted. Starting from general considerations on the nature of measurements, signals, noise, and their relation to a physical reality, we derive the information Hamiltonian, the source field, propagator, and interaction terms. Free IFT reproduces the well-known Wiener-filter theory. Interacting IFT can be diagrammatically expanded, for which we provide the Feynman rules in position-, Fourier-, and spherical-harmonics space, and the Boltzmann-Shannon information measure. The theory should be applicable in many fields. However, here, two cosmological signal recovery problems are discussed in their IFT formulation. (1) Reconstruction of the cosmic large-scale structure matter distribution from discrete galaxy counts in incomplete galaxy surveys within a simple model of galaxy formation. We show that a Gaussian signal, which should resemble the initial density perturbations of the Universe, observed with a strongly nonlinear, incomplete and Poissonian-noise affected response, as the processes of structure and galaxy formation and observations provide, can be reconstructed thanks to the virtue of a response-renormalization flow equation. (2) We design a filter to detect local nonlinearities in the cosmic microwave background, which are predicted from some early-Universe inflationary scenarios, and expected due to measurement imperfections. This filter is the optimal Bayes’ estimator up to linear order in the nonlinearity parameter and can be used even to construct sky maps of nonlinearities in the data.
On the generation of nonlinear travelling waves in confined geometries using electric fields.
Cimpeanu, R; Papageorgiou, D T
2014-07-28
We investigate electrostatically induced interfacial instabilities and subsequent generation of nonlinear coherent structures in immiscible, viscous, dielectric multi-layer stratified flows confined in small-scale channels. Vertical electric fields are imposed across the channel to produce interfacial instabilities that would normally be absent in such flows. In situations when the imposed vertical fields are constant, interfacial instabilities emerge due to the presence of electrostatic forces, and we follow the nonlinear dynamics via direct numerical simulations. We also propose and illustrate a novel pumping mechanism in microfluidic devices that does not use moving parts. This is achieved by first inducing interfacial instabilities using constant background electric fields to obtain fully nonlinear deformations. The second step involves the manipulation of the imposed voltage on the lower electrode (channel wall) to produce a spatio-temporally varying voltage there, in the form of a travelling wave with pre-determined properties. Such travelling wave dielectrophoresis methods are shown to generate intricate fluid-surface-structure interactions that can be of practical value since they produce net mass flux along the channel and thus are candidates for microfluidic pumps without moving parts. We show via extensive direct numerical simulations that this pumping phenomenon is a result of an externally induced nonlinear travelling wave that forms at the fluid-fluid interface and study the characteristics of the generated velocity field inside the channel. PMID:24936019
On the generation of nonlinear travelling waves in confined geometries using electric fields
Cimpeanu, R; Papageorgiou, D. T
2014-01-01
We investigate electrostatically induced interfacial instabilities and subsequent generation of nonlinear coherent structures in immiscible, viscous, dielectric multi-layer stratified flows confined in small-scale channels. Vertical electric fields are imposed across the channel to produce interfacial instabilities that would normally be absent in such flows. In situations when the imposed vertical fields are constant, interfacial instabilities emerge due to the presence of electrostatic forces, and we follow the nonlinear dynamics via direct numerical simulations. We also propose and illustrate a novel pumping mechanism in microfluidic devices that does not use moving parts. This is achieved by first inducing interfacial instabilities using constant background electric fields to obtain fully nonlinear deformations. The second step involves the manipulation of the imposed voltage on the lower electrode (channel wall) to produce a spatio-temporally varying voltage there, in the form of a travelling wave with pre-determined properties. Such travelling wave dielectrophoresis methods are shown to generate intricate fluid–surface–structure interactions that can be of practical value since they produce net mass flux along the channel and thus are candidates for microfluidic pumps without moving parts. We show via extensive direct numerical simulations that this pumping phenomenon is a result of an externally induced nonlinear travelling wave that forms at the fluid–fluid interface and study the characteristics of the generated velocity field inside the channel. PMID:24936019
Exactly solvable model for nonlinear light-matter interaction in an arbitrary time-dependent field
Brown, J. M.; Lotti, A.; Teleki, A.; Kolesik, M.
2011-12-15
Exact analytic expressions are derived for the dipole moment and nonlinear current of a one-dimensional quantum particle subject to a short-range attractive potential and an arbitrary time-dependent electric field. An efficient algorithm for the current evaluation is described and a robust implementation suitable for numerical simulations is demonstrated.
NASA Astrophysics Data System (ADS)
Titov, Serguey V.; Déjardin, Pierre-Michel; El Mrabti, Halim; Kalmykov, Yuri P.
2010-09-01
The nonlinear ac response of the magnetization M(t) of a uniaxially anisotropic superparamagnetic nanoparticle subjected to both ac and dc bias magnetic fields of arbitrary strengths and orientations is determined by averaging Gilbert’s equation augmented by a random field with Gaussian white-noise properties in order to calculate exactly the relevant statistical averages. It is shown that the magnetization dynamics of the uniaxial particle driven by a strong ac field applied at an angle to the easy axis of the particle (so that the axial symmetry is broken) alters drastically leading to different nonlinear effects due to coupling of the thermally activated magnetization reversal mode with the precessional modes of M(t) via the driving ac field.
ON THE STABILITY OF NON-FORCE-FREE MAGNETIC EQUILIBRIA IN STARS
Duez, V.; Braithwaite, J.; Mathis, S.
2010-11-20
The existence of stable magnetic configurations in white dwarfs, neutron stars, and various non-convective stellar regions is now well recognized. It has recently been shown numerically that various families of equilibria, including axisymmetric mixed poloidal-toroidal configurations, are stable. Here we test the stability of an analytically derived non-force-free magnetic equilibrium resulting from an initial relaxation (self-organization) process, using three-dimensional magnetohydrodynamic simulations: the obtained mixed configuration is compared with the dynamical evolution of its purely poloidal and purely toroidal components, both known to be unstable. The mixed equilibrium shows no sign of instability under white noise perturbations. This configuration therefore provides a good description of magnetic equilibrium topology inside non-convective stellar objects and will be useful to initialize magneto-rotational transport in stellar evolution codes and in multi-dimensional magnetohydrodynamic simulations.
The coeliac disease task force " Free from Gluten," " Improved knowledge to cure coeliac disease".
Greco, L; Percopo, S
1996-05-01
Gluten has recently been introduced into the diet of the Mediterranean and European population, but a considerable proportion has not adapted to this change and has developed intolerance to gluten. At least one million EEC citizens are gluten intolerant. In Italy each year 12 million ECU is spent in the diagnosis of uncomplicated gluten intolerance, 10 million ECU for complex diagnosis and 32 million ECU for long-term complications and malignancies. The total financial load of gluten intolerance, in its present state, is about 150 million ECU/year in Italy. Four million ECU is actually needed to develop a genetic probe, which may make the population screening feasible. A National Task Force "Free from Gluten" has been set up by the Italian Coeliac Society to stimulate fund-raising activities supporting genetic and basic research on gluten intolerance. PMID:8783751
Solution to the nonlinear field equations of ten dimensional supersymmetric Yang-Mills theory
NASA Astrophysics Data System (ADS)
Mafra, Carlos R.; Schlotterer, Oliver
2015-09-01
In this paper, we present a formal solution to the nonlinear field equations of ten-dimensional super Yang-Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher-mass dimensions are defined and their equations of motion are spelled out.
Yu, L.-L. Li, F.-Y.; Chen, M.; Weng, S.-M.; Schroeder, C. B.; Benedetti, C.; Esarey, E.; Sheng, Z.-M.
2014-12-15
Control of transverse wakefields in the nonlinear laser-driven bubble regime using a combination of Hermite-Gaussian laser modes is proposed. By controlling the relative intensity ratio of the two laser modes, the focusing force can be controlled, enabling matched beam propagation for emittance preservation. A ring bubble can be generated with a large longitudinal accelerating field and a transverse focusing field suitable for positron beam focusing and acceleration.
Effect of nonlinear absorption on electric field applied lead chloride by Z-scan technique
NASA Astrophysics Data System (ADS)
Rejeena, I.; Lillibai, Rahimkutty, M. H.; Nampoori, V. P. N.; Radhakrishnan, P.
2014-10-01
The preparation, spectral response and optical nonlinearity of gel grown lead chloride single crystals subjected to electric field of 20V using parallel plate arrangements have been investigated. Optical band gap of the samples were determined using linear absorption spectra. Open aperture z-scan was employed for the determination of nonlinear absorption coefficient of PbCl2 solution. The normalized transmittance curve exhibits a valley shows reverse saturable absorption. The non linear absorption at different input fluences were recorded using a single Gaussian laser beam in tight focus geometry. The RSA nature of the sample makes it suitable for optical limiting applications.
Modulation of dendritic patterns during electrodeposition: A nonlinear phase-field model
NASA Astrophysics Data System (ADS)
Chen, Lei; Zhang, Hao Wei; Liang, Lin Yun; Liu, Zhe; Qi, Yue; Lu, Peng; Chen, James; Chen, Long-Qing
2015-12-01
A nonlinear phase-field model, accounting for the Butler-Volmer electrochemical reaction kinetics, is developed to investigate the dendritic patterns during an electrodeposition process. Using lithium electrodeposition as an example, the proposed model is first verified by comparison with the Nernst equation in a 1D equilibrium system. The nonlinear electrochemical kinetics is also confirmed at non-equilibrium condition. The dendritic patterns are examined as a function of applied voltage and initial electrode surface morphology. A design map is proposed to tailor the electrode surface morphology and the applied voltage to avoid undesired dendritic patterns.
NASA Astrophysics Data System (ADS)
Podbielski, Jan; Heitmann, Detlef; Grundler, Dirk
2007-11-01
We have studied the spin dynamics of microscopic permalloy rings at GHz frequencies. Increasing the irradiation power, we observe first nonlinear spin dynamics and second microwave-assisted switching (MAS). We explore the MAS phase diagram as a function of microwave power and frequency f and, in particular, extract the critical microwave field hc(f). Its frequency dependence reflects characteristic eigenfrequencies from both the linear and nonlinear spin-wave spectrum. By comparing hc(f) with the different susceptibilities, we gain insight into the microscopic processes which might be the basis of a predictive theory of MAS.
Effect of nonlinear absorption on electric field applied lead chloride by Z-scan technique
Rejeena, I.; Lillibai,; Nampoori, V. P. N.; Radhakrishnan, P.; Rahimkutty, M. H.
2014-10-15
The preparation, spectral response and optical nonlinearity of gel grown lead chloride single crystals subjected to electric field of 20V using parallel plate arrangements have been investigated. Optical band gap of the samples were determined using linear absorption spectra. Open aperture z-scan was employed for the determination of nonlinear absorption coefficient of PbCl{sub 2} solution. The normalized transmittance curve exhibits a valley shows reverse saturable absorption. The non linear absorption at different input fluences were recorded using a single Gaussian laser beam in tight focus geometry. The RSA nature of the sample makes it suitable for optical limiting applications.
High-sensitivity dc field magnetometer using nonlinear resonance magnetoelectric effect
NASA Astrophysics Data System (ADS)
Burdin, D. A.; Chashin, D. V.; Ekonomov, N. A.; Fetisov, Y. K.; Stashkevich, A. A.
2016-05-01
The design and operation principle of dc field magnetometer using nonlinear resonance magnetoelectric effect in a ferromagnetic-piezoelectric structure are described. It is shown that under action of ac pumping magnetic field the structure generates the output voltage containing higher harmonics whose amplitudes depend on the dc magnetic field. Best performance of the device is obtained if the signal of the third harmonics is used for the dc field measurement. The sensitivity can be considerably (by approximately three orders of magnitude) increased if advantage is taken of the acoustic resonance of the structure at this frequency. There exists the optimal pumping field ensuring the highest sensitivity. Further increasing of this field expands the range of measurable dc fields at the expense of deteriorated sensitivity. The magnetometer fabricated on the basis of a planar langatate-Metglas structure had sensitivity up to ~1 V/Oe and allowed detection of the fields as low as ~10-5 Oe.
Nonlinear effects at high flux-flow electric fields.
Huebener, R P
2009-06-24
Ohm's law with the linear relation between resistive voltage and electric current is strictly valid only in the limit of infinitesimally small voltages. On the other hand, at finite electric voltages nonlinearities in the electric resistance can develop due to the energy picked up by the charge carriers in the electric field. This can lead to important effects both in the case of semiconductors and of superconductors, where the energy rise of the charge carriers or the quasiparticles can become relatively large. In this paper we limit our discussion to the flux-flow voltage in the mixed state of a type-II superconductor. At sufficiently low temperatures the energy dependence of the quasiparticle density of states and, hence, of the quasiparticle scattering rate can cause distinct nonlinear effects in the flux-flow resistance. The recent advances in thin-film sample preparation provided new opportunities for observing nonlinear effects of the latter kind. PMID:21828432
Nano-imaging collagen by atomic force, near-field and nonlinear microscope
NASA Astrophysics Data System (ADS)
Lim, Ken Choong; Tang, Jinkai; Li, Hao; Ng, Boon Ping; Kok, Shaw Wei; Wang, Qijie; Zhang, Ying
2015-03-01
As the most abundant protein in the human body, collagen has a very important role in vast numbers of bio-medical applications. The unique second order nonlinear properties of fibrillar collagen make it a very important index in nonlinear optical imaging based disease diagnosis of the brain, skin, liver, colon, kidney, bone, heart and other organs in the human body. The second-order nonlinear susceptibility of collagen has been explored at the macroscopic level and was explained as a volume-averaged molecular hyperpolarizability. However, details about the origin of optical second harmonic signals from collagen fibrils at the molecular level are still not clear. Such information is necessary for accurate interpolation of bio-information from nonlinear optical imaging techniques. The later has shown great potential in collagen based disease diagnosis methodologies. In this paper, we report our work using an atomic force microscope (AFM), near field (SNOM) and nonlinear laser scanning microscope (NLSM) to study the structure of collagen fibrils and other pro-collagen structures.
Construction and exact solution of a nonlinear quantum field model in quasi-higher dimension
NASA Astrophysics Data System (ADS)
Kundu, Anjan
2015-10-01
Nonperturbative exact solutions are allowed for quantum integrable models in one space-dimension. Going beyond this class we propose an alternative Lax matrix approach, exploiting the hidden multi-space-time concept in integrable systems and construct a novel nonlinear Schrödinger quantum field model in quasi-two dimensions. An intriguing field commutator is discovered, confirming the integrability of the model and yielding its exact Bethe ansatz solution with rich scattering and bound-state properties. The universality of the scheme is expected to cover diverse models, opening up a new direction in the field.
Light bending by nonlinear electrodynamics under strong electric and magnetic field
Kim, Jin Young; Lee, Taekoon E-mail: tlee@kunsan.ac.kr
2011-11-01
We calculate the bending angles of light under the strong electric and magnetic fields by a charged black hole and a magnetized neutron star according to the nonlinear electrodynamics of Euler-Heisenberg interaction. The bending angle of light by the electric field of charged black hole is computed from geometric optics and a general formula is derived for light bending valid for any orientation of the magnetic dipole. The astronomical significance of the light bending by magnetic field of a neutron star is discussed.
Nonlinear resonance of the rotating circular plate under static loads in magnetic field
NASA Astrophysics Data System (ADS)
Hu, Yuda; Wang, Tong
2015-11-01
The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating circular plate under static loads in magnetic field, the nonlinear vibration equation about the spinning circular plate is derived according to Hamilton principle. The algebraic expression of the initial deflection and the magneto elastic forced disturbance differential equation are obtained through the application of Galerkin integral method. By mean of modified Multiple scale method, the strongly nonlinear amplitude-frequency response equation in steady state is established. The amplitude frequency characteristic curve and the relationship curve of amplitude changing with the static loads and the excitation force of the plate are obtained according to the numerical calculation. The influence of magnetic induction intensity, the speed of rotation and the static loads on the amplitude and the nonlinear characteristics of the spinning plate are analyzed. The proposed research provides the theory reference for the research of nonlinear resonance of rotating plates in engineering.
Spata, Michael
2012-08-01
An experiment was conducted at Jefferson Lab's Continuous Electron Beam Accelerator Facility to develop a beam-based technique for characterizing the extent of the nonlinearity of the magnetic fields of a beam transport system. Horizontally and vertically oriented pairs of air-core kicker magnets were simultaneously driven at two different frequencies to provide a time-dependent transverse modulation of the beam orbit relative to the unperturbed reference orbit. Fourier decomposition of the position data at eight different points along the beamline was then used to measure the amplitude of these frequencies. For a purely linear transport system one expects to find solely the frequencies that were applied to the kickers with amplitudes that depend on the phase advance of the lattice. In the presence of nonlinear fields one expects to also find harmonics of the driving frequencies that depend on the order of the nonlinearity. Chebyshev polynomials and their unique properties allow one to directly quantify the magnitude of the nonlinearity with the minimum error. A calibration standard was developed using one of the sextupole magnets in a CEBAF beamline. The technique was then applied to a pair of Arc 1 dipoles and then to the magnets in the Transport Recombiner beamline to measure their multipole content as a function of transverse position within the magnets.
Nonlinear and extra-classical receptive field properties and the statistics of natural scenes.
Zetzsche, C; Röhrbein, F
2001-08-01
-stopping, complex-cell properties and extra-classical receptive field properties, but the 'ideal' complex cells seem only to occur with PCA. Thus, a combination of ON/OFF nonlinearities with an integrated PCA-ICA strategy seems necessary to exploit the statistical properties of natural images. PMID:11563533
Effect of Transverse Magnetic Fields on Cold-Atom Nonlinear Magneto-Optical Rotation
NASA Astrophysics Data System (ADS)
Meyer, David; Kunz, Paul; Fatemi, Fredrik; Quraishi, Qudsia
2016-05-01
We investigate nonlinear magneto-optical rotation (NMOR) in cold atoms in the presence of a transverse magnetic field where alignment-to-orientation conversion (AOC) dominates. The AOC mechanism, which relies on AC-Stark shifts generated by a strong, off-resonant probe beam, significantly alters the NMOR resonance. When an additional magnetic field is present, parallel to the electric field of the light, a nested feature within this NMOR resonance manifests. Unlike similar features observed with lower optical power in warm vapors, attributed to optical pumping through nearby hyperfine levels, this feature is due solely to the AOC mechanism. Using numerical simulations, a perturbative solution, and experimental observations we characterize the feature with respect to optical power, optical polarization, magnetic field strength, and magnetic field direction. These results shed further light on the AOC mechanism common to NMOR-based experiments and we demonstrate a potential application to measure transverse DC magnetic fields and spatial gradients.
Contributions of the substrate electric field to the molecular adsorbate optical nonlinearities
Zouari, M.; Villaeys, A.A.
2005-10-15
The nonlinear optical response of an adsorbate, whose structure is altered by the inhomogeneous electrostatic field of the substrate, has been evaluated with a particular emphasis on the sum-frequency generation process. In the limiting case of an homogeneous electrostatic field, besides the contributions associated with the induced dipole moments, we have additional contributions which only exist if the adsorbed molecule has permanent dipole moments. Also, the Franck-Condon factors of the unperturbed molecule weight the internal couplings induced by the electrostatic field. For the more general inhomogeneous electrostatic field case, while the main observations remain valid, the Franck-Condon factors are modified by the molecular structure changes induced by the electrostatic field. In addition, we have a strong redistribution of the vibronic couplings resulting from the analytical Q dependence of the partial charge distribution which is a signature of the field inhomogeneities.
Nonlinear dynamics of superparamagnetic beads in a traveling magnetic-field wave.
Yellen, Benjamin B; Virgin, Lawrence N
2009-07-01
The nonlinear dynamic behavior of superparamagnetic beads exposed to a periodic array of micromagnets and an external rotating field is simulated as a function of the relative size of the bead with respect to the micromagnet size and the strength of the external field relative to the pole density of the substrate. For large bead sizes, it is confirmed that the motion of the beads corresponds to the dynamics of an overdamped nonlinear harmonic oscillator. For lower bead sizes, additional subharmonic locking effects are observed along with the emergence of bounded orbits. These results qualitatively support previous experimental investigations of traveling-wave magnetophoresis and provide guidelines for achieving nearly infinite separation resolution between differently sized beads. PMID:19658704
NASA Astrophysics Data System (ADS)
Yang, K. F.; Liu, H. W.; Mishima, T. D.; Santos, M. B.; Nagase, K.; Hirayama, Y.
2011-08-01
The spin polarization (P) of high-density InSb two-dimensional electron systems (2DESs) has been measured using both parallel and tilted magnetic fields. P is found to exhibit a superlinear increase with the total field B. This P-B nonlinearity results in a difference in spin susceptibility between its real value χs and χgm~ m*g* (m* and g* are the effective mass and g factor, respectively) as routinely used in experiments. We demonstrate that such a P-B nonlinearity originates from the linearly P-dependent g* due to the exchange coupling of electrons rather than from the electron correlation as predicted for the low-density 2DES.
Tensor of the nonlinear polarizability of anisotropic medium and ``local'' field method
NASA Astrophysics Data System (ADS)
Lavric, V. V.; Ovander, L. N.; Shunyakov, V. T.
1983-08-01
The nonlinear polarizability tensor (NPT) for a molecular crystal of arbitrary symmetry has been obtained within the framework of polariton theory. Use of the Göppert-Mayer unitary transformation for the Hamiltonian of the crystal plus quantized electromagnetic field system made it possible to represent finally the result for the NPT in a compact form and to compare with results of semiphenomenological calculation of the NPT and to go out of the framework of the Gaitler-London approximation.
NASA Astrophysics Data System (ADS)
Hong, Woo-Pyo; Jung, Young-Dae
2013-10-01
We find the existence conditions for stationary dipole and tripole surface solitons formed at the interface of a nonlocal nonlinear medium and a lattice with linearly modulated frequency. We investigate how the degree of nonlocality, the depth, and the modulation frequency of the optical lattice field affect on the existence of the surface solitons and their dynamics. The relationship between the power and the model parameters is identified. The stability of the surface dipole and tripole solitons is numerically investigated.
The hysteresis-free negative capacitance field effect transistors using non-linear poly capacitance
NASA Astrophysics Data System (ADS)
Fan, S.-T.; Yan, J.-Y.; Lai, D.-C.; Liu, C. W.
2016-08-01
A gate structure design for negative capacitance field effect transistors (NCFETs) is proposed. The hysteresis loop in current-voltage performances is eliminated by the nonlinear C-V dependence of polysilicon in the gate dielectrics. Design considerations and optimizations to achieve the low SS and hysteresis-free transfer were elaborated. The effects of gate-to-source/drain overlap, channel length scaling, interface trap states and temperature impact on SS are also investigated.
Nonlinear optical tuning of photonic crystal microcavities by near-field probe
Vignolini, Silvia; Zani, Margherita; Riboli, Francesco; Vinattieri, Anna; Wiersma, Diederik S.; Gurioli, Massimo; Intonti, Francesca; Balet, Laurent; Li, Lianhe; Colocci, Marcello; Francardi, Marco; Gerardino, Annamaria; Fiore, Andrea
2008-07-14
We report on a nonlinear way to control and tune the dielectric environment of photonic crystal microcavities exploiting the local heating induced by near-field laser excitation at different excitation powers. The temperature gradient due to the optical absorption results in an index of refraction gradient which modifies the dielectric surroundings of the cavity and shifts the optical modes. Reversible tuning can be obtained either by changing the excitation power density or by exciting in different points of the photonic crystal microcavity.
NASA Astrophysics Data System (ADS)
Ucuncuoglu, Suleyman; Schneider, David A.; Dunlap, David; Finzi, Laura
2014-03-01
RNA Polymerase I (Pol I) conducts more than 60% of all the transcriptional activity in cells and also is responsible for synthesizing the RNA structure of the ribosome in eukaryotic cells. It is evident in many studies that Pol I transcription is affected by tumor suppressors and oncogenes which makes Pol I as a target for the anticancer therapeutics. The mechanistic pathways and kinetics of the Pol I transcription needs to be understood more precisely. Even though previous bulk studies measured the kinetics of the Pol I transcription, the results may hinder the intermediate states such as processivity and pausing during elongation. Here we used the single molecule approach to show that Pol I pauses more than Pol II during elongation step by using a novel single molecule instrument, multiplexed tethered particle motion microscopy (TPM). Our in-house developed TPM equipment is able to concurrently observe hundreds of single molecules. TPM technique has a major advantage to observe pausing under force-free condition unlike other single molecule techniques such as magnetic tweezers and optical tweezers. We also report that the processivity of Pol I is very low where only one out of fifteen transcription event reached the run-off site. We anticipate that our single molecule assays paved the way for observing more sophisticated aspects of Pol I transcription and it's relation with initiation and transcriptional factors.
ANALYSIS OF HIGH FIELD NON-LINEAR LOSSES ON SRF SURFACES DUE TO SPECIFIC TOPOGRAPHIC ROUGHNESS
Chen Xu,Charles Reece,Michael Kelley
2012-07-01
The high-field performance of SRF cavities will eventually be limited by the realization of fundamental material limits, whether it is Hc1 or Hsh, or some derivative thereof, at which the superconductivity is lost. Before reaching this fundamental field limit at the macro level, it must be encountered at localized, perhaps microscopic, sites of field enhancement due to local topography. If such sites are small enough, they may produce thermally stabilized normal-conducting regions which contribute non-linear losses when viewed from the macro resonant field perspective, and thus produce degradation in Q0. We have undertaken a calculation of local surface magnetic field enhancement from specific fine topographic structure by conformal mapping method and numerically. A solution of the resulting normal conducting volume has been derived and the corresponding RF Ohmic loss simulated.
Nonlinear Fluctuating Hydrodynamics in One Dimension: The Case of Two Conserved Fields
NASA Astrophysics Data System (ADS)
Spohn, Herbert; Stoltz, Gabriel
2015-08-01
We study the BS model, which is a one-dimensional lattice field theory taking real values. Its dynamics is governed by coupled differential equations plus random nearest neighbor exchanges. The BS model has two locally conserved fields. The peak structure of their steady state space-time correlations is determined through numerical simulations and compared with nonlinear fluctuating hydrodynamics, which predicts a traveling peak with KPZ scaling function and a standing peak with a scaling function given by the maximally asymmetric Lévy distribution with parameter . As a by-product, we completely classify the universality classes for two coupled stochastic Burgers equations with arbitrary coupling coefficients.
Nonlinear amplification of Langmuir waves in a plasma with regular and random magnetic fields
NASA Astrophysics Data System (ADS)
Krivitskii, V. S.; Priadko, Iu. M.; Tsytovich, V. N.
1990-07-01
The nonlinear interaction of Langmuir waves in a turbulent plasma with random resonance magnetic fields in the presence of an external regular magnetic field is investigated analytically. In particular, attention is given to the possibility of Langmuir wave amplification using the plasma maser effect. The frequency and angle dependences of the amplification increment (attenuation decrement) of Langmuir waves are determined in the isotropic case and in the presence of anisotropy. For an anisotropic particle distribution function, the amplification increment of Langmuir waves may reach values of the order of the plasma frequency.
On the Transition Regime of Nonlinear Error Field Penetration in Toroidal Plasmas
NASA Astrophysics Data System (ADS)
Wang, Huihui; Wang, Zhengxiong; Ding, Yonghua; Rao, Bo
2015-07-01
The error field penetration is numerically studied in the frame of the visco-resistive magnetohydrodynamics (MHD) model. A transition scaling is obtained to link the Rutherford and Waelbroeck regimes in the nonlinear phase of error field penetration process. Furthermore, a transition density scaling of [br/BT]crit ∼ ne½ is obtained in accord with recent experimental observations in the J-TEXT tokamak. supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2014GB124001 and 2013GB102000) and National Natural Science Foundation of China (Nos. 11322549, 11275043 and 11275080)
NASA Astrophysics Data System (ADS)
Toida, Mieko
2016-07-01
The electric field parallel to the magnetic field in nonlinear magnetosonic waves in three component plasmas (two-ion-species plasma and electron-positron-ion plasma) is theoretically studied based on a three-fluid model. In a two-ion-species plasma, a magnetosonic mode has two branches, high-frequency mode and low-frequency mode. The parallel electric field E ∥ and its integral along the magnetic field, F = - ∫ E ∥ d s , in the two modes propagating quasiperpendicular to the magnetic field are derived as functions of the wave amplitude ɛ and the density ratio and cyclotron frequency ratio of the two ion species. The theory shows that the magnitude of F in the high-frequency-mode pulse is much greater than that in the low-frequency-mode pulse. Theoretical expressions for E ∥ and F in nonlinear magnetosonic pulses in an electron-positron-ion plasma are also obtained under the assumption that the wave amplitudes are in the range of ( m e / m i ) 1 / 2 < ɛ < 1 , where m e / m i is the electron to ion mass ratio.
Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators
NASA Astrophysics Data System (ADS)
Driben, R.; Konotop, V. V.; Malomed, B. A.; Meier, T.
2016-07-01
The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3 +3 harmonic-oscillator p -wave eigenfunctions with orbital and magnetic quantum numbers l =1 and m =1 , 0, -1 . The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p -wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l =1 .
Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators.
Driben, R; Konotop, V V; Malomed, B A; Meier, T
2016-07-01
The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3+3 harmonic-oscillator p-wave eigenfunctions with orbital and magnetic quantum numbers l=1 and m=1, 0, -1. The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p-wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l=1. PMID:27575123
Nonlinear tearing mode interactions and mode locking in reversed field pinches
Hegna, C.C.
1996-06-01
The nonlinear interaction of a set of tearing instabilities and plasma flow is studied in a cylindrical plasma. An analytic theory of mode locking is developed which includes the effects of the localized electromagnetic torques, plasma inertia and cross-field viscosity. The calculation is specialized for the case of mode locking on the Madison Symmetric Torus (MST) reversed field pinch. In MST plasmas, a set of m = 1 tearing instabilities become phase locked and form a toroidally localized, rotating magnetic disturbance. An evolution equation for the phase velocity of this magnetic disturbance is derived which accounts for two types of electromagnetic torques. The external torques describe the interaction of the tearing modes with static magnetic perturbations located outside the plasma region. The interior torques describe the nonlinear interaction of three tearing modes which satisfy a wave number resonance condition. For conditions typical of MST, the internal torques dominate the external torques, which suggest the nonlinear interaction of tearing instabilities play a prominent role in the momentum degradation and mode locking.
A Theoretical Method for Characterizing Nonlinear Effects in Paul Traps with Added Octopole Field.
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Chen, Suming; Nie, Zongxiu
2015-08-01
In comparison with numerical methods, theoretical characterizations of ion motion in the nonlinear Paul traps always suffer from low accuracy and little applicability. To overcome the difficulties, the theoretical harmonic balance (HB) method was developed, and was validated by the numerical fourth-order Runge-Kutta (4th RK) method. Using the HB method, analytical ion trajectory and ion motion frequency in the superimposed octopole field, ε, were obtained by solving the nonlinear Mathieu equation (NME). The obtained accuracy of the HB method was comparable with that of the 4th RK method at the Mathieu parameter, q = 0.6, and the applicable q values could be extended to the entire first stability region with satisfactory accuracy. Two sorts of nonlinear effects of ion motion were studied, including ion frequency shift, Δβ, and ion amplitude variation, Δ(C(2n)/C0) (n ≠ 0). New phenomena regarding Δβ were observed, although extensive studies have been performed based on the pseudo-potential well (PW) model. For instance, the |Δβ| at ε = 0.1 and ε = -0.1 were found to be different, but they were the same in the PW model. This is the first time the nonlinear effects regarding Δ(C(2n)/C0) (n ≠ 0) are studied, and the associated study has been a challenge for both theoretical and numerical methods. The nonlinear effects of Δ(C(2n)/C0) (n ≠ 0) and Δβ were found to share some similarities at q < 0.6: both of them were proportional to ε, and the square of the initial ion displacement, z(0)(2). PMID:25924875
Nonlinear magneto-optical rotation with modulated light in tilted magnetic fields
Pustelny, S.; Gawlik, W.; Rochester, S. M.; Kimball, D. F. Jackson; Yashchuk, V. V.; Budker, D.
2006-12-15
Larmor precession of laser-polarized atoms contained in antirelaxation-coated cells, detected via nonlinear magneto-optical rotation (NMOR), is a promising technique for a new generation of ultrasensitive atomic magnetometers. For magnetic fields directed along the light propagation direction, resonances in NMOR appear when linearly polarized light is frequency or amplitude modulated at twice the Larmor frequency. Because the frequency of these resonances depends on the magnitude but not the direction of the field, they are useful for scalar magnetometry. Additional NMOR resonances at the Larmor frequency appear when the magnetic field is tilted away from the light propagation direction in the plane defined by the light propagation and polarization vectors. These resonances, studied both experimentally and with a density matrix calculation in the present work, offer a convenient method of achieving additional information about a direction of the magnetic field.
Fully non-linear cosmological perturbations of multicomponent fluid and field systems
NASA Astrophysics Data System (ADS)
Hwang, Jai-chan; Noh, Hyerim; Park, Chan-Gyung
2016-09-01
We present fully non-linear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. We include the anisotropic stress. Even in the absence of anisotropic stress of individual component, the multiple component nature introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and the uniform-expansion gauge conditions, present the Newtonian hydrodynamic equations in the presence of general relativistic pressure in the zero-shear gauge, and present the fully non-linear equations and the third-order perturbation equations of the non-relativistic pressure fluids in the CDM-comoving gauge.
Nan, Fan; Xie, Fang-Ming; Liang, Shan; Ma, Liang; Yang, Da-Jie; Liu, Xiao-Li; Wang, Jia-Hong; Cheng, Zi-Qiang; Yu, Xue-Feng; Zhou, Li; Wang, Qu-Quan; Zeng, Jie
2016-06-01
This paper describes a facile method for the synthesis of Au/AuAg/Ag2S/PbS core-multishell nanorods with double trapping layers. The synthesis, in sequence, involved deposition of Ag shells onto the surfaces of Au nanorod seeds, formation of AuAg shells by a galvanic replacement reaction, and overgrowth of the Ag2S shells and PbS shells. The resulting core-multishell nanorod possesses an air gap between the Au core and the AuAg shell. Together with the Ag2S shell, the air gap can efficiently trap light, causing strong field confinement and nonlinear enhancement. The as-prepared Au/AuAg/Ag2S/PbS core-multishell nanorods display distinct localized surface plasmon resonance and nonlinear optical properties, demonstrating an effective pathway for maneuvering the optical properties of nanocavities. PMID:27241031
Fan, Li; Ge, Huan; Zhang, Shu-yi; Gao, Hai-fei; Liu, Yong-hui; Zhang, Hui
2013-06-01
Nonlinear acoustic fields in transmission-line acoustic metamaterials based on a cylindrical pipe with periodically arranged side holes are studied, in which the dispersions and characteristic parameters of the nonlinear acoustic waves are obtained with the Bloch theory, and meanwhile the distributions of the fundamental wave (FW) and second harmonic wave (SHW) in the metamaterial are simulated. Three characteristic frequency bands are defined according to the relations between the frequencies of the FW, SHW, and the low-frequency forbidden band (LFB) in the metamaterial. Especially, when the FW is in the LFB while the SHW is outside the LFB, the SHW can transmit through the metamaterial although the FW is blocked, which exhibits the possibility to extract the information from the SHW instead of the FW. In addition, experiments are carried out to measure the distributions of the acoustic pressures for the FW and SHW along the metamaterial and the experimental results are in agreement with the theory. PMID:23742339
Ruyer, C; Gremillet, L; Bonnaud, G; Riconda, C
2016-08-01
The formation of collisionless shocks mediated by the ion Weibel instability is addressed theoretically and numerically in the nonrelativistic limit. First, the model developed in C. Ruyer et al., Phys. Plasmas 22, 032102 (2015) for the weakly nonlinear ion Weibel instability in a symmetric two-stream system is shown to be consistent with recent experimental and simulation results. Large-scale kinetic simulations are then performed to clarify the spatiotemporal evolution of the magnetic-field and plasma properties in the subsequent strongly nonlinear phase leading to shock formation. A simple analytical model is proposed which captures the simulation results up to a point close to ion isotropization. Electron screening effects are found important in the instability dynamics, so that numerical simulations using a nonphysical electron mass should be considered with caution. PMID:27541468
Analytical Predictions of Field and Plasma Dynamics during Nonlinear Weibel-Mediated Flow Collisions
NASA Astrophysics Data System (ADS)
Ruyer, C.; Gremillet, L.; Bonnaud, G.; Riconda, C.
2016-08-01
The formation of collisionless shocks mediated by the ion Weibel instability is addressed theoretically and numerically in the nonrelativistic limit. First, the model developed in C. Ruyer et al., Phys. Plasmas 22, 032102 (2015) for the weakly nonlinear ion Weibel instability in a symmetric two-stream system is shown to be consistent with recent experimental and simulation results. Large-scale kinetic simulations are then performed to clarify the spatiotemporal evolution of the magnetic-field and plasma properties in the subsequent strongly nonlinear phase leading to shock formation. A simple analytical model is proposed which captures the simulation results up to a point close to ion isotropization. Electron screening effects are found important in the instability dynamics, so that numerical simulations using a nonphysical electron mass should be considered with caution.
NASA Astrophysics Data System (ADS)
Stark, Thomas Spencer
Generally, nonlinear optics studies investigate optically-induced changes in refraction or absorption, and their application to spectroscopy or device fabrication. The photorefractive effect is a nonlinear optical effect that occurs in solids, where transport of an optically-induced free-carrier population results in an internal space-charge field, which produces an index change via the linear electrooptic effect. The photorefractive effect has been widely studied for a variety of materials and device applications, mainly because it allows large index changes to be generated with laser beams having only a few milliwatts of average power. Compound semiconductors are important photorefractive materials because they offer a near-infrared optical response, and because their carrier transport properties allow the index change to be generated quickly and efficiently. While many researchers have attempted to measure the fundamental temporal dynamics of the photorefractive effect in semiconductors using continuous-wave, nanosecond- and picosecond-pulsed laser beams, these investigations have been unsuccessful. However, studies with this goal are of clear relevance because they provide information about the fundamental physical processes that produce this effect, as well as the material's speed and efficiency limitations for device applications. In this dissertation, for the first time, we time-resolve the temporal dynamics of the photorefractive nonlinearities in two zincblende semiconductors, semi- insulating GaAs and undoped CdTe. While CdTe offers a lattice-match to the infrared material HgxCd1-xTe, semi-insulating GaAs has been widely used in optoelectronic and high- speed electronic applications. We use a novel transient- grating experimental method that allows picosecond temporal resolution and high sensitivity. Our results provide a clear and detailed picture of the picosecond photorefractive response of both materials, showing nonlinearities due to hot
Nonlinear magnetic field enhancement and turbulence in laboratory and astrophysical plasmas
NASA Astrophysics Data System (ADS)
Tiwary, Prem Pyari; Modi, K. V.; Sharma, Swati; Singh, Ram Kishor; Uma, R.; Sharma, R. P.
2016-03-01
The transient response of nonlinear coupling between relatively high frequency magnetosonic wave (HMSW) and low frequency magnetosonic wave (LMSW) in the overdense plasma has been presented in this paper. Along with this, the adiabatic response of HMSW also has been studied for low value of magnetic field in the underdense plasma. The ponderomotive force of relatively high frequency and high power pump magnetosonic wave is expected to excite the low frequency magnetosonic wave. The dynamical equation of LMSW in the presence of ponderomotive force of HMSW (pump wave) has been derived for this purpose. Using this coupled system of dynamical equations, the nonlinear behavior of the pump HMSW was studied, and the resulting turbulent spectrum has been presented. Numerical simulation has been carried out for dimensionless nonlinear coupled equations of HMSW and LMSW, and the results show quite complex localized structures that grow with time. The ensemble averaged power spectrum has also been studied which shows that the spectral index follows an approximate scaling of the order of ˜ k - 1.67 at larger scales and scaling of the order of ˜ k - 3.4 at smaller scales. The results indicate considerable randomness in the spatial structure of the magnetic field profile which gives sufficient indication of turbulence. In this context, filamentation of high frequency magnetosonic wave has been considered to be responsible for magnetic turbulence during the laser plasma interaction. The results of the present paper are found relevant with two different experimental observations. Such a nonlinear interaction is quite important in understanding turbulence in the astrophysical phenomenon.
NASA Astrophysics Data System (ADS)
Nan, Fan; Xie, Fang-Ming; Liang, Shan; Ma, Liang; Yang, Da-Jie; Liu, Xiao-Li; Wang, Jia-Hong; Cheng, Zi-Qiang; Yu, Xue-Feng; Zhou, Li; Wang, Qu-Quan; Zeng, Jie
2016-06-01
This paper describes a facile method for the synthesis of Au/AuAg/Ag2S/PbS core-multishell nanorods with double trapping layers. The synthesis, in sequence, involved deposition of Ag shells onto the surfaces of Au nanorod seeds, formation of AuAg shells by a galvanic replacement reaction, and overgrowth of the Ag2S shells and PbS shells. The resulting core-multishell nanorod possesses an air gap between the Au core and the AuAg shell. Together with the Ag2S shell, the air gap can efficiently trap light, causing strong field confinement and nonlinear enhancement. The as-prepared Au/AuAg/Ag2S/PbS core-multishell nanorods display distinct localized surface plasmon resonance and nonlinear optical properties, demonstrating an effective pathway for maneuvering the optical properties of nanocavities.This paper describes a facile method for the synthesis of Au/AuAg/Ag2S/PbS core-multishell nanorods with double trapping layers. The synthesis, in sequence, involved deposition of Ag shells onto the surfaces of Au nanorod seeds, formation of AuAg shells by a galvanic replacement reaction, and overgrowth of the Ag2S shells and PbS shells. The resulting core-multishell nanorod possesses an air gap between the Au core and the AuAg shell. Together with the Ag2S shell, the air gap can efficiently trap light, causing strong field confinement and nonlinear enhancement. The as-prepared Au/AuAg/Ag2S/PbS core-multishell nanorods display distinct localized surface plasmon resonance and nonlinear optical properties, demonstrating an effective pathway for maneuvering the optical properties of nanocavities. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr09151a
Li, Yue; Ho, Janet; Wang, Jianchuan; Li, Zhong-Ming; Zhong, Gan-Ji; Zhu, Lei
2016-01-13
Understanding nonlinear dielectric behavior in polar polymers is crucial to their potential application as next generation high energy density and low loss dielectrics. In this work, we studied nonlinear dielectric properties of a biaxially oriented poly(vinylidene fluoride) (BOPVDF) film under both low and high electric fields. For fundamental nonlinear dielectric constants at low fields (<30 MV/m), Novocontrol high-voltage broadband dielectric spectroscopy (HVBDS) was accurate enough to measure up to the third harmonics. It was observed that the low-field dielectric nonlinearity for the BOPVDF disappeared above 10 Hz at room temperature, suggesting that the low-field dielectric nonlinearity originated from ionic migration of impurity ions rather than dipolar relaxation of the amorphous segments. Above the coercive field (EC ≈ 70 MV/m), bipolar electric displacement-electric field (D-E) loop tests were used to extract the nonlinear behavior for pure PVDF crystals, which had a clear origin of ferroelectric switching of polar crystalline dipoles and domains and nonpolar-to-polar (α → δ → β) phase transformations. By using HVBDS, it was observed that the ferroelectric switching of polar crystalline dipoles and domains in BOPVDF above the EC always took place between 20 and 500 Hz regardless of a broad range of temperature from -30 to 100 °C. This behavior was drastically different from that of the amorphous PVDF dipoles, which had a strong dependence on frequency over orders of magnitude. PMID:26698912
Meinecke, Jena; Tzeferacos, Petros; Bell, Anthony; Bingham, Robert; Clarke, Robert; Churazov, Eugene; Crowston, Robert; Doyle, Hugo; Drake, R. Paul; Heathcote, Robert; Koenig, Michel; Kuramitsu, Yasuhiro; Kuranz, Carolyn; Lee, Dongwook; MacDonald, Michael; Murphy, Christopher; Notley, Margaret; Park, Hye-Sook; Pelka, Alexander; Ravasio, Alessandra; Reville, Brian; Sakawa, Youichi; Wan, Willow; Woolsey, Nigel; Yurchak, Roman; Miniati, Francesco; Schekochihin, Alexander; Lamb, Don; Gregori, Gianluca
2015-01-01
The visible matter in the universe is turbulent and magnetized. Turbulence in galaxy clusters is produced by mergers and by jets of the central galaxies and believed responsible for the amplification of magnetic fields. We report on experiments looking at the collision of two laser-produced plasma clouds, mimicking, in the laboratory, a cluster merger event. By measuring the spectrum of the density fluctuations, we infer developed, Kolmogorov-like turbulence. From spectral line broadening, we estimate a level of turbulence consistent with turbulent heating balancing radiative cooling, as it likely does in galaxy clusters. We show that the magnetic field is amplified by turbulent motions, reaching a nonlinear regime that is a precursor to turbulent dynamo. Thus, our experiment provides a promising platform for understanding the structure of turbulence and the amplification of magnetic fields in the universe. PMID:26100873
Meinecke, Jena; Tzeferacos, Petros; Bell, Anthony; Bingham, Robert; Clarke, Robert; Churazov, Eugene; Crowston, Robert; Doyle, Hugo; Drake, R Paul; Heathcote, Robert; Koenig, Michel; Kuramitsu, Yasuhiro; Kuranz, Carolyn; Lee, Dongwook; MacDonald, Michael; Murphy, Christopher; Notley, Margaret; Park, Hye-Sook; Pelka, Alexander; Ravasio, Alessandra; Reville, Brian; Sakawa, Youichi; Wan, Willow; Woolsey, Nigel; Yurchak, Roman; Miniati, Francesco; Schekochihin, Alexander; Lamb, Don; Gregori, Gianluca
2015-07-01
The visible matter in the universe is turbulent and magnetized. Turbulence in galaxy clusters is produced by mergers and by jets of the central galaxies and believed responsible for the amplification of magnetic fields. We report on experiments looking at the collision of two laser-produced plasma clouds, mimicking, in the laboratory, a cluster merger event. By measuring the spectrum of the density fluctuations, we infer developed, Kolmogorov-like turbulence. From spectral line broadening, we estimate a level of turbulence consistent with turbulent heating balancing radiative cooling, as it likely does in galaxy clusters. We show that the magnetic field is amplified by turbulent motions, reaching a nonlinear regime that is a precursor to turbulent dynamo. Thus, our experiment provides a promising platform for understanding the structure of turbulence and the amplification of magnetic fields in the universe. PMID:26100873
Interspecific competition alters nonlinear selection on offspring size in the field.
Marshall, Dustin J; Monro, Keyne
2013-02-01
Offspring size is one of the most important life-history traits with consequences for both the ecology and evolution of most organisms. Surprisingly, formal estimates of selection on offspring size are rare, and the degree to which selection (particularly nonlinear selection) varies among environments remains poorly explored. We estimate linear and nonlinear selection on offspring size, module size, and senescence rate for a sessile marine invertebrate in the field under three different intensities of interspecific competition. The intensity of competition strongly modified the strength and form of selection acting on offspring size. We found evidence for differences in nonlinear selection across the three environments. Our results suggest that the fitness returns of a given offspring size depend simultaneously on their environmental context, and on the context of other offspring traits. Offspring size effects can be more pervasive with regards to their influence on the fitness returns of other traits than previously recognized, and we suggest that the evolution of offspring size cannot be understood in isolation from other traits. Overall, variability in the form and strength of selection on offspring size in nature may reduce the efficacy of selection on offspring size and maintain variation in this trait. PMID:23356607
Rosnitskiy, P. Yuldashev, P. Khokhlova, V.
2015-10-28
An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parameters were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.
NASA Astrophysics Data System (ADS)
Rosnitskiy, P.; Yuldashev, P.; Khokhlova, V.
2015-10-01
An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parameters were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.
Self-mapping the longitudinal field structure of a nonlinear plasma accelerator cavity
Clayton, C. E.; Adli, E.; Allen, J.; An, W.; Clarke, C. I.; Corde, S.; Frederico, J.; Gessner, S.; Green, S. Z.; Hogan, M. J.; Joshi, C.; Litos, M.; Lu, W.; Marsh, K. A.; Mori, W. B.; Vafaei-Najafabadi, N.; Xu, X.; Yakimenko, V.
2016-01-01
The preservation of emittance of the accelerating beam is the next challenge for plasma-based accelerators envisioned for future light sources and colliders. The field structure of a highly nonlinear plasma wake is potentially suitable for this purpose but has not been yet measured. Here we show that the longitudinal variation of the fields in a nonlinear plasma wakefield accelerator cavity produced by a relativistic electron bunch can be mapped using the bunch itself as a probe. We find that, for much of the cavity that is devoid of plasma electrons, the transverse force is constant longitudinally to within ±3% (r.m.s.). Moreover, comparison of experimental data and simulations has resulted in mapping of the longitudinal electric field of the unloaded wake up to 83 GV m−1 to a similar degree of accuracy. These results bode well for high-gradient, high-efficiency acceleration of electron bunches while preserving their emittance in such a cavity. PMID:27527569
Self-mapping the longitudinal field structure of a nonlinear plasma accelerator cavity.
Clayton, C E; Adli, E; Allen, J; An, W; Clarke, C I; Corde, S; Frederico, J; Gessner, S; Green, S Z; Hogan, M J; Joshi, C; Litos, M; Lu, W; Marsh, K A; Mori, W B; Vafaei-Najafabadi, N; Xu, X; Yakimenko, V
2016-01-01
The preservation of emittance of the accelerating beam is the next challenge for plasma-based accelerators envisioned for future light sources and colliders. The field structure of a highly nonlinear plasma wake is potentially suitable for this purpose but has not been yet measured. Here we show that the longitudinal variation of the fields in a nonlinear plasma wakefield accelerator cavity produced by a relativistic electron bunch can be mapped using the bunch itself as a probe. We find that, for much of the cavity that is devoid of plasma electrons, the transverse force is constant longitudinally to within ±3% (r.m.s.). Moreover, comparison of experimental data and simulations has resulted in mapping of the longitudinal electric field of the unloaded wake up to 83 GV m(-1) to a similar degree of accuracy. These results bode well for high-gradient, high-efficiency acceleration of electron bunches while preserving their emittance in such a cavity. PMID:27527569
NASA Astrophysics Data System (ADS)
Richert, Ranko
2016-03-01
A model of non-linear dielectric polarization is studied in which the field induced entropy change is the source of polarization dependent retardation time constants. Numerical solutions for the susceptibilities of the system are obtained for parameters that represent the dynamic and thermodynamic behavior of glycerol. The calculations for high amplitude sinusoidal fields show a significant enhancement of the steady state loss for frequencies below that of the low field loss peak. Also at relatively low frequencies, the third harmonic susceptibility spectrum shows a "hump," i.e., a maximum, with an amplitude that increases with decreasing temperature. Both of these non-linear effects are consistent with experimental evidence. While such features have been used to conclude on a temperature dependent number of dynamically correlated particles, Ncorr, the present result demonstrates that the third harmonic susceptibility display a peak with an amplitude that tracks the variation of the activation energy in a model that does not involve dynamical correlations or spatial scales.
NASA Astrophysics Data System (ADS)
Gapochka, M. G.; Denisov, M. M.; Denisova, I. P.; Kalenova, N. V.; Korolev, A. F.
2015-11-01
The paper is devoted to mathematical modeling of the nonlinear vacuum electrodynamics effect: the action of the strong magnetic field of a pulsar on the propagation of electromagnetic waves. It is shown that, due to the birefringence of the vacuum, for one normal wave, it takes more time to travel from a pulsar to a detector installed on astrophysical satellites than for the other normal wave. The delay of the pulse carried by the second normal wave relative to pulse carried by the first normal wave from the common point of origin to the satellite is calculated.
NASA Astrophysics Data System (ADS)
Kikuchi, Takashi; Horioka, Kazuhiko
2016-06-01
A procedure to obtain a ratio of beam radii at final and initial states in arbitrary particle distributions is proposed, and is applied to the estimation of possible emittance growth for Gaussian and thermal equilibrium distributions. The ratios are estimated for Gaussian and thermal equilibrium distributions as a function of tune depression. The possible emittance growth as a function of tune depression and nonlinear field energy factor is also estimated with and without a constant radius ratio approximation. It is confirmed that the possible emittance growths are almost the same in comparison to the cases with and without the constant radius ratio approximation at each distribution.
NASA Technical Reports Server (NTRS)
Smith, David D.
2002-01-01
This talk will review the linear and nonlinear optical properties of metal nanoparticles and dielectric microparticles, with an emphasis on local field effects, and whispering gallery modes (WGMs), as well as the conjunction of these two effects for enhanced Raman. In particular, enhanced optical properties that result from electromagnetic coupling effects will be discussed in the context of Mie scattering from concentric spheres and bispheres. Predictions of mode splitting and photonic bandgaps in micro-spheres will be presented and will be shown to be analogous to effects that occur in coupled resonator optical waveguides (CROW). Slow and fast light in SCISSOR / CROW configurations will also be discussed.
NASA Astrophysics Data System (ADS)
Zhu, Siqiang; Xu, Yingfeng; Wang, Shaojie
2016-06-01
The nonlinear gyrokinetic equation with full electromagnetic potential perturbations is derived by using the two-step transform procedure. The second-order transformed Hamiltonian can be simplified as /1 2 δ A∥ 2 , instead of /1 2 δ A 2 in the long-wave-length limit. A numerical code based on the I-transform method is improved to compute the gyrocenter orbit in the TFTR tokamak with a ripple field, and the numerical results indicate that the collisionless stochastic diffusion criterion agrees well with the theoretical prediction.
NASA Astrophysics Data System (ADS)
Farrugia, C. J.; Lavraud, B.; Torbert, R. B.; Argall, M.; Kacem, I.; Yu, W.; Alm, L.; Burch, J.; Russell, C. T.; Shuster, J.; Dorelli, J.; Eastwood, J. P.; Ergun, R. E.; Fuselier, S.; Gershman, D.; Giles, B. L.; Khotyaintsev, Y. V.; Lindqvist, P. A.; Matsui, H.; Marklund, G. T.; Phan, T. D.; Paulson, K.; Pollock, C.; Strangeway, R. J.
2016-06-01
We analyze plasma, magnetic field, and electric field data for a flux transfer event (FTE) to highlight improvements in our understanding of these transient reconnection signatures resulting from high-resolution data. The ˜20 s long, reverse FTE, which occurred south of the geomagnetic equator near dusk, was immersed in super-Alfvénic flow. The field line twist is illustrated by the behavior of flows parallel/perpendicular to the magnetic field. Four-spacecraft timing and energetic particle pitch angle anisotropies indicate a flux rope (FR) connected to the Northern Hemisphere and moving southeast. The flow forces evidently overcame the magnetic tension. The high-speed flows inside the FR were different from those outside. The external flows were perpendicular to the field as expected for draping of the external field around the FR. Modeling the FR analytically, we adopt a non-force free approach since the current perpendicular to the field is nonzero. It reproduces many features of the observations.
Volkova, E. A.; Popov, A. M. Tikhonova, O. V.
2013-03-15
The nonlinear polarization response of a quantum system modeling a silver atom in the field of high-intensity radiation in the IR and UV spectral ranges has been studied by direct numerical integration of a nonstationary Schroedinger equation. The domains of applicability of perturbation theory and polarization expansion in powers of the field intensity are determined. The contribution of excited atoms and electrons in a continuum to the atomic polarization response at the field frequency, which arises due to the radiation-induced excitation and photoionization processes, is analyzed. Features of the nonlinear response to an external field under conditions of atom stabilization are considered.
The nonlinear analysis of self-field effects in free-electron lasers
NASA Astrophysics Data System (ADS)
Freund, H. P.; Jackson, R. H.; Pershing, D. E.
1993-07-01
A model of the self-fields associated with the charge density and current of the electron beam is incorporated into three-dimensional nonlinear formulations of the interaction in free-electron lasers for both planar and helical wiggler configurations. The model assumes the existence of a cylindrically symmetric electron beam with a flat-top density profile and a uniform axial velocity, and the self-electric and self-magnetic fields are determined from Poisson's equation and Ampère's law. Diamagnetic and paramagnetic effects due the electron beam interaction with the wiggler field are neglected; hence, the model breaks down when the wiggler-induced transverse displacement is comparable to the beam radius. The nonlinear formulations are based upon the arachne and wigglin codes, which represent slow-time-scale formulations for the evolution of the amplitudes and phases of a multimode superposition of vacuum waveguide modes. The electron dynamics in these codes are treated by means of the complete three-dimensional Lorentz force equations, and the representations for the self-fields are incorporated directly into this formulation. The results of the simulations are compared directly with an experiment at Lawrence Livermore National Laboratory based upon a planar wiggler and experiments at the Massachusetts Institute of Technology and the Naval Research Laboratory, which employed helical wigglers. These experiments employed intense electron beams with current densities of 200-1200 A/cm2 and comparable space-charge depressions of Δγself/γ0≊0.53%-0.78% across the beam. The simulations are in reasonable agreement with the experiments, and indicate that the self-fields tend to (1) reduce saturation efficiencies and (2) enhance beam spreading depending upon the magnitude of external beam focusing.
NASA Astrophysics Data System (ADS)
Timokhin, A. N.; Arons, J.
2013-02-01
. These discharges are similar to those encountered in previous calculations by Timokhin of pair creation when the surface has a high work function and cannot freely emit charge. In cases (b) and (c), the intermittently generated pairs allow the system to simultaneously carry the magnetospherically prescribed currents and adjust the charge density and average electric field to force-free conditions. We also elucidate the conditions for pair creating beam flow to be steady (stationary with small fluctuations in the rotating frame), finding that such steady flows can occupy only a small fraction of the current density parameter space exhibited by the force-free magnetospheric model. The generic polar flow dynamics and pair creation are strongly time dependent. The model has an essential difference from almost all previous quantitative studies, in that we sought the accelerating voltage (with pair creation, when the voltage drops are sufficiently large; without, when they are small) as a function of the applied current. The 1D results described here characterize the dependence of acceleration and pair creation on the magnitude and sign of current. The dependence on the spatial distribution of the current is a multi-dimensional problem, possibly exhibiting more chaotic behaviour. We briefly outline possible relations of the electric field fluctuations observed in the polar flows (both with and without pair creation discharges) to direct emission of radio waves, as well as revive the possible relation of the observed limit cycle behaviour to microstructure in the radio emission. Actually modelling these effects requires the multi-dimensional treatment, to be reported in a later paper.
Effect of a force-free end on the mechanical property of a biopolymer — A path integral approach
NASA Astrophysics Data System (ADS)
Zhou, Zicong; Joós, Béla
2016-08-01
We study the effect of a force-free end on the mechanical property of a stretched biopolymer. The system can be divided into two parts. The first part consists of the segment counted from the fixed point (i.e., the origin) to the forced point in the biopolymer, with arclength L f . The second part consists of the segment counted from the forced point to the force-free end with arclength ΔL. We apply the path integral technique to find the relationship between these two parts. At finite temperature and without any constraint at the end, we show exactly that if we focus on the quantities related to the first part, then we can ignore the second part completely. Monte Carlo simulation confirms this conclusion. In contrast, the effect for the quantities related to the second part is dependent on what we want to observe. A force-free end has little effect on the relative extension, but it affects seriously the value of the end-to-end distance if ΔL is comparable to L f . Project supported by the MOST and the NSERC (Canada).
Cascaded nonlinearity caused by local-field effects in the two-level atom
Dolgaleva, Ksenia; Boyd, Robert W.; Sipe, John E.
2007-12-15
Contributions to the fifth-order nonlinear optical susceptibility {chi}{sup (5)} of a collection of homogeneously broadened two-level atoms that scale as N{sup 2}({gamma}{sub at}{sup (3)}){sup 2} and N{sup 2}|{gamma}{sub at}{sup (3)}|{sup 2}, where {gamma}{sub at}{sup (3)} is the lower-order atomic hyperpolarizability and N is the atomic number density, are predicted theoretically. These 'cascaded' contributions are a consequence of local-field effects. We determine them from a fifth-order solution of the Lorentz-Maxwell-Bloch equations. They are missing from a straightforward generalization of Bloembergen's result for the local field correction to the second order nonlinearity, but are recovered by a careful application of his general approach. We find that at high atomic densities (N>10{sup 15} cm{sup -3}) the value of the cascaded third-order contribution can be as large as the 'direct' fifth-order term in the expression for the fifth-order susceptibility.
Nonlinearity in MCF7 Cell Survival Following Exposure to Modulated 6 MV Radiation Fields
Castiella, Marion; Franceries, Xavier; Cassol, Emmanuelle; Vieillevigne, Laure; Pereda, Veronica; Bardies, Manuel; Courtade-Saïdi, Monique
2015-01-01
The study of cell survival following exposure to nonuniform radiation fields is taking on particular interest because of the increasing evidence of a nonlinear relationship at low doses. We conducted in vitro experiments using the MCF7 breast cancer cell line. A 2.4 × 2.4 cm2 square area of a T25 flask was irradiated by a Varian Novalis accelerator delivering 6 MV photons. Cell survival inside the irradiation field, in the dose gradient zone and in the peripheral zone, was determined using a clonogenic assay for different radiation doses at the isocenter. Increased cell survival was observed inside the irradiation area for doses of 2, 10, and 20 Gy when nonirradiated cells were present at the periphery, while the cells at the periphery showed decreased survival compared to controls. Increased survival was also observed at the edge of the dose gradient zone for cells receiving 0.02 to 0.01 Gy when compared with cells at the periphery of the same flask, whatever the isocenter dose. These data are the first to report cell survival in the dose gradient zone. Radiotherapists must be aware of this nonlinearity in dose response. PMID:26740805
Nonlinear magnetic field gradients can reduce SAR in flow-driven arterial spin labeling measurements
NASA Astrophysics Data System (ADS)
Marro, Kenneth I.; Lee, Donghoon; Hyyti, Outi M.
2007-03-01
This work describes how custom-built gradient coils, designed to generate magnetic fields with amplitudes that vary nonlinearly with position, can be used to reduce the potential for unsafe tissue heating during flow-driven arterial spin labeling processes. A model was developed to allow detailed analysis of the adiabatic excitation process used for flow-driven arterial water stimulation with elimination of tissue signal (FAWSETS) an arterial spin labeling method developed specifically for use in skeletal muscle. The model predicted that, by adjusting the amplitude of the gradient field, the specific absorption rate could be reduced by more than a factor of 6 while still achieving effective labeling. Flow phantom measurements and in vivo measurements from exercising rat hind limb confirmed the accuracy of the model's predictions. The modeling tools were also applied to the more widely used continuous arterial spin labeling (CASL) method and predicted that specially shaped gradients could allow similar reductions in SAR.
Enhanced nonlinear double excitation of He in intense extreme ultraviolet laser fields.
Hishikawa, A; Fushitani, M; Hikosaka, Y; Matsuda, A; Liu, C-N; Morishita, T; Shigemasa, E; Nagasono, M; Tono, K; Togashi, T; Ohashi, H; Kimura, H; Senba, Y; Yabashi, M; Ishikawa, T
2011-12-01
Nonlinear, three-photon double excitation of He in intense extreme ultraviolet free-electron laser fields (∼24.1 eV, ∼5 TW/cm2) is presented. Resonances to the doubly excited states converging to the He+ N=3 level are revealed by the shot-by-shot photoelectron spectroscopy and identified by theoretical calculations based on the time-dependent Schrödinger equation for the two-electron atom under a laser field. It is shown that the three-photon double excitation is enhanced by intermediate Rydberg states below the first ionization threshold, giving a greater contribution to the photoionization yields than the two-photon process by more than 1 order of magnitude. PMID:22242995
Infrared nonlinear neurons using the field shielding effect in CdTe.
Ziari, M; Steier, W H; Devine, R L
1990-05-10
We report on a novel IR neuron device that utilizes the field shielding effect in CdTe:In, wherein optical activation beams create an intensity dependent space-charge field. The induced electrooptic birefringence or index change is used in a neuron-type configuration to demonstrate a high sensitivity nonlinear saturated response with an absorption loss of
NASA Astrophysics Data System (ADS)
Wei, Nijun; Coffey, William T.; Déjardin, Pirre-Michel; Kalmykov, Yuri P.
External dc bias field effects on the nonlinear dielectric relaxation and dynamic Kerr effect of a system of permanent dipoles in a uniaxial mean field potential are studied via the rotational Brownian motion model. Postulated in terms of the infinite hierarchy of differential-recurrence equations for the statistical moments (the expectation value of the Legendre polynomials), the dielectric and Kerr effect ac stationary responses may be evaluated for arbitrary dc bias field strength via perturbation theory in the ac field. We have given two complementary approaches for treating the nonlinear effects. The first is based on perturbation theory allowing one to calculate the nonlinear ac stationary responses using powerful matrix methods. The second approach based on the accurate two-mode approximation [D.A. Garanin, Phys. Rev. E. 54, 3250 (1996)] effectively generalizes the existing results for dipolar systems in superimposed ac and dc fields to a mean field potential. The results apply both to nonlinear dielectric relaxation and dynamic Kerr effect of nematics and to magnetic birefringence relaxation of ferrofluids. Furthermore, the given methods of the solution of infinite hierarchies of multi-term recurrence relations are quite general and can be applied to analogous nonlinear response problems.
NASA Technical Reports Server (NTRS)
Timokhin, A. N.; Arons, J.
2013-01-01
bursts of pair creation. These discharges are similar to those encountered in previous calculations by Timokhin of pair creation when the surface has a high work function and cannot freely emit charge. In cases (b) and (c), the intermittently generated pairs allow the system to simultaneously carry the magnetospherically prescribed currents and adjust the charge density and average electric field to force-free conditions. We also elucidate the conditions for pair creating beam flow to be steady (stationary with small fluctuations in the rotating frame), finding that such steady flows can occupy only a small fraction of the current density parameter space exhibited by the force-free magnetospheric model. The generic polar flow dynamics and pair creation are strongly time dependent. The model has an essential difference from almost all previous quantitative studies, in that we sought the accelerating voltage (with pair creation, when the voltage drops are sufficiently large; without, when they are small) as a function of the applied current.
Beninato, A.; Baglio, S.; Andò, B.; Emery, T.; Bulsara, A. R.; Jenkins, C.; Palkar, V.
2013-12-09
Multiferroic (MF) composites, in which magnetic and ferroelectric orders coexist, represent a very attractive class of materials with promising applications in areas, such as spintronics, memories, and sensors. One of the most important multiferroics is the perovskite phase of bismuth ferrite, which exhibits weak magnetoelectric properties at room temperature; its properties can be enhanced by doping with other elements such as dysprosium. A recent paper has demonstrated that a thin film of Bi{sub 0.7}Dy{sub 0.3}FeO{sub 3} shows good magnetoelectric coupling. In separate work it has been shown that a carefully crafted ring connection of N (N odd and N ≥ 3) ferroelectric capacitors yields, past a critical point, nonlinear oscillations that can be exploited for electric (E) field sensing. These two results represent the starting point of our work. In this paper the (electrical) hysteresis, experimentally measured in the MF material Bi{sub 0.7}Dy{sub 0.3}FeO{sub 3}, is characterized with the applied magnetic field (B) taken as a control parameter. This yields a “blueprint” for a magnetic (B) field sensor: a ring-oscillator coupling of N = 3 Sawyer-Tower circuits each underpinned by a mutliferroic element. In this configuration, the changes induced in the ferroelectric behavior by the external or “target” B-field are quantified, thus providing a pathway for very low power and high sensitivity B-field sensing.
NASA Astrophysics Data System (ADS)
Beninato, A.; Emery, T.; Baglio, S.; Andò, B.; Bulsara, A. R.; Jenkins, C.; Palkar, V.
2013-12-01
Multiferroic (MF) composites, in which magnetic and ferroelectric orders coexist, represent a very attractive class of materials with promising applications in areas, such as spintronics, memories, and sensors. One of the most important multiferroics is the perovskite phase of bismuth ferrite, which exhibits weak magnetoelectric properties at room temperature; its properties can be enhanced by doping with other elements such as dysprosium. A recent paper has demonstrated that a thin film of Bi0.7Dy0.3FeO3 shows good magnetoelectric coupling. In separate work it has been shown that a carefully crafted ring connection of N (N odd and N ≥ 3) ferroelectric capacitors yields, past a critical point, nonlinear oscillations that can be exploited for electric (E) field sensing. These two results represent the starting point of our work. In this paper the (electrical) hysteresis, experimentally measured in the MF material Bi0.7Dy0.3FeO3, is characterized with the applied magnetic field (B) taken as a control parameter. This yields a "blueprint" for a magnetic (B) field sensor: a ring-oscillator coupling of N = 3 Sawyer-Tower circuits each underpinned by a mutliferroic element. In this configuration, the changes induced in the ferroelectric behavior by the external or "target" B-field are quantified, thus providing a pathway for very low power and high sensitivity B-field sensing.
Non-linear dynamics of viscous bilayers subjected to an electric field: 3D phase field simulations
NASA Astrophysics Data System (ADS)
Dritselis, Christos; Karapetsas, George; Bontozoglou, Vasilis
2014-11-01
The scope of this work is to investigate the non-linear dynamics of the electro-hydrodynamic instability of a bilayer of immiscible liquids. We consider the case of two viscous films which is separated from the top electrode by air. We assume that the liquids are perfect dielectrics and consider the case of both flat and patterned electrodes. We develop a computational model using the diffuse interface method and carry out 3D numerical simulations fully accounting for the flow and electric field in all phases. We perform a parametric study and investigate the influence of the electric properties of fluids, applied voltage and various geometrical characteristics of the mask. The authors acknowledge the support by the General Secretariat of Research and Technology of Greece under the action ``Supporting Postdoctoral Researchers'' (Grant Number PE8/906), co-funded by the European Social Fund and National Resources.
NASA Astrophysics Data System (ADS)
Meier, T.; Thomas, P.; Koch, S. W.
2001-07-01
Linear and nonlinear optical absorption spectra are studied theoretically for semiconductor nanorings penetrated by a magnetic field. Due to the Aharanov-Bohm effect the spectral position as well as the oscillator strength of the exciton change periodically as function of the magnetic flux enclosed by the ring. In the nonlinear differential absorption spectra it is found that the magnetic field strongly modifies Coulomb many-body correlations. In particular, the magnetic-field-induced increase of the exciton binding energy is accompanied by a decrease of the biexciton binding energy. The persistence of these effects in the presence of energetic disorder is analyzed.
NASA Astrophysics Data System (ADS)
Li, Yue; Zhu, Lei; Case Western Reserve University Team; Sichuan University Team
Understanding nonlinear dielectric behavior in polar polymers is crucial to their potential application as next genera tion high energy density and low loss dielectrics. In this work, we studied nonlinear dielectric properties of a biaxially oriented poly(vinylidene fluoride) (BOPVDF) film under both low and high electric fields. It was observed that the low-field dielectric nonlinearity for the BOPVDF disappeared above 10 Hz at room temperature, suggesting that the low-field dielectric nonlinearity originated from ionic migration of impurity ions rather than dipolar relaxation of the amorphous segments. Above the coercive field (EC ~70 MV/m), bipolar electric displacement-electric field (D-E) loop tests were used to extract the nonlinear behavior for pure PVDF crystals, which had a clear origin of ferroelectric switching of polar crystalline dipoles and domains and nonpolar-to-polar (α --> δ --> β) phase transformations. Using HVBDS, it was observed that the ferroelectric switching of polar crystalline dipoles and domains in BOPVDF above the EC always took place between 20 and 500 Hz, regardless of a broad range of temperature from -30 to 100 °C. This behavior was drastically different from the amorphous PVDF dipoles, which had a strong dependence on frequency over orders of magnitude. This work is supported by NSF(DMR-1402733).
NASA Astrophysics Data System (ADS)
Sun, Hao-Ran; Huang, Ka-Ma
2015-12-01
In this paper, an experimental set-up based on a novel microstrip cancellation circuit is presented for investigating the effects of external microwave fields on the dielectric properties of polar solution. The circuit consists of a 3 dB Wilkinson power combiner, a conventional 20 dB backward coupler, and a specially designed 20 dB single-sectioned forward coupler. Besides, in order to realize a uniform electric field in the tested solution, a nicked microstrip ring is designed in the circuit. An improvement of measurement sensitivity in the proposed circuit was obtained when compared to the conventional transmission lines method. We exploit interference cancellation processes to suppress the probing signal at the output port under the principle that two identical amplitude signals with 180° phase difference will completely cancel each other. The measurements are carried out at the frequency of 2.45 GHz, and the temperature effects caused by microwave heating are excluded by the flowing fluid. Experimental results show that the dielectric properties of DMSO-methanol/ethanol mixtures change at the electric field intensity of 105 V m - 1 and present a distinctly nonlinear dielectric change with the electric fields. The study of the microwave-material interaction has expanded our insights into the high-power microwave’s industry application.
Modeling of nonlinear microscopy of localized field enhancements in random metal nanostructures
NASA Astrophysics Data System (ADS)
Beermann, Jonas; Bozhevolnyi, Sergey I.; Coello, Victor
2006-03-01
Nonlinear microscopy of localized field enhancements in random metal nanostructures with a tightly focused laser beam scanning over a sample surface is modeled by making use of analytic representations of the Green dyadic in the near- and far-field regions, with the latter being approximated by the part describing the scattering via excitation of surface plasmon polaritons. The developed approach is applied to scanning second-harmonic (SH) microscopy of small gold spheres placed randomly on a gold surface. We calculate self-consistent fundamental harmonic (FH) and SH field distributions at the illuminated sample surface and, thereby, FH and SH images for different polarization configurations of the illuminating and detected fields. The simulated images bear close resemblance to the images obtained experimentally, exhibiting similar sensitivity to the wavelength and polarization, as well as sensitivity to the scattering configuration. We verify directly our conjecture that very bright spots in the SH images occur due to the spatial overlap of properly polarized FH and SH eigenmodes. Applications and further improvements of the developed model are discussed.
Destruction of large-scale magnetic field in non-linear simulations of the shear dynamo
NASA Astrophysics Data System (ADS)
Teed, Robert J.; Proctor, Michael R. E.
2016-05-01
The Sun's magnetic field exhibits coherence in space and time on much larger scales than the turbulent convection that ultimately powers the dynamo. In the past the α-effect (mean-field) concept has been used to model the solar cycle, but recent work has cast doubt on the validity of the mean-field ansatz under solar conditions. This indicates that one should seek an alternative mechanism for generating large-scale structure. One possibility is the recently proposed `shear dynamo' mechanism where large-scale magnetic fields are generated in the presence of a simple shear. Further investigation of this proposition is required, however, because work has been focused on the linear regime with a uniform shear profile thus far. In this paper we report results of the extension of the original shear dynamo model into the non-linear regime. We find that whilst large-scale structure can initially persist into the saturated regime, in several of our simulations it is destroyed via large increase in kinetic energy. This result casts doubt on the ability of the simple uniform shear dynamo mechanism to act as an alternative to the α-effect in solar conditions.
NASA Astrophysics Data System (ADS)
Schuch, Dieter
2014-04-01
Theoretical physics seems to be in a kind of schizophrenic state. Many phenomena in the observable macroscopic world obey nonlinear evolution equations, whereas the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. I claim that linearity in quantum mechanics is not as essential as it apparently seems since quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown where complex Riccati equations appear in time-dependent quantum mechanics and how they can be treated and compared with similar space-dependent Riccati equations in supersymmetric quantum mechanics. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation. Finally, it will be shown that (real and complex) Riccati equations also appear in many other fields of physics, like statistical thermodynamics and cosmology.
Hatsuki, Ryuji; Honda, Ayae; Kajitani, Masayuki; Yamamoto, Takatoki
2015-01-01
Our living sphere is constantly exposed to a wide range of pathogenic viruses, which can be either known, or of novel origin. Currently, there is no methodology for continuously monitoring the environment for viruses in general, much less a methodology that allows the rapid and sensitive identification of a wide variety of viruses responsible for communicable diseases. Traditional approaches, based on PCR and immunodetection systems, only detect known or specifically targeted viruses. We here describe a simple device that can potentially detect any virus between nanogap electrodes using nonlinear impedance spectroscopy. Three test viruses, differing in shape and size, were used to demonstrate the general applicability of this approach: baculovirus, tobacco mosaic virus (TMV), and influenza virus. We show that each of the virus types responded differently in the nanogap to changes in the electric field strength, and the impedance of the virus solutions differed depending both on virus type and virus concentration. These preliminary results show that the three virus types can be distinguished and their approximate concentrations determined. Although further studies are required, the proposed nonlinear impedance spectroscopy method may achieve a sensitivity comparable to that of more traditional, but less versatile, virus detection systems. PMID:26441875
NASA Astrophysics Data System (ADS)
Tukmakov, A. L.
2015-01-01
A model of a multivelocity multitemperature polydisperse gas suspension has been constructed with account taken of coagulation. Calculations of the dynamics of an aerosol of a polydisperse composition in an acoustic resonator have been done and the derived regularities have been described. A system of Navier-Stokes equations for a compressible heat-conducting gas was used to describe the motion of a carrier medium. The dynamics of dispersed fractions is described by a system of equations including continuity, momentum, and internal-energy equations. The equations of motion of the carrier medium and dispersed fractions have been written with account of the interphase exchange of momentum and energy. The Lagrangian model has been used to describe the process of coagulation. The change in the dispersity of the gas suspension in the nonlinear field of an acoustic resonator has been analyzed.
McArthur, Duncan; Hourahine, Ben; Papoff, Francesco
2015-01-01
We model a scheme for the coherent control of light waves and currents in metallic nanospheres which applies independently of the nonlinear multiphoton processes at the origin of waves and currents. Using exact mathematical formulae, we calculate numerically with a custom fortran code the effect of an external control field which enable us to change the radiation pattern and suppress radiative losses or to reduce absorption, enabling the particle to behave as a perfect scatterer or as a perfect absorber. Data are provided in tabular, comma delimited value format and illustrate narrow features in the response of the particles that result in high sensitivity to small variations in the local environment, including subwavelength spatial shifts. PMID:26601699
On some p-Laplacian equation with electromagnetic fields and critical nonlinearity in ℝN
NASA Astrophysics Data System (ADS)
Liang, Sihua; Zhang, Jihui
2015-04-01
In this paper, we consider the existence and multiplicity of solutions for p-Laplacian equation with electromagnetic fields and critical nonlinearity in ℝN: - ɛ p Δ p , A u + V ( x ) |u| p - 2 u = |u| p* - 2 u + h ( x , |u| p ) |u| p - 2 u for x ∈ ℝN, where Δ p , A u ( x ) ≔ div ( |u ∇ u + i A ( x ) u | p - 2 ( ∇ u + i A ( x ) u ) . By using Lions' second concentration compactness principle and concentration compactness principle at infinity to prove that the (PS)c condition holds locally and by variational method, we show that this equation has at least one solution provided that ɛ < E , for any m ∈ ℕ, it has m pairs of solutions if ɛ < E m , where E and E m are sufficiently small positive numbers.
McArthur, Duncan; Hourahine, Ben; Papoff, Francesco
2015-01-01
We model a scheme for the coherent control of light waves and currents in metallic nanospheres which applies independently of the nonlinear multiphoton processes at the origin of waves and currents. Using exact mathematical formulae, we calculate numerically with a custom fortran code the effect of an external control field which enable us to change the radiation pattern and suppress radiative losses or to reduce absorption, enabling the particle to behave as a perfect scatterer or as a perfect absorber. Data are provided in tabular, comma delimited value format and illustrate narrow features in the response of the particles that result in high sensitivity to small variations in the local environment, including subwavelength spatial shifts. PMID:26601699
Role of fluctuations and nonlinearities on field emission nanomechanical self-oscillators
NASA Astrophysics Data System (ADS)
Barois, T.; Perisanu, S.; Vincent, P.; Purcell, S. T.; Ayari, A.
2013-11-01
A theoretical and experimental description of the threshold, amplitude, and stability of a self-oscillating nanowire in a field emission configuration is presented. Two thresholds for the onset of self-oscillation are identified, one induced by fluctuations of the electromagnetic environment and a second revealed by these fluctuations by measuring the probability density function of the current. The ac and dc components of the current and the phase stability are quantified. An ac to dc ratio above 100% and an Allan deviation of 1.3×10-5 at room temperature can be attained. Finally, it is shown that a simple nonlinear model cannot describe the equilibrium effective potential in the self-oscillating regime due to the high amplitude of oscillations.
Self-similar evolution of the nonlinear magnetic buoyancy instability
NASA Technical Reports Server (NTRS)
Shibata, K.; Tajima, T.; Matsumoto, R.
1990-01-01
A new type of self-similar solution of ideal magnetohydrodynamics (MHD) in the nonlinear stage of the undular model (k parallel to B) of the magnetic buoyancy instability (the ballooning instability in fusion plasma physics or the Parker instability in astrophysics) is found through MHD simulation and theory. The linear theory developed agrees well with the simulation in the early (linear) stage. The nonlinear stages of the instability in the simulation show the self-similar evolution. One of the solutions obtained from the nonlinear analysis has the characteristics of nonlinear instability in Lagrangian coordinates; the fluid velocity and the Alfven speed on each magnetic loop increase exponentially with time, because the loop is evacuated by the field-aligned motion of matter resulting from gravitational acceleration. In the later stage of the nonlinear evolution, the solution property changes from exponential to power-law time dependence. The latter corresponds to a force-free expansion solution. The later saturation of the velocity increment is also discussed.
Far-field optical imaging with subdiffraction resolution enabled by nonlinear saturation absorption
Ding, Chenliang; Wei, Jingsong
2016-01-01
The resolution of far-field optical imaging is required to improve beyond the Abbe limit to the subdiffraction or even the nanoscale. In this work, inspired by scanning electronic microscopy (SEM) imaging, in which carbon (or Au) thin films are usually required to be coated on the sample surface before imaging to remove the charging effect while imaging by electrons. We propose a saturation-absorption-induced far-field super-resolution optical imaging method (SAI-SRIM). In the SAI-SRIM, the carbon (or Au) layers in SEM imaging are replaced by nonlinear-saturation-absorption (NSA) thin films, which are directly coated onto the sample surfaces using advanced thin film deposition techniques. The surface fluctuant morphologies are replicated to the NSA thin films, accordingly. The coated sample surfaces are then imaged using conventional laser scanning microscopy. Consequently, the imaging resolution is greatly improved, and subdiffraction-resolved optical images are obtained theoretically and experimentally. The SAI-SRIM provides an effective and easy way to achieve far-field super-resolution optical imaging for sample surfaces with geometric fluctuant morphology characteristics. PMID:26727415
Far-field optical imaging with subdiffraction resolution enabled by nonlinear saturation absorption
NASA Astrophysics Data System (ADS)
Ding, Chenliang; Wei, Jingsong
2016-01-01
The resolution of far-field optical imaging is required to improve beyond the Abbe limit to the subdiffraction or even the nanoscale. In this work, inspired by scanning electronic microscopy (SEM) imaging, in which carbon (or Au) thin films are usually required to be coated on the sample surface before imaging to remove the charging effect while imaging by electrons. We propose a saturation-absorption-induced far-field super-resolution optical imaging method (SAI-SRIM). In the SAI-SRIM, the carbon (or Au) layers in SEM imaging are replaced by nonlinear-saturation-absorption (NSA) thin films, which are directly coated onto the sample surfaces using advanced thin film deposition techniques. The surface fluctuant morphologies are replicated to the NSA thin films, accordingly. The coated sample surfaces are then imaged using conventional laser scanning microscopy. Consequently, the imaging resolution is greatly improved, and subdiffraction-resolved optical images are obtained theoretically and experimentally. The SAI-SRIM provides an effective and easy way to achieve far-field super-resolution optical imaging for sample surfaces with geometric fluctuant morphology characteristics.
Far-field optical imaging with subdiffraction resolution enabled by nonlinear saturation absorption.
Ding, Chenliang; Wei, Jingsong
2016-01-01
The resolution of far-field optical imaging is required to improve beyond the Abbe limit to the subdiffraction or even the nanoscale. In this work, inspired by scanning electronic microscopy (SEM) imaging, in which carbon (or Au) thin films are usually required to be coated on the sample surface before imaging to remove the charging effect while imaging by electrons. We propose a saturation-absorption-induced far-field super-resolution optical imaging method (SAI-SRIM). In the SAI-SRIM, the carbon (or Au) layers in SEM imaging are replaced by nonlinear-saturation-absorption (NSA) thin films, which are directly coated onto the sample surfaces using advanced thin film deposition techniques. The surface fluctuant morphologies are replicated to the NSA thin films, accordingly. The coated sample surfaces are then imaged using conventional laser scanning microscopy. Consequently, the imaging resolution is greatly improved, and subdiffraction-resolved optical images are obtained theoretically and experimentally. The SAI-SRIM provides an effective and easy way to achieve far-field super-resolution optical imaging for sample surfaces with geometric fluctuant morphology characteristics. PMID:26727415
NASA Astrophysics Data System (ADS)
Moawad, S. M.; Ibrahim, D. A.
2016-08-01
The equilibrium properties of three-dimensional ideal magnetohydrodynamics (MHD) are investigated. Incompressible and compressible flows are considered. The governing equations are taken in a steady state such that the magnetic field is parallel to the plasma flow. Equations of stationary equilibrium for both of incompressible and compressible MHD flows are derived and described in a mathematical mode. For incompressible MHD flows, Alfvénic and non-Alfvénic flows with constant and variable magnetofluid density are investigated. For Alfvénic incompressible flows, the general three-dimensional solutions are determined with the aid of two potential functions of the velocity field. For non-Alfvénic incompressible flows, the stationary equilibrium equations are reduced to two differential constraints on the potential functions, flow velocity, magnetofluid density, and the static pressure. Some examples which may be of some relevance to axisymmetric confinement systems are presented. For compressible MHD flows, equations of the stationary equilibrium are derived with the aid of a single potential function of the velocity field. The existence of three-dimensional solutions for these MHD flows is investigated. Several classes of three-dimensional exact solutions for several cases of nonlinear equilibrium equations are presented.
Pazur, Alexander
2003-01-01
Three types of liposomes in aqueous solution were subjected to a low frequency switched weak magnetic field. A differential non-linear dielectric spectroscopy (DNLDS) was performed at 40 degrees C with two planar orthogonal electrodes, positioned parallel and vertical to the earth surface. The difference of the free voltage release (FVR) signals for the two orthogonal directions following electric pulses with an amplitude of 1.0 V and a duration of 25 ms, were Fourier-transformed. An additional magnetic field was switched with a period of 400 ms and a variable amplitude from 0 to 100 G, whose direction was parallel to the vertical electrode plane. With two of the liposomes (egg yolk lecithin (EY), asolectin doped with cholesterol (ASCO)) a decrease of the signal amplitude with increasing magnetic fields could be seen in most of the 25 observed harmonic frequencies (relative to the electric pulse frequency f(0) = 40 Hz). For EY liposomes this decrease was highly significant and not linear for the 1.-5., and above the 20. harmonic frequency, ASCO liposomes showed a similar effect. Asolectin liposomes showed the reverse response. Quantum mechanical conditions of charges on the liposome surface are discussed as a possible origin of these effects PMID:12872934
Experimental investigation of relationship between nonlinear field energy and emittance growth
NASA Astrophysics Data System (ADS)
Young, D.; McCready, S. S.; McHarg, M. G.; Brasure, L. D.
1989-11-01
Understanding the phenomena of emittance growth in space-charge-dominated particle beams is important to any application that requires a small final emittance. Many researchers have looked at the process of emittance growth under these conditions. Wangler, et al., uses the idea of nonlinear field energy to describe emittance growth. In brief, a beam with a nonuniform radial intensity distribution has a potential energy associated with this distribution. As the beam propagates through a solenoidal magnetic field, this potential energy is turned into transverse kinetic energy and manifests itself as emittance growth. The experimental results shows that there is a relationship between the initial intensity profile and the tune ratio to the emittance of charged particle beams in solenoidal focusing fields. The results also agree with the predicted beam intensity profile changes under focusing for peaked and flat beams. This experiment shows that an experiment to verify this theory by using two different beam intensity profiles is feasible. More experimentation in this area is recommended.
Pfirsch, D.; Sudan, R.N.
1996-01-01
It is observed that the recently developed magnetic flux-averaged magnetohydrodynamics (AMHD) [Phys. Plasmas {bold 1}, 2488 (1994)] is incompatible with Taylor{close_quote}s theorem, which states that the lowest-energy state of force-free equilibria based on the conservation of the helicity integral is absolutely stable for vanishingly small resistivity. By a modification of the Lagrangian from which AMHD is derived, a modified version of AMHD that is compatible with Taylor{close_quote}s theorem is obtained. It also provides an energy principle for examining the linear instability of resistive equilibria, which has a great advantage over resistive MHD. {copyright} {ital 1996 American Institute of Physics.}
NASA Astrophysics Data System (ADS)
Moraitis, Kostas; Archontis, Vasilis; Tziotziou, Konstantinos; Georgoulis, Manolis K.
We calculate the instantaneous free magnetic energy and relative magnetic helicity of solar active regions using two independent approaches: a) a non-linear force-free (NLFF) method that requires only a single photospheric vector magnetogram, and b) well known semi-analytical formulas that require the full three-dimensional (3D) magnetic field structure. The 3D field is obtained either from MHD simulations, or from observed magnetograms via respective NLFF field extrapolations. We find qualitative agreement between the two methods and, quantitatively, a discrepancy not exceeding a factor of 4. The comparison of the two methods reveals, as a byproduct, two independent tests for the quality of a given force-free field extrapolation. We find that not all extrapolations manage to achieve the force-free condition in a valid, divergence-free, magnetic configuration. This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: Thales. Investing in knowledge society through the European Social Fund.
NASA Astrophysics Data System (ADS)
Bergmann, Rachelle Ann
The linear generation of electrostatic hydrogen cyclotron (EHC) waves in the auroral acceleration region near an altitude of 1R(,E) is examined. A field-aligned electron drift and an ion beam are included simultaneously in the plasma model. Each of these has the capability to excite EHC waves. Two assumptions are made, (1) that the plasma can be described by three Maxwellian species and, (2) that the properties of observed EHC waves are the same as the properties of the linearly excited modes. With these assumptions and a plasma model based on S3-3 satellite data, it is concluded that EHC waves driven by an electron drift compare more favorably with observed EHC waves than those driven by an ion beam. Further, the temperature of the drifting electrons should be on the order of the temperature of the stationary ions. Saturation of a linearly excited EHC wave by coherent decay to another EHC wave and an ion acoustic mode is considered. Frequency and wave number matching can be satisfied in this three -wave interaction if the daughter ion acoustic mode is oblique to the geomagnetic field. Many three-wave triads exist for a single parent. A calculation of the coupling coefficient between any three electrostatic waves in a uniformly magnetized plasma comprised of drifting Maxwellian species is derived. This is used to find the threshold electric field of a parent wave necessary for the daughter modes to have a positive non-linear growth rate. It is found that this threshold is below observed EHC wave amplitudes, and is zero when the parent EHC wave couples to a linearly marginally stable EHC daughter wave. Thus, this three-wave interaction may occur in the auroral acceleration region. A preliminary investigation into the temporal development of this interaction is conducted. Though the model is incomplete, the results indicate that this decay can act as a saturation mechanism for the linear growth. In the asymptotic state of the time development, it is the linearly
NASA Technical Reports Server (NTRS)
Lobashov, A. A.; Mostepanenko, V. M.
1993-01-01
The theory of quantum effects in nonlinear dielectric media is developed. The nonlinear dielectric media is influenced by an external pumping field. The diagonalization of the Hamiltonian of a quantized field is obtained by the canonical Bogoliubov transformations. The transformations allow us to obtain the general expressions for the number of created photons and for the degree of squeezing. In the case of a plane pumping wave, for example, the results are calculated by using the zero order of the secular perturbation theory, with small parameters characterizing the medium nonlinearity. The Heisenberg equations of motion are obtained for non-stationary case and a commonly used Hamiltonian is derived from the first principles of quantum electrodynamics.
Determination of Coronal Magnetic Fields from Vector Magnetograms
NASA Technical Reports Server (NTRS)
Mikic, Zoran
1997-01-01
During the course of the present contract we developed an 'evolutionary technique' for the determination of force-free coronal magnetic fields from vector magnetograph observations. The method can successfully generate nonlinear force- free fields (with non-constant-a) that match vector magnetograms. We demonstrated that it is possible to determine coronal magnetic fields from photospheric measurements, and we applied it to vector magnetograms of active regions. We have also studied theoretical models of coronal fields that lead to disruptions. Specifically, we have demonstrated that the determination of force-free fields from exact boundary data is a well-posed mathematical problem, by verifying that the computed coronal field agrees with an analytic force-free field when boundary data for the analytic field are used; demonstrated that it is possible to determine active-region coronal magnetic fields from photospheric measurements, by computing the coronal field above active region 5747 on 20 October 1989, AR6919 on 15 November 1991, and AR7260 on 18 August 1992, from data taken with the Stokes Polarimeter at Mees Solar Observatory, University of Hawaii; started to analyze active region 7201 on 19 June 1992 using measurements made with the Advanced Stokes Polarimeter at NSO/Sac Peak; investigated the effects of imperfections in the photospheric data on the computed coronal magnetic field; documented the coronal field structure of AR5747 and compared it to the morphology of footpoint emission in a flare, showing that the 'high- pressure' H-alpha footpoints are connected by coronal field lines; shown that the variation of magnetic field strength along current-carrying field lines is significantly different from the variation in a potential field, and that the resulting near-constant area of elementary flux tubes is consistent with observations; begun to develop realistic models of coronal fields which can be used to study flare trigger mechanisms; demonstrated that
Bias-field controlled phasing and power combination of gyromagnetic nonlinear transmission lines
NASA Astrophysics Data System (ADS)
Reale, D. V.; Bragg, J.-W. B.; Gonsalves, N. R.; Johnson, J. M.; Neuber, A. A.; Dickens, J. C.; Mankowski, J. J.
2014-05-01
Gyromagnetic Nonlinear Transmission Lines (NLTLs) generate microwaves through the damped gyromagnetic precession of the magnetic moments in ferrimagnetic material, and are thus utilized as compact, solid-state, frequency agile, high power microwave (HPM) sources. The output frequency of a NLTL can be adjusted by control of the externally applied bias field and incident voltage pulse without physical alteration to the structure of the device. This property provides a frequency tuning capability not seen in many conventional e-beam based HPM sources. The NLTLs developed and tested are mesoband sources capable of generating MW power levels in the L, S, and C bands of the microwave spectrum. For an individual NLTL the output power at a given frequency is determined by several factors including the intrinsic properties of the ferrimagnetic material and the transmission line structure. Hence, if higher power levels are to be achieved, it is necessary to combine the outputs of multiple NLTLs. This can be accomplished in free space using antennas or in a transmission line via a power combiner. Using a bias-field controlled delay, a transient, high voltage, coaxial, three port, power combiner was designed and tested. Experimental results are compared with the results of a transient COMSOL simulation to evaluate combiner performance.
NASA Astrophysics Data System (ADS)
Pikichyan, H. V.
2016-06-01
It is shown that for the nonlinear boundary value problem of determining the radiation field inside a one-dimensional anisotropic medium illuminated from outside at its boundaries on both sides, the formulas for adding layers in semilinear systems of differential equations for radiative transfer, invariant embedding, and total Ambartsumyan invariance can be used to reduce the equations for the problem to separable equations with initial conditions. The fields travelling to the left and right are thereby found independently of one another. In addition, when one of them has been determined, the other can be found directly using an explicit expression. A general equivalence property of operators with respect to a certain mathematical form, expression, or functional is formulated mathematically. New equations, referred to as kinetic equations of equivalency, are derived from the mutual equivalence of the differential operators of the Boltzmann kinetic equation (the equations of radiative transfer) and the functional equation of the Ambartsumian's complete invariance. Besides separability, these new equations also have the property of linearity. Formulas are also introduced for special problems of single sided illumination of a medium that in this case serve as supplementary information in the initial conditions for formulating Cauchy problems.
Bias-field controlled phasing and power combination of gyromagnetic nonlinear transmission lines.
Reale, D V; Bragg, J-W B; Gonsalves, N R; Johnson, J M; Neuber, A A; Dickens, J C; Mankowski, J J
2014-05-01
Gyromagnetic Nonlinear Transmission Lines (NLTLs) generate microwaves through the damped gyromagnetic precession of the magnetic moments in ferrimagnetic material, and are thus utilized as compact, solid-state, frequency agile, high power microwave (HPM) sources. The output frequency of a NLTL can be adjusted by control of the externally applied bias field and incident voltage pulse without physical alteration to the structure of the device. This property provides a frequency tuning capability not seen in many conventional e-beam based HPM sources. The NLTLs developed and tested are mesoband sources capable of generating MW power levels in the L, S, and C bands of the microwave spectrum. For an individual NLTL the output power at a given frequency is determined by several factors including the intrinsic properties of the ferrimagnetic material and the transmission line structure. Hence, if higher power levels are to be achieved, it is necessary to combine the outputs of multiple NLTLs. This can be accomplished in free space using antennas or in a transmission line via a power combiner. Using a bias-field controlled delay, a transient, high voltage, coaxial, three port, power combiner was designed and tested. Experimental results are compared with the results of a transient COMSOL simulation to evaluate combiner performance. PMID:24880394
Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling
White, Jonathan; Minamitsuji, Masato; Sasaki, Misao E-mail: masato.minamitsuji@ist.utl.pt
2013-09-01
Using the δN formalism we consider the non-linear curvature perturbation in multi-field models of inflation with non-minimal coupling. In particular, we focus on the relation between the δN formalism as applied in the conformally related Jordan and Einstein frames. Exploiting results already known in the Einstein frame, we give expressions for the power spectrum, spectral tilt and non-gaussianity associated with the Jordan frame curvature perturbation. In the case that an adiabatic limit has not been reached, we find that in general these quantities differ from those associated with the Einstein frame curvature perturbation, and also confirm their equivalence in the absence of isocurvature modes. We then proceed to consider two analytically soluble examples, the first involving a non-minimally coupled 'spectator' field and the second being a non-minimally coupled extension of the multi-brid inflation model. In the first model we find that predictions can easily be brought into agreement with the recent Planck results, as the tensor-to-scalar ratio is generally small, the spectral tilt tuneable and the non-gaussianity suppressed. In the second model we find that predictions for all three parameters can differ substantially from those predicted in the minimally coupled case, and that the recent Planck results for the spectral tilt can be used to constrain the non-minimal coupling parameters.
Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling
NASA Astrophysics Data System (ADS)
White, Jonathan; Minamitsuji, Masato; Sasaki, Misao
2013-09-01
Using the δN formalism we consider the non-linear curvature perturbation in multi-field models of inflation with non-minimal coupling. In particular, we focus on the relation between the δN formalism as applied in the conformally related Jordan and Einstein frames. Exploiting results already known in the Einstein frame, we give expressions for the power spectrum, spectral tilt and non-gaussianity associated with the Jordan frame curvature perturbation. In the case that an adiabatic limit has not been reached, we find that in general these quantities differ from those associated with the Einstein frame curvature perturbation, and also confirm their equivalence in the absence of isocurvature modes. We then proceed to consider two analytically soluble examples, the first involving a non-minimally coupled `spectator' field and the second being a non-minimally coupled extension of the multi-brid inflation model. In the first model we find that predictions can easily be brought into agreement with the recent Planck results, as the tensor-to-scalar ratio is generally small, the spectral tilt tuneable and the non-gaussianity suppressed. In the second model we find that predictions for all three parameters can differ substantially from those predicted in the minimally coupled case, and that the recent Planck results for the spectral tilt can be used to constrain the non-minimal coupling parameters.
Bias-field controlled phasing and power combination of gyromagnetic nonlinear transmission lines
Reale, D. V. Bragg, J.-W. B.; Gonsalves, N. R.; Johnson, J. M.; Neuber, A. A.; Dickens, J. C.; Mankowski, J. J.
2014-05-15
Gyromagnetic Nonlinear Transmission Lines (NLTLs) generate microwaves through the damped gyromagnetic precession of the magnetic moments in ferrimagnetic material, and are thus utilized as compact, solid-state, frequency agile, high power microwave (HPM) sources. The output frequency of a NLTL can be adjusted by control of the externally applied bias field and incident voltage pulse without physical alteration to the structure of the device. This property provides a frequency tuning capability not seen in many conventional e-beam based HPM sources. The NLTLs developed and tested are mesoband sources capable of generating MW power levels in the L, S, and C bands of the microwave spectrum. For an individual NLTL the output power at a given frequency is determined by several factors including the intrinsic properties of the ferrimagnetic material and the transmission line structure. Hence, if higher power levels are to be achieved, it is necessary to combine the outputs of multiple NLTLs. This can be accomplished in free space using antennas or in a transmission line via a power combiner. Using a bias-field controlled delay, a transient, high voltage, coaxial, three port, power combiner was designed and tested. Experimental results are compared with the results of a transient COMSOL simulation to evaluate combiner performance.
Technology Transfer Automated Retrieval System (TEKTRAN)
Non-linear regression techniques are used widely to fit weed field emergence patterns to soil microclimatic indices using S-type functions. Artificial neural networks present interesting and alternative features for such modeling purposes. In this work, a univariate hydrothermal-time based Weibull m...
Hong Qin and Ronald C. Davidson
2011-07-19
In a linear trap confining a one-component nonneutral plasma, the external focusing force is a linear function of the configuration coordinates and/or the velocity coordinates. Linear traps include the classical Paul trap and the Penning trap, as well as the newly proposed rotating-radio- frequency traps and the Mobius accelerator. This paper describes a class of self-similar nonlinear solutions of nonneutral plasma in general time-dependent linear focusing devices, with self-consistent electrostatic field. This class of nonlinear solutions includes many known solutions as special cases.
NASA Astrophysics Data System (ADS)
Park, Kwangsoo
In this dissertation, a research effort aimed at development and implementation of a direct field test method to evaluate the linear and nonlinear shear modulus of soil is presented. The field method utilizes a surface footing that is dynamically loaded horizontally. The test procedure involves applying static and dynamic loads to the surface footing and measuring the soil response beneath the loaded area using embedded geophones. A wide range in dynamic loads under a constant static load permits measurements of linear and nonlinear shear wave propagation from which shear moduli and associated shearing strains are evaluated. Shear wave velocities in the linear and nonlinear strain ranges are calculated from time delays in waveforms monitored by geophone pairs. Shear moduli are then obtained using the shear wave velocities and the mass density of a soil. Shear strains are determined using particle displacements calculated from particle velocities measured at the geophones by assuming a linear variation between geophone pairs. The field test method was validated by conducting an initial field experiment at sandy site in Austin, Texas. Then, field experiments were performed on cemented alluvium, a complex, hard-to-sample material. Three separate locations at Yucca Mountain, Nevada were tested. The tests successfully measured: (1) the effect of confining pressure on shear and compression moduli in the linear strain range and (2) the effect of strain on shear moduli at various states of stress in the field. The field measurements were first compared with empirical relationships for uncemented gravel. This comparison showed that the alluvium was clearly cemented. The field measurements were then compared to other independent measurements including laboratory resonant column tests and field seismic tests using the spectral-analysis-of-surface-waves method. The results from the field tests were generally in good agreement with the other independent test results, indicating
NASA Astrophysics Data System (ADS)
Shi, Pengpeng; Jin, Ke; Zheng, Xiaojing
2016-04-01
Weak magnetic nondestructive testing (e.g., metal magnetic memory method) concerns the magnetization variation of ferromagnetic materials due to its applied load and a weak magnetic surrounding them. One key issue on these nondestructive technologies is the magnetomechanical effect for quantitative evaluation of magnetization state from stress-strain condition. A representative phenomenological model has been proposed to explain the magnetomechanical effect by Jiles in 1995. However, the Jiles' model has some deficiencies in quantification, for instance, there is a visible difference between theoretical prediction and experimental measurements on stress-magnetization curve, especially in the compression case. Based on the thermodynamic relations and the approach law of irreversible magnetization, a nonlinear coupled model is proposed to improve the quantitative evaluation of the magnetomechanical effect. Excellent agreement has been achieved between the predictions from the present model and previous experimental results. In comparison with Jiles' model, the prediction accuracy is improved greatly by the present model, particularly for the compression case. A detailed study has also been performed to reveal the effects of initial magnetization status, cyclic loading, and demagnetization factor on the magnetomechanical effect. Our theoretical model reveals that the stable weak magnetic signals of nondestructive testing after multiple cyclic loads are attributed to the first few cycles eliminating most of the irreversible magnetization. Remarkably, the existence of demagnetization field can weaken magnetomechanical effect, therefore, significantly reduces the testing capability. This theoretical model can be adopted to quantitatively analyze magnetic memory signals, and then can be applied in weak magnetic nondestructive testing.
Impact of nonlinear energy transfer on the wave field in Pacific hindcast experiments
NASA Astrophysics Data System (ADS)
Tamura, Hitoshi; Waseda, Takuji; Miyazawa, Yasumasa
2010-12-01
We investigated the impact of nonlinear energy transfer (Snl) on wave fields by performing hindcast experiments for the Pacific Ocean. Specifically, we evaluated model performance using SRIAM, which was developed to accurately reproduce Snl with lower computational cost than more rigorous algorithms. The model results were compared to in situ wave parameters as well as results from another model employing the widely used discrete interaction approximation method (DIA). Comparison of the model results with buoy observations revealed a negligible difference between SRIAM and DIA for significant wave heights. However, the difference for the peak period was quite pronounced, especially around the tropical Pacific, where a persistent bias in peak frequency was improved by using SRIAM. This study also highlights the impact of source terms on spectral shape under a realistic model setting. Detailed analysis of spectral shape indicated that SRIAM can quantitatively capture the overshoot phenomena around the spectral peak during wave growth. In addition, Snl played a major role in maintaining the equilibrium range; it reacted to changes in the net external sources to cancel out the total source term. These results show that the magnitude of high-frequency dissipation controls the spectral tail exponent and that the balanced net external source is responsible for the reproduction of the f-4 power law behavior in the equilibrium range.
Effect of gravity field on the nonequilibrium/nonlinear chemical oscillation reactions
NASA Astrophysics Data System (ADS)
Fujieda, S.; Mori, Y.; Nakazawa, A.; Mogami, Y.
2001-01-01
Biological systems have evolved for a long time under the normal gravity. The Belousov-Zhabotinsky (BZ) reaction is a nonlinear chemical system far from the equilibrium that may be considered as a simplified chemical model of the biological systems so as to study the effect of gravity. The reaction solution is comprised of bromate in sulfuric acid as an oxidizing agent, 1,4-cyclohexanedione as an organic substrate, and ferroin as a metal catalyst. Chemical waves in the BZ reaction-diffusion system are visualized as blue and red patterns of ferriin and ferroin, respectively. After an improvement to the tubular reaction vessels in the experimental setup, the traveling velocity of chemical waves in aqueous solutions was measured in time series under normal gravity, microgravity, hyper-gravity, and normal gravity using the free-fall facility of JAMIC (Japan Microgravity Center), Hokkaido, Japan. Chemical patterns were collected as image data via CCD camera and analyzed by the software of NIH image after digitization. The estimated traveling velocity increased with increasing gravity as expected. It was clear experimentally that the traveling velocity of target patterns in reaction diffusion system was influenced by the effect of convection and correlated closely with the gravity field.
NASA Astrophysics Data System (ADS)
An, Weiming; Joshi, Chan; Mori, Warren; Lu, Wei
2014-10-01
We study the electron beam evolution in a nonlinear blowout PWFA when the accelerated beam has a very small matched spot size that can cause the plasma ions collapsing towards the beam. Contrary to the common belief, very small emittance growth of the accelerated electron beam is found when the plasma ion collapsing destroys the perfect linear focusing force in the plasma wake field. The improved quasi-static PIC code QuickPIC also allows us to use very high resolution and to model asymmetric spot sizes. Simulation results show that the accelerated beam will reach a steady state after several cm propagation in the plasma (which is why we can do simulations and not let the drive beam evolve). We find that for round beams the ion density (which is Li+) enhancement is indeed by factors of 100, but that the emittance only grows by around 20 percent. For asymmetric spot sizes, the ion collapse is less and emittance growth is zero in the plane with the largest emittance and about 20 percent in the other plane.
NASA Astrophysics Data System (ADS)
Sigsbee, K.; Kletzing, C. A.; Pickett, J. S.; Gurnett, D. A.; Schwartz, S. J.; Lefebvre, B.; Lucek, E.; Fazakerley, A. N.; Kucharek, H.
2010-10-01
Langmuir wave characteristics in the Earth's foreshock were examined to identify possible nonlinear wave behavior for two case studies with data from the Cluster Wideband Data Plasma Wave Receiver. The occurrence rates of four types of power spectra near the foreshock edge were determined: (1) spectra with power at the local plasma frequency fpe only, (2) spectra with power at fpe and 2fpe, (3) spectra with double peaks near fpe, and (4) spectra with double peaks near fpe and peaks at low frequencies indicative of ion acoustic waves. For electric field waveform amplitudes between 0.1 and 22.0 mV/m, most power spectra fell into the fpe only and double-peaked categories. The maximum Langmuir wave amplitudes and bump-on-tail reduced electron distribution functions from Cluster PEACE data were more consistent with saturation of wave growth by electrostatic decay than modulational instabilities. However, few spectra had the double peaks near fpe and ion acoustic waves indicative of electrostatic decay, suggesting other processes may also be at work. For amplitudes greater than 22.0 mV/m, most power spectra fell into the fpe and 2fpe category, but many of the harmonics were too weak to be clearly distinguished from harmonics caused by instrumental effects.
NASA Astrophysics Data System (ADS)
Wang, Lin; Chen, Xiaoshuang; Hu, Yibin; Yu, Anqi; Lu, Wei
2014-10-01
Recent observations of the negative differential conductance (NDC) phenomenon in graphene field-effect transistors (FET) open up new opportunities for their application in graphene-based fast switches, frequency multipliers and, most importantly, in high frequency oscillators up to the terahertz regime. Unlike conventional two-terminal NDC devices that rely on resonant tunneling and inter-valley transferring, in the present work, it has been shown that the universal NDC phenomenon of graphene-based FETs originates from their intrinsic nonlinear carrier transport under a strong electric field. The operation of graphene-NDC devices depends strongly on the interface between graphene and dielectric materials, the scattering-limited carrier mobility, and on the saturation velocity. To reveal such NDC behavior, the output characteristics of GFET are investigated rigorously, with both an analytical model and self-consistent transport equation, and with a multi-electrical parameter simulation. It is demonstrated that the contact-induced doping effect plays an important role in the operational efficiency of graphene-based NDC devices, rather than the ambipolar behavior associated with the competition between electron and hole conductances. In the absence of a NDC regime or beyond one, ambipolar transport starts at Vds > 2Vgs at the drain end, and as the dielectric layer begins to thin down, the kink-like saturation output characteristic is enhanced by the quantum capacitance contribution. These observations reveal the intrinsic mechanism of the NDC effect and open up new opportunities for the performance improvement of GFETs in future high-frequency applications, beyond the current paradigm based on two-terminal diodes.Recent observations of the negative differential conductance (NDC) phenomenon in graphene field-effect transistors (FET) open up new opportunities for their application in graphene-based fast switches, frequency multipliers and, most importantly, in high
Breuer; Huber; Petruccione
2000-05-01
The dynamics of periodically driven quantum systems coupled to a thermal environment is investigated. The interaction of the system with the external coherent driving field is taken into account exactly by making use of the Floquet picture. Treating the coupling to the environment within the Born-Markov approximation one finds a Pauli-type master equation for the diagonal elements of the reduced density matrix in the Floquet representation. The stationary solution of the latter yields a quasistationary, time-periodic density matrix which describes the long-time behavior of the system. Taking the example of a periodically driven particle in a box, the stationary solution is determined numerically for a wide range of driving amplitudes and temperatures. It is found that the quasistationary distribution differs substantially from a Boltzmann-type distribution at the temperature of the environment. For large driving fields it exhibits a plateau region describing a nearly constant population of a certain number of Floquet states. This number of Floquet states turns out to be nearly independent of the temperature. The plateau region is sharply separated from an exponential tail of the stationary distribution which expresses a canonical Boltzmann-type distribution over the mean energies of the Floquet states. These results are explained in terms of the structure of the matrix of transition rates for the dissipative quantum system. Investigating the corresponding classical, nonlinear Hamiltonian system, one finds that in the semiclassical range essential features of the quasistationary distribution can be understood from the structure of the underlying classical phase space. PMID:11031530
NASA Astrophysics Data System (ADS)
Sunil; Mahajan, Amit
2009-09-01
A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional for a magnetized ferrofluid layer heated and soluted from below with magnetic field-dependent (MFD) viscosity, for stress-free boundaries. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. For ferrofluids, we find that there is possibility of existence of subcritical instabilities, however, it is noted that in case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effects of magnetic parameter, M3, solute gradient, S1 and MFD viscosity parameter, δ, on the subcritical instability region have also been analyzed.
Force-free gravitational redshift: proposed gravitational Aharonov-Bohm experiment.
Hohensee, Michael A; Estey, Brian; Hamilton, Paul; Zeilinger, Anton; Müller, Holger
2012-06-01
We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom's Compton frequency. In analogy to the Aharonov-Bohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces. PMID:23003927
Force-free currents and the Newman-Penrose tetrad of a Kerr black hole: Exact local solutions
NASA Astrophysics Data System (ADS)
Menon, Govind
2015-07-01
In a previous article we derived a class of solutions to the force-free magnetosphere in a Kerr background. Here, the streaming surface, defined by constant values of the toriodal component of the electromagnetic vector potential A , was generated by constant values of θ . The electromagnetic current vector flowed along the infalling principle null geodesic vector of the geometry. Subsequently, we generalized this to obtain an outgoing principle null geodesic vector as well. In this article, we derive solutions that are complimentary to the above-mentioned criteria. Namely, here the solution has a streaming surface generated by spheres of constant radial coordinate r , and the current vector is generated by linear combinations of m and m⋆, the remaining bases vectors in the Newman-Penrose null tetrad.
NASA Astrophysics Data System (ADS)
Yuan, Yajie; Nalewajko, Krzysztof; Blandford, Roger D.; East, William E.; Zrake, Jonathan
2016-01-01
Many powerful and variable gamma-ray sources, including pulsar wind nebulae, active galactic nuclei and gamma-ray bursts, seem capable of accelerating particles to gamma-ray emitting energies efficiently over short time scales. This might be due to prodigal dissipation in a highly magnetized outflow. In order to understand the generic behavior of relativistic plasma with high magnetization, we consider a class of prototypical force-free equilibria which are shown to be unstable to ideal modes (East et al 2015 PRL 115, 095002). Kinetic simulations are carried out to follow the evolution of the instability and to study the basic mechanisms of particle acceleration, especially in the radiation-reaction-limited regime. We find that the instability naturally produces current layers and these are sites for efficient particle acceleration. Detailed calculations of the gamma ray spectrum, the evolution of the particle distribution function and the dynamical consequences of radiation reaction will be presented.
NASA Astrophysics Data System (ADS)
Sateesh, V. L.; Upadhyay, C. S.; Venkatesan, C.
2010-07-01
Polarization-electric-field (P-E) interaction results in rendering the stress tensor non-symmetric and in a nonlinear force term in the equilibrium equation. In this paper, an attempt is made to study these (P-E) nonlinear effects on the static response of laminated composite plates with piezo actuators. Further, this paper also focuses on finding the most effective piezo lay-up and ply orientation which gives the maximum deflections. Four different piezo lay-up configurations and three ply orientations are considered. It has been observed from the study that width-wise strips show more transverse bending and twisting. However, full length piezo layers show maximum longitudinal bending. The results of nonlinear analysis show a more considerable softening trend in deformations than that of the linear analysis in the case of longitudinal bending and twisting. In the case of transverse bending this nonlinear effect shows a hardening trend. Further, it has been observed that the influence of P-E nonlinearity depends on the stiffness of the core material, the geometric arrangement of piezo patches, the boundary conditions and the actuation voltage.
NASA Astrophysics Data System (ADS)
Hüter, Claas; Friák, Martin; Weikamp, Marc; Neugebauer, Jörg; Goldenfeld, Nigel; Svendsen, Bob; Spatschek, Robert
2016-06-01
We investigate nonlinear elastic deformations in the phase field crystal model and derived amplitude equation formulations. Two sources of nonlinearity are found, one of them is based on geometric nonlinearity expressed through a finite strain tensor. This strain tensor is based on the inverse right Cauchy-Green deformation tensor and correctly describes the strain dependence of the stiffness for anisotropic and isotropic behavior. In isotropic one- and two-dimensional situations, the elastic energy can be expressed equivalently through the left deformation tensor. The predicted isotropic low-temperature nonlinear elastic effects are directly related to the Birch-Murnaghan equation of state with bulk modulus derivative K'=4 for bcc. A two-dimensional generalization suggests K2D '=5 . These predictions are in agreement with ab initio results for large strain bulk deformations of various bcc elements and graphene. Physical nonlinearity arises if the strain dependence of the density wave amplitudes is taken into account and leads to elastic weakening. For anisotropic deformation, the magnitudes of the amplitudes depend on their relative orientation to the applied strain.
NASA Astrophysics Data System (ADS)
Yuan, Yajie; Nalewajko, Krzysztof; Zrake, Jonathan; East, William E.; Blandford, Roger D.
2016-09-01
Many powerful and variable gamma-ray sources, including pulsar wind nebulae, active galactic nuclei and gamma-ray bursts, seem capable of accelerating particles to gamma-ray emitting energies efficiently over very short timescales. These are likely due to the rapid dissipation of electromagnetic energy in a highly magnetized, relativistic plasma. In order to understand the generic features of such processes, we have investigated simple models based on the relaxation of unstable force-free magnetostatic equilibria. In this work, we make the connection between the corresponding plasma dynamics and the expected radiation signal, using 2D particle-in-cell simulations that self-consistently include synchrotron radiation reactions. We focus on the lowest order unstable force-free equilibrium in a 2D periodic box. We find that rapid variability, with modest apparent radiation efficiency as perceived by a fixed observer, can be produced during the evolution of the instability. The “flares” are accompanied by an increased polarization degree in the high energy band, with rapid variation in the polarization angle. Furthermore, the separation between the acceleration sites and the synchrotron radiation sites for the highest energy particles facilitates acceleration beyond the synchrotron radiation reaction limit. We also discuss the dynamical consequences of the radiation reaction, and some astrophysical applications of this model. Our current simulations with numerically tractable parameters are not yet able to reproduce the most dramatic gamma-ray flares, e.g., from the Crab Nebula. Higher magnetization studies are promising and will be carried out in the future.
NASA Astrophysics Data System (ADS)
Zhu, J.; Winter, C. L.; Wang, Z.
2015-11-01
Computational experiments are performed to evaluate the effects of locally heterogeneous conductivity fields on regional exchanges of water between stream and aquifer systems in the Middle Heihe River basin (MHRB) of northwestern China. The effects are found to be nonlinear in the sense that simulated discharges from aquifers to streams are systematically lower than discharges produced by a base model parameterized with relatively coarse effective conductivity. A similar, but weaker, effect is observed for stream leakage. The study is organized around three hypotheses: (H1) small-scale spatial variations of conductivity significantly affect regional exchanges of water between streams and aquifers in river basins, (H2) aggregating small-scale heterogeneities into regional effective parameters systematically biases estimates of stream-aquifer exchanges, and (H3) the biases result from slow paths in groundwater flow that emerge due to small-scale heterogeneities. The hypotheses are evaluated by comparing stream-aquifer fluxes produced by the base model to fluxes simulated using realizations of the MHRB characterized by local (grid-scale) heterogeneity. Levels of local heterogeneity are manipulated as control variables by adjusting coefficients of variation. All models are implemented using the MODFLOW (Modular Three-dimensional Finite-difference Groundwater Flow Model) simulation environment, and the PEST (parameter estimation) tool is used to calibrate effective conductivities defined over 16 zones within the MHRB. The effective parameters are also used as expected values to develop lognormally distributed conductivity (K) fields on local grid scales. Stream-aquifer exchanges are simulated with K fields at both scales and then compared. Results show that the effects of small-scale heterogeneities significantly influence exchanges with simulations based on local-scale heterogeneities always producing discharges that are less than those produced by the base model
NASA Astrophysics Data System (ADS)
Zhu, J.; Winter, C. L.; Wang, Z.
2015-08-01
Computational experiments are performed to evaluate the effects of locally heterogeneous conductivity fields on regional exchanges of water between stream and aquifer systems in the Middle Heihe River Basin (MHRB) of northwestern China. The effects are found to be nonlinear in the sense that simulated discharges from aquifers to streams are systematically lower than discharges produced by a base model parameterized with relatively coarse effective conductivity. A similar, but weaker, effect is observed for stream leakage. The study is organized around three hypotheses: (H1) small-scale spatial variations of conductivity significantly affect regional exchanges of water between streams and aquifers in river basins, (H2) aggregating small-scale heterogeneities into regional effective parameters systematically biases estimates of stream-aquifer exchanges, and (H3) the biases result from slow-paths in groundwater flow that emerge due to small-scale heterogeneities. The hypotheses are evaluated by comparing stream-aquifer fluxes produced by the base model to fluxes simulated using realizations of the MHRB characterized by local (grid-scale) heterogeneity. Levels of local heterogeneity are manipulated as control variables by adjusting coefficients of variation. All models are implemented using the MODFLOW simulation environment, and the PEST tool is used to calibrate effective conductivities defined over 16 zones within the MHRB. The effective parameters are also used as expected values to develop log-normally distributed conductivity (K) fields on local grid scales. Stream-aquifer exchanges are simulated with K fields at both scales and then compared. Results show that the effects of small-scale heterogeneities significantly influence exchanges with simulations based on local-scale heterogeneities always producing discharges that are less than those produced by the base model. Although aquifer heterogeneities are uncorrelated at local scales, they appear to induce
NASA Astrophysics Data System (ADS)
Hamimid, M.; Mimoune, S. M.; Feliachi, M.
2013-01-01
In this paper, a time stepping finite volume method (FVM) associated with the modified inverse Jiles-Atherton model for the nonlinear electromagnetic field computation is presented. To describe the dynamic behavior in the conducting media, the effective field is modified by adding two counter-fields associated respectively to the eddy current and excess losses. The hysteresis loss can be estimated by the integration over the obtained hysteresis loop at each frequency. To examine the validity of the proposed dynamic model coupled with FVM, the computed total losses and hysteresis loops are compared to experiments.
Generalized mean-field or master equation for nonlinear cavities with transverse effects.
Dunlop, A M; Firth, W J; Heatley, D R; Wright, E M
1996-06-01
We present a general form of master equation for nonlinear-optical cavities that can be described by an ABCD matrix. It includes as special cases some previous models of spatiotemporal effects in lasers. PMID:19876153
Luo, Zhaochu; Xiong, Chengyue; Zhang, Xu; Guo, Zhen-Gang; Cai, Jianwang; Zhang, Xiaozhong
2016-04-01
The anomalous Hall effect of a magnetic material is coupled to the nonlinear transport effect of a semiconductor material in a simple structure to achieve a large geometric magnetoresistance (MR) based on a diode-assisted mechanism. An extremely large MR (>10(4) %) at low magnetic fields (1 mT) is observed at room temperature. This MR device shows potential for use as a logic gate for the four basic Boolean logic operations. PMID:26857904
Nonlinear control design for stressed power systems using normal forms of vector fields
NASA Astrophysics Data System (ADS)
Jang, Gilsoo
Large stressed interconnected power systems exhibit complicated dynamic behavior when subjected to disturbances. This nonlinear complex behavior is not well analyzed with present tools, and a complete theoretical analysis of this is not feasible in large systems. In stressed power systems, due to the presence of increased nonlinearity and the existence of nonlinear modal interactions, there exist some limitation to the use of conventional linear control design techniques. Therefore there is a need to understand the nature of nonlinear modal interactions and their influences on control performance for optimal controller setting. This work deals with control design in power systems using the method of normal forms. The objective of this work is to understand the effect of the nonlinear modal interaction on control performance and to develop a procedure to design controls incorporating the nonlinear information. For power systems equipped with fast exciters, the exciter gains have crucial influence on the system dynamic behavior. In order to be able to tune the exciter gains for optimal system performance, one has to understand, how the system response changes with different gain settings. In linear analysis, this consists of determining the eigenvalues for various gains, and computing the sensitivity of the eigenvalues under gain variations. If one takes into account the influence of the second order normal forms on the system response, then the corresponding interaction coefficients and their sensitivity with respect to gain variations has to be studied as well. This is the topic of the study presented here. The concept of nonlinear participation factors, and sensitivity of the normal forms coefficient, together with linear participation factors and eigenvalue sensitivity are used to vary control settings. The control settings are varied to obtain improved stability and to reduce the nonlinearity in the system. The proposed procedure was applied to the 50-generator
NASA Astrophysics Data System (ADS)
Ata, Metin; Kitaura, Francisco-Shu; Müller, Volker
2015-02-01
We present a Bayesian reconstruction algorithm to generate unbiased samples of the underlying dark matter field from halo catalogues. Our new contribution consists of implementing a non-Poisson likelihood including a deterministic non-linear and scale-dependent bias. In particular we present the Hamiltonian equations of motions for the negative binomial (NB) probability distribution function. This permits us to efficiently sample the posterior distribution function of density fields given a sample of galaxies using the Hamiltonian Monte Carlo technique implemented in the ARGO code. We have tested our algorithm with the Bolshoi N-body simulation at redshift z = 0, inferring the underlying dark matter density field from subsamples of the halo catalogue with biases smaller and larger than one. Our method shows that we can draw closely unbiased samples (compatible within 1-σ) from the posterior distribution up to scales of about k ˜ 1 h Mpc-1 in terms of power-spectra and cell-to-cell correlations. We find that a Poisson likelihood including a scale-dependent non-linear deterministic bias can yield reconstructions with power spectra deviating more than 10 per cent at k = 0.2 h Mpc-1. Our reconstruction algorithm is especially suited for emission line galaxy data for which a complex non-linear stochastic biasing treatment beyond Poissonity becomes indispensable.
NASA Technical Reports Server (NTRS)
Shih, C. C.
1973-01-01
In order to establish a foundation of scaling laws for the highly nonlinear waves associated with the launch vehicle, the basic knowledge of the relationships among the paramaters pertinent to the energy dissipation process associated with the propagation of nonlinear pressure waves in thermoviscous media is required. The problem of interest is to experimentally investigate the temporal and spacial velocity profiles of fluid flow in a 3-inch open-end pipe of various lengths, produced by the propagation of nonlinear pressure waves for various diaphragm burst pressures of a pressure wave generator. As a result, temporal and spacial characteristics of wave propagation for a parametric set of nonlinear pressure waves in the pipe containing air under atmospheric conditions were determined. Velocity measurements at five sections along the pipes of up to 210 ft. in length were made with hot-film anemometers for five pressure waves produced by a piston. The piston was derived with diaphragm burst pressures at 20, 40, 60, 80 and 100 psi in the driver chamber of the pressure wave generator.
NASA Astrophysics Data System (ADS)
Li, Fang; Yin, Xie-Yuan; Yin, Xie-Zhen
2016-05-01
A one-dimensional electrified viscoelastic model is built to study the nonlinear behavior of a slightly viscoelastic, perfectly conducting liquid jet under a radial electric field. The equations are solved numerically using an implicit finite difference scheme together with a boundary element method. The electrified viscoelastic jet is found to evolve into a beads-on-string structure in the presence of the radial electric field. Although the radial electric field greatly enhances the linear instability of the jet, its influence on the decay of the filament thickness is limited during the nonlinear evolution of the jet. On the other hand, the radial electric field induces axial non-uniformity of the first normal stress difference within the filament. The first normal stress difference in the center region of the filament may be greatly decreased by the radial electric field. The regions with/without satellite droplets are illuminated on the χ (the electrical Bond number)-k (the dimensionless wave number) plane. Satellite droplets may be formed for larger wave numbers at larger radial electric fields.
NASA Astrophysics Data System (ADS)
Amooshahi, M.
2016-08-01
Modeling a nonlinear anisotropic magnetodielectric medium with spatial-temporal dispersion by two continuum collections of three dimensional harmonic oscillators, a fully canonical quantization of the electromagnetic field is demonstrated in the presence of such a medium. Some coupling tensors of various ranks are introduced that couple the magnetodielectric medium with the electromagnetic field. The polarization and magnetization fields of the medium are defined in terms of the coupling tensors and the oscillators modeling the medium. The electric and magnetic susceptibility tensors of the medium are obtained in terms of the coupling tensors. It is shown that the electric field satisfy an integral equation in frequency domain. The integral equation is solved by an iteration method and the electric field is found up to an arbitrary accuracy.
NASA Astrophysics Data System (ADS)
Namboodiri, Mahesh; Khan, Tahirzeb; Karki, Khadga; Kazemi, Mehdi Mohammad; Bom, Sidhant; Flachenecker, Günter; Namboodiri, Vinu; Materny, Arnulf
2014-04-01
The combination of near-field microscopy along with nonlinear optical spectroscopic techniques is presented here. The scanning near-field imaging technique can be integrated with nonlinear spectroscopic techniques to improve spatial and axial resolution of the images. Additionally, ultrafast dynamics can be probed down to nano-scale dimension. The review shows some examples for this combination, which resulted in an exciton map and vibrational contrast images with sub-wavelength resolution. Results of two-color femtosecond time-resolved pump-probe experiments using scanning near-field optical microscopy (SNOM) on thin films of the organic semiconductor 3,4,9,10 Perylenetetracarboxylic dianhydride (PTCDA) are presented. While nonlinear Raman techniques have been used to obtain highly resolved images in combination with near-field microscopy, the use of femtosecond laser pulses in electronic resonance still constitutes a big challenge. Here, we present our first results on coherent anti-Stokes Raman scattering (fs-CARS) with femtosecond laser pulses detected in the near-field using SNOM. We demonstrate that highly spatially resolved images can be obtained from poly(3-hexylthiophene) (P3HT) nano-structures where the fs-CARS process was in resonance with the P3HT absorption and with characteristic P3HT vibrational modes without destruction of the samples. Sub-diffraction limited lateral resolution is achieved. Especially the height resolution clearly surpasses that obtained with standard microCARS. These results will be the basis for future investigations of mode-selective dynamics in the near-field.
Dynamics of atom-field probability amplitudes in a coupled cavity system with Kerr non-linearity
Priyesh, K. V.; Thayyullathil, Ramesh Babu
2014-01-28
We have investigated the dynamics of two cavities coupled together via photon hopping, filled with Kerr non-linear medium and each containing a two level atom in it. The evolution of various atom (field) state probabilities of the coupled cavity system in two excitation sub space are obtained numerically. Detailed analysis has been done by taking different initial conditions of the system, with various coupling strengths and by varying the susceptibility of the medium. The role of susceptibility factor, on the dynamics atom field probability has been examined. In a coupled cavity system with strong photon hopping it is found that the susceptibility factor modifies the behaviour of probability amplitudes.
NASA Astrophysics Data System (ADS)
Ren, C.; Mori, W. B.
2004-05-01
The nonlinear and finite spot size effects for short laser pulses propagating in a plasma across a constant magnetic field (ordinary and extraordinary modes) have been studied. Starting from a fluid Lagrangian for magnetized plasmas with immobile ions, we derive the envelope equation for the laser and also the equation for the plasma wake in a three-dimensional geometry. The derived equations reveal that the external magnetic field reduces the strength of ponderomotive self-focusing, causes astigmatic self-focusing, and leads to the possibility of deflecting a short and narrow laser pulse in a magnetized plasma.
NASA Astrophysics Data System (ADS)
Shi, L.; Yan, Z. W.
2016-06-01
In the present work, the optical properties of GaAs/AlxGa1-xAs/GaAs multi-shell ellipsoidal quantum dot heterostructures with a shallow hydrogenic impurity in the presence of an external electric field have been studied. The results show how the linear and nonlinear optical absorption coefficients and refraction index changes are changed by the variations of the size and shape of the multi-shell structure. Moreover, how the optical properties of this structure are affected by the electric field has also been shown. The physical reasons for the results have been discussed in detail.
Liu, Tian; Spincemaille, Pascal; de Rochefort, Ludovic; Wong, Richard; Prince, Martin; Wang, Yi
2010-01-01
Superparamagnetic iron oxide (SPIO) particles generate signal void regions on gradient echo images due to their strong magnetization. In practice, the signal void region might be indistinguishable from that generated by air. However, the response of SPIO to an externally applied magnetic field is non-linear. Magnetization of SPIO saturates at around 1 Tesla while magnetization of water and air increase linearly with field strength. Phantom experiment and mice experiments demonstrated the feasibility of a non-ambiguous identification of superparamagnetic contrast agents. PMID:20688448
NASA Astrophysics Data System (ADS)
Dehghani, Z.; Saievar Iranizad, E.; Nadafan, M.
2015-01-01
Third order nonlinearity of Fe3O4 nanoparticles (NPs) doped in nematic liquid crystals (NLCs) was evaluated due to laser induced self-phase modulation. The influence of electric field on the nonlinear optical responses of the NLCs doped with Fe3O4 NPs was considered in different voltages. The measurements were performed for two commonly initial alignments (homogeneous and homeotropic) with different small compositional percentages of magnetic NPs. The experimental results show that the homogenous- aligned cell was considerably affected on the applied electric field while the nonlinearity of homeotropic-aligned NLCs with the Fe3O4 NPs did not approximately change in the presence of electric field.
Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm
Chen, C.; Xia, J.; Liu, J.; Feng, G.
2006-01-01
Using a genetic algorithm to solve an inverse problem of complex nonlinear geophysical equations is advantageous because it does not require computer gradients of models or "good" initial models. The multi-point search of a genetic algorithm makes it easier to find the globally optimal solution while avoiding falling into a local extremum. As is the case in other optimization approaches, the search efficiency for a genetic algorithm is vital in finding desired solutions successfully in a multi-dimensional model space. A binary-encoding genetic algorithm is hardly ever used to resolve an optimization problem such as a simple geophysical inversion with only three unknowns. The encoding mechanism, genetic operators, and population size of the genetic algorithm greatly affect search processes in the evolution. It is clear that improved operators and proper population size promote the convergence. Nevertheless, not all genetic operations perform perfectly while searching under either a uniform binary or a decimal encoding system. With the binary encoding mechanism, the crossover scheme may produce more new individuals than with the decimal encoding. On the other hand, the mutation scheme in a decimal encoding system will create new genes larger in scope than those in the binary encoding. This paper discusses approaches of exploiting the search potential of genetic operations in the two encoding systems and presents an approach with a hybrid-encoding mechanism, multi-point crossover, and dynamic population size for geophysical inversion. We present a method that is based on the routine in which the mutation operation is conducted in the decimal code and multi-point crossover operation in the binary code. The mix-encoding algorithm is called the hybrid-encoding genetic algorithm (HEGA). HEGA provides better genes with a higher probability by a mutation operator and improves genetic algorithms in resolving complicated geophysical inverse problems. Another significant
Tam, Leo K.; Galiana, Gigi; Stockmann, Jason P.; Constable, R. Todd
2012-01-01
To increase image acquisition efficiency, we develop alternative gradient encoding strategies designed to provide spatial encoding complementary to the spatial encoding provided by the multiple receiver coil elements in parallel image acquisitions. Intuitively, complementary encoding is achieved when the magnetic field encoding gradients are designed to encode spatial information where receiver spatial encoding is ambiguous, for example, along sensitivity isocontours. Specifically, the method generates a basis set for the null space of the coil sensitivities with the singular value decomposition (SVD) and calculates encoding fields from the null space vectors. A set of nonlinear gradients is used as projection imaging readout magnetic fields, replacing the conventional linear readout field and phase encoding. Multiple encoding fields are used as projections to capture the null space information, hence the term Null Space Imaging (NSI). The method is compared to conventional Cartesian SENSitivity Encoding (SENSE) as evaluated by mean squared error and robustness to noise. Strategies for developments in the area of nonlinear encoding schemes are discussed. The NSI approach yields a parallel imaging method that provides high acceleration factors with a limited number of receiver coil array elements through increased time efficiency in spatial encoding. PMID:22190380
Young-Gonzales, Amanda R; Samanta, Subarna; Richert, Ranko
2015-09-14
For glycerol and three monohydroxy alcohols, we have measured the non-linear dielectric effects resulting from the application and removal of a high dc bias electric field. The field effects are detected by virtue of a small amplitude harmonic field, from which time resolved changes in the dielectric loss are derived. The changes in permittivity are dominated by modifications of the time constants (rather than amplitudes) which display two contributions: a heating-like decrease of relaxation times that originates from the time dependent field when the bias is switched on and off and a slowing down of the dynamics resulting from the field induced reduction of configurational entropy. As observed for the electro-optical Kerr effect, the rise of the entropy change is slower than its decay, a feature that we rationalize on the basis of the quadratic dependence of the entropy change on polarization. For glycerol, the observed steady state level of the field induced shift of the glass transition temperature (+84 mK) matches the expectation based on the entropy change and its impact on dynamics via the Adam-Gibbs relation (+88 mK). For the alcohols, these non-linear effects rise and decay on the time scales of the prominent dielectric Debye process, underscoring the relation of these features to polarization anisotropy, opposed to mechanical or enthalpy relaxation which are orders of magnitude faster in these systems. A model is discussed which captures the observed magnitudes as well as time dependences in a near quantitative fashion. It is demonstrated that the high bias field modifies the response of polarization to the ac field, including a temporary change in the low field susceptibility. PMID:26374047
Zapata, Alejandro; Acosta, Ruben E; Mora-Ramos, Miguel E; Duque, Carlos A
2012-01-01
: The exciton binding energy of an asymmetrical GaAs-Ga1-xAlxAs cylindrical quantum dot is studied with the use of the effective mass approximation and a variational calculation procedure. The influence on this quantity of the application of a direct-current electric field along the growth direction of the cylinder, together with that of an intense laser field, is particularly considered. The resulting states are used to calculate the exciton-related nonlinear optical absorption and optical rectification, whose corresponding resonant peaks are reported as functions of the external probes, the quantum dot dimensions, and the aluminum molar fraction in the potential barrier regions. PMID:22971418
Generalized mean-field or master equation for nonlinear cavities with transverse effects
Dunlop, A.M.; Firth, W.J.; Heatley, D.R.; Wright, E.
1996-06-01
We present a general form of master equation for nonlinear-optical cavities that can be described by an {ital ABCD}matrix. It includes as special cases some previous models of spatiotemporal effects in lasers. {copyright} {ital 1996 Optical Society of America.}
NASA Astrophysics Data System (ADS)
LeFloch, Philippe G.; Ma, Yue
2016-01-01
The Hyperboloidal Foliation Method (introduced by the authors in 2014) is extended here and applied to the Einstein equations of general relativity. Specifically, we establish the nonlinear stability of Minkowski spacetime for self-gravitating massive scalar fields, while existing methods only apply to massless scalar fields. First of all, by analyzing the structure of the Einstein equations in wave coordinates, we exhibit a nonlinear wave-Klein-Gordon model defined on a curved background, which is the focus of the present paper. For this model, we prove here the existence of global-in-time solutions to the Cauchy problem, when the initial data have sufficiently small Sobolev norms. A major difficulty comes from the fact that the class of conformal Killing fields of Minkowski space is significantly reduced in the presence of a massive scalar field, since the scaling vector field is not conformal Killing for the Klein-Gordon operator. Our method relies on the foliation (of the interior of the light cone) of Minkowski spacetime by hyperboloidal hypersurfaces and uses Lorentz-invariant energy norms. We introduce a frame of vector fields adapted to the hyperboloidal foliation and we establish several key properties: Sobolev and Hardy-type inequalities on hyperboloids, as well as sup-norm estimates, which correspond to the sharp time decay for the wave and the Klein-Gordon equations. These estimates allow us to control interaction terms associated with the curved geometry and the massive field by distinguishing between two levels of regularity and energy growth and by a successive use of our key estimates in order to close a bootstrap argument.
Detection and analysis of coherent groups in three-dimensional fully-nonlinear potential wave fields
NASA Astrophysics Data System (ADS)
Sanina, E. V.; Suslov, S. A.; Chalikov, D.; Babanin, A. V.
2016-07-01
We investigate the emergence of coherent groups in three-dimensional fully-nonlinear potential deep water waves whose initial spectrum is assumed to be of the JONSWAP type with directional distribution given by cos nθ, where n is the integer varying from 1 to 16. The analysis is based on the results of long-term wave simulations performed using a numerical solution of a three-dimensional Laplace equation for the velocity potential subject to nonlinear kinematic and dynamic boundary conditions at the free surface. The main characteristics of wave groups such as their average velocity, maximum group wave height, lifetime and length are analysed. The statistics of extreme waves occurring in the detected groups are discussed. Spatial and temporal scale characteristics of wave groups are compared to the previous results.
Mapping nonlinear receptive field structure in primate retina at single cone resolution.
Freeman, Jeremy; Field, Greg D; Li, Peter H; Greschner, Martin; Gunning, Deborah E; Mathieson, Keith; Sher, Alexander; Litke, Alan M; Paninski, Liam; Simoncelli, Eero P; Chichilnisky, E J
2015-01-01
The function of a neural circuit is shaped by the computations performed by its interneurons, which in many cases are not easily accessible to experimental investigation. Here, we elucidate the transformation of visual signals flowing from the input to the output of the primate retina, using a combination of large-scale multi-electrode recordings from an identified ganglion cell type, visual stimulation targeted at individual cone photoreceptors, and a hierarchical computational model. The results reveal nonlinear subunits in the circuity of OFF midget ganglion cells, which subserve high-resolution vision. The model explains light responses to a variety of stimuli more accurately than a linear model, including stimuli targeted to cones within and across subunits. The recovered model components are consistent with known anatomical organization of midget bipolar interneurons. These results reveal the spatial structure of linear and nonlinear encoding, at the resolution of single cells and at the scale of complete circuits. PMID:26517879
Singh, A.; Huisman, S. R.; Ctistis, G. Mosk, A. P.; Pinkse, P. W. H.; Korterik, J. P.; Herek, J. L.
2015-01-21
We have measured the photonic bandstructure of GaAs photonic-crystal waveguides with high resolution in energy as well as in momentum using near-field scanning optical microscopy. Intriguingly, we observe additional bands that are not predicted by eigenmode solvers, as was recently demonstrated by Huisman et al. [Phys. Rev. B 86, 155154 (2012)]. We study the presence of these additional bands by performing measurements of these bands while varying the incident light power, revealing a non-linear power dependence. Here, we demonstrate experimentally and theoretically that the observed additional bands are caused by a waveguide-specific near-field tip effect not previously reported, which can significantly phase-modulate the detected field.
NASA Astrophysics Data System (ADS)
Singh, A.; Ctistis, G.; Huisman, S. R.; Korterik, J. P.; Mosk, A. P.; Herek, J. L.; Pinkse, P. W. H.
2015-01-01
We have measured the photonic bandstructure of GaAs photonic-crystal waveguides with high resolution in energy as well as in momentum using near-field scanning optical microscopy. Intriguingly, we observe additional bands that are not predicted by eigenmode solvers, as was recently demonstrated by Huisman et al. [Phys. Rev. B 86, 155154 (2012)]. We study the presence of these additional bands by performing measurements of these bands while varying the incident light power, revealing a non-linear power dependence. Here, we demonstrate experimentally and theoretically that the observed additional bands are caused by a waveguide-specific near-field tip effect not previously reported, which can significantly phase-modulate the detected field.
Relativistic weak lensing from a fully non-linear cosmological density field
NASA Astrophysics Data System (ADS)
Thomas, D. B.; Bruni, M.; Wands, D.
2015-09-01
In this paper we examine cosmological weak lensing on non-linear scales and show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the post-Friedmann formalism, a post-Newtonian type framework for cosmology, to derive the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity. We show that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term. We use this deflection angle to analyse the vector and tensor contributions to the E- and B- mode cosmic shear power spectra. In our approach, once the gravitational theory has been specified, the metric components are related to the matter content in a well-defined manner. Specifying General Relativity, we write down a complete set of equations for a GR+ΛCDM universe for computing all of the possible lensing terms from Newtonian N-body simulations. We illustrate this with the vector potential and show that, in a GR+ΛCDM universe, its contribution to the E-mode is negligible with respect to that of the conventional Newtonian scalar potential, even on non-linear scales. Thus, under the standard assumption that Newtonian N-body simulations give a good approximation of the matter dynamics, we show that the standard ray tracing approach gives a good description for a ΛCDM cosmology.
NASA Technical Reports Server (NTRS)
Liu, Ansheng; Chuang, S.-L.; Ning, C. Z.; Woo, Alex (Technical Monitor)
1999-01-01
Second-order nonlinear optical processes including second-harmonic generation, optical rectification, and difference-frequency generation associated with intersubband transitions in wurtzite GaN/AlGaN quantum well (QW) are investigated theoretically. Taking into account the strain-induced piezoelectric (PZ) effects, we solve the electronic structure of the QW from coupled effective-mass Schrodinger equation and Poisson equation including the exchange-correlation effect under the local-density approximation. We show that the large PZ field in the QW breaks the symmetry of the confinement potential profile and leads to large second-order susceptibilities. We also show that the interband optical pump-induced electron-hole plasma results in an enhancement in the maximum value of the nonlinear coefficients and a redshift of the peak position in the nonlinear optical spectrum. By use of the difference-frequency generation, THz radiation can be generated from a GaN/Al(0.75)Ga(0.25)N with a pump laser of 1.55 micron.
Watts, C.A.
1993-09-01
In this dissertation the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas is investigated. To properly assess this possibility, data from both numerical simulations and experiment are analyzed. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos in the data. These tools include phase portraits and Poincare sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low dimensional chaos and simple determinism. Experimental date were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or low simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.
NASA Astrophysics Data System (ADS)
Zhou, Hao-Miao; Li, Meng-Han; Li, Xiao-Hong; Zhang, Da-Guang
2016-08-01
For a giant magnetostrictive rod under the action of multiple physical loads, such as an external magnetic field, temperature and axial pre-stress, this paper proposes a general one-dimensional nonlinear magneto-thermo-mechanical coupled constitutive model. This model is based on the Taylor expansion of the elastic Gibbs free energy of giant magnetostrictive material and thermodynamic relations from the perspective of macro continuum mechanics. Predictions made using this model are in good agreement with experimental data for magnetization and the magnetostrictive strain curve under the collective effect of pre-stress and temperature. Additionally, the model overcomes the drawback of the existing magneto-thermo-mechanical constitutive model that cannot accurately predict the magnetization and magnetostrictive strain curve for different temperatures and pre-stresses. Furthermore, the constitutive model does not contain an implicit function and is compact, and can thus be applied in both situations of tensile and compressive stress and to both positive and negative magnetostrictive materials, and it is thus appropriate for engineering applications. Comprehensive analysis shows that the model fully describes the nonlinear coupling properties of a magnetic field, magnetostrictive strain and elasticity of a magnetostrictive material subjected to stress, a magnetic field and heat.
NASA Astrophysics Data System (ADS)
Kozelov, B. V.; Golovchanskaya, I. V.; Mingalev, O. V.
2011-08-01
We investigate time evolution of scaling index αA that characterizes auroral luminosity fluctuations at the beginning of substorm expansion. With the use of UVI images from the Polar satellite, it is shown that αA typically varies from values less than unity to ~1.5, increasing with breakup progress. Similar scaling features were previously reported for fluctuations at smaller scales from all-sky TV observations. If this signature is interpreted in terms of non-linear interactions between scales, it means that the power of small-scale fluctuations is transferred with time to larger scales, a kind of the inverse cascade. Scaling behavior in the aurora during substorm activity is compared with that in the field-aligned currents simulated numerically in the model of non-linear interactions of Alfvénic coherent structures, according to the Chang et al. (2004) scenario. This scenario also suggests an inverse cascade, manifesting in clustering of small-scale field-aligned current filaments of the same polarity and formation of "coarse-grained" structures of field-aligned currents.
Mehdian, H.; Mohammadzahery, Z.; Hasanbeigi, A.
2014-01-15
In this work, we study the defect mode and bistability behavior of 1-D photonic band gap structure with magnetized plasma and coupled nonlinear defects. The transfer matrix method has been employed to investigate the magnetic field effect on defect mode frequency and bistability threshold. The obtained results show that the frequency of defect mode and bistability threshold can be altered, without changing the structure of the photonic multilayer. Therefore, the bistability behavior of the subjected structure in the presence of magnetized plasma can be utilized in manufacturing wide frequency range devices.
A filament supported by different magnetic field configurations
NASA Astrophysics Data System (ADS)
Guo, Y.; Schmieder, B.; Démoulin, P.; Wiegelmann, T.; Aulanier, G.; Török, T.; Bommier, V.
2011-08-01
A nonlinear force-free magnetic field extrapolation of vector magnetogram data obtained by THEMIS/MTR on 2005 May 27 suggests the simultaneous existence of different magnetic configurations within one active region filament: one part of the filament is supported by field line dips within a flux rope, while the other part is located in dips within an arcade structure. Although the axial field chirality (dextral) and the magnetic helicity (negative) are the same along the whole filament, the chiralities of the filament barbs at different sections are opposite, i.e., right-bearing in the flux rope part and left-bearing in the arcade part. This argues against past suggestions that different barb chiralities imply different signs of helicity of the underlying magnetic field. This new finding about the chirality of filaments will be useful to associate eruptive filaments and magnetic cloud using the helicity parameter in the Space Weather Science.
NASA Astrophysics Data System (ADS)
Yesilgul, U.; Al, E. B.; Martínez-Orozco, J. C.; Restrepo, R. L.; Mora-Ramos, M. E.; Duque, C. A.; Ungan, F.; Kasapoglu, E.
2016-08-01
In the present study, the effects of electric and magnetic fields on the linear and third-order nonlinear optical absorption coefficients and relative change of the refractive index in asymmetric GaAs/GaAlAs double quantum wells under intense laser fields are theoretically investigated. The electric field is oriented along the growth direction of the heterostructure while the magnetic field is taken in-plane. The intense laser field is linear polarization along the growth direction. Our calculations are made using the effective-mass approximation and the compact density-matrix approach. Intense laser effects on the system are investigated with the use of the Floquet method with the consequent change in the confinement potential of heterostructures. Our results show that the increase of the electric and magnetic fields blue-shifts the peak positions of the total absorption coefficient and of the total refractive index while the increase of the intense laser field firstly blue-shifts the peak positions and later results in their red-shifting.
Okuzumi, Satoshi; Inutsuka, Shu-ichiro
2015-02-10
The ionization state of the gas plays a key role in the magnetohydrodynamics (MHD) of protoplanetary disks. However, the ionization state can depend on the gas dynamics, because electric fields induced by MHD turbulence can heat up plasmas and thereby affect the ionization balance. To study this nonlinear feedback, we construct an ionization model that includes plasma heating by electric fields and impact ionization by heated electrons, as well as charging of dust grains. We show that when plasma sticking onto grains is the dominant recombination process, the electron abundance in the gas decreases with increasing electric field strength. This is a natural consequence of electron-grain collisions whose frequency increases with the electron's random velocity. The decreasing electron abundance may lead to a self-regulation of MHD turbulence. In some cases, not only the electron abundance but also the electric current decreases with increasing field strength in a certain field range. The resulting N-shaped current-field relation violates the fundamental assumption of the non-relativistic MHD that the electric field is uniquely determined by the current density. At even higher field strengths, impact ionization causes an abrupt increase of the electric current as expected by previous studies. We find that this discharge current is multi-valued (i.e., the current-field relation is S-shaped) under some circumstances, and that the intermediate branch is unstable. The N/S-shaped current-field relations may yield hysteresis in the evolution of MHD turbulence in some parts of protoplanetary disks.
NASA Astrophysics Data System (ADS)
Okuzumi, Satoshi; Inutsuka, Shu-ichiro
2015-02-01
The ionization state of the gas plays a key role in the magnetohydrodynamics (MHD) of protoplanetary disks. However, the ionization state can depend on the gas dynamics, because electric fields induced by MHD turbulence can heat up plasmas and thereby affect the ionization balance. To study this nonlinear feedback, we construct an ionization model that includes plasma heating by electric fields and impact ionization by heated electrons, as well as charging of dust grains. We show that when plasma sticking onto grains is the dominant recombination process, the electron abundance in the gas decreases with increasing electric field strength. This is a natural consequence of electron-grain collisions whose frequency increases with the electron's random velocity. The decreasing electron abundance may lead to a self-regulation of MHD turbulence. In some cases, not only the electron abundance but also the electric current decreases with increasing field strength in a certain field range. The resulting N-shaped current-field relation violates the fundamental assumption of the non-relativistic MHD that the electric field is uniquely determined by the current density. At even higher field strengths, impact ionization causes an abrupt increase of the electric current as expected by previous studies. We find that this discharge current is multi-valued (i.e., the current-field relation is S-shaped) under some circumstances, and that the intermediate branch is unstable. The N/S-shaped current-field relations may yield hysteresis in the evolution of MHD turbulence in some parts of protoplanetary disks.
NASA Astrophysics Data System (ADS)
Choudhury, Raja Roy; Choudhury, Arundhati Roy; Ghose, Mrinal Kanti
2013-09-01
To characterize nonlinear optical fiber, a semi-analytical formulation using variational principle and the Nelder-Mead Simplex method for nonlinear unconstrained minimization is proposed. The number of optimizing parameters in order to optimize core parameter U has been increased to incorporate more flexibility in the formulation of an innovative form of fundamental modal field. This formulation provides accurate analytical expressions for modal dispersion parameter (g) of optical fiber with Kerr nonlinearity. The minimization of core parameter (U), which involves Kerr nonlinearity through the nonstationary expression of propagation constant, is carried out by the Nelder-Mead Simplex method of nonlinear unconstrained minimization, suitable for problems with nonsmooth functions as the method does not require any derivative information. This formulation has less computational burden for calculation of modal parameters than full numerical methods.
Sabaeian, Mohammad Shahzadeh, Mohammadreza; Farbod, Mansoor
2014-12-15
In this work, the effects of vertical electric field on the electronic and optical properties of strained semi-spheroid-shaped InAs/GaAs quantum dot (QD) coupled to its wetting layer (WL) aimed to enhance the nonlinear optical properties were investigated. The dependence of energy eigenvalues of S- and P- states and intersubband P-to-S transition energy on applied electric field was studied. A ∼∓10 meV Stark shift in the intersubband P-to-S transition energy was calculated for a semi-spheroid-shaped QD with height of 5 nm and base-length of 20 nm when bias voltage was varied from 0 V to ±0.8V. The dependence of transition dipole moment and linear and nonlinear optical properties of the system on bias voltage was also studied. It was concluded that increasing the bias voltage from -0.8V to +0.8V leads to increase in figure of merit of the system from ∼0.153 to ∼0.198.
Mapping nonlinear receptive field structure in primate retina at single cone resolution
Li, Peter H; Greschner, Martin; Gunning, Deborah E; Mathieson, Keith; Sher, Alexander; Litke, Alan M; Paninski, Liam
2015-01-01
The function of a neural circuit is shaped by the computations performed by its interneurons, which in many cases are not easily accessible to experimental investigation. Here, we elucidate the transformation of visual signals flowing from the input to the output of the primate retina, using a combination of large-scale multi-electrode recordings from an identified ganglion cell type, visual stimulation targeted at individual cone photoreceptors, and a hierarchical computational model. The results reveal nonlinear subunits in the circuity of OFF midget ganglion cells, which subserve high-resolution vision. The model explains light responses to a variety of stimuli more accurately than a linear model, including stimuli targeted to cones within and across subunits. The recovered model components are consistent with known anatomical organization of midget bipolar interneurons. These results reveal the spatial structure of linear and nonlinear encoding, at the resolution of single cells and at the scale of complete circuits. DOI: http://dx.doi.org/10.7554/eLife.05241.001 PMID:26517879
Nonlinear time series analysis of the fluctuations of the geomagnetic horizontal field
NASA Astrophysics Data System (ADS)
George, B.; Renuka, G.; Satheesh Kumar, K.; Kumar, C. P. Anil; Venugopal, C.
2002-02-01
A detailed nonlinear time series analysis of the hourly data of the geomagnetic horizontal intensity H measured at Kodaikanal (10.2° N; 77.5° E; mag: dip 3.5° N) has been carried out to investigate the dynamical behaviour of the fluctuations of H. The recurrence plots, spatiotemporal entropy and the result of the surrogate data test show the deterministic nature of the fluctuations, rejecting the hypothesis that H belong to the family of linear stochastic signals. The low dimensional character of the dynamics is evident from the estimated value of the correlation dimension and the fraction of false neighbours calculated for various embedding dimensions. The exponential decay of the power spectrum and the positive Lyapunov exponent indicate chaotic behaviour of the underlying dynamics of H. This is also supported by the results of the comparison of the chaotic characteristics of the time series of H with the pseudo-chaotic characteristics of coloured noise time series. We have also shown that the error involved in the short-term prediction of successive values of H, using a simple but robust, zero-order nonlinear prediction method, increases exponentially. It has also been suggested that there exists the possibility of characterizing the geomagnetic fluctuations in terms of the invariants in chaos theory, such as Lyapunov exponents and correlation dimension. The results of the analysis could also have implications in the development of a suitable model for the daily fluctuations of geomagnetic horizontal intensity.
NASA Astrophysics Data System (ADS)
Lu, Lin; Chang, Yunlong; Li, Yingmin; He, Youyou
2013-05-01
A transverse magnetic field was introduced to the arc plasma in the process of welding stainless steel tubes by high-speed Tungsten Inert Gas Arc Welding (TIG for short) without filler wire. The influence of external magnetic field on welding quality was investigated. 9 sets of parameters were designed by the means of orthogonal experiment. The welding joint tensile strength and form factor of weld were regarded as the main standards of welding quality. A binary quadratic nonlinear regression equation was established with the conditions of magnetic induction and flow rate of Ar gas. The residual standard deviation was calculated to adjust the accuracy of regression model. The results showed that, the regression model was correct and effective in calculating the tensile strength and aspect ratio of weld. Two 3D regression models were designed respectively, and then the impact law of magnetic induction on welding quality was researched.
NASA Astrophysics Data System (ADS)
Gao, L.; Igumenshchev, I. V.; Hu, S. X.; Stoeckl, C.; Froula, D. H.; Nilson, P. M.; Davies, J. R.; Betti, R.; Meyerhofer, D. D.; Haines, M. G.
2012-10-01
Magnetic field generation during the nonlinear phase of the Rayleigh--Taylor (RT) instability in an ablatively driven plasma using ultrafast laser-driven proton radiography has been measured. Thin plastic foils were irradiated with ˜4-kJ, 2.5-ns laser pulses focused to an intensity of ˜10^14 W/cm^2 on the OMEGA EP Laser System. Target modulations were seeded by laser nonuniformities and amplified during target acceleration by the RT instability. The experimental data show the hydrodynamic evolution of the target and MG-level magnetic fields generated in the broken foil. The experimental data are in good agreement with predictions from 2-D magnetohydrodynamic simulations. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-08NA28302.
Computation of linear and nonlinear site response for near field ground motion
NASA Astrophysics Data System (ADS)
Bonilla, Luis Fabian
The near-surface geological site conditions in the upper tens of meters are one of the dominant factors in controlling the amplitude and variation of strong ground motion during large earthquakes. The understanding of these site effects comes primarily from surface recordings. For instance, different methods to estimate site response and their variability are studied using aftershock data for the 17 January 1994 M6.7 Northridge, California earthquake. A second approach corresponds to borehole measurements. We use the Garner Valley Downhole Array (GVDA), which consists of a set of seven downhole strong-motion instruments ranging from 0 to 500 meters depth, to study site response effects. The GVDA velocity structure is first studied, then the H/ V is evaluated, and finally some considerations of 2D and 3D basin effects are also shown. These previous studies considered small to moderate earthquakes, where strain levels are small enough, so that linear wave propagation is assumed. However, for strong motions produced during large earthquakes, the soils behave nonlinearly. In this study we present evidence that nonlinearity can be directly observed in acceleration time histories such as Wildlife Refuge, 1987 Superstition Hills, CA; Kushiro Port station, 1993 Kushiro-Oki, Japan; among others. To understand the nature of nonlinear soil dynamics, we developed a model that includes anelastic dissipation of energy due to hysteresis. The hysteresis is described by the generalized Masing rules. This new hysteresis formulation, based on the classical Masing rules, has a functional representation, and depends only on one parameter that can be related to damping ratio tests. The coupling with pore pressure generation shows the degradation of the shear modulus and the yield stress during the cyclic response of the material. The simulations show amplitude reduction as well as the shift of the fundamental frequency to lower frequencies as observed on vertical arrays. The synthetic
Steady-state axisymmetric nonlinear magnetohydrodynamic solutions with various boundary conditions
NASA Astrophysics Data System (ADS)
Wang, Lile; Lou, Yu-Qing
2014-04-01
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main-sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars, magnetars, isolated neutron stars, etc.] and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method and finite-element method schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso, finding that their separable semi-analytic non-linear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. Similar situations of multiple non-linear solutions with the same boundary conditions actually also happen to force-free magnetic field models of Low & Lou. The multiplicity of non-linear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as well as in the asymptotic behaviours approaching infinity, which may in turn explain why numerical solvers tend to converge to a non-linear solution with a lower energy than the corresponding separable semi-analytic one. By properly adjusting model parameters, we invoke semi-analytic and numerical solutions to describe different kinds of scenarios, including nearly parallel case and the situation in which the misalignment between the plasma flow and magnetic field is considerable. We propose that these MHD models are capable of describing the magnetospheres of MWDs as examples of applications with moderate conditions (including magnetic field) where the typical values of several important parameters are consistent with observations. Physical parameters can also be estimated based on such MHD models directly. We discuss the challenges
Ultrafast Rotation of Light Fields Applied to Highly Non-Linear Optics
NASA Astrophysics Data System (ADS)
Quéré, Fabien
2014-05-01
Femtosecond laser beams can exhibit spatio-temporal couplings (STC), i.e. a temporal dependence of their spatial properties, or vice versa. Although these couplings have long been considered as detrimental for high-intensity and ultrafast experiments, moderate and controlled STC provide a powerful means of controlling high-intensity laser-matter interactions. This talk will first explain the basics of a particular STC, where the propagation direction of laser light rotates in time on the femtosecond time scale. Laser pulses with such ultrafast wavefront rotation can be used to generate attosecond pulses of light through non-linear optical processes. We show that these pulses, periodically generated in each laser cycle, can then be emitted in spatially separated beamlets. This effects provides a new type of light sources called attosecond lighthouses, and can be exploited for ultrafast measurements with femtosecond resolution, in a scheme called photonic streaking.
NASA Astrophysics Data System (ADS)
Dähmlow, Patricia; Müller, Stefan C.
2015-04-01
Labyrinth-like Turing patterns are investigated under the influence of an electric field. The patterns form in the ferroin-catalyzed Belousov-Zhabotinsky reaction embedded in the sodium-bis (2-ethylhexyl) sulfosuccinate (AOT) water-in-oil microemulsion. For two different values of the droplet fraction above and below the percolation transition of the system, the electric field induced drift of the patterns is different. Above the percolation transition, a linear increase of the drift velocity with increasing electric field strength is found. However, below the percolation transition, this increase shows an exponential behavior. The patterns are also observed to reorient under high electrical field strength, such that they are arranged perpendicular with respect to the field lines.
Dähmlow, Patricia; Müller, Stefan C
2015-04-01
Labyrinth-like Turing patterns are investigated under the influence of an electric field. The patterns form in the ferroin-catalyzed Belousov-Zhabotinsky reaction embedded in the sodium-bis (2-ethylhexyl) sulfosuccinate (AOT) water-in-oil microemulsion. For two different values of the droplet fraction above and below the percolation transition of the system, the electric field induced drift of the patterns is different. Above the percolation transition, a linear increase of the drift velocity with increasing electric field strength is found. However, below the percolation transition, this increase shows an exponential behavior. The patterns are also observed to reorient under high electrical field strength, such that they are arranged perpendicular with respect to the field lines. PMID:25933665
NASA Astrophysics Data System (ADS)
Morais, C. V.; Zimmer, F. M.; Lazo, M. J.; Magalhães, S. G.; Nobre, F. D.
2016-06-01
The behavior of the nonlinear susceptibility χ3 and its relation to the spin-glass transition temperature Tf in the presence of random fields are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue λAT (replicon) on the random fields is analyzed. Particularly, in the absence of random fields, the temperature Tf can be traced by a divergence in the spin-glass susceptibility χSG, which presents a term inversely proportional to the replicon λAT. As a result of a relation between χSG and χ3, the latter also presents a divergence at Tf, which comes as a direct consequence of λAT=0 at Tf. However, our results show that, in the presence of random fields, χ3 presents a rounded maximum at a temperature T* which does not coincide with the spin-glass transition temperature Tf (i.e., T*>Tf for a given applied random field). Thus, the maximum value of χ3 at T* reflects the effects of the random fields in the paramagnetic phase instead of the nontrivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that χ3 still maintains a dependence on the replicon λAT, although in a more complicated way as compared with the case without random fields. These results are discussed in view of recent observations in the LiHoxY1 -xF4 compound.
Calculated non-linear magnetic field penetration of plasma opening switches
Mason, R.J.; Jones, M.E.; Wilson, D.C.; Bergman, C.; Thiem, K. ); Grossmann, J.M.; Ottinger, P.F. )
1990-06-15
We examine magnetic field penetration in the Plasma Opening Switch, exploring, in particular, advective field penetration arising in conjunction with radial density gradients across the cathode anode gap. Our calculations have been completed with the implicit multi-fluid, ANTHEM code. We show favored penetration along a radial density jump, unstable plain wave penetration for a 1/(y {minus} y{sub {alpha}+{epsilon}}) density dependence (with y measured from cathode to anode at Y{sub {alpha}}) in planar switches, and the penetration of finger-like magnetic field perturbations, when the fill plasmas bears initial sinusoidal disturbances on its generator interface. 7 refs., 4 figs.
NASA Astrophysics Data System (ADS)
Rudenko, O. V.; Hedberg, C. M.
2015-01-01
The stationary profile in the focal region of a focused nonlinear acoustic wave is described. Three models following from the Khokhlov-Zabolotskaya (KZ) equation with three independent variables are used: (i) the simplified one-dimensional Ostrovsky-Vakhnenko equation, (ii) the system of equations for paraxial series expansion of the acoustic field in powers of transverse coordinates, and (iii) the KZ equation reduced to two independent variables. The structure of the last equation is analogous to the Westervelt equation. Linearization through the Legendre transformation and reduction to the well-studied Euler-Tricomi equation is shown. At high intensities the stationary profiles are periodic sequences of arc sections having singularities of derivative in their matching points. The occurrence of arc profiles was pointed out by Makov. These appear in different nonlinear systems with low-frequency dispersion. Profiles containing discontinuities (shock fronts) change their form while passing through the focal region and are non-stationary waves. The numerical estimations of maximum pressure and intensity in the focus agree with computer calculations and experimental measurements.
NASA Astrophysics Data System (ADS)
Gao, Lan
2014-10-01
The Rayleigh-Taylor (RT) instability has been extensively studied because of its relevance to ignition target designs in inertial confinement fusion, material strength studies in high energy density physics, and astrophysical systems. This talk presents the first measurements of magnetic field generation by the nonlinear RT instability in laser-accelerated planar foils using ultrafast proton radiography at the OMEGA EP Laser System. Thin plastic foils were irradiated with 4-kJ, 2.5-ns laser pulses at focused laser intensities of ~1014 W /cm2. Target modulations were seeded by laser nonuniformities and amplified during the target-acceleration phase by the RT instability growth. A high-energy proton beam tracked the hydrodynamic evolution of the target and mapped the magnetic field spatial distribution with high spatial and temporal resolution. The experimental data show self-similar behavior in the growing cellular magnetic field structures. The calculated magnetic cell-merging rate is consistent with the value determined by earlier x-ray measurements, linking the cellular magnetic field structures with the RT bubble and spike growth. The results are consistent with two-dimensional magnetohydrodynamic simulations, showing MG-level magnetic field generation in the laser-driven foil. The work could benefit the understanding of magnetic-seed-field generation in high energy density plasmas and the flow-driven processes that induce global magnetic structures prior to their turbulent amplification by the dynamo process. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.
NASA Astrophysics Data System (ADS)
Baghshahi, H. R.; Tavassoly, M. K.
2015-03-01
In this paper, we present a model which exhibits two identical Ξ-type three-level atoms interacting with a single-mode field with k-photon transition in an optical cavity enclosed by a Kerr medium. Considering full nonlinear formalism, it is assumed that the single-mode field, atom-field coupling and Kerr medium are all f-deformed. By using the adiabatic elimination method, it is shown that, the Hamiltonian of the considered system can be reduced to an effective Hamiltonian with two two-level atoms and f-deformed Stark shift. In spite of the fact that, the system seems to be complicated, under initial conditions which may be prepared for the atoms (coherent superposition of their ground and upper states) and the field (coherent state), the explicit form of the state vector of the entire system is analytically obtained. Then, the entanglement dynamics between different subsystems ( i.e. "field-two atoms", "atom-(field+atom)" and "atom-atom") are evaluated through appropriate measures like von Neumann entropy, tangle and concurrence. In addition, the effects of intensity-dependent coupling, deformed Kerr medium, detuning parameter, deformed Stark shift and multi-photon process on the considered entanglement measures are numerically analyzed, in detail. It is shown that the degree of entanglement between subsystems can be controlled by selecting the evolved parameters, suitably. Briefly, the Kerr medium highly decreases the amount of different considered measures of entanglement, especially for two-photon transition. This destructive effect preserves even when all other parameters are present, too. Furthermore, we find that the so-called entanglement sudden death and birth can occur in the atom-atom entanglement.
Seidler, T.; Stadnicka, K.; Champagne, B.
2015-03-30
This contribution summarizes our current findings in the field of calculating and predicting the linear and second-order nonlinear electric susceptibility tensor components of organic crystals. The methodology used for this purpose is based on a combination of the electrostatic interaction scheme developed by Munn and his coworkers (RLFT) with high-level electronic structure calculations. We compare the results of calculations with available experimental data for several examples of molecular crystals. We show the quality of the final results is influenced by i) the chromophore geometry, ii) the method used for molecular properties calculations and iii) the partitioning scheme used. In conclusion we summarize further plans to improve the reliability and predictability of the method.
NASA Astrophysics Data System (ADS)
Khan, Najeeb Alam; Riaz, Fatima; Sultan, Faqiha
2014-01-01
The boundary layer flow of an electrically conducting couple stress fluid over a non-linear stretching sheet is investigated in the presence of chemical reaction and magnetic field. The governing partial differential equations are reduced to coupled ordinary differential equations (ODEs) with the corresponding appropriate boundary conditions. The analytical solutions of the resulting ODEs have been obtained via the homotopy analysis method (HAM) in the form of series, and their convergence regions can also be found by the convergence control auxiliary parameter. The influence of pertinent parameters such as the magnetic, the couple stress and the chemical reaction parameters are discussed on the velocity and concentration profiles of the fluid. Hence, a comparison has been made with the previous results in the literature as a limiting case of the considered problem.
Noe, G. Timothy; Lee, Joseph; Woods, Gary L.; Nojiri, Hiroyuki; Léotin, Jean; Kono, Junichiro
2013-12-15
We have developed a mini-coil pulsed magnet system with direct optical access, ideally suited for nonlinear and ultrafast spectroscopy studies of materials in high magnetic fields up to 30 T. The apparatus consists of a small coil in a liquid nitrogen cryostat coupled with a helium flow cryostat to provide sample temperatures down to below 10 K. Direct optical access to the sample is achieved with the use of easily interchangeable windows separated by a short distance of ∼135 mm on either side of the coupled cryostats with numerical apertures of 0.20 and 0.03 for measurements employing the Faraday geometry. As a demonstration, we performed time-resolved and time-integrated photoluminescence measurements as well as transmission measurements on InGaAs quantum wells.
Speck, Thomas; Menzel, Andreas M.; Bialké, Julian; Löwen, Hartmut
2015-06-14
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.
Noe, G Timothy; Nojiri, Hiroyuki; Lee, Joseph; Woods, Gary L; Léotin, Jean; Kono, Junichiro
2013-12-01
We have developed a mini-coil pulsed magnet system with direct optical access, ideally suited for nonlinear and ultrafast spectroscopy studies of materials in high magnetic fields up to 30 T. The apparatus consists of a small coil in a liquid nitrogen cryostat coupled with a helium flow cryostat to provide sample temperatures down to below 10 K. Direct optical access to the sample is achieved with the use of easily interchangeable windows separated by a short distance of ~135 mm on either side of the coupled cryostats with numerical apertures of 0.20 and 0.03 for measurements employing the Faraday geometry. As a demonstration, we performed time-resolved and time-integrated photoluminescence measurements as well as transmission measurements on InGaAs quantum wells. PMID:24387445
Castro, G; Mascali, D; Agnello, R; Celona, L; Leonardi, O; Neri, L; Nicolosi, D; Torrisi, G; Gammino, S
2016-02-01
A characterization of wave-to-plasma interaction in a quasi-flat magnetostatic field at 3.75 GHz has been carried out by using a small-wire movable RF antenna, connected to a spectrum analyzer. The coupling between electromagnetic and electrostatic waves leads to a characteristic spectral emission in low frequency range and around the pumping wave frequency. The most relevant results consist in the broadening of the pumping wave spectrum above critical RF power thresholds and in the generation of sidebands of the pumping frequency, with corresponding components in low frequency domain. The non-linearities are accompanied by the generation of overdense plasmas and intense fluxes of X-rays. PMID:26931915
Versluis, M J; Sutton, B P; de Bruin, P W; Börnert, P; Webb, A G; van Osch, M J
2012-12-01
Spatio-temporal magnetic field changes in the brain caused by breathing or body movements can lead to image artifacts. This is especially a problem in T(2)(*)-weighted sequences. With the acquisition of an extra echo (navigator), it is possible to measure the magnetic field change induced frequency offset for a given slice during image acquisition. However, substantial local variation across a slice can occur. This work describes an extension of the conventional navigator technique that improves the estimation of the magnetic field distribution in the brain during strong field fluctuations. This is done using the combination of signals from multiple coil elements, the coil sensitivity profiles, and frequency encoding: termed sensitivity-encoded navigator echoes. In vivo validation was performed in subjects who performed normal breathing, nose touching, and deep breathing during scanning. The sensitivity-encoded navigator technique leads to an error reduction in estimating the field distribution in the brain of 73% ± 16% compared with 56% ± 14% for conventional estimation. Image quality can be improved via incorporating this navigator information appropriately into the image reconstruction. When the sensitivity-encoded navigator technique was applied to a T(2)(*)-weighted sequence at 7 T, a ghosting reduction of 47% ± 13% was measured during nose touching experiments compared with no correction. PMID:22362637
Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field at focus
Hartemann, F.V.; Fochs, S.N.; Le Sage, G.P.; Luhmann, N.C. Jr.; Woodworth, J.G.; Perry, M.D.; Chen, Y.J.; Kerman, A.K.
1995-05-01
The relativistic dynamics of electrons subjected to the electromagnetic field of an intense, ultrashort laser pulse in vacuum is studied theoretically. The effects of both finite pulse duration and beam focusing are taken into account. It is found that when the quiver amplitude of the electrons driven by the laser field exceeds the focal spot radius of a Gaussian beam, the restoring force acting on the charge decays exponentially, and the electrons are scattered away from the focus. This physical process, known as ponderomotive scattering, effectively terminates the interaction within a laser wavelength, and the electrons can escape with very high energy, as the normalized laser field is of the order of or greater than unity. The relation between the scattering angle and the escape energy is derived analytically from the conservation of canonical momentum and energy in the photon field. For a linearly polarized laser field, the interaction produces two jets of high energy electrons. The theory is supplemented by detailed two-dimensional computer simulations.
Photorefractive nonlinearities caused by the Dember space-charge field in undoped CdTe
NASA Astrophysics Data System (ADS)
Schroeder, W. Andreas; Stark, Thomas S.; Boggess, Thomas F.; Smirl, Arthur L.; Valley, George C.
1991-06-01
The decay of a photorefractive grating in undoped CdTe produced by subband-gap picosecond excitation has been isolated and temporally resolved. The grating is observed to decay completely at the same rate as the free-carrier grating, a rate consistent with the decay of a 1.7 micron-period grating by ambipolar diffusion. This provides convincing evidence that the source of the photorefractive grating is the Dember space-charge field that is established between electron-hole pairs created by band-to-band two-photon absorption. This establishes the Dember field as a source for the photorefractive space-charge field that can be turned on in the dielectric relaxation time and turned off in the ambipolar diffusion time. It also allows the material to recover fully in the recombination lifetime which can be adjusted by doping or damaging the material.
Detection of radio-frequency magnetic fields using nonlinear magneto-optical rotation
Ledbetter, M. P.; Acosta, V. M.; Rochester, S. M.; Budker, D.; Pustelny, S.; Yashchuk, V. V.
2007-02-15
We describe a room-temperature alkali-metal atomic magnetometer for detection of small, high-frequency magnetic fields. The magnetometer operates by detecting optical rotation due to the precession of an aligned ground state in the presence of a small oscillating magnetic field. The resonance frequency of the magnetometer can be adjusted to any desired value by tuning the bias magnetic field. Based on experimentally measured signal-to-noise ratio, we demonstrate a sensitivity of 100 pG/{radical}(Hz) (rms) in a 3.5-cm-diameter paraffin coated cell. Assuming detection at the photon shot-noise limit, we project a sensitivity as low as 25 pG/{radical}(Hz) (rms)
Bubble shape and electromagnetic field in the nonlinear regime for laser wakefield acceleration
Li, X. F.; Yu, Q.; Huang, S.; Kong, Q.; Gu, Y. J.; Kawata, S.
2015-08-15
The electromagnetic field in the electron “bubble” regime for ultra-intense laser wakefield acceleration was solved using the d'Alembert equations. Ignoring the residual electrons, we assume an ellipsoidal bubble forms under ideal conditions, with bubble velocity equal to the speed of light in vacuum. The general solution for bubble shape and electromagnetic field were obtained. The results were confirmed in 2.5D PIC (particle-in-cell) simulations. Moreover, slopes for the longitudinal electric field of larger than 0.5 were found in these simulations. With spherical bubbles, this slope is always smaller than or equal to 0.5. This behavior validates the ellipsoid assumption.
Non-linear non-local molecular electrodynamics with nano-optical fields.
Chernyak, Vladimir Y; Saurabh, Prasoon; Mukamel, Shaul
2015-10-28
The interaction of optical fields sculpted on the nano-scale with matter may not be described by the dipole approximation since the fields may vary appreciably across the molecular length scale. Rather than incrementally adding higher multipoles, it is advantageous and more physically transparent to describe the optical process using non-local response functions that intrinsically include all multipoles. We present a semi-classical approach for calculating non-local response functions based on the minimal coupling Hamiltonian. The first, second, and third order response functions are expressed in terms of correlation functions of the charge and the current densities. This approach is based on the gauge invariant current rather than the polarization, and on the vector potential rather than the electric and magnetic fields. PMID:26520498
NASA Astrophysics Data System (ADS)
Hu, Q.; Qiu, J.; Krucker, S.; Wang, L.; Wang, B.; Chen, Y.; Moestl, C.
2014-12-01
We report on the detailed and systematic study of field-line twist and length distributions within magnetic flux ropes embedded in Interplanetary Coronal Mass Ejections (ICMEs). In particular we will utilize energetic electron burst observations at 1 AU together with associated type III radio emissions detected by the Wind spacecraft to provide unique measurements of magnetic field-line lengths within selected ICME events. These direct measurements will be compared with flux-rope model calculations to help assess the fidelity of different models and to provide diagnostics of internal structures. The Grad-Shafranov reconstruction method will be utilized together with a constant-twist nonlinear force-free (Gold-Hoyle) flux rope model and the commonly known Lundquist (linear force-free) model to reveal the close relation between the field-line twist and length in cylindrical flux ropes, based on in-situ Wind spacecraft magnetic field and plasma measurements. We show that our initial analysis of field-line twist indicates clear deviation from the Lundquist model, but better consistency with the Gold-Hoyle model. We will also discuss the implications of our analysis of flux-rope structures on the origination and evolution processes in their corresponding solar source regions.
Nonlinear inversion for wave fields monitoring data in hierarchic heterogeneous media
NASA Astrophysics Data System (ADS)
Hachay, Olga; Khachay, Andrey; Khachay, Oleg
2016-04-01
Geological medium is an open system which is influenced by outer and inner factors that can lead it to a unstable state. That non stability is as a rule occurred locally and these zones are named as dynamically active elements, which are indicators of potential catastrophic sources. These objects differ from the embedded geological medium by their structural forms, which often are of hierarchical type. The process of their activisation can be searched, using wave fields monitoring. For that purpose it is needed to develop new algorithms of modeling wave fields propagation through the local objects with hierarchical structure. Also it is needed to develop new theory of interpretation the distribution of wave fields for defining the contours of these local hierarchical objects. It had been constructed an algorithm for 3D modeling electromagnetic field for arbitrary type of source of excitation in N-layered medium with a hierarchic conductive intrusion, located in the layer number J. It had been constructed algorithms for 2D modeling of sound diffraction and linear polarized transversal seismic wave on an intrusion of hierarchic structure, located in the layer number J of N-layered elastic medium. We used the method of integral and integral-differential equations for a space frequency presentation of wave fields distribution. It is developed an algorithm for constructing the equation of theoretical inverse problem for 2-D electromagnetic field of E and H polarization and linear polarized longitudinal elastic wave by excitation of the N-layered conductive or elastic medium with hierarchic conductive or elastic inclusion located in the ν -th layer. From the theory it is obviously that for such complicated medium each wave field contains its own information about the inner structure of the hierarchical inclusion. Therefore it is needed to interpret the monitoring data for each wave field apart, and not mixes the data base. These results will be the base for constructing
Non-linear magnetic behavior around zero field of an assembly of superparamagnetic nanoparticles.
de Montferrand, Caroline; Lalatonne, Yoann; Bonnin, Dominique; Motte, Laurence; Monod, Philippe
2012-05-21
The MIAplex® device is a miniaturized detector, devoted to the high sensitive detection of superparamagnetic nanoprobes for multiparametric immunoassays. It measures a signal corresponding to the second derivative of the magnetization around zero field. Like any new technology, the real success of the MIAplex® detector can only be exploited through a deep understanding of the magnetic signature. In this letter, we study the magnetic behavior around zero-field of diluted lab-made and commercial ferrofluids by comparing together conventional SQUID magnetization and MIAplex® signature. PMID:22441242
Unsteady three-dimensional thermal field prediction in turbine blades using nonlinear BEM
NASA Technical Reports Server (NTRS)
Martin, Thomas J.; Dulikravich, George S.
1993-01-01
A time-and-space accurate and computationally efficient fully three dimensional unsteady temperature field analysis computer code has been developed for truly arbitrary configurations. It uses boundary element method (BEM) formulation based on an unsteady Green's function approach, multi-point Gaussian quadrature spatial integration on each panel, and a highly clustered time-step integration. The code accepts either temperatures or heat fluxes as boundary conditions that can vary in time on a point-by-point basis. Comparisons of the BEM numerical results and known analytical unsteady results for simple shapes demonstrate very high accuracy and reliability of the algorithm. An example of computed three dimensional temperature and heat flux fields in a realistically shaped internally cooled turbine blade is also discussed.
Proton Beam Fast Ignition Fusion: Nonlinear Generation of Bθ-Fields by Knock-on Electrons
NASA Astrophysics Data System (ADS)
Stefan, V. Alexander
2011-10-01
The knock-on electrons, generated by the fast proton beam in interaction with the free and bound electrons in a precompressed DT fusion pellet, outrun the proton beam, generating the Bθ-fields ahead of the beam, which may lead to the defocusing of the beam, if Bθ < 0. The Bθ-fields are generated due to the magnetic instability, ∂Bθ/ ∂t ~ (c/ σ) ∇ x jne, where jne is the knock-on electron current density, σ is the background plasma conductivity, and c the speed of light. The instability growth rate compensates for relatively low knock-on generation efficiency by a proton beam. The saturation level,(electron trapping mechanism), of the B-field ahead of the beam, is of the order of 10 MG and is reached on the time scale of 10 ps. M. Roth et al, Phys. Rev. Lett. 86, 436 (2001); M. Tabak et al, Phys. Plasmas 1 (5), 1626 (1994); H. L. Buchanan, F. W. Chambers, E. P. Lee, S. S. Yu, R. J. Briggs, and M. N. Rosenbluth, LLNL, UCRL Report 82586, 1979.
NASA Astrophysics Data System (ADS)
SjöBerg, Daniel
2003-04-01
We investigate the propagation of electromagnetic waves in a cylindrical waveguide with an arbitrary cross section filled with a nonlinear material. The electromagnetic field is expanded in the usual eigenmodes of the waveguide, and the coupling between the modes is quantified. We derive the wave equations governing each mode with special emphasis on the situation with a dominant TE mode. The result is a strictly hyperbolic system of nonlinear partial differential equations for the dominating mode, whereas the minor modes satisfy hyperbolic systems of linear, nonstationary, and partial differential equations. A growth estimate is given for the minor modes.
Smith, S.J.
1985-01-01
In the experimental program described, we deliberately broaden a well-stabilized single mode laser beam by introducing fluctuations to the laser frequency, in order to synthesize laser power spectra for which the fluctuations are well-characterized to all orders in a statistical sense. With this technique we are able to produce single mode laser fields which have nearly Lorentzian power spectra at one limit, essentially Gaussian power spectra at the other limit, and which may be varied continuously between these two limits. 16 refs., 6 figs.
Nonlinear theory of a free electron laser with a helical wiggler and an axial guide magnetic field
NASA Astrophysics Data System (ADS)
Ginzburg, N. S.; Peskov, N. Yu.
2013-09-01
A 1D nonlinear theory of a free electron laser (FEL) with a helical wiggler and an axial guide magnetic field is developed based on averaged equations of the electron motion. By averaging we separated two different cases of the e-beam/rf-wave interaction. The first one corresponds to the traditional wiggler synchronism (resonance) of rf wave with the electrons moving along stationary helical trajectories. The second one corresponds to combination resonances distinguishing by excitation of oscillation of the electrons near the stationary helical trajectory. Comparative analysis of the FEL operation in different regimes has been studied under the traditional wiggler synchronism condition. It was shown that FELs operated far from cyclotron resonance (including a reversed guide field orientation) possess low sensitivity to the initial velocity spread in the driving beam resulting in high electron efficiency. In contrast, under the weak guide field (the gyrofrequency is less than the bounce frequency) of a conventional orientation, the FEL efficiency is restricted by a significant increase in the transverse velocity of the electrons during the interaction with the rf wave that results in violation of the synchronism conditions and is accompanied by electron current losses. An additional mechanism of FEL efficiency enhancement under the conventional guide field orientation in the conditions when the gyrofrequency is higher than the bounce frequency, based on the dependence of the effective mass of the oscillating electrons on their energy, was demonstrated. Results of the theoretical analysis are compared with the results of experimental studies of FEL oscillators. The specific features of energy extraction from the electron beam under condition of an abnormal Doppler effect in the case of the combination resonance are described. This regime is beneficial to increase radiation frequency keeping wiggler period and electron energies.
NASA Astrophysics Data System (ADS)
Karabulut, Ibrahim; Paspalakis, Emmanuel
2016-07-01
We study theoretically the intensity-dependent nonlinear optical properties of an asymmetric coupled quantum well under a static electric field. Effects such as nonlinear absorption, optical rectification and refractive index are investigated theoretically by using the density matrix equations including the permanent dipole terms. Our results show that the effects of the permanent dipoles on the corresponding optical processes depend crucially on the direction and strength of the static electric field, especially for large optical intensities. Another interesting result of this work is that the nonlinear optical spectra studied here saturate with an increasing optical intensity and specifically the optical spectra in the case that the permanent dipoles are considered reach saturation for lower intensities than when the permanent dipoles are not considered.
Orel, V E; Dziatkovs'ka, I I; Nikolov, M O; Romanov, A V; Mel'nyk, Iu H; Dziatkovs'ka, N M
2010-07-01
While local hyperthermia application the intratumoral blood flow is enhancing, leading to oxygenation and vascular permeability for antitumoral medicines. The work objective was to investigate the dependence of the development kinetics in carcinoma Gereni (CG) from combined action of doxorubicin (DR) and the kind of thermal impact, a contact one--due to a contact delivery of heat from a water heater and without contact - due to the tumor electromagnetic irradiation (EMI) using heterogenous electromagnetic field (EMF). DR was injected to the animals in a mass concentration of 1,5 mg on 1 kg of their body mass. The DR injection, a contact heating and EMI were started on the 8th day after the tumor reinoculation and kept on conducting once a 2 days. The course had included 5 injections and/or 5 seances of a contact heating and/or EMF. The combined action of DR and EMI, using spatially heterogenous EMF of applicator in environment of physiological hyperthermia, have had influenced mostly the inhibition of a nonlinear dynamics in CG development. Antitumoral action of DR in the animals with CG was influenced by thermal and nonthermal effects, which were initiated by spatially heterogenous EMF. Nonlinear dynamics of a CG development in animals did not depend from horizontal direction of isolines of a spatially heterogenous EMF of inductive applicator towards the tumor and duration of the irradiation procedure (15 or 30 minutes) after DR injection. The data obtained were exploited in clinical practice for the inductothermy optimal regimes elaboration while conducting complex treatment of patients, suffering oncological diseases. PMID:20825095
Bykov, Andrei M.; Osipov, Sergei M.; Ellison, Donald C.; Vladimirov, Andrey E. E-mail: osm2004@mail.ru E-mail: avenovo@gmail.com
2014-07-10
We present a nonlinear Monte Carlo model of efficient diffusive shock acceleration where the magnetic turbulence responsible for particle diffusion is calculated self-consistently from the resonant cosmic-ray (CR) streaming instability, together with non-resonant short- and long-wavelength CR-current-driven instabilities. We include the backpressure from CRs interacting with the strongly amplified magnetic turbulence which decelerates and heats the super-Alfvénic flow in the extended shock precursor. Uniquely, in our plane-parallel, steady-state, multi-scale model, the full range of particles, from thermal (∼eV) injected at the viscous subshock to the escape of the highest energy CRs (∼PeV) from the shock precursor, are calculated consistently with the shock structure, precursor heating, magnetic field amplification, and scattering center drift relative to the background plasma. In addition, we show how the cascade of turbulence to shorter wavelengths influences the total shock compression, the downstream proton temperature, the magnetic fluctuation spectra, and accelerated particle spectra. A parameter survey is included where we vary shock parameters, the mode of magnetic turbulence generation, and turbulence cascading. From our survey results, we obtain scaling relations for the maximum particle momentum and amplified magnetic field as functions of shock speed, ambient density, and shock size.
Ong, P. V.; Kioussis, Nicholas; Amiri, P. Khalili; Wang, K. L.
2016-01-01
Voltage-induced switching of magnetization, as opposed to current-driven spin transfer torque switching, can lead to a new paradigm enabling ultralow-power and high density instant-on nonvolatile magnetoelectric random access memory (MeRAM). To date, however, a major bottleneck in optimizing the performance of MeRAM devices is the low voltage-controlled magnetic anisotropy (VCMA) efficiency (change of interfacial magnetic anisotropy energy per unit electric field) leading in turn to high switching energy and write voltage. In this work, employing ab initio electronic structure calculations, we show that epitaxial strain, which is ubiquitous in MeRAM heterostructures, gives rise to a rich variety of VCMA behavior with giant VCMA coefficient (~1800 fJ V−1m−1) in Au/FeCo/MgO junction. The heterostructure also exhibits a strain-induced spin-reorientation induced by a nonlinear magnetoelastic coupling. The results demonstrate that the VCMA behavior is universal and robust in magnetic junctions with heavy metal caps across the 5d transition metals and that an electric-field-driven magnetic switching at low voltage is achievable by design. These findings open interesting prospects for exploiting strain engineering to harvest higher efficiency VCMA for the next generation MeRAM devices. PMID:27424885
Ong, P V; Kioussis, Nicholas; Amiri, P Khalili; Wang, K L
2016-01-01
Voltage-induced switching of magnetization, as opposed to current-driven spin transfer torque switching, can lead to a new paradigm enabling ultralow-power and high density instant-on nonvolatile magnetoelectric random access memory (MeRAM). To date, however, a major bottleneck in optimizing the performance of MeRAM devices is the low voltage-controlled magnetic anisotropy (VCMA) efficiency (change of interfacial magnetic anisotropy energy per unit electric field) leading in turn to high switching energy and write voltage. In this work, employing ab initio electronic structure calculations, we show that epitaxial strain, which is ubiquitous in MeRAM heterostructures, gives rise to a rich variety of VCMA behavior with giant VCMA coefficient (~1800 fJ V(-1)m(-1)) in Au/FeCo/MgO junction. The heterostructure also exhibits a strain-induced spin-reorientation induced by a nonlinear magnetoelastic coupling. The results demonstrate that the VCMA behavior is universal and robust in magnetic junctions with heavy metal caps across the 5d transition metals and that an electric-field-driven magnetic switching at low voltage is achievable by design. These findings open interesting prospects for exploiting strain engineering to harvest higher efficiency VCMA for the next generation MeRAM devices. PMID:27424885
NASA Astrophysics Data System (ADS)
Ong, P. V.; Kioussis, Nicholas; Amiri, P. Khalili; Wang, K. L.
2016-07-01
Voltage-induced switching of magnetization, as opposed to current-driven spin transfer torque switching, can lead to a new paradigm enabling ultralow-power and high density instant-on nonvolatile magnetoelectric random access memory (MeRAM). To date, however, a major bottleneck in optimizing the performance of MeRAM devices is the low voltage-controlled magnetic anisotropy (VCMA) efficiency (change of interfacial magnetic anisotropy energy per unit electric field) leading in turn to high switching energy and write voltage. In this work, employing ab initio electronic structure calculations, we show that epitaxial strain, which is ubiquitous in MeRAM heterostructures, gives rise to a rich variety of VCMA behavior with giant VCMA coefficient (~1800 fJ V‑1m‑1) in Au/FeCo/MgO junction. The heterostructure also exhibits a strain-induced spin-reorientation induced by a nonlinear magnetoelastic coupling. The results demonstrate that the VCMA behavior is universal and robust in magnetic junctions with heavy metal caps across the 5d transition metals and that an electric-field-driven magnetic switching at low voltage is achievable by design. These findings open interesting prospects for exploiting strain engineering to harvest higher efficiency VCMA for the next generation MeRAM devices.
Topological complexity and tangential discontinuity in magnetic fields
Janse, A. M.; Low, B. C.; Parker, E. N.
2010-09-15
This is a study of the topological magnetostatic problem. A magnetic field embedded in a perfectly conducting fluid and rigidly anchored at its boundary has a specific topology invariant for all time. Subject to that topology, the force-free state of such a field generally requires the presence of tangential discontinuities (TDs). This property proposed and demonstrated by Parker [Spontaneous Current Sheets in Magnetic Fields (Oxford University Press, New York, 1994)] is explained in terms of (i) the overdetermined nature of the magnetostatic partial differential equations nonlinearly coupled to the integral equations imposing the field topology and (ii) the hyperbolic nature of the partial differential equation for the twist function {alpha} of the force-free field. The mathematical analysis elucidates a basic incompatibility between preserving a complex field topology and attaining equilibrium, if analyticity is assumed. Physics avoids this incompatibility via TD formation as a natural consequence of perfect conductivity. The study relates TD formation to topological complexity in two-dimensional and three-dimensional fields, as well as the topological connectivity and geometric shape of the field domain. Mathematical points made are given physical interpretations, but important topological concepts for understanding spontaneous TDs have remained incomplete. As an application, examples are presented to define twisted and untwisted potential fields found in simply and multiply connected domains, clarifying a confusion in several recent publications. Appendix A treats the expression of the frozen-in condition by a continuum of conserved, total generalized helicities. Appendix B reports briefly on concurrent developments showing that a published objection to the theory of spontaneous TDs is based upon a misunderstanding of the theory.
NASA Astrophysics Data System (ADS)
Chaikovsky, S. A.; Oreshkin, V. I.; Datsko, I. M.; Labetskaya, N. A.; Rybka, D. V.; Ratakhin, N. A.
2015-11-01
The paper presents the results of an experimental study of the skin explosion of cylindrical conductors of diameter 1-3 mm (copper, aluminum, titanium, steel 3, and stainless steel) at a peak magnetic field of 200-600 T. The experiments were carried out on the MIG pulsed power generator at a current of up to 2.5 MA and a current rise time of 100 ns. The surface explosion of a conductor was identified by the appearance of a flash of extreme ultraviolet radiation. A minimum magnetic induction has been determined below which no plasma is generated at the conductor surface. For copper, aluminum, steel 3, titanium, and stainless steel, the minimum magnetic induction has been estimated to be (to within 10%) 375, 270, 280, 220, and 245 T, respectively.
Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field
NASA Technical Reports Server (NTRS)
Chen, J.; Palmadesso, P. J.
1986-01-01
The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.
Chaikovsky, S. A.; Datsko, I. M.; Labetskaya, N. A.; Rybka, D. V.; Ratakhin, N. A.; Oreshkin, V. I.
2015-11-15
The paper presents the results of an experimental study of the skin explosion of cylindrical conductors of diameter 1–3 mm (copper, aluminum, titanium, steel 3, and stainless steel) at a peak magnetic field of 200–600 T. The experiments were carried out on the MIG pulsed power generator at a current of up to 2.5 MA and a current rise time of 100 ns. The surface explosion of a conductor was identified by the appearance of a flash of extreme ultraviolet radiation. A minimum magnetic induction has been determined below which no plasma is generated at the conductor surface. For copper, aluminum, steel 3, titanium, and stainless steel, the minimum magnetic induction has been estimated to be (to within 10%) 375, 270, 280, 220, and 245 T, respectively.
ERIC Educational Resources Information Center
Donoso, Guillermo; Ladera, Celso L.
2012-01-01
We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the…
NASA Astrophysics Data System (ADS)
El-Dib, Yusry O.
1996-04-01
The nonlinear stability of surface waves propagating between two superposed streaming magnetic fluids is investigated. The fluids are stressed by a constant tangential magnetic field and a vertical periodic acceleration. The solution employs the method of multiple scales. Owing to the periodicity, resonant cases appear. Two parametrically nonlinear Schrödinger equations are derived for the resonant cases to describe the elevation of weakly nonlinear capillary waves. The standard nonlinear Schrödinger equation is satisfied for the non resonant cases. Necessary and sufficient conditions for stability are obtained. A formula for the surface elevation is obtained in each case. It is found that the magnetic field, the velocities and the frequency of the applied periodic force play dual roles in the resonant region. Investigation of the stability criterion by nonlinear perturbation shows that an increase in the acceleration frequency has a stabilizing effect. The stabilizing role of the frequency is due to the destabilizing effect of the amplitude of the periodic acceleration.
Mirus, K.A.
1998-06-01
In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Roessler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high-dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.
Stability of bumps in piecewise smooth neural fields with nonlinear adaptation
NASA Astrophysics Data System (ADS)
Kilpatrick, Zachary P.; Bressloff, Paul C.
2010-06-01
We study the linear stability of stationary bumps in piecewise smooth neural fields with local negative feedback in the form of synaptic depression or spike frequency adaptation. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Discontinuities in the adaptation variable associated with a bump solution means that bump stability cannot be analyzed by constructing the Evans function for a network with a sigmoidal gain function and then taking the high-gain limit. In the case of synaptic depression, we show that linear stability can be formulated in terms of solutions to a system of pseudo-linear equations. We thus establish that sufficiently strong synaptic depression can destabilize a bump that is stable in the absence of depression. These instabilities are dominated by shift perturbations that evolve into traveling pulses. In the case of spike frequency adaptation, we show that for a wide class of perturbations the activity and adaptation variables decouple in the linear regime, thus allowing us to explicitly determine stability in terms of the spectrum of a smooth linear operator. We find that bumps are always unstable with respect to this class of perturbations, and destabilization of a bump can result in either a traveling pulse or a spatially localized breather.
NASA Astrophysics Data System (ADS)
Mirus, Kevin Andrew
In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Rossler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high- dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.
Modeling of Field Effect Transistor Channel as a Nonlinear Transmission Line for Terahertz Detection
NASA Astrophysics Data System (ADS)
Ibrahim, Nihal Y.; Rafat, Nadia H.; Elnahwy, Salah E. A.
2013-10-01
This paper revisits the theory of operation of field effect transistor in the extremely high frequency scale, where the analysis has gone beyond the conventional cutoff frequency of the transistor. In this range, which is typically the terahertz (THz) and sub-terahertz range, the transistor blocks the high frequency signal and generates a rectified signal related to the input high frequency signal. An analytical model is derived for the channel of the FET in the linear mode of operation in non-resonant THz detection conditions. A transmission line distributed circuit model is applied. This is, from the authors' point of view, the suitable model for high frequency non-quasi static operation and the characteristic parameters of this model are derived from the differential equation governing the electron gas in the channel. A comparison is presented for the calculated photoresponse with previously published experimental one showing good agreement away from the threshold potential. Finally, the effects of coupling between the present model and the external input circuit have been taken into account including the loading effects of the antenna and a discussion is given for the effect on frequency selectivity of the FET.
Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics
NASA Astrophysics Data System (ADS)
Freeman, Walter J.; Vitiello, Giuseppe
2006-06-01
Neural activity patterns related to behavior occur at many scales in time and space from the atomic and molecular to the whole brain. Patterns form through interactions in both directions, so that the impact of transmitter molecule release can be analyzed to larger scales through synapses, dendrites, neurons, populations and brain systems to behavior, and control of that release can be described step-wise through transforms to smaller scales. Here we explore the feasibility of interpreting neurophysiological data in the context of many-body physics by using tools that physicists have devised to analyze comparable hierarchies in other fields of science. We focus on a mesoscopic level that offers a multi-step pathway between the microscopic functions of neurons and the macroscopic functions of brain systems revealed by hemodynamic imaging. We use electroencephalographic (EEG) records collected from high-density electrode arrays fixed on the epidural surfaces of primary sensory and limbic areas in rabbits and cats trained to discriminate conditioned stimuli (CS) in the various modalities. High temporal resolution of EEG signals with the Hilbert transform gives evidence for diverse intermittent spatial patterns of amplitude (AM) and phase modulations (PM) of carrier waves that repeatedly re-synchronize in the beta and gamma ranges in very short time lags over very long distances. The dominant mechanism for neural interactions by axodendritic synaptic transmission should impose distance-dependent delays on the EEG oscillations owing to finite propagation velocities and sequential synaptic delays. It does not. EEGs show evidence for anomalous dispersion: neural populations have a low velocity range of information and energy transfers, and a high velocity range of the spread of phase transitions. This distinction labels the phenomenon but does not explain it. In this report we analyze these phenomena using concepts of energy dissipation, the maintenance by cortex of
NASA Astrophysics Data System (ADS)
Guasp, J.; Pastor, I.; Álvarez-Estrada, R. F.; Castejón, F.
2015-02-01
Analytical results obtained recently of the ab-initio classical incoherent Thomson Scattering (TS) spectrum from a single-electron (Alvarez-Estrada et al 2012 Phys. Plasmas 19 062302) have been numerically implemented in a paralelized code to efficiently compute the TS emission from a given electron distribution function, irrespective of its characteristics and/or the intensity of the incoming radiation. These analytical results display certain differences, when compared with other authors, in the general case of incoming linearly and circularly polarized radiation and electrons with arbitrary initial directions. We regard such discrepancies and the ubiquitous interest in TS as motivations for this work. Here, we implement some analytical advances (like generalized Bessel functions for incoming linearly polarized radiation) in TS. The bulk of this work reports on the efficient computation of TS spectra (based upon our analytical approach), for an electron population having an essentially arbitrary distribution function and for both incoming linearly and circularly polarized radiation. A detailed comparison between the present approach and a previous Monte Carlo one (Pastor et al 2011 Nuclear Fusion 51 043011), dealing with the ab-initio computation of TS spectra, is reported. Both approaches are shown to fully agree with each other. As key computational improvements, the analytical technique yields a × 30 to × 100 gain in computation time and is a very flexible tool to compute the scattered spectrum and eventually the scattered electromagnetic fields in the time domain. The latter are computed explicitly here for the first time, as far as we know. Scaling laws for the power integrated over frequency versus initial kinetic energy are studied for the case of isotropic and monoenergetic electron distribution functions and their potential application as diagnostic tools for high-energy populations is briefly discussed. Finally, we discuss the application of these
NASA Astrophysics Data System (ADS)
De Conti, Alberto; Silveira, Fernando H.; Visacro, Silvério
2014-05-01
This paper investigates the influence of corona on currents and electromagnetic fields predicted by a return-stroke model that represents the lightning channel as a nonuniform transmission line with time-varying (nonlinear) resistance. The corona model used in this paper allows the calculation of corona currents as a function of the radial electric field in the vicinity of the channel. A parametric study is presented to investigate the influence of corona parameters, such as the breakdown electric field and the critical electric field for the stable propagation of streamers, on predicted currents and electromagnetic fields. The results show that, regardless of the assumed corona parameters, the incorporation of corona into the nonuniform and nonlinear transmission line model under investigation modifies the model predictions so that they consistently reproduce most of the typical features of experimentally observed lightning electromagnetic fields and return-stroke speed profiles. In particular, it is shown that the proposed model leads to close vertical electric fields presenting waveforms, amplitudes, and decay with distance in good agreement with dart leader electric field changes measured in triggered lightning experiments. A comparison with popular engineering return-stroke models further confirms the model's ability to predict consistent electric field waveforms in the close vicinity of the channel. Some differences observed in the field amplitudes calculated with the different models can be related to the fact that current distortion, while present in the proposed model, is ultimately neglected in the considered engineering return-stroke models.
NASA Astrophysics Data System (ADS)
Strubbe, David A.; Andrade, Xavier; Rubio, Angel; Louie, Steve G.
2009-03-01
Chloroform is often used as a solvent and reference when measuring non-linear optical properties of organic molecules. We calculate directly the non-linear susceptibilities of liquid chloroform at optical frequencies, using molecular dynamics and the Sternheimer equation in time-dependent density-functional theory [X. Andrade et al., J. Chem. Phys. 126, 184106 (2007)]. We compare the results to those of chloroform in the gas and solid phases, and experimental values, and make an ab initio calculation of the local-field factors which are needed to extract molecular properties from liquid calculations and experimental measurements.
NASA Astrophysics Data System (ADS)
Hayden, Lorien; Sethna, James
We systematically analyze the nonlinear invariant scaling variables at bifurcations in the renormalization-group flow, and apply our methods to the two-dimensional random-field Ising model (RFIM). At critical points, the universal scaling functions are usually written in terms of homogeneous invariant combinations of variables, like Ltν in the finite-size scaling form for the magnetization M (T | L) ~t-β M (Ltν) , where t ~Tc - T . The renormalization-group flow for the RFIM has a pitchfork bifurcation in two dimensions, where the correlation length has been argued to diverge exponentially, ξ ~ exp 1 / 2 At2 , leading to the invariant scaling combination L / ξ ~ L / exp 1 / 2 At2 . Our analysis, inspired by normal-form theory, suggests that this exponential divergence can take a richer, more general scaling form at a generic pitchfork bifurcation. We explore possible consequences for simulations. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. . DGE-1144153.
NASA Astrophysics Data System (ADS)
Bretherton, Christopher S.
1988-09-01
In Part I, an idealized model of nonprecipitating moist convection in a shallow conditionally unstable layer of viscous and diffusive air between two parallel plates was introduced, and the `linear' instability of an exactly saturated static state maintained by diffusion was investigated. If there are initially many clouds, the `linear' theory predicted that weaker clouds are suppressed by the subsidence warming and drying from the ever-growing stronger clouds, and the average cloud spacing becomes arbitrarily large as time goes on. Each growing cloud is surrounded by compensating subsidence, which decreases away from the cloud with a characteristic decay scale Rs, the subsidence radius, which can be understood from gravity wave arguments.In Part II, fields of finite amplitude clouds are considered. An asymptotic analysis is performed in which the moist Rayleigh number Nc2 exceeds by only a small amount the value Nc02 necessary for the onset of convection. This leads to a nonlinear set of `cloud field equations' which predict how the amplitudes and positions of all the clouds evolve in time. These equations predict a minimum stable cloud spacing c Rslog(1). If the cloud spacing < c, slight differences in the strengths of neighboring clouds increase until the weaker clouds are suppressed. Unevenly spaced clouds drift until they become evenly spaced, ultimately resulting in a steady field of identical clouds with uniform spacing > c.Numerical experiments with dry stability Nd = Nc corroborate the conclusions from the cloud field equations when Nc2/Nc02 is less than ten. As Nc2 increases, the numerically determined c. becomes approximately 1.8Rs 1.8Nd. There is a second threshold spacing t 1.6Nd
Assadi, S.
1994-01-01
Linear and nonlinear magnetohydrodynamic (MHD) stability of current-driven modes are studied in the MST reversed field pinch. Measured low frequency (f < 35 kHz) magnetic fluctuations are consistent with the global resistive tearing instabilities predicted by 3-D MHD simulations. At frequencies above 35 kHz, the magnetic fluctuations were detected to be localized and externally resonant. Discrete dynamo events, ``sawtooth oscillations,`` have been observed in the experimental RFP plasmas. This phenomenon causes the plasma to become unstable to m = 1 tearing modes. The modes that may be important in different phases of these oscillations are identified. These results then assist in nonlinear studies and also help to interpret the spectral broadening of the measured data during a discrete dynamo event. Three-wave nonlinear coupling of spectral Fourier modes is measured in the MST by applying bispectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 poloidal and 32 toroidal modes. Comparison to bispectra predicted by resistive MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomitant with a broadened k-spectrum. During the sawtooth formation the plasma is undergoing a pure diffusive process. The dynamo only occurs during the sawtooth crash. High frequency activity prior to a sawtooth crash is caused by nonlinear frequency (small-scale) mode coupling. Growth rate and coupling coefficients of toroidal mode spectra are calculated by statistical modeling. Temporal evolution of edge toroidal mode spectra has been predicted by transfer function analysis. The driving sources of electrostatic fields are different than for the magnetic fields. The characteristics of tearing modes can be altered by external field errors and addition of impurities to the plasma.
Correa, J. D.; Mora-Ramos, M. E.; Duque, C. A.
2014-06-07
We report a study on the optical absorption coefficient associated to hydrogenic impurity interstate transitions in zinc-blende GaN quantum wires of cylindrical shape taking into account the effects of externally applied static electric and magnetic fields. The electron states emerge within the effective mass approximation, via the exact diagonalization of the donor-impurity Hamiltonian with parabolic confinement and external field effects. The nonlinear optical absorption is calculated using a recently derived expression for the dielectric susceptibility, obtained via a nonperturbative solution of the density-matrix Bloch equation. Our results show that this treatment eliminates not only the intensity-dependent bleaching effect but also the change in sign of the nonlinear contribution due to the combined effect of asymmetric impurity location and the applied electric field.
NASA Astrophysics Data System (ADS)
Correa, J. D.; Mora-Ramos, M. E.; Duque, C. A.
2014-06-01
We report a study on the optical absorption coefficient associated to hydrogenic impurity interstate transitions in zinc-blende GaN quantum wires of cylindrical shape taking into account the effects of externally applied static electric and magnetic fields. The electron states emerge within the effective mass approximation, via the exact diagonalization of the donor-impurity Hamiltonian with parabolic confinement and external field effects. The nonlinear optical absorption is calculated using a recently derived expression for the dielectric susceptibility, obtained via a nonperturbative solution of the density-matrix Bloch equation. Our results show that this treatment eliminates not only the intensity-dependent bleaching effect but also the change in sign of the nonlinear contribution due to the combined effect of asymmetric impurity location and the applied electric field.
NASA Astrophysics Data System (ADS)
Geiges, A.; Nowak, W.; Rubin, Y.
2013-12-01
Stochastic models of sub-surface systems generally suffer from parametric and conceptual uncertainty. To reduce the model uncertainty, model parameters are calibrated using additional collected data. These data often come from costly data acquisition campaigns that need to be optimized to collect the data with the highest data utility (DU) or value of information. In model-based approaches, the DU is evaluated based on the uncertain model itself and is therefore uncertain as well. Additionally, for non-linear models, data utility depends on the yet unobserved measurement values and can only be estimated as an expected value over an assumed distribution of possible measurement values. Both factors introduce uncertainty into the optimization of field campaigns. We propose and investigate a sequential interaction scheme between campaign optimization, data collection and model calibration. The field campaign is split in individual segments. Each segment consists of optimization, segment-wise data collection, and successive model calibration or data assimilation. By doing so, (1) the expected data utility for the newly collected data is replaced by their actual one, (2) the calibration restricts both conceptual and parametric model uncertainty, and thus (3) the distribution of possible future data values for the subsequent campaign segments also changes. Hence, the model to describe the real system improves successively with each collected data segment, and so does the estimate of the yet remaining data requirements to achieve the overall investigation goals. We will show that using the sequentially improved model for the optimal design (OD) of the remaining field campaign leads to superior and more targeted designs.However, this traditional sequential OD optimizes small data segments one-by-one. In such a strategy, possible mutual dependencies with the possible data values and the optimization of data values collection in later segments are neglected. This allows a
Sims, Jared A.; Pollard, Andrew E.; White, Peter S.; Knisley, Stephen B.
2011-01-01
Cardiac electric field stimulation is critical for the mechanism of defibrillation. The presence of certain inactive epicardial conductors in the field during defibrillation can decrease the defibrillation threshold. We hypothesized this decrease is due to stimulatory effects of current across the interface between the inactive conductor and the heart during field stimulation. To examine this current and its possible stimulatory effects, we imaged transmittance of indium-tin-oxide (ITO) conductors, tested for indium with x-ray diffraction, created a computer model containing realistic ITO interfacial properties, and optically mapped excitation of rabbit heart during electric field stimulation in the presence of an ITO conductor. Reduction of ITO to indium decreased transmittance at the edge facing the anodal shock electrode when trans-interfacial voltage exceeded standard reduction potential. The interfacial current-voltage relationship was nonlinear, producing larger conductances at higher currents. This nonlinearity concentrated the interfacial current near edges in images and in a computer model. The edge current was stimulatory, producing early postshock excitation of rabbit ventricles. Thus, darkening of ITO indicates interfacial current by indium reduction. Interfacial nonlinearity concentrates current near the edge where it can excite the heart. Stimulatory current at edges may account for the reported decrease in defibrillation threshold by inactive conductors. PMID:19605317
NASA Astrophysics Data System (ADS)
Gassenmeier, M.; Sens-Schönfelder, C.; Eulenfeld, T.; Bartsch, M.; Victor, P.; Tilmann, F.; Korn, M.
2016-03-01
To investigate temporal seismic velocity changes due to earthquake related processes and environmental forcing in Northern Chile, we analyse 8 yr of ambient seismic noise recorded by the Integrated Plate Boundary Observatory Chile (IPOC). By autocorrelating the ambient seismic noise field measured on the vertical components, approximations of the Green's functions are retrieved and velocity changes are measured with Coda Wave Interferometry. At station PATCX, we observe seasonal changes in seismic velocity caused by thermal stress as well as transient velocity reductions in the frequency range of 4-6 Hz. Sudden velocity drops occur at the time of mostly earthquake-induced ground shaking and recover over a variable period of time. We present an empirical model that describes the seismic velocity variations based on continuous observations of the local ground acceleration. The model assumes that not only the shaking of large earthquakes causes velocity drops, but any small vibrations continuously induce minor velocity variations that are immediately compensated by healing in the steady state. We show that the shaking effect is accumulated over time and best described by the integrated envelope of the ground acceleration over the discretization interval of the velocity measurements, which is one day. In our model, the amplitude of the velocity reduction as well as the recovery time are proportional to the size of the excitation. This model with two free scaling parameters fits the data of the shaking induced velocity variation in remarkable detail. Additionally, a linear trend is observed that might be related to a recovery process from one or more earthquakes before our measurement period. A clear relationship between ground shaking and induced velocity reductions is not visible at other stations. We attribute the outstanding sensitivity of PATCX to ground shaking and thermal stress to the special geological setting of the station, where the subsurface material
Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong
2014-02-01
Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects. PMID:24070825
NASA Astrophysics Data System (ADS)
Tautz, R. C.; Lerche, I.
2015-11-01
This note considers the evolution of steady isothermal flow across a uniform magnetic field from an analytic standpoint. This problem is of concern in developments of magnetic fields in the solar corona and for prominence dynamics. Limiting behaviors are obtained to the nonlinear equation describing the flow depending on the value of a single parameter. For the situation where the viscous drag is a small correction to the inviscid flow limiting structures are also outlined. The purpose of the note is to show how one can evaluate some of the analytic properties of the highly nonlinear equation that are of use in considering the numerical evolution as done in Low and Egan [Phys. Plasmas 21, 062105 (2014)].
Tautz, R. C.; Lerche, I.
2015-11-15
This note considers the evolution of steady isothermal flow across a uniform magnetic field from an analytic standpoint. This problem is of concern in developments of magnetic fields in the solar corona and for prominence dynamics. Limiting behaviors are obtained to the nonlinear equation describing the flow depending on the value of a single parameter. For the situation where the viscous drag is a small correction to the inviscid flow limiting structures are also outlined. The purpose of the note is to show how one can evaluate some of the analytic properties of the highly nonlinear equation that are of use in considering the numerical evolution as done in Low and Egan [Phys. Plasmas 21, 062105 (2014)].
NASA Astrophysics Data System (ADS)
Ateto, M. S.
2015-08-01
Entanglement dynamics of two identical non-interacting atoms (qubits) coupled individually with simultaneous classical and quantum fields are studied. The cavity field is filled with a nonlinear Kerr medium and initially prepared in a coherent state. The atoms are initially set up as a Bell-like pure state (BS). We present an approach for diagonalization of time-dependent nonlinear Hamiltonian of the system exactly. Connection between the change in the degree of entanglement and tomography of field state in phase space are also illustrated and interpreted. We demonstrate the possibility of atom-atom (qubit-qubit) entanglement optimization by suitably choosing initial interaction settings. Overall, we show that both classical driving amplitude and detuning as well as Kerr media and initial atomic states acts as the control parameters for the qubit-qubit entanglement. By adjusting of these parameters, accurately, entanglement can be enhanced noticeably and high degree of steady periodical entanglement can be generated. Moreover, starting with initial atomic BSs in presence of classical driving suppresses coherences randomness and considerably accompanied with (for specific values of detuning) slight decrease in their amplitudes. Furthermore, the addition of cross Kerr term suppresses degree of entanglement noticeably, where entanglement creation and enhancement could just be possible if cross Kerr effect is moved out from interaction. Our present approach promises the great advantage of being suitable for large quantum systems of various kinds of nonlinearities.
NASA Technical Reports Server (NTRS)
Maskew, B.
1976-01-01
A discrete singularity method has been developed for calculating the potential flow around two-dimensional airfoils. The objective was to calculate velocities at any arbitrary point in the flow field, including points that approach the airfoil surface. That objective was achieved and is demonstrated here on a Joukowski airfoil. The method used combined vortices and sources ''submerged'' a small distance below the airfoil surface and incorporated a near-field subvortex technique developed earlier. When a velocity calculation point approached the airfoil surface, the number of discrete singularities effectively increased (but only locally) to keep the point just outside the error region of the submerged singularity discretization. The method could be extended to three dimensions, and should improve nonlinear methods, which calculate interference effects between multiple wings, and which include the effects of force-free trailing vortex sheets. The capability demonstrated here would extend the scope of such calculations to allow the close approach of wings and vortex sheets (or vortices).
El-Labany, S. K.; Moslem, Waleed M.; Safy, F. M.
2006-08-15
Nonlinear propagation of dust-acoustic solitary waves (DASWs) in a strong magnetized dusty plasma comprising warm adiabatic variable-charged dust particles, isothermal electrons, and two-temperature ions is investigated. Applying a reductive perturbation theory, a nonlinear Zakharov-Kuznetsov (ZK) equation for the first-order perturbed potential and a linear inhomogeneous ZK-type equation for the second-order perturbed potential are derived. However, at a certain value of high-temperature ion density, the coefficient of the nonlinear terms of both ZK and ZK-type equations vanishes. Therefore, a new set of expansion physical parameters and stretched coordinates are then used to derive a modified Zakharov-Kuznetsov (mZK) equation for the first-order perturbed potential and a mZK-type equation for the second-order perturbed potential. Stationary solutions of these equations are obtained using a renormalization method. A condition for two-temperature ions assumption is examined for various cosmic dust-laden plasma systems. It is found that this condition is satisfied for Saturn's F ring. The effects of two-temperature ions, magnetic field, and higher-order nonlinearity on the behavior of the DASWs are discussed. To obtain the stability condition of the waves, a method based on energy consideration is used and the condition for stable solitons is derived.
NASA Astrophysics Data System (ADS)
Shao, Xuefei; Fu, Yiming; Chen, Yang
2015-05-01
Based on the higher order shear deformation theory and the geometric nonlinear theory, the nonlinear motion equations, to which the effects of the positive and negative piezoelectric and the thermal are introduced by piezoelectric fiber metal laminated (FML) plates in an unsteady temperature, are established by Hamilton’s variational principle. Then, the control algorithm of negative-velocity feedback is applied to realize the vibration control of the piezoelectric FML plates. During the solving process, firstly, the formal functions of the displacements that fulfilled the boundary conditions are proposed. Then, heat conduction equations and nonlinear differential equations are dealt with using the differential quadrature (DQ) and Galerkin methods, respectively. On the basis of the previous processing, the time domain is dispersed by the Newmark-β method. Finally, the whole problem can be investigated by the iterative method. In the numerical examples, the influence of the applied voltage, the temperature loading and geometric parameters on the nonlinear dynamic response of the piezoelectric FML plates is analyzed. Meanwhile, the effect of feedback control gain and the position of the piezoelectric layer, the initial deflection and the external temperature on the active control effect of the piezoelectric layers has been studied. The model development and the research results can serve as a basis for nonlinear vibration analysis of the FML structures.
NASA Astrophysics Data System (ADS)
Tsai, T.; Chang, C.; Lyu, L.
2006-12-01
Nonlinear evolutions of electrostatic (ES) and electromagnetic (EM) instabilities in a field-aligned counter- streaming plasma are studied by means of a full particle code simulation and a Vlasov simulation. Our simulation results show that field-aligned counter-streaming plasma can lead to fast growing electrostatic two- stream instability to heat electrons along the background magnetic field directions. If the background magnetic field is not strong enough, the field-aligned heating can easily make the system unstable to the electromagnetic fire-hose instability. The nonlinear kinetic Alfven waves generated by the fire-hose instability can isotropize the electron pressure and heat ions by both ion-cyclotron instability and non-adiabatic ion gyro- reflections. Additional instabilities generated by the gyro-reflecting events can heat the plasma in a very efficient way. The importance of the cross-scale coupling between the ES instabilities and the EM instabilities in the space plasmas with counter-streaming plasma flows will be discussed.
Wei, Kunlin; Stevenson, Ian H; Körding, Konrad P
2010-01-01
When we stand upright, we integrate cues from multiple senses, such as vision and proprioception, to maintain and regulate our vertical posture. How these cues are combined has been the focus of a range of studies. These studies generally measured how subjects deviate from standing upright when confronted with a moving visual stimulus displayed in a virtual environment. Previous research had shown that uncertainty is central in such cue combination problems. Here we wanted to understand, quantitatively, how visual flow fields and uncertainty about them affect human posture. To do so, we combined experimental methods from perceptual psychophysics with methods from motor control studies. We used a two-alternative forced-choice paradigm to measure uncertainty as a function of the magnitude of a random-dot flow field and stimulus coherence. We subsequently measured movement amplitude as a function of visual stimulus parameters. In line with previous research, we find that sensorimotor behavior depends nonlinearly on the stimulus amplitude and, importantly, is affected by uncertainty. We find that this nonlinearity and uncertainty dependence is accurately predicted by standard Bayesian cue combination. Importantly, a Weber's law where visual uncertainty depends on stimulus amplitude is enough to explain the nonlinear behavior. PMID:21131564
Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Ahmad, Bashir
2015-01-01
This article investigates the magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid subject to the convective boundary condition. Flow is generated due to a nonlinear stretching of the surface in two lateral directions. Temperature and nanoparticles concentration distributions are studied through the Brownian motion and thermophoresis effects. Couple stress fluid is considered electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed via boundary layer approach. Nonlinear ordinary differential systems are constructed by employing suitable transformations. The resulting systems have been solved for the convergent series solutions of velocities, temperature and nanoparticles concentration profiles. Graphs are sketched to see the effects of different interesting flow parameters on the temperature and nanoparticles concentration distributions. Numerical values are computed to analyze the values of skin-friction coefficients and Nusselt number. PMID:26714259
Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Ahmad, Bashir
2015-01-01
This article investigates the magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid subject to the convective boundary condition. Flow is generated due to a nonlinear stretching of the surface in two lateral directions. Temperature and nanoparticles concentration distributions are studied through the Brownian motion and thermophoresis effects. Couple stress fluid is considered electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed via boundary layer approach. Nonlinear ordinary differential systems are constructed by employing suitable transformations. The resulting systems have been solved for the convergent series solutions of velocities, temperature and nanoparticles concentration profiles. Graphs are sketched to see the effects of different interesting flow parameters on the temperature and nanoparticles concentration distributions. Numerical values are computed to analyze the values of skin-friction coefficients and Nusselt number. PMID:26714259
BOOTSTRAPPING THE CORONAL MAGNETIC FIELD WITH STEREO: UNIPOLAR POTENTIAL FIELD MODELING
Aschwanden, Markus J.; Sandman, Anne W.
2010-09-15
We investigate the recently quantified misalignment of {alpha}{sub mis} {approx} 20{sup 0}-40{sup 0} between the three-dimensional geometry of stereoscopically triangulated coronal loops observed with STEREO/EUVI (in four active regions (ARs)) and theoretical (potential or nonlinear force-free) magnetic field models extrapolated from photospheric magnetograms. We develop an efficient method of bootstrapping the coronal magnetic field by forward fitting a parameterized potential field model to the STEREO-observed loops. The potential field model consists of a number of unipolar magnetic charges that are parameterized by decomposing a photospheric magnetogram from the Michelson Doppler Imager. The forward-fitting method yields a best-fit magnetic field model with a reduced misalignment of {alpha}{sub PF} {approx} 13{sup 0}-20{sup 0}. We also evaluate stereoscopic measurement errors and find a contribution of {alpha}{sub SE} {approx} 7{sup 0}-12{sup 0}, which constrains the residual misalignment to {alpha}{sub NP} {approx} 11{sup 0}-17{sup 0}, which is likely due to the nonpotentiality of the ARs. The residual misalignment angle, {alpha}{sub NP}, of the potential field due to nonpotentiality is found to correlate with the soft X-ray flux of the AR, which implies a relationship between electric currents and plasma heating.
Zaytsev, Kirill I. Katyba, Gleb M.; Yakovlev, Egor V.; Yurchenko, Stanislav O.; Gorelik, Vladimir S.
2014-06-07
A novel approach for the enhancement of nonlinear optical effects inside globular photonic crystals (PCs) is proposed and systematically studied via numerical simulations. The enhanced optical harmonic generation is associated with two- and three-dimensional PC pumping with the wavelength corresponding to different PC band-gaps. The interactions between light and the PC are numerically simulated using the finite-difference time-domain technique for solving the Maxwell's equations. Both empty and infiltrated two-dimensional PC structures are considered. A significant enhancement of harmonic generation is predicted owing to the highly efficient PC pumping based on the structural light focusing effect inside the PC structure. It is shown that a highly efficient harmonic generation could be attained for both the empty and infiltrated two- and three-dimensional PCs. We are demonstrating the ability for two times enhancement of the parametric decay efficiency, one order enhancement of the second harmonic generation, and two order enhancement of the third harmonic generation in PC structures in comparison to the nonlinear generations in appropriate homogenous media. Obviously, the nonlinear processes should be allowed by the molecular symmetry. The criteria of the nonlinear process efficiency are specified and calculated as a function of pumping wavelength position towards the PC globule diameter. Obtained criterion curves exhibit oscillating characteristics, which indicates that the highly efficient generation corresponds to the various PC band-gap pumping. The highest efficiency of nonlinear conversions could be reached for PC pumping with femtosecond optical pulses; thus, the local peak intensity would be maximized. Possible applications of the observed phenomenon are also discussed.
Friction and nonlinear dynamics
NASA Astrophysics Data System (ADS)
Manini, N.; Braun, O. M.; Tosatti, E.; Guerra, R.; Vanossi, A.
2016-07-01
The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.
Friction and nonlinear dynamics.
Manini, N; Braun, O M; Tosatti, E; Guerra, R; Vanossi, A
2016-07-27
The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction. PMID:27249652
Magnetic Field-line Twist and Length Distributions inside Interplanetary Magnetic Flux Ropes
NASA Astrophysics Data System (ADS)
Hu, Qiang; Qiu, Jiong; Krucker, Sam
2015-04-01
We report on the detailed and systematic study of field-line twist and length distributions within magnetic flux ropes embedded in Interplanetary Coronal Mass Ejections (ICMEs). The Grad-Shafranov reconstruction method is utilized together with a constant-twist nonlinear force-free (Gold-Hoyle) flux rope model and the commonly known Lundquist (linear force-free) model to reveal the close relation between the field-line twist and length in cylindrical flux ropes, based on in-situ spacecraft magnetic field and plasma measurements. In particular, we utilize energetic electron burst observations at 1 AU together with associated type III radio emissions detected by the Wind spacecraft to provide unique measurements of magnetic field-line lengths within selected ICME events. These direct measurements are compared with flux-rope model calculations to help assess the fidelity of different models and to provide diagnostics of internal structures. We show that our initial analysis of field-line twist indicates clear deviation from the Lundquist model, but better consistency with the Gold-Hoyle model. By using the different flux-rope models, we conclude that the in-situ direct measurements of field-line lengths are consistent with a flux-rope structure with spiral field lines of constant and low twist, largely different from that of the Lundquist model, especially for relatively large-scale flux ropes. We will also discuss the implications of our analysis of flux-rope structures on the origination and evolution processes in their corresponding solar source regions.
NASA Astrophysics Data System (ADS)
Robles-Uriza, A. X.; Reyes Gómez, F.; Mejía-Salazar, J. R.
2016-09-01
We report the existence of multiple omnidirectional defect modes in the zero-nbar gap of photonic stacks, made of alternate layers of conventional dielectric and double-negative metamaterial, with a polaritonic defect layer. In the case of nonlinear magnetic metamaterials, the optical bistability phenomenon leads to switching from negligible to perfect transmission around these defect modes. We hope these findings have potential applications in the design and development of multichannel optical filters, power limiters, optical-diodes and optical-transistors.
NASA Astrophysics Data System (ADS)
Babin, Vasile D.; Grigore, Maria; Cojocaru, Laurentiu; Ersen, Simion; Moldovan, Adrian
1998-07-01
In this work we use a technique inspired by the inverse problem in the scattering theory, that is, the calculation of partial derivatives along the characteristic directions of the D'Alembert solution of the wave equation (Maxwell and Euler). In this way, we construct a system of stochastic non-linear differential equations. The analysis of this system, using algebraic invariants, gives more information in comparison with that given by Ghelfand-Levitan-Marcenko, in the inverse problem in the scattering theory.
NASA Astrophysics Data System (ADS)
Kurkin, S. A.; Koronovski, A. A.; Hramov, A. E.
2009-08-01
Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.
Liu, Xiaozhou; Zhang, Shujun; Luo, Jun; Shrout, Thomas R.; Cao, Wenwu
2010-01-01
Through second harmonic measurements, the ultrasonic nonlinearity parameters of [001]c and [111]c polarized 0.70Pb(Mg1∕3Nb2∕3)O3–0.30PbTiO3(PMN–0.3PT) single crystals have been measured as a function of bias electric field. It was found that the nonlinearity parameter increases almost linearly with field at low field but shows a drastic increase near the coercive field. The [111]c polarized single domain crystal has much smaller nonlinearity parameter than that of the [001]c polarized multidomain crystal. Based on effective symmetries of these crystals, we were able to derive the field dependence of several third order elastic constants, which are important parameters for high field applications. PMID:20198132
NASA Astrophysics Data System (ADS)
Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal
2013-01-01
A semi-analytical model with three optimizing parameters and a novel non-Gaussian function as the fundamental modal field solution has been proposed to arrive at an accurate solution to predict various propagation parameters of graded-index fibers with less computational burden than numerical methods. In our semi analytical formulation the optimization of core parameter U which is usually uncertain, noisy or even discontinuous, is being calculated by Nelder-Mead method of nonlinear unconstrained minimizations as it is an efficient and compact direct search method and does not need any derivative information. Three optimizing parameters are included in the formulation of fundamental modal field of an optical fiber to make it more flexible and accurate than other available approximations. Employing variational technique, Petermann I and II spot sizes have been evaluated for triangular and trapezoidal-index fibers with the proposed fundamental modal field. It has been demonstrated that, the results of the proposed solution identically match with the numerical results over a wide range of normalized frequencies. This approximation can also be used in the study of doped and nonlinear fiber amplifier.
2012-01-01
The linear and nonlinear intraband optical absorption coefficients in GaAs three-dimensional single quantum rings are investigated. Taking into account the combined effects of hydrostatic pressure and electric field, applied along the growth direction of the heterostructure, the energies of the ground and first excited states of a donor impurity have been found using the effective mass approximation and a variational method. The energies of these states are examined as functions of the dimensions of the structure, electric field, and hydrostatic pressure. We have also investigated the dependencies of the linear, nonlinear, and total optical absorption coefficients as a function of incident photon energy for several configurations of the system. It is found that the variation of distinct sizes of the structure leads to either a redshift and/or a blueshift of the resonant peaks of the intraband optical spectrum. In addition, we have found that the application of an electric field leads to a redshift, whereas the influence of hydrostatic pressure leads to a blueshift (in the case of on-ring-center donor impurity position) of the resonant peaks of the intraband optical spectrum. PMID:23021497
Barseghyan, Manuk G; Restrepo, Ricardo L; Mora-Ramos, Miguel E; Kirakosyan, Albert A; Duque, Carlos A
2012-01-01
: The linear and nonlinear intraband optical absorption coefficients in GaAs three-dimensional single quantum rings are investigated. Taking into account the combined effects of hydrostatic pressure and electric field, applied along the growth direction of the heterostructure, the energies of the ground and first excited states of a donor impurity have been found using the effective mass approximation and a variational method. The energies of these states are examined as functions of the dimensions of the structure, electric field, and hydrostatic pressure. We have also investigated the dependencies of the linear, nonlinear, and total optical absorption coefficients as a function of incident photon energy for several configurations of the system. It is found that the variation of distinct sizes of the structure leads to either a redshift and/or a blueshift of the resonant peaks of the intraband optical spectrum. In addition, we have found that the application of an electric field leads to a redshift, whereas the influence of hydrostatic pressure leads to a blueshift (in the case of on-ring-center donor impurity position) of the resonant peaks of the intraband optical spectrum. PMID:23021497
Nonlinear Optics and Applications
NASA Technical Reports Server (NTRS)
Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)
2007-01-01
Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.
NASA Astrophysics Data System (ADS)
Isa, Siti Suzilliana Putri Mohamed; Arifin, Norihan Md; Bachok@Lati, Norfifah; Ali, Fadzilah Md.; Nazar, Roslinda Mohd
2015-05-01
A theoretical study has been presented to describe the flow and heat transfer in the boundary layers on a nonlinearly stretching sheet with a variable wall temperature and suction, in the presence of magnetic field and non-uniform heat source. The governing partial differential equations are converted into ordinary differential equations by similarity transformation, which is then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and table for several sets of values of the parameters. The effects of the parameters on the flow and heat transfer characteristics are thoroughly examined.
NASA Technical Reports Server (NTRS)
Bell, T. F.
1984-01-01
A theory is presented of the nonlinear gyroresonance interaction that takes place in the magnetosphere between energetic electrons and coherent VLF waves propagating in the whistler mode at an arbitrary angle psi with respect to the earth's magnetic field B-sub-0. Particularly examined is the phase trapping (PT) mechanism believed to be responsible for the generation of VLF emissions. It is concluded that near the magnetic equatorial plane gradients of psi may play a very important part in the PT process for nonducted waves. Predictions of a higher threshold value for PT for nonducted waves generally agree with experimental data concerning VLF emission triggering by nonducted waves.
[Nonlinear magnetohydrodynamics
Not Available
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday`s law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm`s law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile.
Aschwanden, Markus J.; Sun, Xudong; Liu, Yang E-mail: xudongs@stanford.edu
2014-04-10
We developed a coronal nonlinear force-free field (COR-NLFFF) forward-fitting code that fits an approximate nonlinear force-free field (NLFFF) solution to the observed geometry of automatically traced coronal loops. In contrast to photospheric NLFFF codes, which calculate a magnetic field solution from the constraints of the transverse photospheric field, this new code uses coronal constraints instead, and this way provides important information on systematic errors of each magnetic field calculation method, as well as on the non-force-freeness in the lower chromosphere. In this study we applied the COR-NLFFF code to NOAA Active Region 11158, during the time interval of 2011 February 12-17, which includes an X2.2 GOES-class flare plus 35 M- and C-class flares. We calculated the free magnetic energy with a 6 minute cadence over 5 days. We find good agreement between the two types of codes for the total nonpotential E{sub N} and potential energy E{sub P} but find up to a factor of 4 discrepancy in the free energy E {sub free} = E{sub N} – E{sub P} and up to a factor of 10 discrepancy in the decrease of the free energy ΔE {sub free} during flares. The coronal NLFFF code exhibits a larger time variability and yields a decrease of free energy during the flare that is sufficient to satisfy the flare energy budget, while the photospheric NLFFF code shows much less time variability and an order of magnitude less free-energy decrease during flares. The discrepancy may partly be due to the preprocessing of photospheric vector data but more likely is due to the non-force-freeness in the lower chromosphere. We conclude that the coronal field cannot be correctly calculated on the basis of photospheric data alone and requires additional information on coronal loop geometries.
Particle in cell simulations of tearing modes in reversed-field-pinch-like plasma
Svidzinski, Vladmir; Li, Hui; Albright, Brian
2008-01-01
Particle in cell (PIC) simulations of tearing modes in two-dimensional plane geometry in a force free reversed field pinch (RFP) like plasma equilibrium are performed to study possible kinetic effects on these modes in RFPs. Linear tearing modes are compared in the PIC and two fluid models. The results showed that the growth rates and the profiles of magnetic field components in the two models are very similar, indicating that the kinetic effects on the tearing modes are weak such that the two fluid approximation is rather accurate for modeling these instabilities in RFPs. During the nonlinear evolution of the tearing mode in this geometry small scale secondary instabilities located near the internal layer of the primary tearing instability are excited. These secondary instabilities appear to be driven by the nonlinearly induced local pressure gradient in the regions of unfavorable curvature of the nonlinearly evolved magnetic field. They could also appear in a realistic RFP geometry and play a role during sawtooth crashes in these machines.
``Once Nonlinear, Always Nonlinear''
NASA Astrophysics Data System (ADS)
Blackstock, David T.
2006-05-01
The phrase "Once nonlinear, always nonlinear" is attributed to David F. Pernet. In the 1970s he noticed that nonlinearly generated higher harmonic components (both tones and noise) don't decay as small signals, no matter how far the wave propagates. Despite being out of step with the then widespread notion that small-signal behavior is restored in "old age," Pernet's view is supported by the Burgers-equation solutions of the early 1960s. For a plane wave from a sinusoidally vibrating source in a thermoviscous fluid, the old-age decay of the nth harmonic is e-nαx, not e-n2αx (small-signal expectation), where α is the absorption coefficient at the fundamental frequency f and x is propagation distance. Moreover, for spherical waves (r the distance) the harmonic diminishes as e-nαx/rn, not e-n2αx/r. While not new, these results have special application to aircraft noise propagation, since the large propagation distances of interest imply old age. The virtual source model may be used to explain the "anomalous" decay rates. In old age most of the nth harmonic sound comes from virtual sources close to the receiver. Their strength is proportional to the nth power of the local fundamental amplitude, and that sets the decay law for the nth harmonic.
NASA Astrophysics Data System (ADS)
Verde, E. L.; Landi, G. T.; Carrião, M. S.; Drummond, A. L.; Gomes, J. A.; Vieira, E. D.; Sousa, M. H.; Bakuzis, A. F.
2012-09-01
Further advances in magnetic hyperthermia might be limited by biological constraints, such as using sufficiently low frequencies and low field amplitudes to inhibit harmful eddy currents inside the patient's body. These incite the need to optimize the heating efficiency of the nanoparticles, referred to as the specific absorption rate (SAR). Among the several properties currently under research, one of particular importance is the transition from the linear to the non-linear regime that takes place as the field amplitude is increased, an aspect where the magnetic anisotropy is expected to play a fundamental role. In this paper we investigate the heating properties of cobalt ferrite and maghemite nanoparticles under the influence of a 500 kHz sinusoidal magnetic field with varying amplitude, up to 134 Oe. The particles were characterized by TEM, XRD, FMR and VSM, from which most relevant morphological, structural and magnetic properties were inferred. Both materials have similar size distributions and saturation magnetization, but strikingly different magnetic anisotropies. From magnetic hyperthermia experiments we found that, while at low fields maghemite is the best nanomaterial for hyperthermia applications, above a critical field, close to the transition from the linear to the non-linear regime, cobalt ferrite becomes more efficient. The results were also analyzed with respect to the energy conversion efficiency and compared with dynamic hysteresis simulations. Additional analysis with nickel, zinc and copper-ferrite nanoparticles of similar sizes confirmed the importance of the magnetic anisotropy and the damping factor. Further, the analysis of the characterization parameters suggested core-shell nanostructures, probably due to a surface passivation process during the nanoparticle synthesis. Finally, we discussed the effect of particle-particle interactions and its consequences, in particular regarding discrepancies between estimated parameters and expected
Davidson, R.C.; Chen, C.
1997-08-01
A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B{sup sol}({rvec x}) is developed. The analysis is carried out for a thin beam with characteristic beam radius r{sub b} {much_lt} S, and directed axial momentum {gamma}{sub b}m{beta}{sub b}c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f{sub b}({rvec x},{rvec p},t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B{sub z}(z) = B{sub 0} = const. and for the case of a periodic solenoidal focusing field B{sub z}(z + S) = B{sub z}(z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field {rvec B}{sup sol}({rvec x}) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria.
NASA Astrophysics Data System (ADS)
Ezersky, A. B.; Marin, F.
2008-08-01
This paper reports the results of an experimental and theoretical study of the segregation of heavy (sand) and light [polyvinyl chloride (PVC)] grains under the action of intense nonlinear water waves, solitons. The tests are carried out with initially carefully mixed grains at the bottom of a wave flume used in resonant mode. Ripples form on the bed and the segregation process is considered after the stopping of the wave paddle. The waves are damped and the PVC grains concentrate in a narrow region close to the ripple crest. A theoretical model explaining this grain density segregation is developed.
Ezersky, A B; Marin, F
2008-08-01
This paper reports the results of an experimental and theoretical study of the segregation of heavy (sand) and light [polyvinyl chloride (PVC)] grains under the action of intense nonlinear water waves, solitons. The tests are carried out with initially carefully mixed grains at the bottom of a wave flume used in resonant mode. Ripples form on the bed and the segregation process is considered after the stopping of the wave paddle. The waves are damped and the PVC grains concentrate in a narrow region close to the ripple crest. A theoretical model explaining this grain density segregation is developed. PMID:18850874
NASA Technical Reports Server (NTRS)
Vaidya, P. G.; Wang, K. S.
1977-01-01
Nonlinear acoustic interactions at the second order (so-called weak interactions) of the perturbation scheme have been recognized for a long time. This paper examines the possibility of stronger interactions at the first order which are found in rigid rectangular ducts and to a lesser degree in slightly soft rectangular ducts. The strong interactions occur if any two modes have identical phase speeds, the case of multimode and multifrequency input for example. An important consequence of the strong interaction is the self-generation of subharmonics. Even a small amount of subharmonic can, given the right phase conditions, grow through a strong interaction with a higher harmonic.
EXTRAPOLATION OF THE SOLAR CORONAL MAGNETIC FIELD FROM SDO/HMI MAGNETOGRAM BY A CESE-MHD-NLFFF CODE
Jiang Chaowei; Feng Xueshang E-mail: fengx@spaceweather.ac.cn
2013-06-01
Due to the absence of direct measurement, the magnetic field in the solar corona is usually extrapolated from the photosphere in a numerical way. At the moment, the nonlinear force-free field (NLFFF) model dominates the physical models for field extrapolation in the low corona. Recently, we have developed a new NLFFF model with MHD relaxation to reconstruct the coronal magnetic field. This method is based on CESE-MHD model with the conservation-element/solution-element (CESE) spacetime scheme. In this paper, we report the application of the CESE-MHD-NLFFF code to Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) data with magnetograms sampled for two active regions (ARs), NOAA AR 11158 and 11283, both of which were very non-potential, producing X-class flares and eruptions. The raw magnetograms are preprocessed to remove the force and then inputted into the extrapolation code. Qualitative comparison of the results with the SDO/AIA images shows that our code can reconstruct magnetic field lines resembling the EUV-observed coronal loops. Most important structures of the ARs are reproduced excellently, like the highly sheared field lines that suspend filaments in AR 11158 and twisted flux rope which corresponds to a sigmoid in AR 11283. Quantitative assessment of the results shows that the force-free constraint is fulfilled very well in the strong-field regions but apparently not that well in the weak-field regions because of data noise and numerical errors in the small currents.
Karzova, M.; Cunitz, B.; Kreider, W.; Bailey, M.; Yuldashev, P.; Andriyakhina, Y.; Sapozhnikov, O.; Khokhlova, V.
2015-10-28
Newer imaging and therapeutic ultrasound technologies require higher in situ pressure levels compared to conventional diagnostic values. One example is the recently developed use of focused ultrasonic radiation force to move kidney stones and residual fragments out of the urinary collecting system. A commercial diagnostic 2.3 MHz C5-2 array probe is used to deliver the acoustic pushing pulses. The probe comprises 128 elements equally spaced at the 55 mm long convex cylindrical surface with 38 mm radius of curvature. The efficacy of the treatment can be increased by using higher intensity at the focus to provide stronger pushing force; however, nonlinear acoustic saturation can be a limiting factor. In this work nonlinear propagation effects were analyzed for the C5-2 transducer using a combined measurement and modeling approach. Simulations were based on the 3D Westervelt equation; the boundary condition was set to match the focal geometry of the beam as measured at a low power output. Focal waveforms simulated for increased output power levels were compared with the fiber-optic hydrophone measurements and were found in good agreement. It was shown that saturation effects do limit the acoustic pressure in the focal region of the transducer. This work has application to standard diagnostic probes and imaging.
Karzova, M.; Cunitz, B.; Yuldashev, P.; Andriyakhina, Y.; Kreider, W.; Sapozhnikov, O.; Bailey, M.; Khokhlova, V.
2016-01-01
Newer imaging and therapeutic ultrasound technologies require higher in situ pressure levels compared to conventional diagnostic values. One example is the recently developed use of focused ultrasonic radiation force to move kidney stones and residual fragments out of the urinary collecting system. A commercial diagnostic 2.3 MHz C5-2 array probe is used to deliver the acoustic pushing pulses. The probe comprises 128 elements equally spaced at the 55 mm long convex cylindrical surface with 38 mm radius of curvature. The efficacy of the treatment can be increased by using higher transducer output to provide stronger pushing force; however, nonlinear acoustic saturation effect can be a limiting factor. In this work nonlinear propagation effects were analyzed for the C5-2 transducer using a combined measurement and modeling approach. Simulations were based on the 3D Westervelt equation; the boundary condition was set to match low power pressure beam scans. Focal waveforms simulated for increased output power levels were compared with the fiber-optic hydrophone measurements and were found in good agreement. It was shown that saturation effects do limit the acoustic pressure in the focal region of the transducer. This work has application to standard diagnostic probes and imaging. PMID:27087711
NASA Astrophysics Data System (ADS)
Karzova, M.; Cunitz, B.; Yuldashev, P.; Andriyakhina, Y.; Kreider, W.; Sapozhnikov, O.; Bailey, M.; Khokhlova, V.
2015-10-01
Newer imaging and therapeutic ultrasound technologies require higher in situ pressure levels compared to conventional diagnostic values. One example is the recently developed use of focused ultrasonic radiation force to move kidney stones and residual fragments out of the urinary collecting system. A commercial diagnostic 2.3 MHz C5-2 array probe is used to deliver the acoustic pushing pulses. The probe comprises 128 elements equally spaced at the 55 mm long convex cylindrical surface with 38 mm radius of curvature. The efficacy of the treatment can be increased by using higher intensity at the focus to provide stronger pushing force; however, nonlinear acoustic saturation can be a limiting factor. In this work nonlinear propagation effects were analyzed for the C5-2 transducer using a combined measurement and modeling approach. Simulations were based on the 3D Westervelt equation; the boundary condition was set to match the focal geometry of the beam as measured at a low power output. Focal waveforms simulated for increased output power levels were compared with the fiber-optic hydrophone measurements and were found in good agreement. It was shown that saturation effects do limit the acoustic pressure in the focal region of the transducer. This work has application to standard diagnostic probes and imaging.
NASA Astrophysics Data System (ADS)
Giraldo-Tobón, Eugenio; Ospina, Walter; Miranda-Pedraza, Guillermo L.; Mora-Ramos, Miguel E.
2015-07-01
The coefficients of the second-order nonlinear optical rectification and the generation of second and third harmonics, related to electron energy transitions in a two-dimensional elliptical quantum dot are calculated. The conduction band states are obtained using the finite element method to numerically solve the effective mass Schrödinger differential equation in the parabolic approximation, including the influence of an externally applied static electric field. It comes about that the geometry of the ellipse has a strong influence on the optical response, being the large eccentricity case the more favorable one. Furthermore, it is shown that the application of an electric field is of most importance for achieving well-resolved higher harmonics signals.
Deriving Potential Coronal Magnetic Fields from Vector Magnetograms
NASA Astrophysics Data System (ADS)
Welsch, Brian T.; Fisher, George H.
2016-08-01
The minimum-energy configuration for the magnetic field above the solar photosphere is curl-free (hence, by Ampère's law, also current-free), so can be represented as the gradient of a scalar potential. Since magnetic fields are divergence free, this scalar potential obeys Laplace's equation, given an appropriate boundary condition (BC). With measurements of the full magnetic vector at the photosphere, it is possible to employ either Neumann or Dirichlet BCs there. Historically, the Neumann BC was used with available line-of-sight magnetic field measurements, which approximate the radial field needed for the Neumann BC. Since each BC fully determines the 3D vector magnetic field, either choice will, in general, be inconsistent with some aspect of the observed field on the boundary, due to the presence of both currents and noise in the observed field. We present a method to combine solutions from both Dirichlet and Neumann BCs to determine a hybrid, "least-squares" potential field, which minimizes the integrated square of the residual between the potential and actual fields. We also explore weighting the residuals in the fit by spatially uniform measurement uncertainties. This has advantages both in not overfitting the radial field used for the Neumann BC, and in maximizing consistency with the observations. We demonstrate our methods with SDO/HMI vector magnetic field observations of active region 11158, and find that residual discrepancies between the observed and potential fields are significant, and they are consistent with nonzero horizontal photospheric currents. We also analyze potential fields for two other active regions observed with two different vector magnetographs, and find that hybrid-potential fields have significantly less energy than the Neumann fields in every case - by more than 10^{32} erg in some cases. This has major implications for estimates of free magnetic energy in coronal field models, e.g., non-linear force-free field extrapolations.
Deriving Potential Coronal Magnetic Fields from Vector Magnetograms
NASA Astrophysics Data System (ADS)
Welsch, Brian T.; Fisher, George H.
2016-06-01
The minimum-energy configuration for the magnetic field above the solar photosphere is curl-free (hence, by Ampère's law, also current-free), so can be represented as the gradient of a scalar potential. Since magnetic fields are divergence free, this scalar potential obeys Laplace's equation, given an appropriate boundary condition (BC). With measurements of the full magnetic vector at the photosphere, it is possible to employ either Neumann or Dirichlet BCs there. Historically, the Neumann BC was used with available line-of-sight magnetic field measurements, which approximate the radial field needed for the Neumann BC. Since each BC fully determines the 3D vector magnetic field, either choice will, in general, be inconsistent with some aspect of the observed field on the boundary, due to the presence of both currents and noise in the observed field. We present a method to combine solutions from both Dirichlet and Neumann BCs to determine a hybrid, "least-squares" potential field, which minimizes the integrated square of the residual between the potential and actual fields. We also explore weighting the residuals in the fit by spatially uniform measurement uncertainties. This has advantages both in not overfitting the radial field used for the Neumann BC, and in maximizing consistency with the observations. We demonstrate our methods with SDO/HMI vector magnetic field observations of active region 11158, and find that residual discrepancies between the observed and potential fields are significant, and they are consistent with nonzero horizontal photospheric currents. We also analyze potential fields for two other active regions observed with two different vector magnetographs, and find that hybrid-potential fields have significantly less energy than the Neumann fields in every case - by more than 10^{32} erg in some cases. This has major implications for estimates of free magnetic energy in coronal field models, e.g., non-linear force-free field extrapolations.
Magnetic field line lengths inside interplanetary magnetic flux ropes
NASA Astrophysics Data System (ADS)
Hu, Qiang; Qiu, Jiong; Krucker, Sam
2015-07-01
We report on the detailed and systematic study of field line twist and length distributions within magnetic flux ropes embedded in interplanetary coronal mass ejections (ICMEs). The Grad-Shafranov reconstruction method is utilized together with a constant-twist nonlinear force-free (Gold-Hoyle) flux rope model to reveal the close relation between the field line twist and length in cylindrical flux ropes, based on in situ Wind spacecraft measurements. We show that the field line twist distributions within interplanetary flux ropes are inconsistent with the Lundquist model. In particular, we utilize the unique measurements of magnetic field line lengths within selected ICME events as provided by Kahler et al. () based on energetic electron burst observations at 1 AU and the associated type III radio emissions detected by the Wind spacecraft. These direct measurements are compared with our model calculations to help assess the flux rope interpretation of the embedded magnetic structures. By using the different flux rope models, we show that the in situ direct measurements of field line lengths are consistent with a flux rope structure with spiral field lines of constant and low twist, largely different from that of the Lundquist model, especially for relatively large-scale flux ropes.
Kirtman, Bernard; Springborg, Michael; Rérat, Michel; Ferrero, Mauro; Lacivita, Valentina; Dovesi, Roberto; Orlando, Roberto
2015-01-22
An implementation of the vector potential approach (VPA) for treating the response of infinite periodic systems to static and dynamic electric fields has been initiated within the CRYSTAL code. The VPA method is based on the solution of a time-dependent Hartree-Fock or Kohn-Sham equation for the crystal orbitals wherein the usual scalar potential, that describes interaction with the field, is replaced by the vector potential. This equation may be solved either by perturbation theory or by finite field methods. With some modification all the computational procedures of molecular ab initio quantum chemistry can be adapted for periodic systems. Accessible properties include the linear and nonlinear responses of both the nuclei and the electrons. The programming of static field pure electronic (hyper)polarizabilities has been successfully tested. Dynamic electronic (hyper)polarizabilities, as well as infrared and Raman intensities, are in progress while the addition of finite fields for calculation of vibrational (hyper)polarizabilities, through nuclear relaxation procedures, will begin shortly.
Mehdian, H. Kargarian, A.; Hajisharifi, K.
2015-06-15
In this paper, the effect of an external inhomogeneous magnetic field on the high intensity laser absorption rate in a sub-critical plasma has been investigated by employing a relativistic electromagnetic 1.5 dimensional particle-in-cell code. Relying on the effective nonlinear phenomena such as phase-mixing and scattering, this study shows that in a finite-size plasma the laser absorption increases with inhomogeneity of the magnetic field (i.e., reduction of characteristic length of inhomogeneous magnetic field, λ{sub p}) before exiting a considerable amount of laser energy from the plasma due to scattering process. On the other hand, the presence of the external inhomogeneous magnetic field causes the maximum absorption of laser to occur at a shorter time. Moreover, study of the kinetic results associated with the distribution function of plasma particles shows that, in a special range of the plasma density and the characteristic length of inhomogeneous magnetic field, a considerable amount of laser energy is transferred to the particles producing a population of electrons with kinetic energy along the laser direction.
NASA Astrophysics Data System (ADS)
Gu, Zhan
1998-09-01
A new localized smoothing filter based on the least squares is proposed in this study. It has been found the use of an appropriate smoothing method is critical to the success of numerical prediction of separating flow problems with nonlinear turbulence models. The new smoothing filter effectively eliminated numerical fluctuations due to the nonlineality of the turbulence model and the higher order approximation. The efficiency of using this scheme is very attractive; less than 20% more CPU time is needed for the extra computation in simulations. Modification has been made to the nonlinear model to take into consideration of low Reynolds number effects. The two-dimensional turbulent recirculating flow field behind a V-shaped bluff body has been investigated numerically. Similar bluff bodies are used in combustion chambers for flame stabilization. The study helps to gain a comprehensive understanding of the mechanism of the flame stability and major factors that affect this stability, and thereby establishes a more reasonable physical model. The validation test of turbulent flow over a backward facing step shows that the modified nonlinear turbulence model significantly improved the overall prediction. Predicted results for both mean flow field and turbulence quantities agreed very well experimental results. The prediction error for the characteristic reattachment length has been reduced from 18% to 4% compared with the experimental data. The results of simulation of flow field behind the bluff body are also improved by using this model. The degree of improvement varies for different flow variables. Parametric investigation of the flow field by varying the shape and size of the bluff body is also performed. It has been found that the axial distributions of normalized reverse mass flow rate for different configurations are similar. The maximum reverse mass flow rate increases monotonically with the base height as well as with the included angle of the bluff body, but
Malanushenko, A.; Schrijver, C. J.; DeRosa, M. L.; Wheatland, M. S.
2014-03-10
The shapes of solar coronal loops are sensitive to the presence of electrical currents that are the carriers of the non-potential energy available for impulsive activity. We use this information in a new method for modeling the coronal magnetic field of active region (AR) 11158 as a nonlinear force-free field (NLFFF). The observations used are coronal images around the time of major flare activity on 2011 February 15, together with the surface line-of-sight magnetic field measurements. The data are from the Helioseismic and Magnetic Imager and Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The model fields are constrained to approximate the coronal loop configurations as closely as possible, while also being subject to the force-free constraints. The method does not use transverse photospheric magnetic field components as input and is thereby distinct from methods for modeling NLFFFs based on photospheric vector magnetograms. We validate the method using observations of AR 11158 at a time well before major flaring and subsequently review the field evolution just prior to and following an X2.2 flare and associated eruption. The models indicate that the energy released during the instability is about 1 × 10{sup 32} erg, consistent with what is needed to power such a large eruptive flare. Immediately prior to the eruption, the model field contains a compact sigmoid bundle of twisted flux that is not present in the post-eruption models, which is consistent with the observations. The core of that model structure is twisted by ≈0.9 full turns about its axis.
Anomalous resistivity and the evolution of magnetic field topology
NASA Technical Reports Server (NTRS)
Parker, E. N.
1993-01-01
This paper explores the topological restructuring of a force-free magnetic field caused by the hypothetical sudden onset of a localized region of strong anomalous resistivity. It is shown that the topological complexity increases, with the primitive planar force-free field with straight field lines developing field lines that wrap half a turn around each other, evidently providing a surface of tangential discontinuity in the wraparound region. It is suggested that the topological restructuring contributes to the complexity of the geomagnetic substorm, the aurora, and perhaps some of the flare activity on the sun, or other star, and the Galactic halo.
J.A. Krommes
2009-05-19
Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K-χ theorem is discussed. An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.
Hinterbichler, Kurt; Joyce, Austin; Khoury, Justin E-mail: joyceau@sas.upenn.edu
2012-06-01
The pseudo-conformal scenario is an alternative to inflation in which the early universe is described by an approximate conformal field theory on flat, Minkowski space. Some fields acquire a time-dependent expectation value, which breaks the flat space so(4,2) conformal algebra to its so(4,1) de Sitter subalgebra. As a result, weight-0 fields acquire a scale invariant spectrum of perturbations. The scenario is very general, and its essential features are determined by the symmetry breaking pattern, irrespective of the details of the underlying microphysics. In this paper, we apply the well-known coset technique to derive the most general effective lagrangian describing the Goldstone field and matter fields, consistent with the assumed symmetries. The resulting action captures the low energy dynamics of any pseudo-conformal realization, including the U(1)-invariant quartic model and the Galilean Genesis scenario. We also derive this lagrangian using an alternative method of curvature invariants, consisting of writing down geometric scalars in terms of the conformal mode. Using this general effective action, we compute the two-point function for the Goldstone and a fiducial weight-0 field, as well as some sample three-point functions involving these fields.
NASA Astrophysics Data System (ADS)
Qi, Yusheng; Yue, Dick
2015-11-01
We use direct nonlinear phase-resolved simulations based on a High-Order Spectral (HOS) method (Dommermuth & Yue 1987) to understand and quantify wave-breaking dissipation in the evolution of general irregular short-crested wave-fields. We achieve this by incorporating a robust phenomenological-based wave breaking model in HOS simulations to account for energy dissipation. This model can automatically simulate the onset of wave breaking, and the simulated wave-breaking dissipation strength differentiates corresponding to different wave breaking type (such as spilling or plunging breaking waves). The efficacy of this model is confirmed by direct comparisons against measurements for the energy loss in 2D and 3D breaking events. By comparing simulated wave-fields with and without the dissipation model in HOS, we obtain the dissipation field, which provides the times, locations and intensity of wave breaking events. From the dissipation field we further calculate the distribution of total length of breaking wave front per unit surface area per unit increment of breaking velocity (Phillips 1985), and obtain qualitative agreement with Phillips theoretical power-law.
Sedaghat, M.; Ettehadi-Abari, M.; Shokri, B. Ghorbanalilu, M.
2015-03-15
Laser absorption in the interaction between ultra-intense femtosecond laser and solid density plasma is studied theoretically here in the intensity range Iλ{sup 2}≃10{sup 14}−10{sup 16}Wcm{sup −2}μm{sup 2}. The collisional effect is found to be significant when the incident laser intensity is less than 10{sup 16}Wcm{sup −2}μm{sup 2}. In the current work, the propagation of a high frequency electromagnetic wave, for underdense collisional plasma in the presence of an external magnetic field is investigated. It is shown that, by considering the effect of the ponderomotive force in collisional magnetized plasmas, the increase of laser pulse intensity leads to steepening of the electron density profile and the electron bunches of plasma makes narrower. Moreover, it is found that the wavelength of electric and magnetic fields oscillations increases by increasing the external magnetic field and the density distribution of electrons also grows in comparison with the unmagnetized collisional plasma. Furthermore, the spatial damping rate of laser energy and the nonlinear bremsstrahlung absorption coefficient are obtained in the collisional regime of magnetized plasma. The other remarkable result is that by increasing the external magnetic field in this case, the absorption coefficient increases strongly.
Davidson, R.C.; Lee, W.W.; Stoltz, P.
1997-08-01
This paper presents a detailed formulation and analysis of the rate equations for statistically-averaged quantities for an intense nonneutral beam propagating through a periodic solenoidal focusing field B{sup sol}(x). The analysis is based on the nonlinear Vlasov-Maxwell equations in the electrostatic approximation, assuming a thin beam with characteristic beam radius r{sub b} {much_lt} S. The results are applied to investigate the nonlinear evolution of the generalized entropy, mean canonical angular momentum {l_angle}P{sub {theta}}{r_angle}, center-of-mass motion for {l_angle}X{r_angle} and {l_angle}Y{r_angle}, mean kinetic energy (1/2) {l_angle}X{sup {prime}2} + Y{sup {prime}2}{r_angle}, mean-square beam radius {l_angle}X{sup 2} + Y{sup 2}{r_angle}, and coupled rate equations for the unnormalized transverse emittance {epsilon}(s) and root-mean-square beam radius R{sub b}(s) = {l_angle}X{sup 2} + Y{sup 2}{r_angle}{sup 1/2}. Global energy balance is discussed, and the coupled rate equations for {epsilon}(s) and R{sub b}(s) are examined for the class of axisymmetric beam distributions F{sub b}.
NASA Astrophysics Data System (ADS)
Zhang, Li
2015-11-01
Based on the compact density matrix approach, the linear and nonlinear refractive index change (RIC) and optical rectification (OR) coefficients in a GaN-based step QW with strong built-in electric field (BEF) have been theoretically deduced and investigated in detail. The analytical electronic state is derived by the two airy functions. And the band nonparabolicity is taken into account by using an energy dependence effective mass (EDEM) method. Numerical calculations on a four-layer AlN/GaN/AlxGa1-xN/AlN step QW are performed, and the curves for the geometric factors, the linear, the nonlinear, the total RICs and the OR coefficients as functions of the structural parameters of the step QW are discussed. The features for these curves were specified and reasons for the features were explained reasonably. It is found that the decreasing of well width Lw, and step barrier width Lb and the doped concentration x in step barrier will result in the significant enhancement of the RICs. With the decrease of Lw, Lb and x, the resonant photon energies of RIC and OR coefficients have obvious blue-shift. Moreover, the RIC and OR coefficients behave different dependence on the structural parameters of the GaN-based step QWs. The profound physical reasons are also analyzed.
Thakur, Pramodsingh H.; Fitzgerald, Paul J.; Lane, John W.; Hsiao, Steven S.
2007-01-01
We investigate the position invariant receptive field properties of neurons in the macaque second somatosensory (SII) cortical region. Previously we reported that many SII region neurons show orientation tuning in the center of multiple finger pads of the hand and further that the tuning is similar on different pads, which can be interpreted as position invariance. Here we study the receptive field properties of a single finger pad for a subset (n = 61) of those 928 neurons, using a motorized oriented bar that we positioned at multiple locations across the pad. We calculate both vector fields and linear receptive fields of the finger pad to characterize the receptive field properties that give rise to the tuning, and we perform an additional regression analysis to quantify linearity, invariance, or both in individual neurons. We show that orientation tuning of SII region neurons is based on a variety of mechanisms. For some neurons, the tuning is explained by simple excitatory regions, simple inhibitory regions, or some combination of these structures. However, a large fraction of the neurons (n = 20 of 61, 33%) show position invariance that is not explained well by their linear receptive fields. Finding invariance within a finger pad, coupled with the previous result of similar tuning on different pads, indicates that some SII region neurons may exhibit similar tuning throughout large regions of the hand. We hypothesize that invariant neurons play an important role in tactile form recognition. PMID:17192440
Nonlinear diffusion and superconducting hysteresis
Mayergoyz, I.D.
1996-12-31
Nonlinear diffusion of electromagnetic fields in superconductors with ideal and gradual resistive transitions is studied. Analytical results obtained for linear and nonlinear polarizations of electromagnetic fields are reported. These results lead to various extensions of the critical state model for superconducting hysteresis.
Bennett, Kochise Mukamel, Shaul
2014-01-28
The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field that are initially in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, the susceptibility of a collection of N non-interacting molecules is additive and scales as N. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as N{sup 2}.
NASA Technical Reports Server (NTRS)
Wheeler, A. A.; Mcfadden, G. B.; Coriell, S. R.; Hurle, D. T. J.
1990-01-01
The effect of a constant electric current on the crystal-melt interface morphology during directional solidification at constant velocity of a binary alloy is considered. A linear temperature field is assumed, and thermoelectric effects and Joule heating are neglected; electromigration and differing electrical conductivities of crystal and melt are taken into account. A two-dimensional weakly nonlinear analysis is carried out to third order in the interface amplitude, resulting in a cubic amplitude equation that describes whether the bifurcation from the planar state is supercritical or subcritical. For wavelengths corresponding to the most dangerous mode of linear theory, the demarcation between supercritical and subcritical behavior is calculated as a function of processing conditions and material parameters. The bifurcation behavior is a sensitive function of the magnitude and direction of the electric current and of the electrical conductivity ratio.
Hramov, A. E.; Koronovskii, A. A.; Kurkin, S. A.; Filatova, A. E.
2012-11-15
The report is devoted to the results of the numerical study of the virtual cathode (VC) formation conditions in the relativistic electron beam (REB) under the influence of the self-magnetic and external axial magnetic fields. The azimuthal instability of the relativistic electron beam leading to the formation of the vortex electron structure in the system was found out. This instability is determined by the influence of the self-magnetic fields of the relativistic electron beam, and it leads to the decrease of the critical value of the electron beam current (current when the non-stationary virtual cathode is formed in the drift space). The typical dependencies of the critical current on the external uniform magnetic field value were discovered. The effect of the beam thickness on the virtual cathode formation conditions was also analyzed.
NASA Astrophysics Data System (ADS)
Ghatak, Kamakhya P.
1990-08-01
An attempt is made to study the photoemission :eron 3D quantum well boxes (QWBs) of nonlinear optical materials in the presence of crossed electric and magnetic fields, taking ternary chalcopyrite semiconductors as an example. Consi3ering the anisotropic crystal potential in the Harniltonian, we have formulated the generalized electron energy spectrum taking into account the anisotropies of the 0ther energy band par arne ter s, within the fr sine work of theory. We have then derlved.the photoernission from 3D QWBs of ternary chalCopyrite compounds by using the modified dispersion law under cross field configuration in the said material. It is found, taking 3D QWBs of n-CdGeAs2 as an example, that the photoernission exhibits ladder like dependence with incident photon energy as found in quanturn Hall effect and the corresponding results for three and two-band Kane models together with that of parabolic energy bands have been obtained from the present generalized exjressions as special cases. The photoeinission decreases with increasing magnetic field and decreasing electron concentration respectively. The oscillations in accordance with the present generalized model show up much more significantly and are in agreement with the experimental results as given elsewhere.
NASA Astrophysics Data System (ADS)
Li, Haipeng; Xu, Hu; Shen, Xiaopeng; Han, Kui; Bi, Zetong; Xu, Runfeng
2016-06-01
We investigated the electronic properties and second hyperpolarizabilities of hydrogenated silicon nanoclusters (H-SiNCs) by using the density functional theory method. The effects of cluster size, external electric field and incident frequency on the second hyperpolarizability were also examined, respectively. We found that small H-SiNCs exhibit large second hyperpolarizability. With the increase of the number of silicon atoms in H-SiNCs, the frontier molecular orbital energy gap decreases, attributed to the enhancement of the second hyperpolarizability. Interestingly, we also found the electric-field-induced gigantic enhancement of the second hyperpolarizability for H-SiNCs due to the change of electron density distributions. In addition, our results demonstrate a significant dependence on the frequency of incident light.
Li, Haipeng; Xu, Hu; Shen, Xiaopeng; Han, Kui; Bi, Zetong; Xu, Runfeng
2016-01-01
We investigated the electronic properties and second hyperpolarizabilities of hydrogenated silicon nanoclusters (H-SiNCs) by using the density functional theory method. The effects of cluster size, external electric field and incident frequency on the second hyperpolarizability were also examined, respectively. We found that small H-SiNCs exhibit large second hyperpolarizability. With the increase of the number of silicon atoms in H-SiNCs, the frontier molecular orbital energy gap decreases, attributed to the enhancement of the second hyperpolarizability. Interestingly, we also found the electric-field-induced gigantic enhancement of the second hyperpolarizability for H-SiNCs due to the change of electron density distributions. In addition, our results demonstrate a significant dependence on the frequency of incident light. PMID:27305957
Li, Haipeng; Xu, Hu; Shen, Xiaopeng; Han, Kui; Bi, Zetong; Xu, Runfeng
2016-01-01
We investigated the electronic properties and second hyperpolarizabilities of hydrogenated silicon nanoclusters (H-SiNCs) by using the density functional theory method. The effects of cluster size, external electric field and incident frequency on the second hyperpolarizability were also examined, respectively. We found that small H-SiNCs exhibit large second hyperpolarizability. With the increase of the number of silicon atoms in H-SiNCs, the frontier molecular orbital energy gap decreases, attributed to the enhancement of the second hyperpolarizability. Interestingly, we also found the electric-field-induced gigantic enhancement of the second hyperpolarizability for H-SiNCs due to the change of electron density distributions. In addition, our results demonstrate a significant dependence on the frequency of incident light. PMID:27305957
NASA Technical Reports Server (NTRS)
Bell, T. F.
1986-01-01
A recently developed theory is used to calculate the wave magnetic field amplitude threshold, B-tau, necessary to allow the nonlinear trapping of energetic gyroresonant and Landau resonant electrons by VLF whistler mode waves in the magnetosphere propagating at an arbitrary angle, psi, with respect to the earth's magnetic field. A detailed raytracing study is carried out to establish the variation of psi with position along each magnetic shell in the range L = 2-5 and for frequencies 5-17.8 kHz. It is found that the minimum values of B-tau along each L shell generally occur at points of second-order resonance. In general, for nonducted fixed frequency signals there is only one point of second-order resonance on each L shell, and this is located within a few degrees of the magnetic equator. However, over a narrow range of L, there are as many as three points of second-order resonance and as many as three associated minima in B-tau. At least one of these points is located more than 10 deg from the magnetic equator.
NASA Astrophysics Data System (ADS)
Auzinsh, M.; Berzins, A.; Ferber, R.; Gahbauer, F.; Kalvans, L.; Mozers, A.; Spiss, A.
2015-05-01
We studied alignment-to-orientation conversion caused by excited-state level crossings in a nonzero magnetic field of both atomic rubidium isotopes. Experimental measurements were performed on the transitions of the D2 line of rubidium. These measured signals were described by a theoretical model that takes into account all neighboring hyperfine transitions, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. In the experiments, laser-induced fluorescence components were observed at linearly polarized excitation and their difference was taken afterwards. By observing the two oppositely circularly polarized components, we were able to see structures not visible in the difference graphs, which give deeper insight into the processes responsible for these signals. We studied how these signals are dependent on intensity and how they are affected when the exciting laser is tuned to different hyperfine transitions. The comparison between experiment and theory was carried out fulfilling the nonlinear absorption conditions. The theoretical curves described the experimental measurements satisfactorily, reproducing even small features in the shapes of the curves.
Coronal magnetic fields produced by photospheric shear
NASA Technical Reports Server (NTRS)
Sturrock, P. A.; Yang, W.-H.
1987-01-01
The magneto-frictional method is used for computing force free fields to examine the evolution of the magnetic field of a line dipole, when there is relative shearing motion between the two polarities. It found that the energy of the sheared field can be arbitrarily large compared with the potential field. It is also found that it is possible to fit the magnetic energy, as a function of shear, by a simple functional form.
NASA Astrophysics Data System (ADS)
Wang, Rui; Liu, Ying D.; Dai, Xinghua; Yang, Zhongwei; Huang, Chong; Hu, Huidong
2015-11-01
We study the role of the coronal magnetic field configuration of an active region (AR) in determining the propagation direction of a coronal mass ejection (CME). The CME occurred in the AR 11944 (S09W01) near the disk center on 2014 January 7 and was associated with an X1.2 flare. A new CME reconstruction procedure based on a polarimetric technique is adopted, which shows that the CME changed its propagation direction by around 28° in latitude within 2.5 {R}⊙ and 43° in longitude within 6.5 {R}⊙ with respect to the CME source region. This significant non-radial motion is consistent with the finding of Möstl et al. We use nonlinear force-free field and potential field source surface extrapolation methods to determine the configurations of the coronal magnetic field. We also calculate the magnetic energy density distributions at different heights based on the extrapolations. Our results show that the AR coronal magnetic field has a strong influence on the CME propagation direction. This is consistent with the “channeling” by the AR coronal magnetic field itself, rather than deflection by nearby structures. These results indicate that the AR coronal magnetic field configuration has to be taken into account in order to determine CME propagation direction correctly.
NASA Astrophysics Data System (ADS)
Banerjee, Tanmoy; Biswas, Debabrata
2013-12-01
We explore and experimentally demonstrate the phenomena of amplitude death (AD) and the corresponding transitions through synchronized states that lead to AD in coupled intrinsic time-delayed hyperchaotic oscillators interacting through mean-field diffusion. We identify a novel synchronization transition scenario leading to AD, namely transitions among AD, generalized anticipatory synchronization (GAS), complete synchronization (CS), and generalized lag synchronization (GLS). This transition is mediated by variation of the difference of intrinsic time-delays associated with the individual systems and has no analogue in non-delayed systems or coupled oscillators with coupling time-delay. We further show that, for equal intrinsic time-delays, increasing coupling strength results in a transition from the unsynchronized state to AD state via in-phase (complete) synchronized states. Using Krasovskii-Lyapunov theory, we derive the stability conditions that predict the parametric region of occurrence of GAS, GLS, and CS; also, using a linear stability analysis, we derive the condition of occurrence of AD. We use the error function of proper synchronization manifold and a modified form of the similarity function to provide the quantitative support to GLS and GAS. We demonstrate all the scenarios in an electronic circuit experiment; the experimental time-series, phase-plane plots, and generalized autocorrelation function computed from the experimental time series data are used to confirm the occurrence of all the phenomena in the coupled oscillators.
Large scale reconstruction of the solar coronal magnetic field
NASA Astrophysics Data System (ADS)
Amari, T.; Aly, J.-J.; Chopin, P.; Canou, A.; Mikic, Z.
2014-10-01
It is now becoming necessary to access the global magnetic structure of the solar low corona at a large scale in order to understand its physics and more particularly the conditions of energization of the magnetic fields and the multiple connections between distant active regions (ARs) which may trigger eruptive events in an almost coordinated way. Various vector magnetographs, either on board spacecraft or ground-based, currently allow to obtain vector synoptic maps, composite magnetograms made of multiple interactive ARs, and full disk magnetograms. We present a method recently developed for reconstructing the global solar coronal magnetic field as a nonlinear force-free magnetic field in spherical geometry, generalizing our previous results in Cartesian geometry. This method is implemented in the new code XTRAPOLS, which thus appears as an extension of our active region scale code XTRAPOL. We apply our method by performing a reconstruction at a specific time for which we dispose of a set of composite data constituted of a vector magnetogram provided by SDO/HMI, embedded in a larger full disk vector magnetogram provided by the same instrument, finally embedded in a synoptic map provided by SOLIS. It turns out to be possible to access the large scale structure of the corona and its energetic contents, and also the AR scale, at which we recover the presence of a twisted flux rope in equilibrium.
Nonlinear phased array imaging
NASA Astrophysics Data System (ADS)
Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.
2016-04-01
A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.
Callen, J. D.
2002-11-04
The primary efforts this year have focused on exploring the nonlinear evolution of localized interchange instabilities, some extensions of neoclassical tearing mode theory, and developing a model for the dynamic electrical conductivity in a bumpy cylinder magnetic field. In addition, we have vigorously participated in the computationally-focused NIMROD and CEMM projects.
NASA Astrophysics Data System (ADS)
Rosnitskiy, P. B.; Yuldashev, P. V.; Khokhlova, V. A.
2015-05-01
Certain modern applications of high-intensity focused ultrasound (HIFU) in medicine use the nonlinear effect of shock front formation in the focal waveform. However, an important problem remains unsolved: determination of transducer parameters that provide the given pressure levels of the shock wave field at the focus required for a specific application. In this paper, simulations based on the Khokhlov-Zabolotskaya equation are performed to test and confirm the hypothesis that angular aperture of the transducer is the main parameter that determines the characteristic amplitude of the shock front and corresponding values for the peak positive and negative pressures at the focus. A criterion for formation of a developed shock in the acoustic waveform, as well as a method for determining its amplitude is proposed. Quantitative dependences of the amplitude of the developed shock and the peak pressures in the wave profile on the angular aperture of the transducer are calculated. The effects of saturation and the range of changes of the shock waveform parameters at the focus are analyzed for a typical HIFU transducer.
NASA Astrophysics Data System (ADS)
Moorthy, V.
2016-01-01
Unexplored ferromagnetic phenomena of non-linear distortion of tangential magnetic field (HT) and that of excitation voltage (VE) across the electromagnetic (EM) yoke, in the presence of a ferromagnetic material between the poles of the EM yoke, have been uniquely correlated in this study. Both the HT and VE show similar distortion behaviour, but in the opposite direction, with unique shape for each ferromagnetic sample with different microstructural conditions. Interestingly unique correlation between (dVE / dt) and (dHT / dt) profiles and their ability to distinguish different magnetisation behaviour of ferromagnetic material with different microstructures have also been discussed in this study. One to one correlation between the distortion of HT and VE shown in this study is clear evidence that both these parameters are strongly influenced by the same mechanism of magnetisation process, but in different ways. The systematic changes in the height and position of the peak and the trough on the time derivative profiles of VE and HT reflect the subtle differences in the magnetisation process for each microstructural condition of the steel. This study reveals the new scientific insight and good potential of this novel as well as very simple approach of distortion analysis of HT and VE for understanding the influence of material properties on the mechanism of magnetisation process and also their suitability for variety of applications related to materials evaluation of ferromagnetic components and structures.
NASA Astrophysics Data System (ADS)
Yates, Travis Fred
Magnetic fluctuation-induced particle transport and density fluctuations have been investigated in the Madison Symmetric Torus (MST) reversed-filed pinch using a far infrared (FIR) laser based interferometer-polarimetry system. An extensive study focuses on the particle transport and density fluctuations during the sawtooth crash where the stochastic magnetic field is largest. Particle flux arising from the inieraction between density fluctuations and magnetic fluctuations has been measured to be significant at the reversal surface where modes with poloidal mode number m = 0 are resonant. The particle flux is comparable to that measured in the core where m = 1 modes dominate. The origin of density fluctuations has been studied experimentally. It is found that density fluctuations not only result from linear advection but also non-linear three-wave interactions. This is different from the previously reported results that indicated that the edge density fluctuations originate from linear advection. The results reported here reveal that m = 0 modes play an important role in density fluctuations and particle flux. An experiment where m = 0 modes are greatly reduced, by removing the reversal surface from the plasma, indicates that particle flux and density fluctuations are reduced significantly, which further confirms the importance of edge resonant modes in particle transport.
Palazzo, S.; Vagliasindi, G.; Arena, P.; Murari, A.; Mazon, D.; De Maack, A.; Collaboration: JET-EFDA Contributors
2010-08-15
In the past years cameras have become increasingly common tools in scientific applications. They are now quite systematically used in magnetic confinement fusion, to the point that infrared imaging is starting to be used systematically for real-time machine protection in major devices. However, in order to guarantee that the control system can always react rapidly in case of critical situations, the time required for the processing of the images must be as predictable as possible. The approach described in this paper combines the new computational paradigm of cellular nonlinear networks (CNNs) with field-programmable gate arrays and has been tested in an application for the detection of hot spots on the plasma facing components in JET. The developed system is able to perform real-time hot spot recognition, by processing the image stream captured by JET wide angle infrared camera, with the guarantee that computational time is constant and deterministic. The statistical results obtained from a quite extensive set of examples show that this solution approximates very well an ad hoc serial software algorithm, with no false or missed alarms and an almost perfect overlapping of alarm intervals. The computational time can be reduced to a millisecond time scale for 8 bit 496x560-sized images. Moreover, in our implementation, the computational time, besides being deterministic, is practically independent of the number of iterations performed by the CNN - unlike software CNN implementations.