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.
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
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
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 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
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.
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
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.
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.
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
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.
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.
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.
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.
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.
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
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)
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.
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
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})
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.
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.
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.
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
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.
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
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.
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.
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.
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)
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.
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.
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)
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 .
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.
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.
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
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
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.
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
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
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
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.