Excitation of slow waves in front of an ICRF antenna in a basic plasma experiment

NASA Astrophysics Data System (ADS)

Soni, Kunal; van Compernolle, Bart; Crombe, Kristel; van Eester, Dirk

2017-10-01

Recent results of ICRF experiments at the Large Plasma Device (LAPD) indicate parasitic coupling to the slow wave by the fast wave antenna. Plasma parameters in LAPD are similar to the scrape-off layer of current fusion devices. The machine has a 17 m long, 60 cm diameter magnetized plasma column with typical plasma parameters ne 1012 -1013 cm-3, Te 1 - 10 eV and B0 1000 G. It was found that coupling to the slow mode occurs when the plasma density in front of the antenna is low enough such that the lower hybrid resonance is present in the plasma. The radial density profile is tailored to allow for fast mode propagation in the high density core and slow mode propagation in the low density edge region. Measurements of the wave fields clearly show two distinct modes, one long wavelength m=1 fast wave mode in the core and a short wavelength backward propagating mode in the edge. Perpendicular wave numbers compare favorably to the predicted values. The experiment was done for varying frequencies, ω /Ωi = 25 , 6 and 1.5. Future experiments will investigate the dependence on antenna tilt angle with respect to the magnetic field, with and without Faraday screen. This work is performed at the Basic Plasma Science Facility, sponsored jointly by DOE and NSF.

Mode conversion in ICRF experiments on Alcator C-Mod

NASA Astrophysics Data System (ADS)

Lin, Y.; Wukitch, S. J.; Edlund, E.; Ennever, P.; Hubbard, A. E.; Porkolab, M.; Rice, J.; Wright, J.

2017-10-01

In recent three-ion species (majority D and H plus a trace level of 3He) ICRF heating experiment on Alcator C-Mod, double mode conversion on both sides of the 3He cyclotron resonance has been observed using the phase contrast imaging (PCI) system. The MC locations are used to estimate the species concentrations in the plasma. Simulation using TORIC shows that with the 3He level <1%, most RF power is absorbed by the 3He ions and the process can generate energetic 3He ions. In recent mode conversion flow drive experiment in D(3He) plasma at 8 T, MC waves were also monitored by PCI. The MC ion cyclotron wave (ICW) amplitude and wavenumber kR have been found to correlate with the flow drive force. The MC efficiency, wave-number k of the MC ICW and their dependence on plasma parameters like Te0 are shown to play important roles. Based on the experimental observation and numerical study of the dispersion solutions, a hypothesis of the flow drive mechanism has been proposed. Supported by USDoE awards DE-FC02-99ER54512.

Progress on the development of FullWave, a Hot and Cold Plasma Parallel Full Wave Code

NASA Astrophysics Data System (ADS)

Spencer, J. Andrew; Svidzinski, Vladimir; Zhao, Liangji; Kim, Jin-Soo

2017-10-01

FullWave is being developed at FAR-TECH, Inc. to simulate RF waves in hot inhomogeneous magnetized plasmas without making small orbit approximations. FullWave is based on a meshless formulation in configuration space on non-uniform clouds of computational points (CCP) adapted to better resolve plasma resonances, antenna structures and complex boundaries. The linear frequency domain wave equation is formulated using two approaches: for cold plasmas the local cold plasma dielectric tensor is used (resolving resonances by particle collisions), while for hot plasmas the conductivity kernel is calculated. The details of FullWave and some preliminary results will be presented, including: 1) a monitor function based on analytic solutions of the cold-plasma dispersion relation; 2) an adaptive CCP based on the monitor function; 3) construction of the finite differences for approximation of derivatives on adaptive CCP; 4) results of 2-D full wave simulations in the cold plasma model in tokamak geometry using the formulated approach for ECRH, ICRH and Lower Hybrid range of frequencies. Work is supported by the U.S. DOE SBIR program.

Effects of ICRF power on SOL density profiles and LH coupling during simultaneous LH and ICRF operation on Alcator C-Mod

NASA Astrophysics Data System (ADS)

Lau, C.; Lin, Y.; Wallace, G.; Wukitch, S. J.; Hanson, G. R.; Labombard, B.; Ochoukov, R.; Shiraiwa, S.; Terry, J.

2013-09-01

A dedicated experiment during simultaneous lower hybrid (LH) and ion cyclotron range-of-frequencies (ICRF) operations is carried out to evaluate and understand the effects of ICRF power on the scrape-off-layer (SOL) density profiles and on the resultant LH coupling for a wide range of plasma parameters on Alcator C-Mod. Operation of the LH launcher with the adjacent ICRF antenna significantly degrades LH coupling while operation with the ICRF antenna that is not magnetically connected to the LH launcher minimally affects LH coupling. An X-mode reflectometer system at three poloidal locations adjacent to the LH launcher and a visible video camera imaging the LH launcher are used to measure local SOL density profile and emissivity modifications with the application of LH and LH + ICRF power. These measurements confirm that the density in front of the LH launcher depends strongly on the magnetic field line mapping of the active ICRF antenna. Reflectometer measurements also observe both ICRF-driven and LH-driven poloidal density profile asymmetries, especially a strong density depletion at certain poloidal locations in front of the LH launcher during operation with a magnetically connected ICRF antenna. The results indicate that understanding both LH-driven flows and ICRF sheath driven flows may be necessary to understand the observed density profile modifications and LH coupling results during simultaneous LH + ICRF operation.

Measurement of ICRF wave propagation using a microwave reflectometer with fast antenna switching on GAMMA 10

NASA Astrophysics Data System (ADS)

Ikezoe, R.; Ichimura, M.; Itagaki, J.; Hirata, M.; Sumida, S.; Jang, S.; Izumi, K.; Tanaka, A.; Sekine, R.; Kubota, Y.; Shima, Y.; Kohagura, J.; Yoshikawa, M.; Sakamoto, M.; Nakashima, Y.

2017-12-01

Slow Alfvén wave in ion cyclotron range of frequency (ICRF) is a powerful tool to heat ions confined in a mirror field. In spite of its efficient heating effect that has been attained in the central cell of GAMMA 10, there are still unknown characteristics concerning boundary condition, transient variation of heating effect, exact picture of cyclotron damping, and so on. To study these characteristics in detail, a multi-point measurement of the waves inside the hot plasma has been recently developed by using a microwave reflectometer. In addition to a radial profile measurement that is available by a usual reflectometer, an axial measurement has been achieved by arraying transmitting and receiving horn antennas in the axial direction, which are repeatedly switched in time during a discharge with PIN diode switches. Another transmitting and receiving horn antenna pair was newly added to the system and probing at five cross sections was achieved in a single discharge with time resolution of about 1 ms at each antenna pair position. With the upgraded reflectometer system, axial and radial distributions of wave-induced fluctuations and those temporal behavior were clearly observed, offering valuable data on wave physics in a hot mirror plasma.

Aspects of ICRF-3

NASA Astrophysics Data System (ADS)

Ma, Chopo; MacMillan, Daniel; Le Bail, Karine; Gordon, David

2016-12-01

The Second Realization of the International Celestial Reference Frame (ICRF2) used dual-frequency VLBI data acquired for geodetic and astrometric purposes from 1979-2009 by organizations coordinated by the IVS and various precursor networks. Since 2009 the data set has been significantly broadened, especially by observations in the southern hemisphere. While the new southern data have ameliorated the north/south imbalance of observations, they appear to produce a systematic zonal declination change in the catalog positions. Over the 35 years of the ICRF data set the effect of galactic aberration may be significant. Geophysical and tropospheric models also may affect the source positions. All these effects need to be addressed in preparation for ICRF-3.

Considerations for ICRF-3

NASA Astrophysics Data System (ADS)

Ma, Chopo; MacMillan, Daniel; Gordon, David

2015-08-01

The Second Realization of the International Celestial Reference Frame (ICRF) used dual-frequency VLBI data acquired for geodetic and astrometric purposes from 1979-2009 by organizations now coordinated by the International VLBI Service for Geodesy and Astrometry (IVS) and analyzed according to the Conventions of the International Earth Rotation and Reference Systems Service (IERS). Since 2009 the data set has been significantly broadened, especially by observations in the Southern Hemisphere, and modeling of astronomical, geophysical and tropospheric effects has progressed. The new southern data appear to cause a systematic zonal declination change in the catalog positions. Over the three decades of the ICRF data set the effect of galactic aberration may be significant. Geophysical and tropospheric models also may affect the source positions. All these effects need to be addressed in preparation for ICRF-3.

Recent ICRF coupling experiments on EAST

NASA Astrophysics Data System (ADS)

Yuqing, YANG; Xinjun, ZHANG; Yanping, ZHAO; Chengming, QIN; Yan, CHENG; Yuzhou, MAO; Hua, YANG; Jianhua, WANG; Shuai, YUAN; Lei, WANG; Songqing, JU; Gen, CHEN; Xu, DENG; Kai, ZHANG; Baonian, WAN; Jiangang, LI; Yuntao, SONG; Xianzu, GONG; Jinping, QIAN; Tao, ZHANG

2018-04-01

Recent ion cyclotron resonance frequency (ICRF) coupling experiments for optimizing ICRF heating in high power discharge were performed on EAST. The coupling experiments were focus on antenna phasing and gas puffing, which were performed separately on two ports of the ion cyclotron resonance heating (ICRH) system of EAST. The antenna phasing was performed on the I-port antenna, which consists of four toroidally spaced radiating straps operating in multiple phasing cases; the coupling performance was better under low wave number | {k}\\parallel | (ranging from 4.5 to 6.5). By fuelling the plasma from gas injectors, placed as uniformly spaced array from top to bottom at each side limiter of the B-port antenna, which works in dipole phasing, the coupling resistance of the B-port antenna increased obviously. Furthermore, the coupling resistance of the I-port antenna was insensitive to a smaller rate of gas puffing but when the gas injection rate was more than a certain value (>1021s‑1), a sharp increase in the coupling resistance of the I-port antenna occurred, which was mainly caused by the toroidal asymmetric boundary density arising from gas puffing. A more specific analysis is given in the paper.

The behavior of neutron emissions during ICRF minority heating of plasma at EAST

NASA Astrophysics Data System (ADS)

Zhong, Guoqiang; Cao, Hongrui; Hu, Liqun; Zhou, Ruijie; Xiao, Min; Li, Kai; Pu, Neng; Huang, Juan; Liu, Guangzhu; Lin, Shiyao; Lyu, Bo; Liu, Haiqing; Zhang, Xinjun; EAST Team

2016-07-01

Ion cyclotron radio frequency (ICRF) wave heating is a primary method to heat ions in the Experimental Advanced Superconducting Tokamak (EAST). Through neutron diagnostics, effective ion heating was observed in hydrogenminority heating (MH) scenarios. At present, investigation of deuterium-deuterium (DD) fusion neutrons is mostly based on time-resolved flux monitor and spectrometer measurements. When the ICRF was applied, the neutron intensity became one order higher. The H/H  +  D ratio was in the range of 5-10%, corresponding to the hydrogen MH dominated scenario, and a strong high energy tail was not displayed on the neutron spectrum that was measured by a liquid scintillator. Moreover, ion temperature in the plasma center (T i) was inversely calculated by the use of neutron source strength (S n) and the plasma density based on classical fusion reaction equations. This result indicates that T i increases by approximately 30% in L-mode plasma, and by more than 50% in H-mode plasma during ICRF heating, which shows good agreement with x-ray crystal spectrometer (XCS) diagnostics. Finally, the DD neutron source strength scaling law, with regard to plasma current (I P) and ICRF coupling power (P RF) on the typical minority heating condition, was obtained by statistical analysis.

Recent progress on improving ICRF coupling and reducing RF-specific impurities in ASDEX Upgrade

NASA Astrophysics Data System (ADS)

Zhang, Wei; Bobkov, Volodymyr; Noterdaeme, Jean-Marie; Tierens, Wouter; Aguiam, Diogo; Bilato, Roberto; Coster, David; Colas, Laurent; Crombé, Kristel; Fuenfgelder, Helmut; Faugel, Helmut; Feng, Yuhe; Jacquot, Jonathan; Jacquet, Philippe; Kallenbach, Arne; Kostic, Ana; Lunt, Tilmann; Maggiora, Riccardo; Ochoukov, Roman; Silva, Antonio; Suárez, Guillermo; Tuccilo, Angelo A.; Tudisco, Onofrio; Usoltceva, Mariia; Van Eester, Dirk; Wang, Yongsheng; Yang, Qingxi

2017-10-01

The recent scientific research on ASDEX Upgrade (AUG) has greatly advanced solutions to two issues of Radio Frequency (RF) heating in the Ion Cyclotron Range of Frequencies (ICRF): (a) the coupling of ICRF power to the plasma is significantly improved by density tailoring with local gas puffing; (b) the release of RF-specific impurities is significantly reduced by minimizing the RF near field with 3-strap antennas. This paper summarizes the applied methods and reviews the associated achievements.

Implementation of the new multichannel X-mode edge density profile reflectometer for the ICRF antenna on ASDEX Upgrade

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguiam, D. E., E-mail: daguiam@ipfn.tecnico.ulisboa.pt; Silva, A.; Carvalho, P. J.

A new multichannel frequency modulated continuous-wave reflectometry diagnostic has been successfully installed and commissioned on ASDEX Upgrade to measure the plasma edge electron density profile evolution in front of the Ion Cyclotron Range of Frequencies (ICRF) antenna. The design of the new three-strap ICRF antenna integrates ten pairs (sending and receiving) of microwave reflectometry antennas. The multichannel reflectometer can use three of these to measure the edge electron density profiles up to 2 × 10{sup 19} m{sup −3}, at different poloidal locations, allowing the direct study of the local plasma layers in front of the ICRF antenna. ICRF power coupling,more » operational effects, and poloidal variations of the plasma density profile can be consistently studied for the first time. In this work the diagnostic hardware architecture is described and the obtained density profile measurements were used to track outer radial plasma position and plasma shape.« less

Towards a Future ICRF Realization

NASA Technical Reports Server (NTRS)

Ma, Chopo; Gordon, D.; MacMillan, D.; Petrov, L.; Smith, David E. (Technical Monitor)

2001-01-01

The data and analysis for the ICRF were completed in 1995 to define a frame to which the Hipparcos optical catalog could be fixed. Additional observations on most of the 608 sources in the overall ICRF catalog have been acquired using a small portion of geodetic observing time as well as astrometric sessions concentrating on the southern hemisphere. Positions of new sources have been determined, including approx.1200 from a VLBA phase calibrator survey. A future ICRF realization will require improved geophysical modeling, sophisticated treatment of position variations and/or source structure, optimized data selection and weighting, and reidentification of defining sources. The motivation for the next realization could be significant improvement in accuracy and density or preparation for optical extragalactic catalogs with microarcsecond precision.

Towards a Future ICRF Realization

NASA Technical Reports Server (NTRS)

Ma, Chopo; Gordon, David; MacMillan, Daniel; Petrov, Leonid

2002-01-01

The data and analysis for the ICRF were completed in 1995 to define a frame to which the Hipparcos optical catalog could be fixed. Additional observations on most of the 608 sources in the overall ICRF catalog have been acquired using a small portion of geodetic observing time as well as astrometric sessions concentrating on the Southern Hemisphere. Positions of new sources have been determined, including approximately 1200 from a VLBA phase calibrator survey. A future ICRF realization will require improved geophysical modeling, sophisticated treatment of position variations and/or source structure, optimized data selection and weighting, and re-identification of defining sources. The motivation for the next realization could be significant improvement in accuracy and density or preparation for optical extragalactic catalogs with microarcsecond precision.

ICRF-187 in clinical oncology.

PubMed

Poster, D S; Penta, J S; Bruno, S; Macdonald, J S

1981-01-01

Although the mechanism of action of ICRF-159 and 187 has not been clearly defined, it is evident from both preclinical and early clinical studies that these compounds are of interest. There are three distinct characteristics of these ICRF compounds that deserve careful clinical evaluation. First, these drugs are apparently alkylating agents with modest, predictable and noncumulative bone marrow toxicity that makes them good potential candidates for combination chemotherapy regimens. The second characteristic that should be investigated is the suggestion that combination of ICRF-187 with an anthracycline may ameliorate the cardiac toxicity of the latter. The third factor in the preclinical evaluation of the bis-diketopiperazines that may have clinical application is the evidence that suggests that these drugs have an antimetastatic effect.

Refinement of the ICRF

NASA Technical Reports Server (NTRS)

Ma, Chopo

2004-01-01

Since the ICRF was generated in 1995, VLBI modeling and estimation, data quality: source position stability analysis, and supporting observational programs have improved markedly. There are developing and potential applications in the areas of space navigation Earth orientation monitoring and optical astrometry from space that would benefit from a refined ICRF with enhanced accuracy, stability and spatial distribution. The convergence of analysis, focused observations, and astrometric needs should drive the production of a new realization in the next few years.

RF current distribution and topology of RF sheath potentials in front of ICRF antennae

NASA Astrophysics Data System (ADS)

Colas, L.; Heuraux, S.; Brémond, S.; Bosia, G.

2005-08-01

The 2D (radial/poloidal) spatial topology of RF-induced convective cells developing radially in front of ion cyclotron range of frequency (ICRF) antennae is investigated, in relation to the spatial distribution of RF currents over the metallic structure of the antenna. This is done via a Green's function, determined from the ICRF wave coupling equations, and well-suited to open field lines extending toroidally far away on both sides of the antenna. Using such formalism, combined with a full-wave calculation using the 3D antenna code ICANT (Pécoul S. et al 2000 Comput. Phys. Commun. 146 166-87), two classes of convective cells are analysed. The first one appears in front of phased arrays of straps, and depending on the strap phasing, its topology is interpreted using the poloidal profiles of either the RF current or the RF voltage of the strip line theory. The other class of convective cells is specific to antenna box corners and is evidenced for the first time. Based on such analysis, general design rules are worked out in order to reduce the RF-sheath potentials, which generalize those proposed in the earlier literature, and concrete antenna design options are tested numerically. The merits of aligning all strap centres on the same (tilted) flux tube, and of reducing the antenna box toroidal conductivity in its lower and upper parts, are discussed.

ICRF Mode Conversion Flow Drive Experiments on Alcator C-Mod

NASA Astrophysics Data System (ADS)

Lin, Y.; Reinke, M. L.; Rice, J. E.; Wukitch, S. J.; Granetz, R.; Greenwald, M.; Hubbard, A. E.; Marmar, E. S.; Podpaly, Y. A.; Porkolab, M.; Tsujii, N.; Wolfe, S.

2011-12-01

We have carried out a detailed study of the dependence of ICRF mode conversion flow drive (MCFD) on plasma and RF parameters. The flow drive efficiency is found to depend strongly on the 3He concentration in D(3He) plasmas, a key parameter separating the ICRF minority heating regime and mode conversion regime. At +90 ° antenna phasing (waves in the co-Ip direction) and dipole phasing, the driven flow is in the co-Ip direction, and the change of the rotation velocity increases with both PRF and Ip, and scales unfavorably vs. plasma density and antenna frequency. When MCFD is applied to I-mode plasmas, the plasma rotation increases until the onset of MHD modes triggered by large sawtooth crashes. Very high performance I-mode plasmas with HITER98,y2˜1.4 and Te0˜8 keV have been obtained in these experiments.

Extending the ICRF to Higher Radio Frequencies

NASA Technical Reports Server (NTRS)

Jacobs, C. S.; Jones, D. L.; Lanyi, G. E.; Lowe, S. T.; Naudet, C. J.; Resch, G. M.; Steppe, J. A.; Zhang, L. D.; Ulvestad, J. S.; Taylor, G. B.

2002-01-01

The ICRF forms the basis for all astrometry including use as the inertial coordinate system for navigating deep space missions. This frame was defined using S/X-band observations over the past 20+ years. In January 2002, the VLBA approved our proposal for observing time to extend the ICRF to K-band (24 GHz) and Q-band (43 GHz). The first step will be observations at K- and Q-bands on a subset of ICRF sources. Eventually, K- and Q-band multi-epoch observations will be used to estimate positions, flux density and source structure for a large fraction of the current S/X-band ICRF source list. This work will benefit the radio astronomy community by extending the VLBA calibrator list at these bands. In the longer term, we would also like to extend the ICRF to Ka-band (32 GHz). A celestial reference frame will be needed at this frequency to support deep space navigation. A navigation demonstration is being considered for NASA's Mars 2005 mission. The initial K- and Q-band work will serve to identify candidate sources at Ka-band for use with that mission.

Estimation of sheath potentials in front of ASDEX upgrade ICRF antenna with SSWICH asymptotic code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Křivská, A., E-mail: alena.krivska@rma.ac.be; Bobkov, V.; Jacquot, J.

Multi-megawatt Ion Cyclotron Range of Frequencies (ICRF) heating became problematic in ASDEX Upgrade (AUG) tokamak after coating of ICRF antenna limiters and other plasma facing components by tungsten. Strong impurity influx was indeed produced at levels of injected power markedly lower than in the previous experiments. It is assumed that the impurity production is mainly driven by parallel component of Radio-Frequency (RF) antenna electric near-field E// that is rectified in sheaths. In this contribution we estimate poloidal distribution of sheath Direct Current (DC) potential in front of the ICRF antenna and simulate its relative variations over the parametric scans performedmore » during experiments, trying to reproduce some of the experimental observations. In addition, relative comparison between two types of AUG ICRF antenna configurations, used for experiments in 2014, has been performed. For this purpose we use the Torino Polytechnic Ion Cyclotron Antenna (TOPICA) code and asymptotic version of the Self-consistent Sheaths and Waves for Ion Cyclotron Heating (SSWICH) code. Further, we investigate correlation between amplitudes of the calculated oscillating sheath voltages and the E// fields computed at the lateral side of the antenna box, in relation with a heuristic antenna design strategy at IPP Garching to mitigate RF sheaths.« less

A full-wave Helmholtz model for continuous-wave ultrasound transmission.

PubMed

Huttunen, Tomi; Malinen, Matti; Kaipio, Jari P; White, Phillip Jason; Hynynen, Kullervo

2005-03-01

A full-wave Helmholtz model of continuous-wave (CW) ultrasound fields may offer several attractive features over widely used partial-wave approximations. For example, many full-wave techniques can be easily adjusted for complex geometries, and multiple reflections of sound are automatically taken into account in the model. To date, however, the full-wave modeling of CW fields in general 3D geometries has been avoided due to the large computational cost associated with the numerical approximation of the Helmholtz equation. Recent developments in computing capacity together with improvements in finite element type modeling techniques are making possible wave simulations in 3D geometries which reach over tens of wavelengths. The aim of this study is to investigate the feasibility of a full-wave solution of the 3D Helmholtz equation for modeling of continuous-wave ultrasound fields in an inhomogeneous medium. The numerical approximation of the Helmholtz equation is computed using the ultraweak variational formulation (UWVF) method. In addition, an inverse problem technique is utilized to reconstruct the velocity distribution on the transducer which is used to model the sound source in the UWVF scheme. The modeling method is verified by comparing simulated and measured fields in the case of transmission of 531 kHz CW fields through layered plastic plates. The comparison shows a reasonable agreement between simulations and measurements at low angles of incidence but, due to mode conversion, the Helmholtz model becomes insufficient for simulating ultrasound fields in plates at large angles of incidence.

Theory and Practice in ICRF Antennas for Long Pulse Operation

NASA Astrophysics Data System (ADS)

Colas, L.; Faudot, E.; Brémond, S.; Heuraux, S.; Mitteau, R.; Chantant, M.; Goniche, M.; Basiuk, V.; Bosia, G.; Tore Supra Team

2005-09-01

Long plasma discharges on the Tore Supra (TS) tokamak were extended in 2004 towards higher powers and plasma densities by combined Lower Hybrid (LH) and Ion Cyclotron Range of Frequencies (ICRF) waves. RF pulses of 20s×8MW and 60s×4MW were produced. TS is equipped with 3 ICRF antennas, whose front faces are ready for CW operation. This paper reports on their behaviour over high power long pulses, as observed with infrared (IR) thermography and calorimetric measurements. Edge parasitic losses, although modest, are concentrated on a small surface and can raise surface temperatures close to operational limits. A complex hot spot pattern was revealed with at least 3 physical processes involved : convected power, electron acceleration in the LH near field, and a RF-specific phenomenon compatible with RF sheaths. LH coupling was also perturbed in the antenna shadow. This was attributed to RF-induced DC E×B0 convection. This motivated sheath modelling in two directions. First, the 2D topology of RF potentials was investigated in relation with the RF current distribution over the antenna, via a Green's function formalism and full-wave calculation using the ICANT code. In front of phased arrays of straps, convective cells were interpreted using the RF current profiles of strip line theory. Another class of convective cells, specific to antenna box corners, was evidenced for the first time. Within 1D sheath models assuming independent flux tubes, RF and rectified DC potentials are proportional. 2D fluid models couple nearby flux tubes via transverse polarisation currents. Unexpectedly this does not necessarily smooth RF potential maps. Peak DC potentials can even be enhanced. The experience gained on TS and the numerical tools are valuable for designing steady state high power antennas for next step devices. General rules to reduce RF potentials as well as concrete design options are discussed.

Uses of the ICRF and implications for future VLBI

NASA Technical Reports Server (NTRS)

Ma, Chopo

2006-01-01

Since its inception on 1 Jan 1998, the fundamental ICRF has been set by the VLBI positions of 212 "defining" extragalactic radio sources. In all there are approx.3000 sources with usefully accurate (< few mas) positions consistent with the ICRF. The uses of the ICRF include fundamental astrometry, monitoring of Earth orientation, and spacecraft navigation. For fundamental astrometry, stability and accuracy are most important, and realizations at different frequencies must be in proper registration. However, there is no preferred frequency, and the GAIA mission has the potential for an optical ICRF with 500,000 objects at the 50 microarcsec level some time after the planned 2011 launch. The radio ICRF should be properly prepared for a transition to assure long term stability and consistency. Earth orientation monitoring requires objects attached to the solid Earth, and VLBI will continue to be the fundamental technique. For this purpose it is essential that the new VLBI stations contemplated in the VLBI20l0 report be capable of observing a sufficiently large and well-distributed set of stable sources, and identifying these sources is an on-going effort. Spacecraft navigation by differential VLBI is planned using the Ka-band telemetry signal, and work has begun towards an ICRF realization suitable for this purpose. The balancing of different needs related to the VLBI ICRF will be discussed.

International Celestial Reference Frame (ICRF): mantenimiento y extensión

NASA Astrophysics Data System (ADS)

Ma, C.; Arias, E. F.; Eubanks, T.; Fey, A. L.; Gontier, A.-M.; Jacobs, C. S.; Sovers, O. J.; Archinal, B. A.; Charlot, P.

A partir de enero de 1998 el sistema de referencia celeste convencional está representado por el International Celestial Reference System (ICRS) y materializado a través de las coordenadas VLBI del conjunto de radiofuentes extragalácticas que conforman el International Celestial Reference Frame (ICRF). La primera realización del ICRF, fue elaborada en 1995 por un grupo de expertos designado por la IAU, la que encomendó al International Earth Rotation Service el mantenimiento del ICRS, del ICRF y del vínculo con marcos de referencia en otras frecuencias. Una primera extensión del ICRF se realizó entre abril y junio de 1999, con el objetivo primario de proveer posiciones de radiofuentes extragalácticas observadas a partir de julio de 1995 y de mejorar las posiciones de las fuentes ``candidatas" con la inclusión de observaciones adicionales. Objetivos secundarios fueron monitorear a las radiofuentes para verificar que siguen siendo adecuadas para realizar al ICRF y mejorar las técnicas de análisis de datos. Como resultado del nuevo análisis se obtuvo una solución a partir de la cual se construyó la primera extensión del ICRF, denominada ICRF - Ext.1. Ella representa al ICRS, sus fuentes de definición se mantienen con las mismas posiciones y errores que en la primera realización del ICRF; las demás radiofuentes tienen coordenadas mejor determinadas que en ICRF; el marco de referencia se densificó con el agregado de 59 nuevas radiofuentes.

Angular spectral framework to test full corrections of paraxial solutions.

PubMed

Mahillo-Isla, R; González-Morales, M J

2015-07-01

Different correction methods for paraxial solutions have been used when such solutions extend out of the paraxial regime. The authors have used correction methods guided by either their experience or some educated hypothesis pertinent to the particular problem that they were tackling. This article provides a framework so as to classify full wave correction schemes. Thus, for a given solution of the paraxial wave equation, we can select the best correction scheme of those available. Some common correction methods are considered and evaluated under the proposed scope. Another remarkable contribution is obtained by giving the necessary conditions that two solutions of the Helmholtz equation must accomplish to accept a common solution of the parabolic wave equation as a paraxial approximation of both solutions.

A PIC-MCC code RFdinity1d for simulation of discharge initiation by ICRF antenna

NASA Astrophysics Data System (ADS)

Tripský, M.; Wauters, T.; Lyssoivan, A.; Bobkov, V.; Schneider, P. A.; Stepanov, I.; Douai, D.; Van Eester, D.; Noterdaeme, J.-M.; Van Schoor, M.; ASDEX Upgrade Team; EUROfusion MST1 Team

2017-12-01

Discharges produced and sustained by ion cyclotron range of frequency (ICRF) waves in absence of plasma current will be used on ITER for (ion cyclotron-) wall conditioning (ICWC, Te = 3{-}5 eV, ne < 1018 m-3 ). In this paper, we present the 1D particle-in-cell Monte Carlo collision (PIC-MCC) RFdinity1d for the study the breakdown phase of ICRF discharges, and its dependency on the RF discharge parameters (i) antenna input power P i , (ii) RF frequency f, (iii) shape of the electric field and (iv) the neutral gas pressure pH_2 . The code traces the motion of both electrons and ions in a narrow bundle of magnetic field lines close to the antenna straps. The charged particles are accelerated in the parallel direction with respect to the magnetic field B T by two electric fields: (i) the vacuum RF field of the ICRF antenna E_z^RF and (ii) the electrostatic field E_zP determined by the solution of Poisson’s equation. The electron density evolution in simulations follows exponential increase, {\\dot{n_e} ∼ ν_ion t } . The ionization rate varies with increasing electron density as different mechanisms become important. The charged particles are affected solely by the antenna RF field E_z^RF at low electron density ({ne < 1011} m-3 , {≤ft \\vert E_z^RF \\right \\vert \\gg ≤ft \\vert E_zP \\right \\vert } ). At higher densities, when the electrostatic field E_zP is comparable to the antenna RF field E_z^RF , the ionization frequency reaches the maximum. Plasma oscillations propagating toroidally away from the antenna are observed. The simulated energy distributions of ions and electrons at {ne ∼ 1015} m-3 correspond a power-law Kappa energy distribution. This energy distribution was also observed in NPA measurements at ASDEX Upgrade in ICWC experiments.

Effects of Earth's curvature in full-wave modeling of VLF propagation

NASA Astrophysics Data System (ADS)

Qiu, L.; Lehtinen, N. G.; Inan, U. S.; Stanford VLF Group

2011-12-01

We show how to include curvature in the full-wave finite element approach to calculate ELF/VLF wave propagation in horizontally stratified earth-ionosphere waveguide. A general curvilinear stratified system is considered, and the numerical solutions of full-wave method in curvilinear system are compared with the analytic solutions in the cylindrical and spherical waveguides filled with an isotropic medium. We calculate the attenuation and height gain for modes in the Earth-ionosphere waveguide, taking into account the anisotropicity of ionospheric plasma, for different assumptions about the Earth's curvature, and quantify the corrections due to the curvature. The results are compared with the results of previous models, such as LWPC, as well as with ground and satellite observations, and show improved accuracy compared with full-wave method without including the curvature effect.

Anti-alias filter in AORSA for modeling ICRF heating of DT plasmas in ITER

NASA Astrophysics Data System (ADS)

Berry, L. A.; Batchelor, D. B.; Jaeger, E. F.; RF SciDAC Team

2011-10-01

The spectral wave solver AORSA has been used extensively to model full-field, ICRF heating scenarios for DT plasmas in ITER. In these scenarios, the tritium (T) second harmonic cyclotron resonance is positioned near the magnetic axis, where fast magnetosonic waves are efficiently absorbed by tritium ions. In some cases, a fundamental deuterium (D) cyclotron layer can also be located within the plasma, but close to the high field boundary. In this case, the existence of multiple ion cyclotron resonances presents a serious challenge for numerical simulation because short-wavelength, mode-converted waves can be excited close to the plasma edge at the ion-ion hybrid layer. Although the left hand circularly polarized component of the wave field is partially shielded from the fundamental D resonance, some power penetrates, and a small fraction (typically <10%) can be absorbed by the D ions. We find that an anti-aliasing filter is required in AORSA to calculate this fraction correctly while including up-shift and down-shift in the parallel wave spectrum. Work supported by U.S. DOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

The Second International Celestial Reference Frame (ICRF2)

NASA Technical Reports Server (NTRS)

Ma, Chopo

2010-01-01

The ICRF2 catalog was constructed by the IERS/IVS Working Group with oversight by the IAU Working Group. Derived using data from August 1979 through March 2009, it is a great improvement over the original ICRF with 3414 extragalactic radio source positions, a noise floor of 40 microarcsec, and axis stability of 10 microarcsec. Significant refinements were made in the selection of defining sources, modeling, and the integration of CRF, TRF, and EOP. The adoption of the ICRF2 was approved by the IAU in Resolution B3 at the XXVII IAU General Assembly and became effective 1 January 2010.

VizieR Online Data Catalog: VLBI ICRF2 (Fey+, 2015)

NASA Astrophysics Data System (ADS)

Fey, A. L.; Gordon, D.; Jacobs, C. S.; Ma, C.; Gaume, R. A.; Arias, E. F.; Bianco, G.; Boboltz, D. A.; Bockmann, S.; Bolotin, S.; Charlot, P.; Collioud, A.; Engelhardt, G.; Gipson, J.; Gontier, A.-M.; Heinkelmann, R.; Kurdubov, S.; Lambert, S.; Lytvyn, S.; MacMillan, D. S.; Malkin, Z.; Nothnagel, A.; Ojha, R.; Skurikhina, E.; Sokolova, J.; Souchay, J.; Sovers, O. J.; Tesmer, V.; Titov, O.; Wang, G.; Zharov, V.

2016-01-01

We present the second realization of the International Celestial Reference Frame (ICRF2) at radio wavelengths using nearly 30 years of Very Long Baseline Interferometry observations. The earliest observations used are from 1979 August and the latest are from 2009 March. ICRF2 consists of accurate positions of 295 new "defining" sources and positions of 3119 additional compact radio sources to densify the frame. ICRF2 has more than 5 times as many sources as ICRF1 (Ma et al. 1997, cat. I/251), is roughly 5-6 times more accurate, and is nearly twice as stable in the orientation of its axes. (3 data files).

Modeling RF Fields in Hot Plasmas with Parallel Full Wave Code

NASA Astrophysics Data System (ADS)

Spencer, Andrew; Svidzinski, Vladimir; Zhao, Liangji; Galkin, Sergei; Kim, Jin-Soo

2016-10-01

FAR-TECH, Inc. is developing a suite of full wave RF plasma codes. It is based on a meshless formulation in configuration space with adapted cloud of computational points (CCP) capability and using the hot plasma conductivity kernel to model the nonlocal plasma dielectric response. The conductivity kernel is calculated by numerically integrating the linearized Vlasov equation along unperturbed particle trajectories. Work has been done on the following calculations: 1) the conductivity kernel in hot plasmas, 2) a monitor function based on analytic solutions of the cold-plasma dispersion relation, 3) an adaptive CCP based on the monitor function, 4) stencils to approximate the wave equations on the CCP, 5) the solution to the full wave equations in the cold-plasma model in tokamak geometry for ECRH and ICRH range of frequencies, and 6) the solution to the wave equations using the calculated hot plasma conductivity kernel. We will present results on using a meshless formulation on adaptive CCP to solve the wave equations and on implementing the non-local hot plasma dielectric response to the wave equations. The presentation will include numerical results of wave propagation and absorption in the cold and hot tokamak plasma RF models, using DIII-D geometry and plasma parameters. Work is supported by the U.S. DOE SBIR program.

Theory and Practice in ICRF Antennas for Long Pulse Operation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Colas, L.; Bremond, S.; Mitteau, R.

2005-09-26

Long plasma discharges on the Tore Supra (TS) tokamak were extended in 2004 towards higher powers and plasma densities by combined Lower Hybrid (LH) and Ion Cyclotron Range of Frequencies (ICRF) waves. RF pulses of 20sx8MW and 60sx4MW were produced. TS is equipped with 3 ICRF antennas, whose front faces are ready for CW operation. This paper reports on their behaviour over high power long pulses, as observed with infrared (IR) thermography and calorimetric measurements. Edge parasitic losses, although modest, are concentrated on a small surface and can raise surface temperatures close to operational limits. A complex hot spot patternmore » was revealed with at least 3 physical processes involved : convected power, electron acceleration in the LH near field, and a RF-specific phenomenon compatible with RF sheaths. LH coupling was also perturbed in the antenna shadow. This was attributed to RF-induced DC ExB0 convection. This motivated sheath modelling in two directions. First, the 2D topology of RF potentials was investigated in relation with the RF current distribution over the antenna, via a Green's function formalism and full-wave calculation using the ICANT code. In front of phased arrays of straps, convective cells were interpreted using the RF current profiles of strip line theory. Another class of convective cells, specific to antenna box corners, was evidenced for the first time. Within 1D sheath models assuming independent flux tubes, RF and rectified DC potentials are proportional. 2D fluid models couple nearby flux tubes via transverse polarisation currents. Unexpectedly this does not necessarily smooth RF potential maps. Peak DC potentials can even be enhanced. The experience gained on TS and the numerical tools are valuable for designing steady state high power antennas for next step devices. General rules to reduce RF potentials as well as concrete design options are discussed.« less

Helical localized wave solutions of the scalar wave equation.

PubMed

Overfelt, P L

2001-08-01

A right-handed helical nonorthogonal coordinate system is used to determine helical localized wave solutions of the homogeneous scalar wave equation. Introducing the characteristic variables in the helical system, i.e., u = zeta - ct and v = zeta + ct, where zeta is the coordinate along the helical axis, we can use the bidirectional traveling plane wave representation and obtain sets of elementary bidirectional helical solutions to the wave equation. Not only are these sets bidirectional, i.e., based on a product of plane waves, but they may also be broken up into right-handed and left-handed solutions. The elementary helical solutions may in turn be used to create general superpositions, both Fourier and bidirectional, from which new solutions to the wave equation may be synthesized. These new solutions, based on the helical bidirectional superposition, are members of the class of localized waves. Examples of these new solutions are a helical fundamental Gaussian focus wave mode, a helical Bessel-Gauss pulse, and a helical acoustic directed energy pulse train. Some of these solutions have the interesting feature that their shape and localization properties depend not only on the wave number governing propagation along the longitudinal axis but also on the normalized helical pitch.

Influence of ICRF heating on the stability of TAEs

NASA Astrophysics Data System (ADS)

Sears, J.; Burke, W.; Parker, R. R.; Snipes, J. A.; Wolfe, S.

2007-11-01

Unstable toroidicity-induced Alfv'en eigenmodes (TAEs) can appear spontaneously due to resonant interaction with fast particles such as fusion alphas, raising concern that TAEs may threaten ITER performance. This work investigates the progression of stable TAE damping rates toward instability during a scan of ICRF heating power up to 3.1 MW. Stable eigenmodes are identified in Alcator C-Mod by the Active MHD diagnostic. Unstable TAEs are observed to appear spontaneously in C-Mod limited L-mode plasmas at sufficient tail energies generated by >3 MW of ICRF heating. However preliminary analysis of experiments with moderate ICRF heating power show that TAE stability may not simply degrade with overall fast particle content. There are hints that the stability of some TAEs may be enhanced in the presence of fast particle distribution tails. Furthermore, the radial profile of the energetic particle distribution relative to the safety factor profile affects the ICRF power influence on TAE stability.

High-Performance Computational Modeling of ICRF Physics and Plasma-Surface Interactions in Alcator C-Mod

NASA Astrophysics Data System (ADS)

Jenkins, Thomas; Smithe, David

2016-10-01

Inefficiencies and detrimental physical effects may arise in conjunction with ICRF heating of tokamak plasmas. Large wall potential drops, associated with sheath formation near plasma-facing antenna hardware, give rise to high-Z impurity sputtering from plasma-facing components and subsequent radiative cooling. Linear and nonlinear wave excitations in the plasma edge/SOL also dissipate injected RF power and reduce overall antenna efficiency. Recent advances in finite-difference time-domain (FDTD) modeling techniques allow the physics of localized sheath potentials, and associated sputtering events, to be modeled concurrently with the physics of antenna near- and far-field behavior and RF power flow. The new methods enable time-domain modeling of plasma-surface interactions and ICRF physics in realistic experimental configurations at unprecedented spatial resolution. We present results/animations from high-performance (10k-100k core) FDTD/PIC simulations spanning half of Alcator C-Mod at mm-scale resolution, exploring impurity production due to localized sputtering (in response to self-consistent sheath potentials at antenna surfaces) and the physics of parasitic slow wave excitation near the antenna hardware and SOL. Supported by US DoE (Award DE-SC0009501) and the ALCC program.

The IAU Division A Working Group on the Third Realization of the ICRF: Background, Goals, Plans

NASA Astrophysics Data System (ADS)

Gaume, Ralph

2015-08-01

The XXVIII General Assembly of the IAU (Beijing, 2012) established the Division A Working Group on the Third Realization of the International Celestial Reference Frame (ICRF). The adopted charter of the ICRF3 Working Group includes a commitment to report on the implementation and execution plans for ICRF3 during the XXIX General Assembly of the IAU along with a targeted completion and presentation of ICRF3 in 2018 to the XXX General Assembly for adoption. This talk will discuss the background, purpose, and overall implementation plan for ICRF3, and motivate the concept, currently under consideration by the ICRF3 Working Group, that future realizations of the ICRF be based on multi-frequency astrometric data, starting with ICRF3.

The Position/Structure Stability of Four ICRF2 Sources

NASA Technical Reports Server (NTRS)

Fomalont, Ed; Johnston, Kenneth; Fey, Alan; Boboltz, Dave; Oyama, Tomoaki; Honma, Mareki

2010-01-01

Four compact radio sources in the International Celestial Reference Frame (ICRF2) catalog were observed using phase referencing with the VLBA at 43, 23, and 8.6-GHz, and with VERA at 23-GHz over a one-year period. The goal was to determine the stability of the radio cores and to assess structure effects associated with positions in the ICRF2. Conclusions are: (1) 43-GHz VLBI high-resolution observations are often needed to determine the location of the radio core. (2) Over the observing period, the relative positions among the four radio cores were constant to 0.02 mas, suggesting that once the true radio core is identified, it remains stationary in the sky to this accuracy. (3) The emission in 0556+238, one of the four sources investigated and one of the 295 ICRF2 defining sources, was dominated by a strong component near the core and moved 0.1 mas during the year. (4) Comparison of the VLBA images at 43, 23, and 8.6-GHz with the ICRF2 positions suggests that the 8-GHz structure is often dominated by a bright non-core component. The measured ICRF2 position can be displaced more than 0.5 mas from the radio core and partake in the motion of the bright jet component.

Effect on the tritium breeding ratio for a distributed ICRF antenna in a DEMO reactor

NASA Astrophysics Data System (ADS)

Garcia, A.; Noterdaeme, J.-M.; Fischer, U.; Dies, J.

2015-12-01

The paper reports results of MCNP-5 calculations to assess the effect on the Tritium Breeding Ratio (TBR) when integrating a distributed Ion Cyclotron Range of Frequencies (ICRF) antenna in the blanket of DEMO fusion power reactor. The calculations consider different parameters such as the ICRF covering ratio and the type of breeding blanket including the Helium Cooled Pebble Bed (HCPB) and the Helium Cooled Lithium Lead (HCLL) concepts. For an antenna with a full toroidal circumference of 360°, located poloidally at 40° with a poloidal extension of 1 m, the reduction of the TBR is -0.349% for the HCPB blanket and -0.532% for the HCLL blanket. The distributed ICRF antenna is thus shown to have only a marginal effect on the TBR of the DEMO reactor.

ICRF mode conversion in three-ion species heating experiment and in flow drive experiment on the Alcator C-Mod tokamak

NASA Astrophysics Data System (ADS)

Lin, Y.; Wukitch, S. J.; Edlund, E.; Ennever, P.; Hubbard, A. E.; Porkolab, M.; Rice, J.; Wright, J.

2017-10-01

In recent three-ion species (majority D and H plus a trace level of 3He) ICRF heating experiments on Alcator C-Mod, double mode conversion on both sides of the 3He cyclotron resonance has been observed using the phase contrast imaging (PCI) system. The MC locations are used to estimate the species concentrations in the plasma. Simulation using TORIC shows that with the 3He level <1%, most RF power is absorbed by the 3He ions and the process can generate energetic 3He ions. In mode conversion (MC) flow drive experiment in D(3He) plasma at 8 T, MC waves were also monitored by PCI. The MC ion cyclotron wave (ICW) amplitude and wavenumber kR have been found to correlate with the flow drive force. The MC efficiency, wave-number k of the MC ICW and their dependence on plasma parameters like Te0 have been studied. Based on the experimental observation and numerical study of the dispersion solutions, a hypothesis of the flow drive mechanism has been proposed.

ICRF operation with improved antennas in ASDEX Upgrade with W wall

NASA Astrophysics Data System (ADS)

Bobkov, V.; Balden, M.; Bilato, R.; Braun, F.; Dux, R.; Herrmann, A.; Faugel, H.; Fünfgelder, H.; Giannone, L.; Kallenbach, A.; Maier, H.; Müller, H. W.; Neu, R.; Noterdaeme, J.-M.; Pütterich, Th.; Rohde, V.; Tsujii, N.; Zeus, F.; Zohm, H.; the ASDEX Upgrade Team

2013-09-01

Experiments with boron-coated side limiters of two antennas operated together in 2012 showed that the side limiters are responsible for more than half of the increased W content in the plasma. Together with the contribution from the other limiter tiles, not replaced in 2012, the limiters account for at least two thirds of the W content. A modified test two-strap ion cyclotron range of frequency (ICRF) antennas in ASDEX Upgrade with broad limiters and narrow straps has shown an improved operation with full W wall in 2011/2012 campaigns with up to a 40% lower rise of W concentration allowing more stable operation at low deuterium gas injection rate. Limiter spectroscopy measurements indicate up to a 40% reduction of the rise of the W sputtering yield during ICRF power, measured under the assumption of negligible influence of geometry variations and reflections on the measurements. The boron limiters on two antennas together with the improved broad-limiter antenna allowed a successful ICRF operation in 2012. As a part of long-term strategy of antenna design development, two three-strap antennas with phase and power balance control for reduction of E‖ are planned for installation in the future.

Effect on the tritium breeding ratio for a distributed ICRF antenna in a DEMO reactor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia, A., E-mail: albert.garcia.hp@gmail.com; Karlsruhe Institute of Technology; Polytechnic University of Catalonia

The paper reports results of MCNP-5 calculations to assess the effect on the Tritium Breeding Ratio (TBR) when integrating a distributed Ion Cyclotron Range of Frequencies (ICRF) antenna in the blanket of DEMO fusion power reactor. The calculations consider different parameters such as the ICRF covering ratio and the type of breeding blanket including the Helium Cooled Pebble Bed (HCPB) and the Helium Cooled Lithium Lead (HCLL) concepts. For an antenna with a full toroidal circumference of 360°, located poloidally at 40° with a poloidal extension of 1 m, the reduction of the TBR is −0.349% for the HCPB blanket andmore » −0.532% for the HCLL blanket. The distributed ICRF antenna is thus shown to have only a marginal effect on the TBR of the DEMO reactor.« less

Development of FullWave : Hot Plasma RF Simulation Tool

NASA Astrophysics Data System (ADS)

Svidzinski, Vladimir; Kim, Jin-Soo; Spencer, J. Andrew; Zhao, Liangji; Galkin, Sergei

2017-10-01

Full wave simulation tool, modeling RF fields in hot inhomogeneous magnetized plasma, is being developed. The wave equations with linearized hot plasma dielectric response are solved in configuration space on adaptive cloud of computational points. The nonlocal hot plasma dielectric response is formulated in configuration space without limiting approximations by calculating the plasma conductivity kernel based on the solution of the linearized Vlasov equation in inhomogeneous magnetic field. This approach allows for better resolution of plasma resonances, antenna structures and complex boundaries. The formulation of FullWave and preliminary results will be presented: construction of the finite differences for approximation of derivatives on adaptive cloud of computational points; model and results of nonlocal conductivity kernel calculation in tokamak geometry; results of 2-D full wave simulations in the cold plasma model in tokamak geometry using the formulated approach; results of self-consistent calculations of hot plasma dielectric response and RF fields in 1-D mirror magnetic field; preliminary results of self-consistent simulations of 2-D RF fields in tokamak using the calculated hot plasma conductivity kernel; development of iterative solver for wave equations. Work is supported by the U.S. DOE SBIR program.

IVS Observation of ICRF2-Gaia Transfer Sources

NASA Astrophysics Data System (ADS)

Le Bail, K.; Gipson, J. M.; Gordon, D.; MacMillan, D. S.; Behrend, D.; Thomas, C. C.; Bolotin, S.; Himwich, W. E.; Baver, K. D.; Corey, B. E.; Titus, M.; Bourda, G.; Charlot, P.; Collioud, A.

2016-03-01

The second realization of the International Celestial Reference Frame (ICRF2), which is the current fundamental celestial reference frame adopted by the International Astronomical Union, is based on Very Long Baseline Interferometry (VLBI) data at radio frequencies in X band and S band. The European Space Agency’s Gaia mission, launched on 2013 December 19, started routine scientific operations in 2014 July. By scanning the whole sky, it is expected to observe ∼500,000 Quasi Stellar Objects in the optical domain an average of 70 times each during the five years of the mission. This means that, in the future, two extragalactic celestial reference frames, at two different frequency domains, will coexist. It will thus be important to align them very accurately. In 2012, the Laboratoire d’Astrophysique de Bordeaux (LAB) selected 195 sources from ICRF2 that will be observed by Gaia and should be suitable for aligning the radio and optical frames: they are called ICRF2-Gaia transfer sources. The LAB submitted a proposal to the International VLBI Service (IVS) to regularly observe these ICRF2-Gaia transfer sources at the same rate as Gaia observes them in the optical realm, e.g., roughly once a month. We describe our successful effort to implement such a program and report on the results. Most observations of the ICRF2-Gaia transfer sources now occur automatically as part of the IVS source monitoring program, while a subset of 37 sources requires special attention. Beginning in 2013, we scheduled 25 VLBI sessions devoted in whole or in part to measuring these 37 sources. Of the 195 sources, all but one have been successfully observed in the 12 months prior to 2015 September 01. Of the sources, 87 met their observing target of 12 successful sessions per year. The position uncertainties of all of the ICRF2-Gaia transfer sources have improved since the start of this observing program. For a subset of 24 sources whose positions were very poorly known, the uncertainty

Circuit-based versus full-wave modelling of active microwave circuits

NASA Astrophysics Data System (ADS)

Bukvić, Branko; Ilić, Andjelija Ž.; Ilić, Milan M.

2018-03-01

Modern full-wave computational tools enable rigorous simulations of linear parts of complex microwave circuits within minutes, taking into account all physical electromagnetic (EM) phenomena. Non-linear components and other discrete elements of the hybrid microwave circuit are then easily added within the circuit simulator. This combined full-wave and circuit-based analysis is a must in the final stages of the circuit design, although initial designs and optimisations are still faster and more comfortably done completely in the circuit-based environment, which offers real-time solutions at the expense of accuracy. However, due to insufficient information and general lack of specific case studies, practitioners still struggle when choosing an appropriate analysis method, or a component model, because different choices lead to different solutions, often with uncertain accuracy and unexplained discrepancies arising between the simulations and measurements. We here design a reconfigurable power amplifier, as a case study, using both circuit-based solver and a full-wave EM solver. We compare numerical simulations with measurements on the manufactured prototypes, discussing the obtained differences, pointing out the importance of measured parameters de-embedding, appropriate modelling of discrete components and giving specific recipes for good modelling practices.

Modelling of combined ICRF and NBI heating in JET hybrid plasmas

NASA Astrophysics Data System (ADS)

Gallart, Dani; Mantsinen, Mervi; Challis, Clive; Frigione, Domenico; Graves, Jonathan; Hobirk, Joerg; Belonohy, Eva; Czarnecka, Agata; Eriksson, Jacob; Goniche, Marc; Hellesen, Carl; Jacquet, Philippe; Joffrin, Emmanuel; Krawczyk, Natalia; King, Damian; Lennholm, Morten; Lerche, Ernesto; Pawelec, Ewa; Sips, George; Solano, Emilia; Tsalas, Maximos; Valisa, Marco

2017-10-01

During the 2015-2016 JET campaigns many efforts have been devoted to the exploration of high performance plasma scenarios envisaged for ITER operation. In this paper we model the combined ICRF+NBI heating in selected key hybrid discharges using PION. The antenna frequency was tuned to match the cyclotron frequency of minority hydrogen (H) at the center of the tokamak coinciding with the second harmonic cyclotron resonance of deuterium. The modelling takes into account the synergy between ICRF and NBI heating through the second harmonic cyclotron resonance of deuterium beam ions which allows us to assess its impact on the neutron rate RNT. We evaluate the influence of H concentration which was varied in different discharges in order to test their role in the heating performance. According to our modelling, the ICRF enhancement of RNT increases by decreasing the H concentration which increases the ICRF power absorbed by deuterons. We find that in the recent hybrid discharges this ICRF enhancement was in the range of 10-25%. Finally, we extrapolate the results to D-T and find that the best performing hybrid discharges correspond to an equivalent fusion power of ˜7.0 MW in D-T.

The International Celestial Reference Frame (ICRF) and the Relationship Between Frames

NASA Technical Reports Server (NTRS)

Ma, Chopo

2000-01-01

The International Celestial Reference Frame (ICRF), a catalog of VLBI source positions, is now the basis for astrometry and geodesy. Its construction and extension/maintenance will be discussed as well as the relationship of the ICRF, ITRF, and EOP/nutation.

Initial operation of high power ICRF system for long pulse in EAST

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qin, C. M., E-mail: chmq@ipp.ac.cn; Zhao, Y. P.; Zhang, X. J.

2015-12-10

The ICRF heating system on EAST upgraded by active cooling aims for long pulse operation. In this paper, the main technical features of the ICRF system are described. One of a major challenges for long pulse operation is RF-edge interactions induced impurity production and heat loading. In EAST, ICRF antenna protections and Faraday screen bars damaged due to LH electron beam are found. Preliminary results for the analysis of the interaction between LHCD and ICRF antenna are discussed. Increase of metal impurities in the plasma during RF pulse and in a larger core radiation are also shown. These RF-edge interactionsmore » at EAST and some preliminary results for the optimizing RF performance will be presented.« less

THE POSITION/STRUCTURE STABILITY OF FOUR ICRF2 SOURCES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fomalont, Ed; Johnston, Kenneth; Fey, Alan

2011-03-15

Four close radio sources in the International Celestial Reference Frame (ICRF) catalog were observed using phase referencing with the VLBA at 43, 23, and 8.6 GHz, and with VERA at 23 GHz over a one-year period. The goal was to determine the stability of the radio cores and to assess structure effects associated with positions in the ICRF. Although the four sources were compact at 8.6 GHz, the VLBA images at 43 GHz with 0.3 mas resolution showed that all were composed of several components. A component in each source was identified as the radio core using some or allmore » of the following emission properties: compactness, spectral index, location at the end of the extended emission region, and stationary in the sky. Over the observing period, the relative positions between the four radio cores were constant to 0.02 mas, the phase-referencing positional accuracy obtained at 23 and 43 GHz among the sources, suggesting that once a radio core is identified, it remains stationary in the sky to this accuracy. Other radio components in two of the four sources had detectable motion in the radio jet direction. Comparison of the 23 and 43 GHz VLBA images with the VLBA 8.6 GHz images and the ICRF positions suggests that some ICRF positions are dominated by a moving jet component; hence, they can be displaced up to 0.5 mas from the radio core and may also reflect the motion of the jet component. Future astrometric efforts to determine a more accurate quasar reference frame at 23 and 43 GHz and from the VLBI2010 project are discussed, and supporting VLBA or European VLBI Network observations of ICRF sources at 43 GHz are recommended in order to determine the internal structure of the sources. A future collaboration between the radio (ICRF) and the optical frame of GAIA is discussed.« less

Beamforming Based Full-Duplex for Millimeter-Wave Communication

PubMed Central

Liu, Xiao; Xiao, Zhenyu; Bai, Lin; Choi, Jinho; Xia, Pengfei; Xia, Xiang-Gen

2016-01-01

In this paper, we study beamforming based full-duplex (FD) systems in millimeter-wave (mmWave) communications. A joint transmission and reception (Tx/Rx) beamforming problem is formulated to maximize the achievable rate by mitigating self-interference (SI). Since the optimal solution is difficult to find due to the non-convexity of the objective function, suboptimal schemes are proposed in this paper. A low-complexity algorithm, which iteratively maximizes signal power while suppressing SI, is proposed and its convergence is proven. Moreover, two closed-form solutions, which do not require iterations, are also derived under minimum-mean-square-error (MMSE), zero-forcing (ZF), and maximum-ratio transmission (MRT) criteria. Performance evaluations show that the proposed iterative scheme converges fast (within only two iterations on average) and approaches an upper-bound performance, while the two closed-form solutions also achieve appealing performances, although there are noticeable differences from the upper bound depending on channel conditions. Interestingly, these three schemes show different robustness against the geometry of Tx/Rx antenna arrays and channel estimation errors. PMID:27455256

Numerical study of nonlinear full wave acoustic propagation

NASA Astrophysics Data System (ADS)

Velasco-Segura, Roberto; Rendon, Pablo L.

2013-11-01

With the aim of describing nonlinear acoustic phenomena, a form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A CLAWPACK based, 2D finite-volume method using Roe's linearization has been implemented to obtain numerically the solution of the proposed equations. In order to validate the code, two different tests have been performed: one against a special Taylor shock-like analytic solution, the other against published results on a HIFU system, both with satisfactory results. The code is written for parallel execution on a GPU and improves performance by a factor of over 50 when compared to the standard CLAWPACK Fortran code. This code can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from modest models of diagnostic and therapeutic HIFU, parametric acoustic arrays, to acoustic wave guides. A couple of examples will be presented showing shock formation and oblique interaction. DGAPA PAPIIT IN110411, PAEP UNAM 2013.

Wave excitation by nonlinear coupling among shear Alfvén waves in a mirror-confined plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ikezoe, R., E-mail: ikezoe@prc.tsukuba.ac.jp; Ichimura, M.; Okada, T.

2015-09-15

A shear Alfvén wave at slightly below the ion-cyclotron frequency overcomes the ion-cyclotron damping and grows because of the strong anisotropy of the ion temperature in the magnetic mirror configuration, and is called the Alfvén ion-cyclotron (AIC) wave. Density fluctuations caused by the AIC waves and the ion-cyclotron range of frequencies (ICRF) waves used for ion heating have been detected using a reflectometer in a wide radial region of the GAMMA 10 tandem mirror plasma. Various wave-wave couplings are clearly observed in the density fluctuations in the interior of the plasma, but these couplings are not so clear in themore » magnetic fluctuations at the plasma edge when measured using a pick-up coil. A radial dependence of the nonlinearity is found, particularly in waves with the difference frequencies of the AIC waves; bispectral analysis shows that such wave-wave coupling is significant near the core, but is not so evident at the periphery. In contrast, nonlinear coupling with the low-frequency background turbulence is quite distinct at the periphery. Nonlinear coupling associated with the AIC waves may play a significant role in the beta- and anisotropy-limits of a mirror-confined plasma through decay of the ICRF heating power and degradation of the plasma confinement by nonlinearly generated waves.« less

Multi-frequency ICRF diagnostic of Tokamak plasmas

NASA Astrophysics Data System (ADS)

Lafonteese, David James

This thesis explores the diagnostic possibilities of a fast wave-based method for measuring the ion density and temperature profiles of tokamak plasmas. In these studies fast waves are coupled to the plasma at frequencies at the second harmonic of the ion gyrofrequency, at which wave energy is absorbed by the finite-temperature ions. As the ion gyrofrequency is dependent upon the local magnetic field, which varies as l/R in a tokamak, this power absorption is radially localized. The simultaneous launching of multiple frequencies, all resonating at different plasma positions, allows local measurements of the ion density and temperature. To investigate the profile applications of wave damping measurements in a simulated tokamak, an inhouse slab-model ICRF code is developed. A variety of analysis methods are presented, and ion density and temperature profiles are reconstructed for hydrogen plasmas for the Electric Tokamak (ET) and ITER parameter spaces. These methods achieve promising results in simulated plasmas featuring bulk ion heating, off-axis RF heating, and density ramps. The experimental results of similar studies on the Electric Tokamak, a high aspect ratio (R/a = 5), low toroidal field (2.2 kG) device are then presented. In these studies, six fast wave frequencies were coupled using a single-strap, low-field-side antenna to ET plasmas. The frequencies were variable, and could be tuned to resonate at different radii for different experiments. Four magnetic pickup loops were used to measure of the toroidal component of the wave magnetic field. The expected greater eigenmode damping of center-resonant frequencies versus edge-resonant frequencies is consistently observed. Comparison of measured aspects of fast wave behavior in ET is made with the slab code predictions, which validate the code simulations under weakly-damped conditions. A density profile is measured for an ET discharge through analysis of the fast wave measurements, and is compared to an

Full wave description of VLF wave penetration through the ionosphere

NASA Astrophysics Data System (ADS)

Kuzichev, Ilya; Shklyar, David

2010-05-01

Of the many problems in whistler study, wave propagation through the ionosphere is among the most important, and the most difficult at the same time. Both satellite and ground-based investigations of VLF waves include considerations of this problem, and it has been in the focus of research since the beginning of whistler study (Budden [1985]; Helliwell [1965]). The difficulty in considering VLF wave passage through the ionosphere is, after all, due to fast variation of the lower ionosphere parameters as compared to typical VLF wave number. This makes irrelevant the consideration in the framework of geometrical optics, which, along with a smooth variations of parameters, is always based on a particular dispersion relation. Although the full wave analysis in the framework of cold plasma approximation does not require slow variations of plasma parameters, and does not assume any particular wave mode, the fact that the wave of a given frequency belongs to different modes in various regions makes numerical solution of the field equations not simple. More specifically, as is well known (e.g. Ginzburg and Rukhadze [1972]), in a cold magnetized plasma, there are, in general, two wave modes related to a given frequency. Both modes, however, do not necessarily correspond to propagating waves. In particular, in the frequency range related to whistler waves, the other mode is evanescent, i.e. it has a negative value of N2 (the refractive index squared). It means that one of solutions of the relevant differential equations is exponentially growing, which makes a straightforward numerical approach to these equations despairing. This well known difficulty in the problem under discussion is usually identified as numerical swamping (Budden [1985]). Resolving the problem of numerical swamping becomes, in fact, a key point in numerical study of wave passage through the ionosphere. As it is typical of work based on numerical simulations, its essential part remains virtually hidden

Modeling of the EAST ICRF antenna with ICANT Code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qin Chengming; Zhao Yanping; Colas, L.

2007-09-28

A Resonant Double Loop (RDL) antenna for ion-cyclotron range of frequencies (ICRF) on Experimental Advanced Superconducting Tokamak (EAST) is under construction. The new antenna is analyzed using the antenna coupling code ICANT which self-consistently determines the surface currents on all antenna parts. In this work, the modeling of the new ICRF antenna using this code is to assess the near-fields in front of the antenna and analysis its coupling capabilities. Moreover, the antenna reactive radiated power computed by ICANT and shows a good agreement with deduced from Transmission Line (TL) theory.

Modeling of the EAST ICRF antenna with ICANT Code

NASA Astrophysics Data System (ADS)

Qin, Chengming; Zhao, Yanping; Colas, L.; Heuraux, S.

2007-09-01

A Resonant Double Loop (RDL) antenna for ion-cyclotron range of frequencies (ICRF) on Experimental Advanced Superconducting Tokamak (EAST) is under construction. The new antenna is analyzed using the antenna coupling code ICANT which self-consistently determines the surface currents on all antenna parts. In this work, the modeling of the new ICRF antenna using this code is to assess the near-fields in front of the antenna and analysis its coupling capabilities. Moreover, the antenna reactive radiated power computed by ICANT and shows a good agreement with deduced from Transmission Line (TL) theory.

Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.

PubMed

Chen, Shihua; Grelu, Philippe; Soto-Crespo, J M

2014-01-01

Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.

Full-wave effects on shear wave splitting

NASA Astrophysics Data System (ADS)

Lin, Yu-Pin; Zhao, Li; Hung, Shu-Huei

2014-02-01

Seismic anisotropy in the mantle plays an important role in our understanding of the Earth's internal dynamics, and shear wave splitting has always been a key observable in the investigation of seismic anisotropy. To date the interpretation of shear wave splitting in terms of anisotropy has been largely based on ray-theoretical modeling of a single vertically incident plane SKS or SKKS wave. In this study, we use sensitivity kernels of shear wave splitting to anisotropic parameters calculated by the normal-mode theory to demonstrate that the interference of SKS with other phases of similar arrival times, near-field effect, and multiple reflections in the crust lead to significant variations of SKS splitting with epicentral distance. The full-wave kernels not only widen the possibilities in the source-receiver geometry in making shear wave splitting measurements but also provide the capability for tomographic inversion to resolve vertical and lateral variations in the anisotropic structures.

Full-wave and half-wave rectification in second-order motion perception

NASA Technical Reports Server (NTRS)

Solomon, J. A.; Sperling, G.

1994-01-01

Microbalanced stimuli are dynamic displays which do not stimulate motion mechanisms that apply standard (Fourier-energy or autocorrelational) motion analysis directly to the visual signal. In order to extract motion information from microbalanced stimuli, Chubb and Sperling [(1988) Journal of the Optical Society of America, 5, 1986-2006] proposed that the human visual system performs a rectifying transformation on the visual signal prior to standard motion analysis. The current research employs two novel types of microbalanced stimuli: half-wave stimuli preserve motion information following half-wave rectification (with a threshold) but lose motion information following full-wave rectification; full-wave stimuli preserve motion information following full-wave rectification but lose motion information following half-wave rectification. Additionally, Fourier stimuli, ordinary square-wave gratings, were used to stimulate standard motion mechanisms. Psychometric functions (direction discrimination vs stimulus contrast) were obtained for each type of stimulus when presented alone, and when masked by each of the other stimuli (presented as moving masks and also as nonmoving, counterphase-flickering masks). RESULTS: given sufficient contrast, all three types of stimulus convey motion. However, only one-third of the population can perceive the motion of the half-wave stimulus. Observers are able to process the motion information contained in the Fourier stimulus slightly more efficiently than the information in the full-wave stimulus but are much less efficient in processing half-wave motion information. Moving masks are more effective than counterphase masks at hampering direction discrimination, indicating that some of the masking effect is interference between motion mechanisms, and some occurs at earlier stages. When either full-wave and Fourier or half-wave and Fourier gratings are presented simultaneously, there is a wide range of relative contrasts within which the

Full-wave generalizations of the fundamental Gaussian beam.

PubMed

Seshadri, S R

2009-12-01

The basic full wave corresponding to the fundamental Gaussian beam was discovered for the outwardly propagating wave in a half-space by the introduction of a source in the complex space. There is a class of extended full waves all of which reduce to the same fundamental Gaussian beam in the appropriate limit. For the extended full Gaussian waves that include the basic full Gaussian wave as a special case, the sources are in the complex space on different planes transverse to the propagation direction. The sources are cylindrically symmetric Gaussian distributions centered at the origin of the transverse planes, the axis of symmetry being the propagation direction. For the special case of the basic full Gaussian wave, the source is a point source. The radiation intensity of the extended full Gaussian waves is determined and their characteristics are discussed and compared with those of the fundamental Gaussian beam. The extended full Gaussian waves are also obtained for the oppositely propagating outwardly directed waves in the second half-space. The radiation intensity distributions in the two half-spaces have reflection symmetry about the midplane. The radiation intensity distributions of the various extended full Gaussian waves are not significantly different. The power carried by the extended full Gaussian waves is evaluated and compared with that of the fundamental Gaussian beam.

Resonance localization in tokamaks excited with ICRF waves

NASA Astrophysics Data System (ADS)

Kerbel, G. D.; McCoy, M. G.

1985-06-01

Advanced wave model used to evaluate ICRH in tokamaks typically used warm plasma theory and allow inhomogeneity in one dimension. The majority of these calculations neglect the fact that gyrocenters experience the inhomogeneity via their motion parallel to the magnetic field. In strongly driven systems, wave damping can distort the particle distribution function supporting the wave and this produces changes in the absorption. A bounce-averaged Fokker-Planck quasilinear computational model which evolves the population of particles on more realistic orbits is presented. Each wave-particle resonance has its own specific interaction amplitude within any given volume element; these data need only be generated once, and appropriately stored for efficient retrieval. The wave-particle resonant interaction then serves as a mechanism by which the diffusion of particle populations can proceed among neighboring orbits. The local specific spectral energy absorption rate is directly calculable once the orbit geometry and populations are determined. The code is constructed in such fashion as to accommodate wave propagation models which provide the wave spectral energy density on a poloidal cross-section. Information provided by the calculation includes the local absorption properties of the medium which can then be exploited to evolve the wave field.

Rogue-wave solutions of the Zakharov equation

NASA Astrophysics Data System (ADS)

Rao, Jiguang; Wang, Lihong; Liu, Wei; He, Jingsong

2017-12-01

Using the bilinear transformation method, we derive general rogue-wave solutions of the Zakharov equation. We present these Nth-order rogue-wave solutions explicitly in terms of Nth-order determinants whose matrix elements have simple expressions. We show that the fundamental rogue wave is a line rogue wave with a line profile on the plane ( x, y) arising from a constant background at t ≪ 0 and then gradually tending to the constant background for t ≫ 0. Higher-order rogue waves arising from a constant background and later disappearing into it describe the interaction of several fundamental line rogue waves. We also consider different structures of higher-order rogue waves. We present differences between rogue waves of the Zakharov equation and of the first type of the Davey-Stewartson equation analytically and graphically.

Full-wave modeling of EMIC waves near the He + gyrofrequency

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Eun -Hwa; Johnson, Jay R.

Electromagnetic ion cyclotron (EMIC) waves are known to be excited by the cyclotron instability associated with hot and anisotropic ion distributions in the equatorial region of the magnetosphere and are thought to play a key role in radiation belt losses. Although detection of these waves at the ground can provide a global view of the EMIC wave environment, it is not clear what signatures, if any, would be expected. One of the significant scientific issues concerning EMIC waves is to understand how these waves are detected at the ground. In order to solve this puzzle, it is necessary to understandmore » the propagation characteristics of the field-aligned EMIC waves, which include polarization reversal, cutoff, resonance, and mode coupling between different wave modes, in a dipolar magnetic field. However, the inability of ray tracing to adequately describe wave propagation near the crossover cutoff-resonance frequencies in multi-ion plasmas is one of reasons why these scientific questions remain unsolved. Using a recently developed 2-D full-wave code that solves the full-wave equations in global magnetospheric geometry, we demonstrate how EMIC waves propagate from the equatorial region to higher magnetic latitude in an electron-proton-He+ plasma. We find that polarization reversal occurs at the crossover frequency from left-hand polarization (LHP) to right-hand (RHP) polarization and such RHP EMIC waves can either propagate to the inner magnetosphere or reflect to the outer magnetosphere at the Buchsbaum resonance location. Lastly, we also find that mode coupling from guided LHP EMIC waves to unguided RHP or LHP waves (i.e., fast mode) occurs.« less

Full-wave modeling of EMIC waves near the He + gyrofrequency

DOE PAGES

Kim, Eun -Hwa; Johnson, Jay R.

2016-01-06

Electromagnetic ion cyclotron (EMIC) waves are known to be excited by the cyclotron instability associated with hot and anisotropic ion distributions in the equatorial region of the magnetosphere and are thought to play a key role in radiation belt losses. Although detection of these waves at the ground can provide a global view of the EMIC wave environment, it is not clear what signatures, if any, would be expected. One of the significant scientific issues concerning EMIC waves is to understand how these waves are detected at the ground. In order to solve this puzzle, it is necessary to understandmore » the propagation characteristics of the field-aligned EMIC waves, which include polarization reversal, cutoff, resonance, and mode coupling between different wave modes, in a dipolar magnetic field. However, the inability of ray tracing to adequately describe wave propagation near the crossover cutoff-resonance frequencies in multi-ion plasmas is one of reasons why these scientific questions remain unsolved. Using a recently developed 2-D full-wave code that solves the full-wave equations in global magnetospheric geometry, we demonstrate how EMIC waves propagate from the equatorial region to higher magnetic latitude in an electron-proton-He+ plasma. We find that polarization reversal occurs at the crossover frequency from left-hand polarization (LHP) to right-hand (RHP) polarization and such RHP EMIC waves can either propagate to the inner magnetosphere or reflect to the outer magnetosphere at the Buchsbaum resonance location. Lastly, we also find that mode coupling from guided LHP EMIC waves to unguided RHP or LHP waves (i.e., fast mode) occurs.« less

Fast-ion distributions from third harmonic ICRF heating studied with neutron emission spectroscopy

NASA Astrophysics Data System (ADS)

Hellesen, C.; Gatu Johnson, M.; Andersson Sundén, E.; Conroy, S.; Ericsson, G.; Eriksson, J.; Sjöstrand, H.; Weiszflog, M.; Johnson, T.; Gorini, G.; Nocente, M.; Tardocchi, M.; Kiptily, V. G.; Pinches, S. D.; Sharapov, S. E.; EFDA Contributors, JET

2013-11-01

The fast-ion distribution from third harmonic ion cyclotron resonance frequency (ICRF) heating on the Joint European Torus is studied using neutron emission spectroscopy with the time-of-flight spectrometer TOFOR. The energy dependence of the fast deuteron distribution function is inferred from the measured spectrum of neutrons born in DD fusion reactions, and the inferred distribution is compared with theoretical models for ICRF heating. Good agreements between modelling and measurements are seen with clear features in the fast-ion distribution function, that are due to the finite Larmor radius of the resonating ions, replicated. Strong synergetic effects between ICRF and neutral beam injection heating were also seen. The total energy content of the fast-ion population derived from TOFOR data was in good agreement with magnetic measurements for values below 350 kJ.

Numerical modelling of nonlinear full-wave acoustic propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx

2015-10-28

The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on amore » GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.« less

The Role of Combined ICRF and NBI Heating in JET Hybrid Plasmas in Quest for High D-T Fusion Yield

NASA Astrophysics Data System (ADS)

Mantsinen, Mervi; Challis, Clive; Frigione, Domenico; Graves, Jonathan; Hobirk, Joerg; Belonohy, Eva; Czarnecka, Agata; Eriksson, Jacob; Gallart, Dani; Goniche, Marc; Hellesen, Carl; Jacquet, Philippe; Joffrin, Emmanuel; King, Damian; Krawczyk, Natalia; Lennholm, Morten; Lerche, Ernesto; Pawelec, Ewa; Sips, George; Solano, Emilia R.; Tsalas, Maximos; Valisa, Marco

2017-10-01

Combined ICRF and NBI heating played a key role in achieving the world-record fusion yield in the first deuterium-tritium campaign at the JET tokamak in 1997. The current plans for JET include new experiments with deuterium-tritium (D-T) plasmas with more ITER-like conditions given the recently installed ITER-like wall (ILW). In the 2015-2016 campaigns, significant efforts have been devoted to the development of high-performance plasma scenarios compatible with ILW in preparation of the forthcoming D-T campaign. Good progress was made in both the inductive (baseline) and the hybrid scenario: a new record JET ILW fusion yield with a significantly extended duration of the high-performance phase was achieved. This paper reports on the progress with the hybrid scenario which is a candidate for ITER longpulse operation (˜1000 s) thanks to its improved normalized confinement, reduced plasma current and higher plasma beta with respect to the ITER reference baseline scenario. The combined NBI+ICRF power in the hybrid scenario was increased to 33 MW and the record fusion yield, averaged over 100 ms, to 2.9x1016 neutrons/s from the 2014 ILW fusion record of 2.3x1016 neutrons/s. Impurity control with ICRF waves was one of the key means for extending the duration of the high-performance phase. The main results are reviewed covering both key core and edge plasma issues.

Localized light waves: Paraxial and exact solutions of the wave equation (a review)

NASA Astrophysics Data System (ADS)

Kiselev, A. P.

2007-04-01

Simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation. Much attention has been paid to exact solutions (which date back to the Bateman findings) that describe wave beams (including Bessel-Gauss beams) and wave packets with a Gaussian localization with respect to the spatial variables and time. Their asymptotics with respect to free parameters and at large distances are presented. A similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied. Higher-order modes are considered systematically using the separation of variables method. The application of the Bateman solutions of the wave equation to the construction of solutions to equations with dispersion and nonlinearity and their use in wavelet analysis, as well as the summation of Gaussian beams, are discussed. In addition, solutions localized at infinity known as the Moses-Prosser “acoustic bullets”, as well as their harmonic in time counterparts, “ X waves”, waves from complex sources, etc., have been considered. Everywhere possible, the most elementary mathematical formalism is used.

Initial Simulations of RF Waves in Hot Plasmas Using the FullWave Code

NASA Astrophysics Data System (ADS)

Zhao, Liangji; Svidzinski, Vladimir; Spencer, Andrew; Kim, Jin-Soo

2017-10-01

FullWave is a simulation tool that models RF fields in hot inhomogeneous magnetized plasmas. The wave equations with linearized hot plasma dielectric response are solved in configuration space on adaptive cloud of computational points. The nonlocal hot plasma dielectric response is formulated by calculating the plasma conductivity kernel based on the solution of the linearized Vlasov equation in inhomogeneous magnetic field. In an rf field, the hot plasma dielectric response is limited to the distance of a few particles' Larmor radii, near the magnetic field line passing through the test point. The localization of the hot plasma dielectric response results in a sparse matrix of the problem thus significantly reduces the size of the problem and makes the simulations faster. We will present the initial results of modeling of rf waves using the Fullwave code, including calculation of nonlocal conductivity kernel in 2D Tokamak geometry; the interpolation of conductivity kernel from test points to adaptive cloud of computational points; and the results of self-consistent simulations of 2D rf fields using calculated hot plasma conductivity kernel in a tokamak plasma with reduced parameters. Work supported by the US DOE ``SBIR program.

Analytical and numerical solution for wave reflection from a porous wave absorber

NASA Astrophysics Data System (ADS)

Magdalena, Ikha; Roque, Marian P.

2018-03-01

In this paper, wave reflection from a porous wave absorber is investigated theoretically and numerically. The equations that we used are based on shallow water type model. Modification of motion inside the absorber is by including linearized friction term in momentum equation and introducing a filtered velocity. Here, an analytical solution for wave reflection coefficient from a porous wave absorber over a flat bottom is derived. Numerically, we solve the equations using the finite volume method on a staggered grid. To validate our numerical model, comparison of the numerical reflection coefficient is made against the analytical solution. Further, we implement our numerical scheme to study the evolution of surface waves pass through a porous absorber over varied bottom topography.

Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas

NASA Astrophysics Data System (ADS)

Hu, Wen-Qiang; Gao, Yi-Tian; Jia, Shu-Liang; Huang, Qian-Min; Lan, Zhong-Zhou

2016-11-01

In this paper, a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation is investigated, which has been presented as a model for the shallow water wave in fluids or the electrostatic wave potential in plasmas. By virtue of the binary Bell polynomials, the bilinear form of this equation is obtained. With the aid of the bilinear form, N -soliton solutions are obtained by the Hirota method, periodic wave solutions are constructed via the Riemann theta function, and breather wave solutions are obtained according to the extended homoclinic test approach. Travelling waves are constructed by the polynomial expansion method as well. Then, the relations between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure. Furthermore, we obtain some new solutions of this equation by the standard extended homoclinic test approach. Finally, we give a generalized form of this equation, and find that similar analytical solutions can be obtained from the generalized equation with arbitrary coefficients.

VizieR Online Data Catalog: Radio fluxes of 195 ICRF2-Gaia transfer sources (Le Bail+, 2016)

NASA Astrophysics Data System (ADS)

Le Bail, K.; Gipson, J. M.; Gordon, D.; MacMillan, D. S.; Behrend, D.; Thomas, C. C.; Bolotin, S.; Himwich, W. E.; Baver, K. D.; Corey, B. E.; Titus, M.; Bourda, G.; Charlot, P.; Collioud, A.

2016-07-01

The second realization of the International Celestial Reference Frame (ICRF2) is based on Very Long Baseline Interferometry (VLBI) data at radio frequencies in X band and S band. The European Space Agency's Gaia mission, launched on 2013 December 19, started routine scientific operations in 2014 July. By scanning the whole sky, it is expected to observe ~500000 Quasi Stellar Objects in the optical domain. This means that, in the future, two extragalactic celestial reference frames, at two different frequency domains, will coexist. It will thus be important to align them very accurately. In 2012, the Laboratoire d'Astrophysique de Bordeaux (LAB) selected 195 sources from ICRF2 that will be observed by Gaia and should be suitable for aligning the radio and optical frames: they are called ICRF2-Gaia transfer sources. The LAB submitted a proposal to the International VLBI Service (IVS) to regularly observe these ICRF2-Gaia transfer sources at the same rate as Gaia observes them in the optical realm, e.g., roughly once a month. Of the 195 sources, all but one have been successfully observed in the 12 months prior to 2015 September 01. Table1 lists the 195 ICRF2-Gaia transfer sources. Beginning in 2003 June, the Goddard VLBI group developed a program to purposefully monitor when sources were observed and to increase the observations of "under-observed" sources. In 2013 March, we added all 195 ICRF2-Gaia transfer sources to the IVS source monitoring program with an observation target of 12 successful sessions per year. (1 data file).

Long-Term Variations of the EOP and ICRF2

NASA Technical Reports Server (NTRS)

Zharov, Vladimir; Sazhin, Mikhail; Sementsov, Valerian; Sazhina, Olga

2010-01-01

We analyzed the time series of the coordinates of the ICRF radio sources. We show that part of the radio sources, including the defining sources, shows a significant apparent motion. The stability of the celestial reference frame is provided by a no-net-rotation condition applied to the defining sources. In our case this condition leads to a rotation of the frame axes with time. We calculated the effect of this rotation on the Earth orientation parameters (EOP). In order to improve the stability of the celestial reference frame we suggest a new method for the selection of the defining sources. The method consists of two criteria: the first one we call cosmological and the second one kinematical. It is shown that a subset of the ICRF sources selected according to cosmological criteria provides the most stable reference frame for the next decade.

Full Spectrum Conversion Using Traveling Pulse Wave Quantization

DTIC Science & Technology

2017-03-01

Full Spectrum Conversion Using Traveling Pulse Wave Quantization Michael S. Kappes Mikko E. Waltari IQ-Analog Corporation San Diego, California...temporal-domain quantization technique called Traveling Pulse Wave Quantization (TPWQ). Full spectrum conversion is defined as the complete...pulse width measurements that are continuously generated hence the name “traveling” pulse wave quantization. Our TPWQ-based ADC is composed of a

Several reverse-time integrable nonlocal nonlinear equations: Rogue-wave solutions

NASA Astrophysics Data System (ADS)

Yang, Bo; Chen, Yong

2018-05-01

A study of rogue-wave solutions in the reverse-time nonlocal nonlinear Schrödinger (NLS) and nonlocal Davey-Stewartson (DS) equations is presented. By using Darboux transformation (DT) method, several types of rogue-wave solutions are constructed. Dynamics of these rogue-wave solutions are further explored. It is shown that the (1 + 1)-dimensional fundamental rogue-wave solutions in the reverse-time NLS equation can be globally bounded or have finite-time blowing-ups. It is also shown that the (2 + 1)-dimensional line rogue waves in the reverse-time nonlocal DS equations can be bounded for all space and time or develop singularities in critical time. In addition, the multi- and higher-order rogue waves exhibit richer structures, most of which have no counterparts in the corresponding local nonlinear equations.

High field side launch of RF waves: A new approach to reactor actuators

NASA Astrophysics Data System (ADS)

Wallace, G. M.; Baek, S. G.; Bonoli, P. T.; Faust, I. C.; LaBombard, B. L.; Lin, Y.; Mumgaard, R. T.; Parker, R. R.; Shiraiwa, S.; Vieira, R.; Whyte, D. G.; Wukitch, S. J.

2015-12-01

Launching radio frequency (RF) waves from the high field side (HFS) of a tokamak offers significant advantages over low field side (LFS) launch with respect to both wave physics and plasma material interactions (PMI). For lower hybrid (LH) waves, the higher magnetic field opens the window between wave accessibility (n∥≡c k∥/ω >√{1 -ωpi 2/ω2+ωpe 2/ωce 2 }+ωp e/|ωc e| ) and the condition for strong electron Landau damping (n∥˜√{30 /Te } with Te in keV), allowing LH waves from the HFS to penetrate into the core of a burning plasma, while waves launched from the LFS are restricted to the periphery of the plasma. The lower n∥ of waves absorbed at higher Te yields a higher current drive efficiency as well. In the ion cyclotron range of frequencies (ICRF), HFS launch allows for direct access to the mode conversion layer where mode converted waves absorb strongly on thermal electrons and ions, thus avoiding the generation of energetic minority ion tails. The absence of turbulent heat and particle fluxes on the HFS, particularly in double null configuration, makes it the ideal location to minimize PMI damage to the antenna structure. The quiescent SOL also eliminates the need to couple LH waves across a long distance to the separatrix, as the antenna can be located close to plasma without risking damage to the structure. Improved impurity screening on the HFS will help eliminate the long-standing issues of high Z impurity accumulation with ICRF. Looking toward a fusion reactor, the HFS is the only possible location for a plasma-facing RF antenna that will survive long-term. By integrating the antenna into the blanket module it is possible to improve the tritium breeding ratio compared with an antenna occupying an equatorial port plug. Blanket modules will require remote handling of numerous cooling pipes and electrical connections, and the addition of transmission lines will not substantially increase the level of complexity. The obvious engineering

Global Confinement, Sawtooth Mixing, and Stochastic Diffusion Ripple Loss of Fast ICRF-driven H+ Minority Ions in TFTR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petrov, M.P.; Bell, R.; Budny, R.V.

1998-07-01

This paper presents studies of ICRF-driven H+ minority ions in TFTR (Tokamak Fusion Test Reator) deuterium plasmas using primarily passive Ho flux detection in the energy range of 0.2-1.0 MeV with some corroborating active (lithium pellet charge exchange) measurements. It is shown that in the passive mode the main donors for the neutralization of H+ ions in this energy range are C5+ ions. The measured effective H+ tail temperatures range from 0.15 MeV at an ICRF power of 2 MW to 0.35 MeV at 6 MW. Analysis of the ICRF-driven H+ ion energy balance has been performed on the basismore » of the dependence of effective H+ temperatures on the plasma parameters. The analysis showed that H+ confinement times are comparable with their slowing-down times and tended to decrease with increasing ICRF power. Radial redistribution of ICRF-driven H+ ions was detected when giant sawtooth crashes occurred during the ICRF heating. The redistribution affected ions with energy below 0.7-0.8 MeV. The sawtooth crashes displace H+ ions outward along the plasma major radius into the stochastic ripple diffusion domain were those ions are lost in about 10 milliseconds. These observations are consistent with the model of the redistribution of energetic particles developed previously to explain the results of deuterium-tritium alpha-particle redistribution due to sawteeth observed in TFTR. The experimental data are also consistent with ORBIT code simulations of H+ stochastic ripple diffusion losses.« less

Generalization of the Euler-type solution to the wave equation

NASA Astrophysics Data System (ADS)

Borisov, Victor V.

2001-08-01

Generalization of the Euler-type solution to the wave equation is given. Peculiarities of the space-time structure of obtained waves are considered. For some particular cases interpretation of these waves as `subliminal' and `superluminal' is discussed. The possibility of description of electromagnetic waves by means of the scalar solutions is shown.

Arc detection for the ICRF system on ITER

NASA Astrophysics Data System (ADS)

D'Inca, R.

2011-12-01

The ICRF system for ITER is designed to respect the high voltage breakdown limits. However arcs can still statistically happen and must be quickly detected and suppressed by shutting the RF power down. For the conception of a reliable and efficient detector, the analysis of the mechanism of arcs is necessary to find their unique signature. Numerous systems have been conceived to address the issues of arc detection. VSWR-based detectors, RF noise detectors, sound detectors, optical detectors, S-matrix based detectors. Until now, none of them has succeeded in demonstrating the fulfillment of all requirements and the studies for ITER now follow three directions: improvement of the existing concepts to fix their flaws, development of new theoretically fully compliant detectors (like the GUIDAR) and combination of several detectors to benefit from the advantages of each of them. Together with the physical and engineering challenges, the development of an arc detection system for ITER raises methodological concerns to extrapolate the results from basic experiments and present machines to the ITER scale ICRF system and to conduct a relevant risk analysis.

Northern Hemisphere observations of ICRF sources on the USNO stellar catalogue frame

NASA Astrophysics Data System (ADS)

Fienga, A.; Andrei, A. H.

2004-06-01

The most recent USNO stellar catalogue, the USNO B1.0 (Monet et al. \\cite{Monet03}), provides positions for 1 042 618 261 objects, with a published astrometric accuracy of 200 mas and five-band magnitudes with a 0.3 mag accuracy. Its completeness is believed to be up to magnitude 21th in V-band. Such a catalogue would be a very good tool for astrometric reduction. This work investigates the accuracy of the USNO B1.0 link to ICRF and give an estimation of its internal and external accuracies by comparison with different catalogues, and by computation of ICRF sources using USNO B1.0 star positions.

ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. II. LAMB, SURFACE, AND CENTRIFUGAL WAVES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peralta, J.; López-Valverde, M. A.; Imamura, T.

2014-07-01

This paper is the second in a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases where the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the backgroundmore » wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere.« less

Asymptotic traveling wave solution for a credit rating migration problem

NASA Astrophysics Data System (ADS)

Liang, Jin; Wu, Yuan; Hu, Bei

2016-07-01

In this paper, an asymptotic traveling wave solution of a free boundary model for pricing a corporate bond with credit rating migration risk is studied. This is the first study to associate the asymptotic traveling wave solution to the credit rating migration problem. The pricing problem with credit rating migration risk is modeled by a free boundary problem. The existence, uniqueness and regularity of the solution are obtained. Under some condition, we proved that the solution of our credit rating problem is convergent to a traveling wave solution, which has an explicit form. Furthermore, numerical examples are presented.

The ITER ICRF Antenna Design with TOPICA

NASA Astrophysics Data System (ADS)

Milanesio, Daniele; Maggiora, Riccardo; Meneghini, Orso; Vecchi, Giuseppe

2007-11-01

TOPICA (Torino Polytechnic Ion Cyclotron Antenna) code is an innovative tool for the 3D/1D simulation of Ion Cyclotron Radio Frequency (ICRF), i.e. accounting for antennas in a realistic 3D geometry and with an accurate 1D plasma model [1]. The TOPICA code has been deeply parallelized and has been already proved to be a reliable tool for antennas design and performance prediction. A detailed analysis of the 24 straps ITER ICRF antenna geometry has been carried out, underlining the strong dependence and asymmetries of the antenna input parameters due to the ITER plasma response. We optimized the antenna array geometry dimensions to maximize loading, lower mutual couplings and mitigate sheath effects. The calculated antenna input impedance matrices are TOPICA results of a paramount importance for the tuning and matching system design. Electric field distributions have been also calculated and they are used as the main input for the power flux estimation tool. The designed optimized antenna is capable of coupling 20 MW of power to plasma in the 40 -- 55 MHz frequency range with a maximum voltage of 45 kV in the feeding coaxial cables. [1] V. Lancellotti et al., Nuclear Fusion, 46 (2006) S476-S499

Millimetre-Wave Backhaul for 5G Networks: Challenges and Solutions

PubMed Central

Feng, Wei; Li, Yong; Jin, Depeng; Su, Li; Chen, Sheng

2016-01-01

The trend for dense deployment in future 5G mobile communication networks makes current wired backhaul infeasible owing to the high cost. Millimetre-wave (mm-wave) communication, a promising technique with the capability of providing a multi-gigabit transmission rate, offers a flexible and cost-effective candidate for 5G backhauling. By exploiting highly directional antennas, it becomes practical to cope with explosive traffic demands and to deal with interference problems. Several advancements in physical layer technology, such as hybrid beamforming and full duplexing, bring new challenges and opportunities for mm-wave backhaul. This article introduces a design framework for 5G mm-wave backhaul, including routing, spatial reuse scheduling and physical layer techniques. The associated optimization model, open problems and potential solutions are discussed to fully exploit the throughput gain of the backhaul network. Extensive simulations are conducted to verify the potential benefits of the proposed method for the 5G mm-wave backhaul design. PMID:27322265

Millimetre-Wave Backhaul for 5G Networks: Challenges and Solutions.

PubMed

Feng, Wei; Li, Yong; Jin, Depeng; Su, Li; Chen, Sheng

2016-06-16

The trend for dense deployment in future 5G mobile communication networks makes current wired backhaul infeasible owing to the high cost. Millimetre-wave (mm-wave) communication, a promising technique with the capability of providing a multi-gigabit transmission rate, offers a flexible and cost-effective candidate for 5G backhauling. By exploiting highly directional antennas, it becomes practical to cope with explosive traffic demands and to deal with interference problems. Several advancements in physical layer technology, such as hybrid beamforming and full duplexing, bring new challenges and opportunities for mm-wave backhaul. This article introduces a design framework for 5G mm-wave backhaul, including routing, spatial reuse scheduling and physical layer techniques. The associated optimization model, open problems and potential solutions are discussed to fully exploit the throughput gain of the backhaul network. Extensive simulations are conducted to verify the potential benefits of the proposed method for the 5G mm-wave backhaul design.

Collision broadened resonance localization in tokamaks excited with ICRF waves

NASA Astrophysics Data System (ADS)

Kerbel, G. D.; McCoy, M. G.

1985-08-01

Advanced wave models used to evaluate ICRH in tokamaks typically use warm plasma theory and allow inhomogeneity in one dimension. The authors have developed a bounce-averaged Fokker-Planck quasilinear computational model which evolves the population of particles on more realistic orbits. Each wave-particle resonance has its own specific interaction amplitude within any given volume element. These data need only be generated once, and appropriately stored for efficient retrieval. The wave-particle resonant interaction then serves as a mechanism by which the diffusion of particle populations can proceed among neighboring orbits. Collisions affect the absorption of RF energy by two quite distinct processes: In addition to the usual relaxation towards the Maxwellian distribution creating velocity gradients which drive quasilinear diffusion, collisions also affect the wave-particle resonance through the mechanism of gyro-phase diffusion. The local specific spectral energy absorption rate is directly calculable once the orbit geometry and populations are determined. The code is constructed in such fashion as to accommodate wave propagation models which provide the wave spectral energy density on a poloidal cross-section. Information provided by the calculation includes the local absorption properties of the medium which can then be exploited to evolve the wave field.

Large-amplitude hydromagnetic waves in collisionless relativistic plasma - Exact solution for the fast-mode magnetoacoustic wave

NASA Technical Reports Server (NTRS)

Barnes, A.

1983-01-01

An exact nonlinear solution is found to the relativistic kinetic and electrodynamic equations (in their hydromagnetic limit) that describes the large-amplitude fast-mode magnetoacoustic wave propagating normal to the magnetic field in a collisionless, previously uniform plasma. It is pointed out that a wave of this kind will be generated by transverse compression of any collisionless plasma. The solution is in essence independent of the detailed form of the particle momentum distribution functions. The solution is obtained, in part, through the method of characteristics; the wave exhibits the familiar properties of steepening and shock formation. A detailed analysis is given of the ultrarelativistic limit of this wave.

RF wave simulation for cold edge plasmas using the MFEM library

NASA Astrophysics Data System (ADS)

Shiraiwa, S.; Wright, J. C.; Bonoli, P. T.; Kolev, T.; Stowell, M.

2017-10-01

A newly developed generic electro-magnetic (EM) simulation tool for modeling RF wave propagation in SOL plasmas is presented. The primary motivation of this development is to extend the domain partitioning approach for incorporating arbitrarily shaped SOL plasmas and antenna to the TORIC core ICRF solver, which was previously demonstrated in the 2D geometry [S. Shiraiwa, et. al., "HISTORIC: extending core ICRF wave simulation to include realistic SOL plasmas", Nucl. Fusion in press], to larger and more complicated simulations by including a 3D realistic antenna and integrating RF rectified sheath potential model. Such an extension requires a scalable high fidelity 3D edge plasma wave simulation. We used the MFEM [http://mfem.org], open source scalable C++ finite element method library, and developed a Python wrapper for MFEM (PyMFEM), and then a radio frequency (RF) wave physics module in Python. This approach allows for building a physics layer rapidly, while separating the physics implementation being apart from the numerical FEM implementation. An interactive modeling interface was built on pScope [S Shiraiwa, et. al. Fusion Eng. Des. 112, 835] to work with an RF simulation model in a complicated geometry.

A folded waveguide ICRF antenna for PBX-M and TFTR

NASA Astrophysics Data System (ADS)

Bigelow, T. S.; Carter, M. D.; Fogelman, C. H.; Yugo, J. J.; Baity, F. W.; Bell, G. L.; Gardner, W. L.; Goulding, R. H.; Hoffman, D. J.; Ryan, P. M.; Swain, D. W.; Taylor, D. J.; Wilson, R.; Bernabei, S.; Kugel, H.; Ono, M.

1996-02-01

The folded waveguide (FWG) antenna is an advanced ICRF launcher under development at ORNL that offers many significant advantages over current-strap type antennas. These features are particularly beneficial for reactor-relevant applications such as ITER and TPX. Previous tests of a development folded waveguide with a low density plasma load have shown a factor of 5 increase in power capability over loop antennas into similar plasma conditions. The performance and reliability of a FWG with an actual tokamak plasma load must now be verified for further acceptance of this concept. A 58 MHz, 4 MW folded waveguide is being designed and built for the PBX-M and TFTR tokamaks at Princeton Plasma Physics Laboratory. This design has a square cross-section that can be installed as either a fast wave (FW) or ion-Bernstein wave (IBW) launcher by 90° rotation. Two new features of the design are: a shorter quarter-wavelength resonator configuration and a rear-feed input power coupling loop. Loading calculations with a standard shorting plate indicate that a launched power level of 4 MW is possible on either machine. Mechanical and disruption force analysis indicates that bolted construction will withstand the disruption loads. An experimental program is planned to characterize the plasma loading, heating effectiveness, power capability, impurity generation and other factors for both FW and IBW cases. High power tests of the new configuration are being performed with a development FWG unit on RFTF at ORNL.

Existence and numerical simulation of periodic traveling wave solutions to the Casimir equation for the Ito system

NASA Astrophysics Data System (ADS)

Abbasbandy, S.; Van Gorder, R. A.; Hajiketabi, M.; Mesrizadeh, M.

2015-10-01

We consider traveling wave solutions to the Casimir equation for the Ito system (a two-field extension of the KdV equation). These traveling waves are governed by a nonlinear initial value problem with an interesting nonlinearity (which actually amplifies in magnitude as the size of the solution becomes small). The nonlinear problem is parameterized by two initial constant values, and we demonstrate that the existence of solutions is strongly tied to these parameter values. For our interests, we are concerned with positive, bounded, periodic wave solutions. We are able to classify parameter regimes which admit such solutions in full generality, thereby obtaining a nice existence result. Using the existence result, we are then able to numerically simulate the positive, bounded, periodic solutions. We elect to employ a group preserving scheme in order to numerically study these solutions, and an outline of this approach is provided. The numerical simulations serve to illustrate the properties of these solutions predicted analytically through the existence result. Physically, these results demonstrate the existence of a type of space-periodic structure in the Casimir equation for the Ito model, which propagates as a traveling wave.

Stokes waves revisited: Exact solutions in the asymptotic limit

NASA Astrophysics Data System (ADS)

Davies, Megan; Chattopadhyay, Amit K.

2016-03-01

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic "secular variation" in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n -ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

Linking Deep Astrometric Standards to the ICRF

NASA Astrophysics Data System (ADS)

Frey, S.; Platais, I.; Fey, A. L.

2007-07-01

The next-generation large aperature and large field-of-view telescopes will address fundamantal questions of astrophysica and cosmology such as the nature of dark matter and dark energy. For a variety of applications, the CCD mosaic detectors in the focal plane arrays require astronomic calibrationat the milli-arcsecond (mas) level. The existing optical reference frames are insufficient to support such calibrations. To address this problem, deep optical astronomic fields are being established near the Galactic plane. In order to achiev a 5-10-mas or better positional accuracyfor the Deepp Astrometric Standards (DAS), and to obtain bsolute stellar proper motions for the study of Galactic structure, it is crucial to link these fields to the International Celestial Reference Frame (ICRF). To this end, we selected 15 candidate compact extragalactic radio sources in the Gemini-Orion-Taurus (GOT) field. These sources were observed with the European VLBI Network (EVN) at 5 GHz in phase-reference mode. The bright compact calibrator source J0603+2159 and seven other sources were detected and imaged at the angular resolution of -1.5-8 mas. Relative astrometric positions were derived for these sources at a milli-arcsecond accuracy level. The detection of the optical counterparts of these extragalactic radio sources will allow us to establish a direct link to the ICRF locally in the GOT field.

Solitary-wave solutions of the Benjamin equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Albert, J.P.; Bona, J.L.; Restrepo, J.M.

1999-10-01

Considered here is a model equation put forward by Benjamin that governs approximately the evolution of waves on the interface of a two-fluid system in which surface-tension effects cannot be ignored. The principal focus is the traveling-wave solutions called solitary waves, and three aspects will be investigated. A constructive proof of the existence of these waves together with a proof of their stability is developed. Continuation methods are used to generate a scheme capable of numerically approximating these solitary waves. The computer-generated approximations reveal detailed aspects of the structure of these waves. They are symmetric about their crests, but unlikemore » the classical Korteqeg-de Vries solitary waves, they feature a finite number of oscillations. The derivation of the equation is also revisited to get an idea of whether or not these oscillatory waves might actually occur in a natural setting.« less

A stationary phase solution for mountain waves with application to mesospheric mountain waves generated by Auckland Island

NASA Astrophysics Data System (ADS)

Broutman, Dave; Eckermann, Stephen D.; Knight, Harold; Ma, Jun

2017-01-01

A relatively general stationary phase solution is derived for mountain waves from localized topography. It applies to hydrostatic, nonhydrostatic, or anelastic dispersion relations, to arbitrary localized topography, and to arbitrary smooth vertically varying background temperature and vector wind profiles. A simple method is introduced to compute the ray Jacobian that quantifies the effects of horizontal geometrical spreading in the stationary phase solution. The stationary phase solution is applied to mesospheric mountain waves generated by Auckland Island during the Deep Propagating Gravity Wave Experiment. The results are compared to a Fourier solution. The emphasis is on interpretations involving horizontal geometrical spreading. The results show larger horizontal geometrical spreading for nonhydrostatic waves than for hydrostatic waves in the region directly above the island; the dominant effect of horizontal geometrical spreading in the lower ˜30 km of the atmosphere, compared to the effects of refraction and background density variation; and the enhanced geometrical spreading due to directional wind in the approach to a critical layer in the mesosphere.

Optical Spectra of Candidate International Celestial Reference Frame (ICRF) Flat-spectrum Radio Sources. III.

NASA Astrophysics Data System (ADS)

Titov, O.; Pursimo, T.; Johnston, Helen M.; Stanford, Laura M.; Hunstead, Richard W.; Jauncey, David L.; Zenere, Katrina A.

2017-04-01

In extending our spectroscopic program, which targets sources drawn from the International Celestial Reference Frame (ICRF) Catalog, we have obtained spectra for ˜160 compact, flat-spectrum radio sources and determined redshifts for 112 quasars and radio galaxies. A further 14 sources with featureless spectra have been classified as BL Lac objects. Spectra were obtained at three telescopes: the 3.58 m European Southern Observatory New Technology Telescope, and the two 8.2 m Gemini telescopes in Hawaii and Chile. While most of the sources are powerful quasars, a significant fraction of radio galaxies is also included from the list of non-defining ICRF radio sources.

Optical Spectra of Candidate International Celestial Reference Frame (ICRF) Flat-spectrum Radio Sources. III

DOE Office of Scientific and Technical Information (OSTI.GOV)

Titov, O.; Stanford, Laura M.; Pursimo, T.

In extending our spectroscopic program, which targets sources drawn from the International Celestial Reference Frame (ICRF) Catalog, we have obtained spectra for ∼160 compact, flat-spectrum radio sources and determined redshifts for 112 quasars and radio galaxies. A further 14 sources with featureless spectra have been classified as BL Lac objects. Spectra were obtained at three telescopes: the 3.58 m European Southern Observatory New Technology Telescope, and the two 8.2 m Gemini telescopes in Hawaii and Chile. While most of the sources are powerful quasars, a significant fraction of radio galaxies is also included from the list of non-defining ICRF radiomore » sources.« less

Soliton-cnoidal interactional wave solutions for the reduced Maxwell-Bloch equations

NASA Astrophysics Data System (ADS)

Huang, Li-Li; Qiao, Zhi-Jun; Chen, Yong

2018-02-01

Based on nonlocal symmetry method, localized excitations and interactional solutions are investigated for the reduced Maxwell-Bloch equations. The nonlocal symmetries of the reduced Maxwell-Bloch equations are obtained by the truncated Painleve expansion approach and the Mobious invariant property. The nonlocal symmetries are localized to a prolonged system by introducing suitable auxiliary dependent variables. The extended system can be closed and a novel Lie point symmetry system is constructed. By solving the initial value problems, a new type of finite symmetry transformations is obtained to derive periodic waves, Ma breathers and breathers travelling on the background of periodic line waves. Then rich exact interactional solutions are derived between solitary waves and other waves including cnoidal waves, rational waves, Painleve waves, and periodic waves through similarity reductions. In particular, several new types of localized excitations including rogue waves are found, which stem from the arbitrary function generated in the process of similarity reduction. By computer numerical simulation, the dynamics of these localized excitations and interactional solutions are discussed, which exhibit meaningful structures.

Discrimination of Mixed Taste Solutions using Ultrasonic Wave and Soft Computing

NASA Astrophysics Data System (ADS)

Kojima, Yohichiro; Kimura, Futoshi; Mikami, Tsuyoshi; Kitama, Masataka

In this study, ultrasonic wave acoustic properties of mixed taste solutions were investigated, and the possibility of taste sensing based on the acoustical properties obtained was examined. In previous studies, properties of solutions were discriminated based on sound velocity, amplitude and frequency characteristics of ultrasonic waves propagating through the five basic taste solutions and marketed beverages. However, to make this method applicable to beverages that contain many taste substances, further studies are required. In this paper, the waveform of an ultrasonic wave with frequency of approximately 5 MHz propagating through mixed solutions composed of sweet and salty substance was measured. As a result, differences among solutions were clearly observed as differences in their properties. Furthermore, these mixed solutions were discriminated by a self-organizing neural network. The ratio of volume in their mixed solutions was estimated by a distance-type fuzzy reasoning method. Therefore, the possibility of taste sensing was shown by using ultrasonic wave acoustic properties and the soft computing, such as the self-organizing neural network and the distance-type fuzzy reasoning method.

Measurement of fast minority /sub 3/He/sup + +/ energy distribution during ICRF heating

DOEpatents

Post, D.E. Jr.; Grisham, L.R.; Medley, S.S.

A method and means for measuring the fast /sub 3/He/sup + +/ distribution during /sub 3/He/sup + +/ minority Ion Cyclotron Resonance Frequency (ICRF) heating is disclosed. The present invention involves the use of 10 to 100 keV beams of neutral helium atoms to neutralize the fast /sub 3/He/sup + +/ ions in a heated plasma by double charge exchange (/sub 3/He/sup + +/ + /sub 4/He/sup 0/ ..-->.. /sub 3/He/sup 0/ + /sub 4/He/sup + +/). The neutralized fast /sub 3/He/sup 0/ atoms then escape from the hot plasma confined by a magnetic field and are detected by conventional neutral particle analyzing means. This technique permits the effectiveness of the coupling of the ion cyclotron waves to the /sub 3/He/sup + +/ minority ions to be accurately measured. The present invention is particularly adapted for use in evaluating the effectiveness of the intermediate coupling between the RF heating and the /sub 3/He/sup + +/ in an energetic toroidal plasma.

Possibility designing half-wave and full-wave molecular rectifiers by using single benzene molecule

NASA Astrophysics Data System (ADS)

Abbas, Mohammed A.; Hanoon, Falah H.; Al-Badry, Lafy F.

2018-02-01

This work focused on possibility designing half-wave and full-wave molecular rectifiers by using single and two benzene rings, respectively. The benzene rings were threaded by a magnetic flux that changes over time. The quantum interference effect was considered as the basic idea in the rectification action, the para and meta configurations were investigated. All the calculations are performed by using steady-state theoretical model, which is based on the time-dependent Hamiltonian model. The electrical conductance and the electric current are considered as DC output signals of half-wave and full-wave molecular rectifiers. The finding in this work opens up the exciting potential to use these molecular rectifiers in molecular electronics.

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

Rogue wave solutions for the infinite integrable nonlinear Schrödinger equation hierarchy.

PubMed

Ankiewicz, A; Akhmediev, N

2017-07-01

We present rogue wave solutions of the integrable nonlinear Schrödinger equation hierarchy with an infinite number of higher-order terms. The latter include higher-order dispersion and higher-order nonlinear terms. In particular, we derive the fundamental rogue wave solutions for all orders of the hierarchy, with exact expressions for velocities, phase, and "stretching factors" in the solutions. We also present several examples of exact solutions of second-order rogue waves, including rogue wave triplets.

Closed form solutions of two time fractional nonlinear wave equations

NASA Astrophysics Data System (ADS)

Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

2018-06-01

In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

High-power and steady-state operation of ICRF heating in the large helical device

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mutoh, T., E-mail: mutoh@nifs.ac.jp; Seki, T.; Saito, K.

2015-12-10

Recent progress in an ion cyclotron range of frequencies (ICRF) heating system and experiment results in a Large Helical Device (LHD) are reported. Three kinds of ICRF antenna pairs were installed in the LHD, and the operation power regimes were extended up to 4.5 MW; also, the steady-state operation was extended for more than 45 min in LHD at a MW power level. We studied ICRF heating physics in heliotron configuration using a Hand Shake type (HAS) antenna, Field Aligned Impedance Transforming (FAIT) antenna, and Poloidal Array (PA) antenna, and established the optimum minority-ion heating scenario in an LHD. The FAITmore » antenna having a novel impedance transformer inside the vacuum chamber could reduce the VSWR and successfully injected a higher power to plasma. We tested the PA antennas completely removing the Faraday-shield pipes to avoid breakdown and to increase the plasma coupling. The heating performance was almost the same as other antennas; however, the heating efficiency was degraded when the gap between the antenna and plasma surface was large. Using these three kinds of antennas, ICRF heating could contribute to raising the plasma beta with the second- and third-harmonic cyclotron heating mode, and also to raising the ion temperature as discharge cleaning tools. In 2014, steady-state operation plasma with a line-averaged electron density of 1.2 × 10{sup 19} m{sup −3}, ion and electron temperature of 2 keV, and plasma sustainment time of 48 min was achieved with ICH and ECH heating power of 1.2 MW for majority helium with minority hydrogen. In 2015, the higher-power steady-state operation with a heating power of up to 3 MW was tested with higher density of 3 × 10{sup 19} m{sup −3}.« less

Phase portrait analysis of super solitary waves and flat top solutions

NASA Astrophysics Data System (ADS)

Steffy, S. V.; Ghosh, S. S.

2018-06-01

The phase portrait analysis of super solitary waves has revealed a new kind of intermediate solution which defines the boundary between the two types of super solitary waves, viz., Type I and Type II. A Type I super solitary wave is known to be associated with an intermediate double layer while a Type II solution has no such association. The intermediate solution at the boundary has a flat top structure and is called a flat top solitary wave. Its characteristics resemble an amalgamation of a solitary wave and a double layer. It was found that, mathematically, such kinds of structures may emerge due to the presence of an extra nonlinearity. Although they are relatively unfamiliar in the realm of plasma physics, they have much wider applications in other physical systems.

Impedance of strip-traveling waves on an elastic half space - Asymptotic solution

NASA Technical Reports Server (NTRS)

Crandall, S. H.; Nigam, A. K.

1973-01-01

The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution.

Rogue waves: from nonlinear Schrödinger breather solutions to sea-keeping test.

PubMed

Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco

2013-01-01

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.

Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test

PubMed Central

Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco

2013-01-01

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship. PMID:23405086

LETTER: Study of combined NBI and ICRF enhancement of the D-3He fusion yield with a Fokker-Planck code

NASA Astrophysics Data System (ADS)

Azoulay, M.; George, M. A.; Burger, A.; Collins, W. E.; Silberman, E.

A two-dimensional bounce averaged Fokker-Planck code is used to study the fusion yield and the wave absorption by residual hydrogen ions in higher harmonic ICRF heating of D (120 keV) and 3He (80 keV) beams in the JT-60U tokamak. Both for the fourth harmonic resonance of 3He (ω = 4ωc3He(0), which is accompanied by the third harmonic resonance of hydrogen (ω = 3ωcH) at the low field side, and for the third harmonic resonance of 3He (ω = 4ωcD(0) = 3ωc3He(0)) = 2ωcH(0)), a few per cent of hydrogen ions are found to absorb a large fraction of the ICRF power and to degrade the fusion output power. In the latter case, D beam acceleration due to the fourth harmonic resonance in the 3He(D) regime can enhance the fusion yield more effectively. A discussion is given of the effect of D beam acceleration due to the fifth harmonic resonance (ω = 5ωcD) at the high field side in the case of ω = 4ωc3He(0) and of the optimization of the fusion yield in the case of lower electron density and higher electron temperature

IShTAR ICRF antenna field characterization in vacuum and plasma by using probe diagnostic

NASA Astrophysics Data System (ADS)

Usoltceva, Mariia; Ochoukov, Roman; D'Inca, Rodolphe; Jacquot, Jonathan; Crombé, Kristel; Kostic, Ana; Heuraux, Stéphane; Faudot, Eric; Noterdaeme, Jean-Marie

2017-10-01

RF sheath physics is one of the key topics relevant for improvements of ICRF heating systems, which are present on nearly all modern magnetic fusion machines. This paper introduces developement and validation of a new approach to understanding general RF sheath physics. The presumed reason of enhanced plasma-antenna interactions, parallel electric field, is not measured directly, but proposed to be obtained from simulations in COMSOL Multiphysics® Modeling Software. Measurements of RF magnetic field components with B-dot probes are done on a linear device IShTAR (Ion cyclotron Sheath Test ARrangement) and then compared to simulations. Good resulting accordance is suggested to be the criterion for trustworthiness of parallel electric field estimation as a component of electromagnetic field in modeling. A comparison between simulation and experiment for one magnetic field component in vacuum has demonstrated a close match. An additional complication to this ICRF antenna field characterization study is imposed by the helicon antenna which is used as a plasma ignition tool in the test arrangement. The plasma case, in contrast to the vacuum case, must be approached carefully, since the overlapping of ICRF antenna and helicon antenna fields occurs. Distinguishing of the two fields is done by an analysis of correlation between measurements with both antennas together and with each one separately.

Full-Wave Radio Characterization of Ionospheric Modification at HAARP

DTIC Science & Technology

2015-07-26

Full-Wave Radio Characterization of Ionospheric Modification at HAARP We have studied electrostatic and electromagnetic turbulence stimulated by...radio receivers at HAARP in Alaska, and ground-based radio receivers, incoherent scatter radars, and in-situ measurements from Canadian, ESA, and Polish...363255 San Juan, PR 00936 -3255 31-May-2015 ABSTRACT Final Report: Full-Wave Radio Characterization of Ionospheric Modification at HAARP Report Title We

Evanescent Wave Absorption Based Fiber Sensor for Measuring Glucose Solution Concentration

NASA Astrophysics Data System (ADS)

Marzuki, Ahmad; Candra Pratiwi, Arni; Suryanti, Venty

2018-03-01

An optical fiber sensor based on evanescent wave absorption designed for measuring glucose solution consentration was proposed. The sensor was made to detect absorbance of various wavelength in the glucose solution. The sensing element was fabricated by side polishing of multimode polymer optical fiber to form a D-shape. The sensing element was immersed in different concentration of glucoce solution. As light propagated through the optical fiber, the evanescent wave interacted with the glucose solution. Light was absorbed by the glucose solution. The larger concentration the glucose solution has, the more the evanescent wave was absorbed in particular wavelenght. Here in this paper, light absorbtion as function of glucose concentration was measured as function of wavelength (the color of LED). We have shown that the proposed sensor can demonstrated an increase of light absorption as function of glucose concentration.

Vector-beam solutions of Maxwell's wave equation.

PubMed

Hall, D G

1996-01-01

The Hermite-Gauss and Laguerre-Gauss modes are well-known beam solutions of the scalar Helmholtz equation in the paraxial limit. As such, they describe linearly polarized fields or single Cartesian components of vector fields. The vector wave equation admits, in the paraxial limit, of a family of localized Bessel-Gauss beam solutions that can describe the entire transverse electric field. Two recently reported solutions are members of this family of vector Bessel-Gauss beam modes.

ICRF wall conditioning at TEXTOR-94 in the presence of a 2.25 T magnetic field

NASA Astrophysics Data System (ADS)

Esser, H. G.; Lyssoivan, A.; Freisinger, M.; Koch, R.; van Oost, G.; Weschenfelder, F.; Winter, J.; Textor-Icrh-Team

1997-02-01

To investigate alternative conditioning concepts for future fusion devices with permanent magnetic fields, plasmas produced by the coupling of ICRF power to He and gas mixtures of Helium + silane, have been analyzed in the presence of a 2.25 T toroidal magnetic field at TEXTOR-94. Their qualification for wall conditioning has been investigated for different He-pressures, PHe (1 × 10 -3 < PHe ( Pa) < 1 × 10 -1) and ICRF power, PICRF (100 < PICRF ( kW) < 800). Electron densities n e averaged along different radial lines of sight across the vacuum vessel from the top to the bottom have been obtained in the range 5 × 10 10 < ne ( cm-3) < 3 × 10 12. To study quantitatively the efficiency of hydrogen desorption from the first wall at different ICRF plasma conditions in a reproducible way, the first wall was presaturated by RG-glow discharges in H 2. The amount and the evolution of the H 2 desorption from rf discharge to rf discharge was determined by ion gauge measurements combined with mass spectrometry. To demonstrate the capability of the new method for plasma assisted thin film deposition, different amounts of silane (<50%) were added to the He gas. During the ICRF pulses, the silane molecules were dissociated in the plasma and the Si atoms stick to the wall. A good balance of the amount of Si disappearing from the gas phase and that measured by post mortem surface analyses of collector probes at the wall position was found.

Experimental Study of RF Sheaths due to Shear Alfv'en Waves in the LAPD

NASA Astrophysics Data System (ADS)

Martin, Michael; van Compernolle, Bart; Carter, Troy; Gekelman, Walter; Pribyl, Patrick; D'Ippolito, Daniel A.; Myra, James R.

2012-10-01

Ion cyclotron resonance frequency (ICRF) heating is an important tool in current fusion experiments and will be an essential part of the heating power in ITER. A current limitation of ICRF heating is impurity generation through the formation of radiofrequency (RF) sheaths, both near-field (at the antenna) and far-field (e.g. in the divertor region). Far-field sheaths are thought to be generated through the direct launch of or mode conversion to shear Alfv'en waves. Shear Alfv'en waves have an electric field component parallel to the background magnetic field near the wall that drives an RF sheath.footnotetextD. A. D'Ippolito and J. R. Myra, Phys. Plasmas 19, 034504 (2012) In this study we directly launch the shear Alfv'en wave and measure the plasma potential oscillations and DC potential in the bulk plasma of the LAPD using emissive and Langmuir probes. Measured changes in the DC plasma potential can serve as an indirect measurement of the formation of an RF sheath because of rectification. These measurements will be useful in guiding future experiments to measure the plasma potential profile inside RF sheaths as part of an ongoing campaign.

Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation

NASA Astrophysics Data System (ADS)

Ma, Zhi-Min; Sun, Yu-Huai; Liu, Fu-Sheng

2013-03-01

In this paper, the generalized Boussinesq wave equation utt — uxx + a(um)xx + buxxxx = 0 is investigated by using the bifurcation theory and the method of phase portraits analysis. Under the different parameter conditions, the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained.

Weierstrass traveling wave solutions for dissipative Benjamin, Bona, and Mahony (BBM) equation

NASA Astrophysics Data System (ADS)

Mancas, Stefan C.; Spradlin, Greg; Khanal, Harihar

2013-08-01

In this paper the effect of a small dissipation on waves is included to find exact solutions to the modified Benjamin, Bona, and Mahony (BBM) equation by viscosity. Using Lyapunov functions and dynamical systems theory, we prove that when viscosity is added to the BBM equation, in certain regions there still exist bounded traveling wave solutions in the form of solitary waves, periodic, and elliptic functions. By using the canonical form of Abel equation, the polynomial Appell invariant makes the equation integrable in terms of Weierstrass ℘ functions. We will use a general formalism based on Ince's transformation to write the general solution of dissipative BBM in terms of ℘ functions, from which all the other known solutions can be obtained via simplifying assumptions. Using ODE (ordinary differential equations) analysis we show that the traveling wave speed is a bifurcation parameter that makes transition between different classes of waves.

Periodic solutions for one dimensional wave equation with bounded nonlinearity

NASA Astrophysics Data System (ADS)

Ji, Shuguan

2018-05-01

This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient u (x) satisfies ess infηu (x) > 0 with ηu (x) = 1/2 u″/u - 1/4 (u‧/u)2, which actually excludes the classical constant coefficient model. For the case ηu (x) = 0, it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form T = 2p-1/q (p , q are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition ess infηu (x) > 0.

Absolute instabilities of travelling wave solutions in a Keller-Segel model

NASA Astrophysics Data System (ADS)

Davis, P. N.; van Heijster, P.; Marangell, R.

2017-11-01

We investigate the spectral stability of travelling wave solutions in a Keller-Segel model of bacterial chemotaxis with a logarithmic chemosensitivity function and a constant, sublinear, and linear consumption rate. Linearising around the travelling wave solutions, we locate the essential and absolute spectrum of the associated linear operators and find that all travelling wave solutions have parts of the essential spectrum in the right half plane. However, we show that in the case of constant or sublinear consumption there exists a range of parameters such that the absolute spectrum is contained in the open left half plane and the essential spectrum can thus be weighted into the open left half plane. For the constant and sublinear consumption rate models we also determine critical parameter values for which the absolute spectrum crosses into the right half plane, indicating the onset of an absolute instability of the travelling wave solution. We observe that this crossing always occurs off of the real axis.

Self-sustained peristaltic waves: Explicit asymptotic solutions

NASA Astrophysics Data System (ADS)

Dudchenko, O. A.; Guria, G. Th.

2012-02-01

A simple nonlinear model for the coupled problem of fluid flow and contractile wall deformation is proposed to describe peristalsis. In the context of the model the ability of a transporting system to perform autonomous peristaltic pumping is interpreted as the ability to propagate sustained waves of wall deformation. Piecewise-linear approximations of nonlinear functions are used to analytically demonstrate the existence of traveling-wave solutions. Explicit formulas are derived which relate the speed of self-sustained peristaltic waves to the rheological properties of the transporting vessel and the transported fluid. The results may contribute to the development of diagnostic and therapeutic procedures for cases of peristaltic motility disorders.

An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2004-01-01

The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

Novel Reactor Relevant RF Actuator Schemes for the Lower Hybrid and the Ion Cyclotron Range of Frequencies

NASA Astrophysics Data System (ADS)

Bonoli, Paul

2014-10-01

This paper presents a fresh physics perspective on the onerous problem of coupling and successfully utilizing ion cyclotron range of frequencies (ICRF) and lower hybrid range of frequencies (LHRF) actuators in the harsh environment of a nuclear fusion reactor. The ICRF and LH launchers are essentially first wall components in a fusion reactor and as such will be subjected to high heat fluxes. The high field side (HFS) of the plasma offers a region of reduced heat flux together with a quiescent scrape off layer (SOL). Placement of the ICRF and LHRF launchers on the tokamak HFS also offers distinct physics advantages: The higher toroidal magnetic field makes it possible to couple faster phase velocity LH waves that can penetrate farther into the plasma core and be absorbed by higher energy electrons, thereby increasing the current drive efficiency. In addition, re-location of the LH launcher off the mid-plane (i.e., poloidal ``steering'') allows further control of the deposition location. Also ICRF waves coupled from the HFS couple strongly to mode converted ion Bernstein waves and ion cyclotron waves waves as the minority density is increased, thus opening the possibility of using this scheme for flow drive and pressure control. Finally the quiescent nature of the HFS scrape off layer should minimize the effects of RF wave scattering from density fluctuations. Ray tracing / Fokker Planck simulations will be presented for LHRF applications in devices such as the proposed Advanced Divertor Experiment (ADX) and extending to ITER and beyond. Full-wave simulations will also be presented which demonstrate the possible combinations of electron and ion heating via ICRF mode conversion. Work supported by the US DoE under Contract Numbers DE-FC02-01ER54648 and DE-FC02-99ER54512.

Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions

NASA Astrophysics Data System (ADS)

Merzon, A.; Zhevandrov, P.; Romero Rodríguez, M. I.; De la Paz Méndez, J. E.

2018-06-01

Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction and of finite support in the other. These solutions are quasiperiodic along the structure and exponentially decay in the orthogonal direction. A simple formula for the dispersion relation of these waves is obtained.

MITHRA 1.0: A full-wave simulation tool for free electron lasers

NASA Astrophysics Data System (ADS)

Fallahi, Arya; Yahaghi, Alireza; Kärtner, Franz X.

2018-07-01

Free Electron Lasers (FELs) are a solution for providing intense, coherent and bright radiation in the hard X-ray regime. Due to the low wall-plug efficiency of FEL facilities, it is crucial and additionally very useful to develop complete and accurate simulation tools for better optimizing a FEL interaction. The highly sophisticated dynamics involved in a FEL process was the main obstacle hindering the development of general simulation tools for this problem. We present a numerical algorithm based on finite difference time domain/Particle in cell (FDTD/PIC) in a Lorentz boosted coordinate system which is able to fulfill a full-wave simulation of a FEL process. The developed software offers a suitable tool for the analysis of FEL interactions without considering any of the usual approximations. A coordinate transformation to bunch rest frame makes the very different length scales of bunch size, optical wavelengths and the undulator period transform to values with the same order. Consequently, FDTD/PIC simulations in conjunction with efficient parallelization techniques make the full-wave simulation feasible using the available computational resources. Several examples of free electron lasers are analyzed using the developed software, the results are benchmarked based on standard FEL codes and discussed in detail.

Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach.

PubMed

Geng, Xiaolong; Boufadel, Michel C; Xia, Yuqiang; Li, Hailong; Zhao, Lin; Jackson, Nancy L; Miller, Richard S

2014-09-01

A numerical study was undertaken to investigate the effects of waves on groundwater flow and associated inland-released solute transport based on tracer experiments in a laboratory beach. The MARUN model was used to simulate the density-dependent groundwater flow and subsurface solute transport in the saturated and unsaturated regions of the beach subjected to waves. The Computational Fluid Dynamics (CFD) software, Fluent, was used to simulate waves, which were the seaward boundary condition for MARUN. A no-wave case was also simulated for comparison. Simulation results matched the observed water table and concentration at numerous locations. The results revealed that waves generated seawater-groundwater circulations in the swash and surf zones of the beach, which induced a large seawater-groundwater exchange across the beach face. In comparison to the no-wave case, waves significantly increased the residence time and spreading of inland-applied solutes in the beach. Waves also altered solute pathways and shifted the solute discharge zone further seaward. Residence Time Maps (RTM) revealed that the wave-induced residence time of the inland-applied solutes was largest near the solute exit zone to the sea. Sensitivity analyses suggested that the change in the permeability in the beach altered solute transport properties in a nonlinear way. Due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone, which reached up to 10% of the total mass in some cases, constituted a continuous slow release of solutes to the saturated zone of the beach. This means of control was not addressed in prior studies. Copyright © 2014 Elsevier B.V. All rights reserved.

Symmetry Reductions and Group-Invariant Radial Solutions to the n-Dimensional Wave Equation

NASA Astrophysics Data System (ADS)

Feng, Wei; Zhao, Songlin

2018-01-01

In this paper, we derive explicit group-invariant radial solutions to a class of wave equation via symmetry group method. The optimal systems of one-dimensional subalgebras for the corresponding radial wave equation are presented in terms of the known point symmetries. The reductions of the radial wave equation into second-order ordinary differential equations (ODEs) with respect to each symmetry in the optimal systems are shown. Then we solve the corresponding reduced ODEs explicitly in order to write out the group-invariant radial solutions for the wave equation. Finally, several analytical behaviours and smoothness of the resulting solutions are discussed.

Integral representations of solutions of the wave equation based on relativistic wavelets

NASA Astrophysics Data System (ADS)

Perel, Maria; Gorodnitskiy, Evgeny

2012-09-01

A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincaré group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coefficients on speeds of sources is discussed.

Full wave simulations of helicon wave losses in the scrape-off-layer of the DIII-D tokamak

NASA Astrophysics Data System (ADS)

Lau, Cornwall; Jaeger, Fred; Berry, Lee; Bertelli, Nicola; Pinsker, Robert

2017-10-01

Helicon waves have been recently proposed as an off-axis current drive actuator for DIII-D. Previous modeling using the hot plasma, full wave code AORSA, has shown good agreement with the ray tracing code GENRAY for helicon wave propagation and absorption in the core plasma. AORSA, and a new, reduced finite-element-model show discrepancies between ray tracing and full wave occur in the scrape-off-layer (SOL), especially at high densities. The reduced model is much faster than AORSA, and reproduces most of the important features of the AORSA model. The reduced model also allows for larger parametric scans and for the easy use of arbitrary tokamak geometry. Results of the full wave codes, AORSA and COMSOL, will be shown for helicon wave losses in the SOL are shown for a large range of parameters, such as SOL density profiles, n||, radial and vertical locations of the antenna, and different tokamak vessel geometries. This work was supported by DE-AC05-00OR22725, DE-AC02-09CH11466, and DE-FC02-04ER54698.

Characteristics of solitary waves, quasiperiodic solutions, homoclinic breather solutions and rogue waves in the generalized variable-coefficient forced Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Zou, Li

2017-12-01

In this paper, the generalized variable-coefficient forced Kadomtsev-Petviashvili (gvcfKP) equation is investigated, which can be used to characterize the water waves of long wavelength relating to nonlinear restoring forces. Using a dependent variable transformation and combining the Bell’s polynomials, we accurately derive the bilinear expression for the gvcfKP equation. By virtue of bilinear expression, its solitary waves are computed in a very direct method. By using the Riemann theta function, we derive the quasiperiodic solutions for the equation under some limitation factors. Besides, an effective way can be used to calculate its homoclinic breather waves and rogue waves, respectively, by using an extended homoclinic test function. We hope that our results can help enrich the dynamical behavior of the nonlinear wave equations with variable-coefficient.

Rogue waves and unbounded solutions of the NLSE

NASA Astrophysics Data System (ADS)

Lechuga, Antonio

2017-04-01

Since the pioneering work of Zakharov has been generally admitted that rogue waves can be studied in the framework of the Nonlinear Schrödinger Equation (NLSE). Many researchers, Akhmediev, Peregrine, Matveev among others gave different solutions to this equation that, in some way, could be linked to rogue waves and also to its more important characteristic: its unexpectedness. Janssen (2003, 2004), Onorato (2004, 2006) and Waseda (2006) linked the coefficient of the nonlinear term of the Schrödinger equation with the Benjamin-Feir index (BFI) that, we know, is a measure of the modulational instability of the waves. From this point of view the value of this coefficient of the NLSE could be known from statistics. Thus the relationship between sea states and the mechanism of generation of rogue waves could be found out. Following the well-known Lie group theory researchers have been studying the Lie point symmetries of the NLSE: the scaling transformations, Galilean transformations and phase transformations. Basically these transformations turn the NLSE into a nonlinear ordinary differential equation called Duffing equation (also called eikonal equation). There are different ways to do this, but in most of them the independent variable that could be seen as a space variable is a kind of moving frame with the time incorporated in this way. The main aim of this work is to classify solutions of the Duffing equation (periodic and nonperiodic waves and also bounded and unbounded waves) bearing in mind that the coefficient of the nonlinear term in the NLSE is left unaltered in the process of the transformation.

Exact modelling of the optical bistability in ferroelectics via two-wave mixing: A system with full nonlinearity

NASA Astrophysics Data System (ADS)

Khushaini, Muhammad Asif A.; Ibrahim, Abdel-Baset M. A.; Choudhury, P. K.

2018-05-01

In this paper, we provide a complete mathematical model of the phenomenon of optical bistability (OB) resulting from the degenerate two-wave mixing (TWM) process of laser beams interacting with a single nonlinear layer of ferroelectric material. Starting with the electromagnetic wave equation for optical wave propagating in nonlinear media, a nonlinear coupled wave (CW) system with both self-phase modulation (SPM) and cross-phase modulation (XPM) sources of nonlinearity are derived. The complete CW system with full nonlinearity is solved numerically and a comparison between both the cases of with and without SPM at various combinations of design parameters is given. Furthermore, to provide a reliable theoretical model for the OB via TWM process, the results obtained theoretically are compared with the available experimental data. We found that the nonlinear system without SPM fails to predict the bistable response at lower combinations of the input parameters. However, at relatively higher values, the solution without SPM shows a reduction in the switching contrast and period in the OB response. A comparison with the experimental results shows better agreement with the system with full nonlinearity.

Tunable biasing magnetic field design of ferrite tuner for ICRF heating system in EAST

NASA Astrophysics Data System (ADS)

Manman, XU; Yuntao, SONG; Gen, CHEN; Yanping, ZHAO; Yuzhou, MAO; Guang, LIU; Zhen, PENG

2017-11-01

Ion cyclotron range of frequency (ICRF) heating has been used in tokamaks as one of the most successful auxiliary heating tools and has been adopted in the EAST. However, the antenna load will fluctuate with the change of plasma parameters in the ICRF heating process. To ensure the steady operation of the ICRF heating system in the EAST, fast ferrite tuner (FFT) has been carried out to achieve real-time impedance matching. For the requirements of the FFT impedance matching system, the magnet system of the ferrite tuner (FT) was designed by numerical simulations and experimental analysis, where the biasing magnetic circuit and alternating magnetic circuit were the key researched parts of the ferrite magnet. The integral design goal of the FT magnetic circuit is that DC bias magnetic field is 2000 Gs and alternating magnetic field is ±400 Gs. In the FTT, E-type magnetic circuit was adopted. Ferrite material is NdFeB with a thickness of 30 mm by setting the working point of NdFeB, and the ampere turn of excitation coil is 25 through the theoretical calculation and simulation analysis. The coil inductance to generate alternating magnetic field is about 7 mH. Eddy-current effect has been analyzed, while the magnetic field distribution has been measured by a Hall probe in the medium plane of the biasing magnet. Finally, the test results show the good performance of the biasing magnet satisfying the design and operating requirements of the FFT.

Classification of homoclinic rogue wave solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Osborne, A. R.

2014-01-01

Certain homoclinic solutions of the nonlinear Schrödinger (NLS) equation, with spatially periodic boundary conditions, are the most common unstable wave packets associated with the phenomenon of oceanic rogue waves. Indeed the homoclinic solutions due to Akhmediev, Peregrine and Kuznetsov-Ma are almost exclusively used in scientific and engineering applications. Herein I investigate an infinite number of other homoclinic solutions of NLS and show that they reduce to the above three classical homoclinic solutions for particular spectral values in the periodic inverse scattering transform. Furthermore, I discuss another infinity of solutions to the NLS equation that are not classifiable as homoclinic solutions. These latter are the genus-2N theta function solutions of the NLS equation: they are the most general unstable spectral solutions for periodic boundary conditions. I further describe how the homoclinic solutions of the NLS equation, for N = 1, can be derived directly from the theta functions in a particular limit. The solutions I address herein are actual spectral components in the nonlinear Fourier transform theory for the NLS equation: The periodic inverse scattering transform. The main purpose of this paper is to discuss a broader class of rogue wave packets1 for ship design, as defined in the Extreme Seas program. The spirit of this research came from D. Faulkner (2000) who many years ago suggested that ship design procedures, in order to take rogue waves into account, should progress beyond the use of simple sine waves. 1An overview of other work in the field of rogue waves is given elsewhere: Osborne 2010, 2012 and 2013. See the books by Olagnon and colleagues 2000, 2004 and 2008 for the Brest meetings. The books by Kharif et al. (2008) and Pelinovsky et al. (2010) are excellent references.

Soliton and quasi-periodic wave solutions for b-type Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Singh, Manjit; Gupta, R. K.

2017-11-01

In this paper, truncated Laurent expansion is used to obtain the bilinear equation of a nonlinear evolution equation. As an application of Hirota's method, multisoliton solutions are constructed from the bilinear equation. Extending the application of Hirota's method and employing multidimensional Riemann theta function, one and two-periodic wave solutions are also obtained in a straightforward manner. The asymptotic behavior of one and two-periodic wave solutions under small amplitude limits is presented, and their relations with soliton solutions are also demonstrated.

Traveling wave solutions and conservation laws for nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-02-01

In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated.

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.

2009-07-01

In this paper, we restrict our attention to traveling wave solutions of a reaction-diffusion equation. Firstly we apply the Divisor Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to find a quasi-polynomial first integral of an explicit form to an equivalent autonomous system. Then through this first integral, we reduce the reaction-diffusion equation to a first-order integrable ordinary differential equation, and a class of traveling wave solutions is obtained accordingly. Comparisons with the existing results in the literature are also provided, which indicates that some analytical results in the literature contain errors. We clarify the errors and instead give a refined result in a simple and straightforward manner.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vdovin V.L.

In this report we describe theory and 3D full wave code description for the wave excitation, propagation and absorption in 3-dimensional (3D) stellarator equilibrium high beta plasma in ion cyclotron frequency range (ICRF). This theory forms a basis for a 3D code creation, urgently needed for the ICRF heating scenarios development for the operated LHD, constructed W7-X, NCSX and projected CSX3 stellarators, as well for re evaluation of ICRF scenarios in operated tokamaks and in the ITER . The theory solves the 3D Maxwell-Vlasov antenna-plasma-conducting shell boundary value problem in the non-orthogonal flux coordinates ({Psi}, {theta}, {var_phi}), {Psi} being magneticmore » flux function, {theta} and {var_phi} being the poloidal and toroidal angles, respectively. All basic physics, like wave refraction, reflection and diffraction are self consistently included, along with the fundamental ion and ion minority cyclotron resonances, two ion hybrid resonance, electron Landau and TTMP absorption. Antenna reactive impedance and loading resistance are also calculated and urgently needed for an antenna -generator matching. This is accomplished in a real confining magnetic field being varying in a plasma major radius direction, in toroidal and poloidal directions, through making use of the hot dense plasma wave induced currents with account to the finite Larmor radius effects. We expand the solution in Fourier series over the toroidal ({var_phi}) and poloidal ({theta}) angles and solve resulting ordinary differential equations in a radial like {Psi}-coordinate by finite difference method. The constructed discretization scheme is divergent-free one, thus retaining the basic properties of original equations. The Fourier expansion over the angle coordinates has given to us the possibility to correctly construct the ''parallel'' wave number k{sub //}, and thereby to correctly describe the ICRF waves absorption by a hot plasma. The toroidal harmonics are tightly coupled with

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

PubMed

Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

2014-01-01

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

Analytical solution for the transient wave propagation of a buried cylindrical P-wave line source in a semi-infinite elastic medium with a fluid surface layer

NASA Astrophysics Data System (ADS)

Shan, Zhendong; Ling, Daosheng

2018-02-01

This article develops an analytical solution for the transient wave propagation of a cylindrical P-wave line source in a semi-infinite elastic solid with a fluid layer. The analytical solution is presented in a simple closed form in which each term represents a transient physical wave. The Scholte equation is derived, through which the Scholte wave velocity can be determined. The Scholte wave is the wave that propagates along the interface between the fluid and solid. To develop the analytical solution, the wave fields in the fluid and solid are defined, their analytical solutions in the Laplace domain are derived using the boundary and interface conditions, and the solutions are then decomposed into series form according to the power series expansion method. Each item of the series solution has a clear physical meaning and represents a transient wave path. Finally, by applying Cagniard's method and the convolution theorem, the analytical solutions are transformed into the time domain. Numerical examples are provided to illustrate some interesting features in the fluid layer, the interface and the semi-infinite solid. When the P-wave velocity in the fluid is higher than that in the solid, two head waves in the solid, one head wave in the fluid and a Scholte wave at the interface are observed for the cylindrical P-wave line source.

On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.

PubMed

Yang, Xiao-Jun; Tenreiro Machado, J A; Baleanu, Dumitru; Cattani, Carlo

2016-08-01

This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.

Investigation of electrostatic waves in the ion cyclotron range of frequencies in L-4 and ACT-1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ono, Masayuki

Electrostatic waves in the ion cyclotron range of frequencies (ICRF) were studied in the Princeton L-4 and ACT-1 devices for approximately ten years, from 1975 to 1985. The investigation began in the L-4 linear device, looking for the parametric excitation of electrostatic ion cyclotron waves in multi-ion-species plasmas. In addition, this investigation verified multi-ion-species effects on the electrostatic ion cyclotron wave dispersion religion including the ion-ion hybrid resonance. Finite-Larmor-radius modification of the wave dispersion relation was also observed, even for ion temperatures of T{sub i} {approx} 1/40 eV. Taking advantage of the relatively high field and long device length ofmore » L-4, the existence of the cold electrostatic ion cyclotron wave (CES ICW) was verified. With the arrival of the ACT-1 toroidal device, finite-Larmor-radius (FLR) waves were studied in a relatively collisionless warm-ion hydrogen plasma. Detailed investigations of ion Bernstein waves (IBW) included the verification of mode-transformation in their launching, their wave propagation characteristics, their absorption, and the resulting ion heating. This basic physics activity played a crucial role in developing a new reactor heating concept termed ion Bernstein wave heating. Experimental research in the lower hybrid frequency range confirmed the existence of FLR effects near the lower hybrid resonance, predicted by Stix in 1965. In a neon plasma with a carefully placed phased wave exciter, the neutralized ion Bernstein wave was observed for the first time. Using a fastwave ICRF antenna, two parasitic excitation processes for IBW -- parametric instability and density-gradient-driven excitation -- were also discovered. In the concluding section of this paper, a possible application of externally launched electrostatic waves is suggested for helium ash removal from fusion reactor plasmas.« less

Investigation of electrostatic waves in the ion cyclotron range of frequencies in L-4 and ACT-1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ono, Masayuki.

Electrostatic waves in the ion cyclotron range of frequencies (ICRF) were studied in the Princeton L-4 and ACT-1 devices for approximately ten years, from 1975 to 1985. The investigation began in the L-4 linear device, looking for the parametric excitation of electrostatic ion cyclotron waves in multi-ion-species plasmas. In addition, this investigation verified multi-ion-species effects on the electrostatic ion cyclotron wave dispersion religion including the ion-ion hybrid resonance. Finite-Larmor-radius modification of the wave dispersion relation was also observed, even for ion temperatures of T[sub i] [approx] 1/40 eV. Taking advantage of the relatively high field and long device length ofmore » L-4, the existence of the cold electrostatic ion cyclotron wave (CES ICW) was verified. With the arrival of the ACT-1 toroidal device, finite-Larmor-radius (FLR) waves were studied in a relatively collisionless warm-ion hydrogen plasma. Detailed investigations of ion Bernstein waves (IBW) included the verification of mode-transformation in their launching, their wave propagation characteristics, their absorption, and the resulting ion heating. This basic physics activity played a crucial role in developing a new reactor heating concept termed ion Bernstein wave heating. Experimental research in the lower hybrid frequency range confirmed the existence of FLR effects near the lower hybrid resonance, predicted by Stix in 1965. In a neon plasma with a carefully placed phased wave exciter, the neutralized ion Bernstein wave was observed for the first time. Using a fastwave ICRF antenna, two parasitic excitation processes for IBW -- parametric instability and density-gradient-driven excitation -- were also discovered. In the concluding section of this paper, a possible application of externally launched electrostatic waves is suggested for helium ash removal from fusion reactor plasmas.« less

Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Bertola, Marco; El, Gennady A.; Tovbis, Alexander

2016-10-01

Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrödinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration of multiphase, or finite-band, fNLS solutions of whom the standard SFBs and the structures forming due to their collisions represent particular, degenerate, cases. A generalized rogue wave notion then naturally enters as a large-amplitude localized coherent structure occurring within a finite-band fNLS solution. In this paper, we use the winding of real tori to show the mechanism of the appearance of such generalized rogue waves and derive an analytical criterion distinguishing finite-band potentials of the fNLS equation that exhibit generalized rogue waves.

Gauge invariant gluon spin operator for spinless nonlinear wave solutions

NASA Astrophysics Data System (ADS)

Lee, Bum-Hoon; Kim, Youngman; Pak, D. G.; Tsukioka, Takuya; Zhang, P. M.

2017-04-01

We consider nonlinear wave type solutions with intrinsic mass scale parameter and zero spin in a pure SU(2) quantum chromodynamics (QCD). A new stationary solution which can be treated as a system of static Wu-Yang monopole dressed in off-diagonal gluon field is proposed. A remarkable feature of such a solution is that it possesses a finite energy density everywhere. All considered nonlinear wave type solutions have common features: presence of the mass scale parameter, nonvanishing projection of the color fields along the propagation direction and zero spin. The last property requires revision of the gauge invariant definition of the spin density operator which is supposed to produce spin one states for the massless vector gluon field. We construct a gauge invariant definition of the classical gluon spin density operator which is unique and Lorentz frame independent.

Traveling wave solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-10-01

In this paper, we investigate the traveling soliton and the periodic wave solutions of the nonlinear Schrödinger equation (NLSE) with generalized nonlinear functionality. We also explore the underlying close connection between the well-known KdV equation and the NLSE. It is remarked that both one-dimensional KdV and NLSE models share the same pseudoenergy spectrum. We also derive the traveling wave solutions for two cases of weakly nonlinear mathematical models, namely, the Helmholtz and the Duffing oscillators' potentials. It is found that these models only allow gray-type NLSE solitary propagations. It is also found that the pseudofrequency ratio for the Helmholtz potential between the nonlinear periodic carrier and the modulated sinusoidal waves is always in the range 0.5 ≤ Ω/ω ≤ 0.537285 regardless of the potential parameter values. The values of Ω/ω = {0.5, 0.537285} correspond to the cnoidal waves modulus of m = {0, 1} for soliton and sinusoidal limits and m = 0.5, respectively. Moreover, the current NLSE model is extended to fully NLSE (FNLSE) situation for Sagdeev oscillator pseudopotential which can be derived using a closed set of hydrodynamic fluid equations with a fully integrable Hamiltonian system. The generalized quasi-three-dimensional traveling wave solution is also derived. The current simple hydrodynamic plasma model may also be generalized to two dimensions and other complex situations including different charged species and cases with magnetic or gravitational field effects.

A numerical study of the 3-periodic wave solutions to KdV-type equations

NASA Astrophysics Data System (ADS)

Zhang, Yingnan; Hu, Xingbiao; Sun, Jianqing

2018-02-01

In this paper, by using the direct method of calculating periodic wave solutions proposed by Akira Nakamura, we present a numerical process to calculate the 3-periodic wave solutions to several KdV-type equations: the Korteweg-de Vries equation, the Sawada-Koterra equation, the Boussinesq equation, the Ito equation, the Hietarinta equation and the (2 + 1)-dimensional Kadomtsev-Petviashvili equation. Some detailed numerical examples are given to show the existence of the three-periodic wave solutions numerically.

P-wave fault-plane solutions and the generation of surface waves by earthquakes in the western United States

NASA Astrophysics Data System (ADS)

Patton, Howard J.

1985-08-01

Surface waves recorded at regional distances are used to study the source mechanisms of seven earthquakes in the western United States with magnitudes between 4.3 and 5.5. The source mechanisms of events in or on the margins of the Basin and Range show T-axis with an azimuth of N85°W +/- 16° and a plunge of 12° +/- 16°. Of the seven events, four have P-wave solutions that are inconsistent with surface-wave observations. Azimuths of the T-axis obtained from the surface-wave mechanisms and from the P-wave solutions differ by up to 45°. These events have dip-slip or oblique-slip mechanisms, and the source depths for three of the events are 5 km or less. Their source mechanisms and small magnitudes make identification of the P-wave first motion difficult due to poor signal-to-noise ratio of the initial P-wave and close arrivals of pP or sP with significant amplitude. We suggest that mis-identification of the P-wave first motion and distortion of the body-wave ray paths due to non-planar structure were sources of error in determining the nodal planes for these events.

Traveling wave solution of driven nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-09-01

The traveling solitary and cnoidal wave solutions of the one dimensional driven nonlinear Schrödinger equation with a generalized form of nonlinearity are presented in this paper. We examine the modulation of nonlinear solitary excitations in two known weakly nonlinear models of classic oscillators, namely, the Helmholtz and Duffing oscillators and envelope structure formations for different oscillator and driver parameters. It is shown that two distinct regimes of subcritical and supercritical modulations may occur for nonlinear excitations with propagation speeds v <√{4 F0 } and v >√{4 F0 } , respectively, in which F0 is the driver force strength. The envelope soliton and cnoidal waves in these regimes are observed to be fundamentally different. The effect of pseudoenergy on the structure of the modulated envelope excitations is studied in detail for both sub- and supercritical modulation types. The current model for traveling envelope excitations may be easily extended to pseudopotentials with full nonlinearity relevant to more realistic gases, fluids, and plasmas.

Effect of the scrape-off layer in AORSA full wave simulations of fast wave minority, mid/high harmonic, and helicon heating regimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bertelli, N., E-mail: nbertell@pppl.gov; Gerhardt, S.; Hosea, J. C.

2015-12-10

Several experiments on different machines and in different fast wave (FW) heating regimes, such as hydrogen minority heating and high harmonic fast waves, have found strong interactions between radio-frequency (RF) waves and the scrape-off layer (SOL) region. This paper examines the propagation and the power loss in the SOL by using the full wave code AORSA, in which the edge plasma beyond the last closed flux surface (LCFS) is included in the solution domain and a collisional damping parameter is used as a proxy to represent the real, and most likely nonlinear, damping processes. 3D AORSA results for the Nationalmore » Spherical Torus eXperiment (NSTX), where a full antenna spectrum is reconstructed, are shown, confirming the same behavior found for a single toroidal mode results in Bertelli et al, Nucl. Fusion, 54 083004, 2014, namely, a strong transition to higher SOL power losses (driven by the RF field) when the FW cut-off is moved away from in front of the antenna by increasing the edge density. Additionally, full wave simulations have been extended to “conventional” tokamaks with higher aspect ratios, such as the DIII-D, Alcator C-Mod, and EAST devices. DIII-D results show similar behavior found in NSTX and NSTX-U, consistent with previous DIII-D experimental observations. In contrast, a different behavior has been found for Alcator C-Mod and EAST, which operate in the minority heating regime unlike NSTX/NSTX-U and DIII-D, which operate in the mid/high harmonic regime. A substantial discussion of some of the main aspects, such as (i) the pitch angle of the magnetic field; (ii) minority heating vs. mid/high harmonic regimes is presented showing the different behavior of the RF field in the SOL region for NSTX-U scenarios with different plasma current. Finally, the preliminary results of the impact of the SOL region on the evaluation of the helicon current drive efficiency in DIII-D is presented for the first time and briefly compared with the different

Effect of the scrape-off layer in AORSA full wave simulations of fast wave minority, mid/high harmonic, and helicon heating regimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bertelli, Nicola; Jaeger, E. F.; Lau, Cornwall H

2015-01-01

Several experiments on different machines and in different fast wave (FW) heating regimes, such as hydrogen minority heating and high harmonic fast waves, have found strong interactions between radio-frequency (RF) waves and the scrape-off layer (SOL) region. This paper examines the propagation and the power loss in the SOL by using the full wave code AORSA, in which the edge plasma beyond the last closed flux surface (LCFS) is included in the solution domain and a collisional damping parameter is used as a proxy to represent the real, and most likely nonlinear, damping processes. 3D AORSA results for the Nationalmore » Spherical Torus eXperiment (NSTX), where a full antenna spectrum is reconstructed, are shown, confirming the same behavior found for a single toroidal mode results in Bertelli et al, Nucl. Fusion, 54 083004, 2014, namely, a strong transition to higher SOL power losses (driven by the RF field) when the FW cut-off is moved away from in front of the antenna by increasing the edge density. Additionally, full wave simulations have been extended to "conventional" tokamaks with higher aspect ratios, such as the DIII-D, Alcator C-Mod, and EAST devices. DIII-D results show similar behavior found in NSTX and NSTX-U, consistent with previous DIII-D experimental observations. In contrast, a different behavior has been found for Alcator C-Mod and EAST, which operate in the minority heating regime unlike NSTX/NSTX-U and DIII-D, which operate in the mid/high harmonic regime. A substantial discussion of some of the main aspects, such as (i) the pitch angle of the magnetic field; (ii) minority heating vs. mid/high harmonic regimes is presented showing the different behavior of the RF field in the SOL region for NSTX-U scenarios with different plasma current. Finally, the preliminary results of the impact of the SOL region on the evaluation of the helicon current drive efficiency in DIII-D is presented for the first time and briefly compared with the different

Full wave simulations of fast wave efficiency and power losses in the scrape-off layer of tokamak plasmas in mid/high harmonic and minority heating regimes

DOE PAGES

Bertelli, N.; Jaeger, E. F.; Hosea, J. C.; ...

2015-12-17

Here, several experiments on different machines and in different fast wave (FW) heating regimes, such as hydrogen minority heating and high harmonic fast waves (HHFW), have found strong interaction between radio-frequency (RF) waves and the scrape-off layer (SOL) region. This paper examines the propagation and the power loss in the SOL by using the full wave code AORSA, in which the edge plasma beyond the last closed flux surface (LCFS) is included in the solution domain and a collisional damping parameter is used as a proxy to represent the real, and most likely nonlinear, damping processes. 2D and 3D AORSAmore » results for the National Spherical Torus eXperiment (NSTX) have shown a strong transition to higher SOL power losses (driven by the RF field) when the FW cut-off is removed from in front of the antenna by increasing the edge density. Here, full wave simulations have been extended for 'conventional' tokamaks with higher aspect ratios, such as the DIII-D, Alcator C-Mod, and EAST devices. DIII-D results in HHFW regime show similar behavior found in NSTX and NSTX-U, consistent with previous DIII-D experimental observations. In contrast, a different behavior has been found for C-Mod and EAST, which operate in the minority heating regime.« less

Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions.

PubMed

Kedziora, David J; Ankiewicz, Adrian; Akhmediev, Nail

2013-07-01

We present a systematic classification for higher-order rogue-wave solutions of the nonlinear Schrödinger equation, constructed as the nonlinear superposition of first-order breathers via the recursive Darboux transformation scheme. This hierarchy is subdivided into structures that exhibit varying degrees of radial symmetry, all arising from independent degrees of freedom associated with physical translations of component breathers. We reveal the general rules required to produce these fundamental patterns. Consequently, we are able to extrapolate the general shape for rogue-wave solutions beyond order 6, at which point accuracy limitations due to current standards of numerical generation become non-negligible. Furthermore, we indicate how a large set of irregular rogue-wave solutions can be produced by hybridizing these fundamental structures.

A new B-dot probe-based diagnostic for amplitude, polarization, and wavenumber measurements of ion cyclotron range-of frequency fields on ASDEX Upgrade

NASA Astrophysics Data System (ADS)

Ochoukov, R.; Bobkov, V.; Faugel, H.; Fünfgelder, H.; Noterdaeme, J.-M.

2015-11-01

A new B-dot probe-based diagnostic has been installed on an ASDEX Upgrade tokamak to characterize ion cyclotron range-of frequency (ICRF) wave generation and interaction with magnetized plasma. The diagnostic consists of a field-aligned array of B-dot probes, oriented to measure fast and slow ICRF wave fields and their field-aligned wavenumber (k//) spectrum on the low field side of ASDEX Upgrade. A thorough description of the diagnostic and the supporting electronics is provided. In order to compare the measured dominant wavenumber of the local ICRF fields with the expected spectrum of the launched ICRF waves, in-air near-field measurements were performed on the newly installed 3-strap ICRF antenna to reconstruct the dominant launched toroidal wavenumbers (ktor). Measurements during a strap current phasing scan in tokamak discharges reveal an upshift in k// as strap phasing is moved away from the dipole configuration. This result is the opposite of the ktor trend expected from in-air near-field measurements; however, the near-field based reconstruction routine does not account for the effect of induced radiofrequency (RF) currents in the passive antenna structures. The measured exponential increase in the local ICRF wave field amplitude is in agreement with the upshifted k//, as strap phasing moves away from the dipole configuration. An examination of discharges heated with two ICRF antennas simultaneously reveals the existence of beat waves at 1 kHz, as expected from the difference of the two antennas' operating frequencies. Beats are observed on both the fast and the slow wave probes suggesting that the two waves are coupled outside the active antennas. Although the new diagnostic shows consistent trends between the amplitude and the phase measurements in response to changes applied by the ICRF antennas, the disagreement with the in-air near-field measurements remains. An electromagnetic model is currently under development to address this issue.

A new B-dot probe-based diagnostic for amplitude, polarization, and wavenumber measurements of ion cyclotron range-of frequency fields on ASDEX Upgrade.

PubMed

Ochoukov, R; Bobkov, V; Faugel, H; Fünfgelder, H; Noterdaeme, J-M

2015-11-01

A new B-dot probe-based diagnostic has been installed on an ASDEX Upgrade tokamak to characterize ion cyclotron range-of frequency (ICRF) wave generation and interaction with magnetized plasma. The diagnostic consists of a field-aligned array of B-dot probes, oriented to measure fast and slow ICRF wave fields and their field-aligned wavenumber (k(//)) spectrum on the low field side of ASDEX Upgrade. A thorough description of the diagnostic and the supporting electronics is provided. In order to compare the measured dominant wavenumber of the local ICRF fields with the expected spectrum of the launched ICRF waves, in-air near-field measurements were performed on the newly installed 3-strap ICRF antenna to reconstruct the dominant launched toroidal wavenumbers (k(tor)). Measurements during a strap current phasing scan in tokamak discharges reveal an upshift in k(//) as strap phasing is moved away from the dipole configuration. This result is the opposite of the k(tor) trend expected from in-air near-field measurements; however, the near-field based reconstruction routine does not account for the effect of induced radiofrequency (RF) currents in the passive antenna structures. The measured exponential increase in the local ICRF wave field amplitude is in agreement with the upshifted k(//), as strap phasing moves away from the dipole configuration. An examination of discharges heated with two ICRF antennas simultaneously reveals the existence of beat waves at 1 kHz, as expected from the difference of the two antennas' operating frequencies. Beats are observed on both the fast and the slow wave probes suggesting that the two waves are coupled outside the active antennas. Although the new diagnostic shows consistent trends between the amplitude and the phase measurements in response to changes applied by the ICRF antennas, the disagreement with the in-air near-field measurements remains. An electromagnetic model is currently under development to address this issue.

A new B-dot probe-based diagnostic for amplitude, polarization, and wavenumber measurements of ion cyclotron range-of frequency fields on ASDEX Upgrade

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ochoukov, R.; Bobkov, V.; Faugel, H.

2015-11-15

A new B-dot probe-based diagnostic has been installed on an ASDEX Upgrade tokamak to characterize ion cyclotron range-of frequency (ICRF) wave generation and interaction with magnetized plasma. The diagnostic consists of a field-aligned array of B-dot probes, oriented to measure fast and slow ICRF wave fields and their field-aligned wavenumber (k{sub //}) spectrum on the low field side of ASDEX Upgrade. A thorough description of the diagnostic and the supporting electronics is provided. In order to compare the measured dominant wavenumber of the local ICRF fields with the expected spectrum of the launched ICRF waves, in-air near-field measurements were performedmore » on the newly installed 3-strap ICRF antenna to reconstruct the dominant launched toroidal wavenumbers (k{sub tor}). Measurements during a strap current phasing scan in tokamak discharges reveal an upshift in k{sub //} as strap phasing is moved away from the dipole configuration. This result is the opposite of the k{sub tor} trend expected from in-air near-field measurements; however, the near-field based reconstruction routine does not account for the effect of induced radiofrequency (RF) currents in the passive antenna structures. The measured exponential increase in the local ICRF wave field amplitude is in agreement with the upshifted k{sub //}, as strap phasing moves away from the dipole configuration. An examination of discharges heated with two ICRF antennas simultaneously reveals the existence of beat waves at 1 kHz, as expected from the difference of the two antennas’ operating frequencies. Beats are observed on both the fast and the slow wave probes suggesting that the two waves are coupled outside the active antennas. Although the new diagnostic shows consistent trends between the amplitude and the phase measurements in response to changes applied by the ICRF antennas, the disagreement with the in-air near-field measurements remains. An electromagnetic model is currently under

A novel approach for solitary wave solutions of the generalized fractional Zakharov-Kuznetsov equation

NASA Astrophysics Data System (ADS)

Batool, Fiza; Akram, Ghazala

2018-01-01

In this article the solitary wave solutions of generalized fractional Zakharov-Kuznetsov (GZK) equation which appear in the electrical transmission line model are investigated. The (G'/G)-expansion method is used to obtain the solitary solutions of fractional GZK equation via local fractional derivative. Three classes of solutions, hyperbolic, trigonometric and rational wave solutions of the associated equation are characterized with some free parameters. The obtained solutions reveal that the proposed technique is effective and powerful.

Development of plasma sources for ICRF heating experiment in KMAX mirror device

NASA Astrophysics Data System (ADS)

Sun, Xuan; Liu, Ming; Yi, Hongshen; Lin, Munan; Shi, Peiyun

2016-10-01

KMAX, Keda Mirror with AXisymmeticity, is a tandem mirror machine with a length of 10 meters and diameters of 1.2 meters in the central cell and 0.3 meters in the mirror throat. In the past experiments, the plasma was generated by helicon wave launched from the west end. We obtained the blue core mode in argon discharge, however, it cannot provide sufficient plasma for hydrogen discharge, which is at least 1012 cm-3 required for effective ICRF heating. Several attempts have thus been tried or under design to increase the central cell's plasma density: (1) a washer gun with aperture of 1cm has been successfully tested, and a plasma density of 1013 cm-3 was achieved in the west cell near the gun, however, the plasma is only 1011 cm-3 in the central cell possible due to the mirror trapping and/or neutral quenching effect (2) a larger washer gun with aperture of 2.5 cm and a higher power capacitor bank are being assembled in order to generate more plasmas. In addition, how to mitigate the neutrals is under consideration (3) A hot cathode is been designed and will be tested in combination with plasma gun or alone. Preliminary results from those plasma sources will be presented and discussed.

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.; Manafian, Jalil

2018-03-01

This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

High-order rogue wave solutions of the classical massive Thirring model equations

NASA Astrophysics Data System (ADS)

Guo, Lijuan; Wang, Lihong; Cheng, Yi; He, Jingsong

2017-11-01

The nth-order solutions of the classical massive Thirring model (MTM) equations are derived by using the n-fold Darboux transformation. These solutions are expressed by the ratios of the two determinants consisted of 2n eigenfunctions under the reduction conditions. Using this method, rogue waves are constructed explicitly up to the third-order. Three patterns, i.e., fundamental, triangular and circular patterns, of the rogue waves are discussed. The parameter μ in the MTM model plays the role of the mass in the relativistic field theory while in optics it is related to the medium periodic constant, which also results in a significant rotation and a remarkable lengthening of the first-order rogue wave. These results provide new opportunities to observe rouge waves by using a combination of electromagnetically induced transparency and the Bragg scattering four-wave mixing because of large amplitudes.

A new mathematical approach for shock-wave solution in a dusty plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Das, G.C.; Dwivedi, C.B.; Talukdar, M.

1997-12-01

The problem of nonlinear Burger equation in a plasma contaminated with heavy dust grains has been revisited. As discussed earlier [C. B. Dwivedi and B. P. Pandey, Phys. Plasmas {bold 2}, 9 (1995)], the Burger equation originates due to dust charge fluctuation dynamics. A new alternate mathematical approach based on a simple traveling wave formalism has been applied to find out the solution of the derived Burger equation, and the method recovers the known shock-wave solution. This technique, although having its own limitation, predicts successfully the salient features of the weak shock-wave structure in a dusty plasma with dust chargemore » fluctuation dynamics. It is emphasized that this approach of the traveling wave formalism is being applied for the first time to solve the nonlinear wave equation in plasmas. {copyright} {ital 1997 American Institute of Physics.}« less

Bootstrap and fast wave current drive for tokamak reactors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ehst, D.A.

1991-09-01

Using the multi-species neoclassical treatment of Hirshman and Sigmar we study steady state bootstrap equilibria with seed currents provided by low frequency (ICRF) fast waves and with additional surface current density driven by lower hybrid waves. This study applies to reactor plasmas of arbitrary aspect ratio. IN one limit the bootstrap component can supply nearly the total equilibrium current with minimal driving power (< 20 MW). However, for larger total currents considerable driving power is required (for ITER: I{sub o} = 18 MA needs P{sub FW} = 15 MW, P{sub LH} = 75 MW). A computational survey of bootstrap fractionmore » and current drive efficiency is presented. 11 refs., 8 figs.« less

Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications

NASA Astrophysics Data System (ADS)

Ali, Asghar; Seadawy, Aly R.; Lu, Dianchen

2018-05-01

The aim of this article is to construct some new traveling wave solutions and investigate localized structures for fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) water wave dynamical equation. The simple equation method (SEM) and the modified simple equation method (MSEM) are applied in this paper to construct the analytical traveling wave solutions of AKNS equation. The different waves solutions are derived by assigning special values to the parameters. The obtained results have their importance in the field of physics and other areas of applied sciences. All the solutions are also graphically represented. The constructed results are often helpful for studying several new localized structures and the waves interaction in the high-dimensional models.

Some new traveling wave exact solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli equations.

PubMed

Qi, Jian-ming; Zhang, Fu; Yuan, Wen-jun; Huang, Zi-feng

2014-01-01

We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions ur,2 (z) and simply periodic solutions us,2-6(z) which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results.

An exact solution for effects of topography on free Rayleigh waves

USGS Publications Warehouse

Savage, W.Z.

2004-01-01

An exact solution for the effects of topography on Rayleigh wave amplification is presented. The solution is obtained by incorporating conformal mapping into complex-variable stress functions developed for free Rayleigh wave propagation in an elastic half-space with a flat upper surface. Results are presented for free Rayleigh wave propagation across isolated symmetric ridges and valleys. It is found for wavelengths that are comparable to ridge widths that horizontal Rayleigh wave amplitudes are amplified at ridge crests and that vertical amplitudes are strongly reduced near ridge crests relative to horizontal and vertical amplitudes of free Rayleigh waves in the flat case. Horizontal amplitudes are strongly deamplified at valley bottoms relative to those for the flat case for Rayleigh wavelengths comparable to valley widths. Wave amplitudes in the symmetric ridges and valleys asymptotically approach those for the flat case with increased wavelengths, increased ridge and valley widths, and with horizontal distance from and depth below the isolated ridges and valleys. Also, prograde particle motion is predicted near crests of narrow ridges and near the bottoms of narrow valleys. Finally, application of the theory at two sites known for topographic wave amplification gives a predicted surface wave amplification ratio of 3.80 at the ridge center for a frequency of 1.0 Hz at Robinwood Ridge in northern California and a predicted surface wave amplification ratio of 1.67 at the ridge center for the same frequency at the Cedar Hill Nursery site at Tarzana in southern California.

3D Modeling of Antenna Driven Slow Waves Excited by Antennas Near the Plasma Edge

NASA Astrophysics Data System (ADS)

Smithe, David; Jenkins, Thomas

2016-10-01

Prior work with the 3D finite-difference time-domain (FDTD) plasma and sheath model used to model ICRF antennas in fusion plasmas has highlighted the possibility of slow wave excitation at the very low end of the SOL density range, and thus the prudent need for a slow-time evolution model to treat SOL density modifications due to the RF itself. At higher frequency, the DIII-D helicon antenna has much easier access to a parasitic slow wave excitation, and in this case the Faraday screen provides the dominant means of controlling the content of the launched mode, with antenna end-effects remaining a concern. In both cases, the danger is the same, with the slow-wave propagating into a lower-hybrid resonance layer a short distance ( cm) away from the antenna, which would parasitically absorb power, transferring energy to the SOL edge plasma, primarily through electron-neutral collisions. We will present 3D modeling of antennas at both ICRF and helicon frequencies. We've added a slow-time evolution capability for the SOL plasma density to include ponderomotive force driven rarefaction from the strong fields in the vicinity of the antenna, and show initial application to NSTX antenna geometry and plasma configurations. The model is based on a Scalar Ponderomotive Potential method, using self-consistently computed local field amplitudes from the 3D simulation.

Realistic full wave modeling of focal plane array pixels

DOE PAGES

Campione, Salvatore; Warne, Larry K.; Jorgenson, Roy E.; ...

2017-11-01

Here, we investigate full-wave simulations of realistic implementations of multifunctional nanoantenna enabled detectors (NEDs). We focus on a 2x2 pixelated array structure that supports two wavelengths of operation. We design each resonating structure independently using full-wave simulations with periodic boundary conditions mimicking the whole infinite array. We then construct a supercell made of a 2x2 pixelated array with periodic boundary conditions mimicking the full NED; in this case, however, each pixel comprises 10-20 antennas per side. In this way, the cross-talk between contiguous pixels is accounted for in our simulations. We observe that, even though there are finite extent effects,more » the pixels work as designed, each responding at the respective wavelength of operation. This allows us to stress that realistic simulations of multifunctional NEDs need to be performed to verify the design functionality by taking into account finite extent and cross-talk effects.« less

A Complete Bank of Optical Images of the ICRF QSOs

NASA Astrophysics Data System (ADS)

Humberto Andrei, Alexandre; Taris, Francois; Anton, Sonia; Bourda, Geraldine; Damljanovic, Goran; Souchay, Jean; Vieira Martins, Roberto; Pursimo, Tapio; Barache, Christophe; Nepomuceno da Silva Neto, Dario; Fernandes Coelho, Bruno David

2015-08-01

We have been developing a systematic effort to collect good quality images of the optical counterpart of ICRF sources, in particular for those that have been regularly radio surveyed either for future implementation at high frequencies and/or those that will be the link sources between the ICRF and the Gaia CRF. Observations have been taken at the LNA/Brazil, CASLEO/Argentina, NOT/Spain, LFOA/Austria, Rozhen/Bulgária, and ASV/Serbia. In complement images were collected from the SDSS. As a step to implement such image data bank and make it publicly available through the IERS service we present its description, that comprises for each source the number of measurements, filter, pixel scale, size of field, and seeing at each observation. The photometry analysis is centered on the morphology, since there remain still cases in which the host galaxy is overwhelming, and many cases in which the host asks for a non-stellar PSF modeling. On basis of the neighbor stars we assign magnitudes and variability whenever possible. Finally, assisted by previous literature, the redshift and luminosity are used to derive astrophysical quantities, in special the absolute magnitude, SED and spectral index. Moreover, since Gaia will not obtain direct images of the observed sources, the morphology and magnitude becomes useful as templates onto which assembling and interpreting the one-dimensional and uncontinuous line spread function samplings that will be delivered by Gaia for each QSO.

Analytical Time-Domain Solution of Plane Wave Propagation Across a Viscoelastic Rock Joint

NASA Astrophysics Data System (ADS)

Zou, Yang; Li, Jianchun; Laloui, Lyesse; Zhao, Jian

2017-10-01

The effects of viscoelastic filled rock joints on wave propagation are of great significance in rock engineering. The solutions in time domain for plane longitudinal ( P-) and transverse ( S-) waves propagation across a viscoelastic rock joint are derived based on Maxwell and Kelvin models which are, respectively, applied to describe the viscoelastic deformational behaviour of the rock joint and incorporated into the displacement discontinuity model (DDM). The proposed solutions are verified by comparing with the previous studies on harmonic waves, which are simulated by sinusoidal incident P- and S-waves. Comparison between the predicted transmitted waves and the experimental data for P-wave propagation across a joint filled with clay is conducted. The Maxwell is found to be more appropriate to describe the filled joint. The parametric studies show that wave propagation is affected by many factors, such as the stiffness and the viscosity of joints, the incident angle and the duration of incident waves. Furthermore, the dependences of the transmission and reflection coefficients on the specific joint stiffness and viscosity are different for the joints with Maxwell and Kelvin behaviours. The alternation of the reflected and transmitted waveforms is discussed, and the application scope of this study is demonstrated by an illustration of the effects of the joint thickness. The solutions are also extended for multiple parallel joints with the virtual wave source method and the time-domain recursive method. For an incident wave with arbitrary waveform, it is convenient to adopt the present approach to directly calculate wave propagation across a viscoelastic rock joint without additional mathematical methods such as the Fourier and inverse Fourier transforms.

Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators

NASA Astrophysics Data System (ADS)

Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E.

2016-06-01

Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts. Our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.

Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators

DOE PAGES

Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; ...

2016-02-27

Artificial perceptions of light called phosphenes were motivated by earlier studies. We analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolutionmore » and stability of planar fronts. Moreover, our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.« less

Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.

Artificial perceptions of light called phosphenes were motivated by earlier studies. We analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolutionmore » and stability of planar fronts. Moreover, our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.« less

Explicit and exact nontraveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation

NASA Astrophysics Data System (ADS)

Yuan, Na

2018-04-01

With the aid of the symbolic computation, we present an improved ( G ‧ / G ) -expansion method, which can be applied to seek more types of exact solutions for certain nonlinear evolution equations. In illustration, we choose the (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation to demonstrate the validity and advantages of the method. As a result, abundant explicit and exact nontraveling wave solutions are obtained including two solitary waves solutions, nontraveling wave solutions and dromion soliton solutions. Some particular localized excitations and the interactions between two solitary waves are researched. The method can be also applied to other nonlinear partial differential equations.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

Exact traveling wave solutions for system of nonlinear evolution equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

2016-01-01

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

TOPICA: an accurate and efficient numerical tool for analysis and design of ICRF antennas

NASA Astrophysics Data System (ADS)

Lancellotti, V.; Milanesio, D.; Maggiora, R.; Vecchi, G.; Kyrytsya, V.

2006-07-01

The demand for a predictive tool to help in designing ion-cyclotron radio frequency (ICRF) antenna systems for today's fusion experiments has driven the development of codes such as ICANT, RANT3D, and the early development of TOPICA (TOrino Polytechnic Ion Cyclotron Antenna) code. This paper describes the substantive evolution of TOPICA formulation and implementation that presently allow it to handle the actual geometry of ICRF antennas (with curved, solid straps, a general-shape housing, Faraday screen, etc) as well as an accurate plasma description, accounting for density and temperature profiles and finite Larmor radius effects. The antenna is assumed to be housed in a recess-like enclosure. Both goals have been attained by formally separating the problem into two parts: the vacuum region around the antenna and the plasma region inside the toroidal chamber. Field continuity and boundary conditions allow formulating of a set of two coupled integral equations for the unknown equivalent (current) sources; then the equations are reduced to a linear system by a method of moments solution scheme employing 2D finite elements defined over a 3D non-planar surface triangular-cell mesh. In the vacuum region calculations are done in the spatial (configuration) domain, whereas in the plasma region a spectral (wavenumber) representation of fields and currents is adopted, thus permitting a description of the plasma by a surface impedance matrix. Owing to this approach, any plasma model can be used in principle, and at present the FELICE code has been employed. The natural outcomes of TOPICA are the induced currents on the conductors (antenna, housing, etc) and the electric field in front of the plasma, whence the antenna circuit parameters (impedance/scattering matrices), the radiated power and the fields (at locations other than the chamber aperture) are then obtained. An accurate model of the feeding coaxial lines is also included. The theoretical model and its TOPICA

AORSA full wave calculations of helicon waves in DIII-D and ITER

NASA Astrophysics Data System (ADS)

Lau, C.; Jaeger, E. F.; Bertelli, N.; Berry, L. A.; Green, D. L.; Murakami, M.; Park, J. M.; Pinsker, R. I.; Prater, R.

2018-06-01

Helicon waves have been recently proposed as an off-axis current drive actuator for DIII-D, FNSF, and DEMO tokamaks. Previous ray tracing modeling using GENRAY predicts strong single pass absorption and current drive in the mid-radius region on DIII-D in high beta tokamak discharges. The full wave code AORSA, which is valid to all order of Larmor radius and can resolve arbitrary ion cyclotron harmonics, has been used to validate the ray tracing technique. If the scrape-off-layer (SOL) is ignored in the modeling, AORSA agrees with GENRAY in both the amplitude and location of driven current for DIII-D and ITER cases. These models also show that helicon current drive can possibly be an efficient current drive actuator for ITER. Previous GENRAY analysis did not include the SOL. AORSA has also been used to extend the simulations to include the SOL and to estimate possible power losses of helicon waves in the SOL. AORSA calculations show that another mode can propagate in the SOL and lead to significant (~10%–20%) SOL losses at high SOL densities. Optimizing the SOL density profile can reduce these SOL losses to a few percent.

Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

NASA Astrophysics Data System (ADS)

Elwakil, S. A.; El-Labany, S. K.; Zahran, M. A.; Sabry, R.

2004-04-01

The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D( u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K( u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m>1 is the power of the nonlinear convection term).

Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-09-01

Nonlinear two-dimensional Kadomtsev-Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech-tanh, sinh-cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.

FAST TRACK COMMUNICATION: Soliton solutions of the KP equation with V-shape initial waves

NASA Astrophysics Data System (ADS)

Kodama, Y.; Oikawa, M.; Tsuji, H.

2009-08-01

We consider the initial value problems of the Kadomtsev-Petviashvili (KP) equation for symmetric V-shape initial waves consisting of two semi-infinite line solitons with the same amplitude. Those are particularly important for studies of large amplitude waves such as tsunami in shallow water. Numerical simulations show that the solutions of the initial value problem approach asymptotically to certain exact solutions of the KP equation found recently in [1]. We then use a chord diagram to explain the asymptotic result. This provides an analytical method to study asymptotic behavior for the initial value problem of the KP equation. We also demonstrate a real experiment of shallow water waves which may represent the solution discussed in this communication.

Nonparaxial wave beams and packets with general astigmatism

NASA Astrophysics Data System (ADS)

Kiselev, A. P.; Plachenov, A. B.; Chamorro-Posada, P.

2012-04-01

We present exact solutions of the wave equation involving an arbitrary wave form with a phase closely similar to the general astigmatic phase of paraxial wave optics. Special choices of the wave form allow general astigmatic beamlike and pulselike waves with a Gaussian-type unrestricted localization in space and time. These solutions are generalizations of the known Bateman-type waves obtained from the connection existing between beamlike solutions of the paraxial parabolic equation and relatively undistorted wave solutions of the wave equation. As a technical tool, we present a full description of parametrizations of 2×2 symmetric matrices with positive imaginary part, which arise in the theory of Gaussian beams.

Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions.

PubMed

Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C

2011-06-01

The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.

Travelling Wave Solutions in Multigroup Age-Structured Epidemic Models

NASA Astrophysics Data System (ADS)

Ducrot, Arnaut; Magal, Pierre; Ruan, Shigui

2010-01-01

Age-structured epidemic models have been used to describe either the age of individuals or the age of infection of certain diseases and to determine how these characteristics affect the outcomes and consequences of epidemiological processes. Most results on age-structured epidemic models focus on the existence, uniqueness, and convergence to disease equilibria of solutions. In this paper we investigate the existence of travelling wave solutions in a deterministic age-structured model describing the circulation of a disease within a population of multigroups. Individuals of each group are able to move with a random walk which is modelled by the classical Fickian diffusion and are classified into two subclasses, susceptible and infective. A susceptible individual in a given group can be crisscross infected by direct contact with infective individuals of possibly any group. This process of transmission can depend upon the age of the disease of infected individuals. The goal of this paper is to provide sufficient conditions that ensure the existence of travelling wave solutions for the age-structured epidemic model. The case of two population groups is numerically investigated which applies to the crisscross transmission of feline immunodeficiency virus (FIV) and some sexual transmission diseases.

Interaction between high harmonic fast waves and fast ions in NSTX/NSTX-U plasmas

NASA Astrophysics Data System (ADS)

Bertelli, N.; Valeo, E. J.; Gorelenkova, M.; Green, D. L.; RF SciDAC Team

2016-10-01

Fast wave (FW) heating in the ion cyclotron range of frequency (ICRF) has been successfully used to sustain and control the fusion plasma performance, and it will likely play an important role in the ITER experiment. As demonstrated in the NSTX and DIII-D experiments the interactions between fast waves and fast ions can be so strong to significantly modify the fast ion population from neutral beam injection. In fact, it has been recently found in NSTX that FWs can modify and, under certain conditions, even suppress the energetic particle driven instabilities, such as toroidal Alfvén eigenmodes and global Alfvén eigenmodes and fishbones. This paper examines such interactions in NSTX/NSTX-U plasmas by using the recent extension of the RF full-wave code TORIC to include non-Maxwellian ions distribution functions. Particular attention is given to the evolution of the fast ions distribution function w/ and w/o RF. Tests on the RF kick-operator implemented in the Monte-Carlo particle code NUBEAM is also discussed in order to move towards a self consistent evaluation of the RF wave-field and the ion distribution functions in the TRANSP code. Work supported by US DOE Contract DE-AC02-09CH11466.

AORSA full wave calculations of helicon waves in DIII-D and ITER

DOE PAGES

Lau, Cornwall; Jaeger, E.F.; Bertelli, Nicola; ...

2018-04-11

Helicon waves have been recently proposed as an off-axis current drive actuator for DIII-D, FNSF, and DEMO tokamaks. Previous ray tracing modeling using GENRAY predicts strong single pass absorption and current drive in the mid-radius region on DIII-D in high beta tokamak discharges. The full wave code AORSA, which is valid to all order of Larmor radius and can resolve arbitrary ion cyclotron harmonics, has been used to validate the ray tracing technique. If the scrape-off-layer (SOL) is ignored in the modeling, AORSA agrees with GENRAY in both the amplitude and location of driven current for DIII-D and ITER cases.more » These models also show that helicon current drive can possibly be an efficient current drive actuator for ITER. Previous GENRAY analysis did not include the SOL. AORSA has also been used to extend the simulations to include the SOL and to estimate possible power losses of helicon waves in the SOL. AORSA calculations show that another mode can propagate in the SOL and lead to significant (~10-20%) SOL losses at high SOL densities. Optimizing the SOL density profile can reduce these SOL losses to a few percent.« less

AORSA full wave calculations of helicon waves in DIII-D and ITER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lau, Cornwall; Jaeger, E.F.; Bertelli, Nicola

Helicon waves have been recently proposed as an off-axis current drive actuator for DIII-D, FNSF, and DEMO tokamaks. Previous ray tracing modeling using GENRAY predicts strong single pass absorption and current drive in the mid-radius region on DIII-D in high beta tokamak discharges. The full wave code AORSA, which is valid to all order of Larmor radius and can resolve arbitrary ion cyclotron harmonics, has been used to validate the ray tracing technique. If the scrape-off-layer (SOL) is ignored in the modeling, AORSA agrees with GENRAY in both the amplitude and location of driven current for DIII-D and ITER cases.more » These models also show that helicon current drive can possibly be an efficient current drive actuator for ITER. Previous GENRAY analysis did not include the SOL. AORSA has also been used to extend the simulations to include the SOL and to estimate possible power losses of helicon waves in the SOL. AORSA calculations show that another mode can propagate in the SOL and lead to significant (~10-20%) SOL losses at high SOL densities. Optimizing the SOL density profile can reduce these SOL losses to a few percent.« less

Are There Optical Solitary Wave Solutions in Linear Media with Group Velocity Dispersion?

NASA Technical Reports Server (NTRS)

Li, Zhonghao; Zhou, Guosheng

1996-01-01

A generalized exact optical bright solitary wave solution in a three dimensional dispersive linear medium is presented. The most interesting property of the solution is that it can exist in the normal group-velocity-dispersion (GVD) region. In addition, another peculiar feature is that it may achieve a condition of 'zero-dispersion' to the media so that a solitary wave of arbitrarily small amplitude may be propagated with no dependence on is pulse width.

From supersonic shear wave imaging to full-field optical coherence shear wave elastography

NASA Astrophysics Data System (ADS)

Nahas, Amir; Tanter, Mickaël; Nguyen, Thu-Mai; Chassot, Jean-Marie; Fink, Mathias; Claude Boccara, A.

2013-12-01

Elasticity maps of tissue have proved to be particularly useful in providing complementary contrast to ultrasonic imaging, e.g., for cancer diagnosis at the millimeter scale. Optical coherence tomography (OCT) offers an endogenous contrast based on singly backscattered optical waves. Adding complementary contrast to OCT images by recording elasticity maps could also be valuable in improving OCT-based diagnosis at the microscopic scale. Static elastography has been successfully coupled with full-field OCT (FF-OCT) in order to realize both micrometer-scale sectioning and elasticity maps. Nevertheless, static elastography presents a number of drawbacks, mainly when stiffness quantification is required. Here, we describe the combination of two methods: transient elastography, based on speed measurements of shear waves induced by ultrasonic radiation forces, and FF-OCT, an en face OCT approach using an incoherent light source. The use of an ultrafast ultrasonic scanner and an ultrafast camera working at 10,000 to 30,000 images/s made it possible to follow shear wave propagation with both modalities. As expected, FF-OCT is found to be much more sensitive than ultrafast ultrasound to tiny shear vibrations (a few nanometers and micrometers, respectively). Stiffness assessed in gel phantoms and an ex vivo rat brain by FF-OCT is found to be in good agreement with ultrasound shear wave elastography.

Generation and Sustainment of Plasma Rotation by ICRF Heating

NASA Astrophysics Data System (ADS)

Perkins, F. W.

2000-10-01

When tokamak plasmas are heated by the fundamental minority ion-cyclotron process, they are observed to rotate toroidally, even though this heating process introduces negligable angular momentum. This work proposes and evaluates a physics mechanism which resolves this apparent conflict. The argument has two elements. First, it is assumed that angular momentum transport is governed by a diffusion equation with a v_tor = 0 boundary condition at the plasma surface and a torque-density source. When the source consists of separated regions of positive and negative torque density, a finite central rotation velocity results, even though the volume integrated torque density - the angular momentum input - vanishes. Secondly, ions energized by the ICRF process can generate separated regions of positive and negative torque density. Heating increases their banana widths which leads to radial energetic-particle transport that must be balanced by neutralizing radial currents and a j_rB_pR torque density in the bulk plasma. Additional, comparable torque density results from collisional transfer of mechanical angular momentum from energetic particles to the bulk plasma and particle loss through banana particles impacting the wall. Monte-Carlo calculations utilizing the ORBIT code evaluate all sources of torque density and rigorously assure that no net angular momentum is introduced. Two models of ICRF heating, diffusive and instantaneous, give similar results. When the resonance location is on the LFS, the calculated rotation has the magnitude, profile, and co-current sense of Alcator C-Mod observations. For HFS resonance locations, the model predicts counter-current rotation. Scans of rotational profiles vs. resonance location, initial energy, particle loss, pitch, and qm will be presented as will the location of the velocity shear layer its scaling to a reactor.

Topological soliton solutions for three shallow water waves models

NASA Astrophysics Data System (ADS)

Liu, Jiangen; Zhang, Yufeng; Wang, Yan

2018-07-01

In this article, we investigate three distinct physical structures for shallow water waves models by the improved ansatz method. The method was improved and can be used to obtain more generalized form topological soliton solutions than the original method. As a result, some new exact solutions of the shallow water equations are successfully established and the obtained results are exhibited graphically. The results showed that the improved ansatz method can be applied to solve other nonlinear differential equations arising from mathematical physics.

Dissipative MHD solutions for resonant Alfven waves in 1-dimensional magnetic flux tubes

NASA Technical Reports Server (NTRS)

Goossens, Marcel; Ruderman, Michail S.; Hollweg, Joseph V.

1995-01-01

The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfven waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfven waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions for xi(sub r), and P' across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg for xi(sub r), and P' in terms of double integrals of Hankel functions of complex argument of order 1/3 with compact analytical solutions that allow a straight- forward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpen- dicular to the magnetic field lines xi(sub perpendicular) which enables us to determine the dominant dynamics of resonant Alfven waves in dissipative MHD.

Reinstated JET ICRF ILA: Overview and Results

NASA Astrophysics Data System (ADS)

Dumortier, Pierre; Durodié, Frédéric; Blackman, Trevor; Helou, Walid; Jacquet, Philippe; Lerche, Ernesto; Monakhov, Igor; Noble, Craig; Bobkov, Volodymyr; Goulding, Richard; Kaufman, Michael; Van Eester, Dirk

2017-10-01

The works undertaken to reinstate the JET ICRF ILA are reviewed. The vacuum matching capacitors were replaced, an extensive calibration of all the measurements in the RF circuit was carried out, new simulation tools were created and new control algorithms were implemented for the - toroidal and poloidal - phase control of the array as well as for the matching of the second stage. A review of the contribution of the reinstated ILA to the JET programme during the last campaigns is given showing namely that the new controls allowed extending the range of the operation to lower (29MHz) and higher (51MHz) frequencies than previously achieved and allowed more flexible and reliable operation. Operation with coupled power levels up to 2.8MW and voltages up to 40kV was achieved. ILA results on plasma are discussed and emphasis is given to the features of interest for ITER.

Characterization of the mutual influence of Ion Cyclotron and Lower Hybrid Range of frequencies systems on EAST

NASA Astrophysics Data System (ADS)

Urbanczyk, Guillaume; Zhang, Xinjun; Qin, Chengming; Zhao, Yanping; Zhang, Tao; Zhang, Ling; Li, Jiangang; Yuan, Shuai; Chen, Liang; Zhang, Heng; Zhang, Jiahui; Wang, Jianhua; Yang, Xiuda; Qian, Jinping

2017-10-01

Waves in the Ion Cyclotron (ICRF) and Lower Hybrid (LH) Range of Frequencies are efficient techniques respectively to heat the plasma and drive current. Main difficulties come from a trade-off between good RF coupling and acceptable level of impurities release. The mutual influence of both systems makes such equilibrium often hard to reach [1]. In order to investigate those interactions based on Scrape-Off Layer (SOL) plasma parameters, a new reciprocating probe was designed allying a three tips Langmuir probe with an emissive wire. The emissive filament provides a precise measure of plasma potential [2], which can be used to calibrate Langmuir probe's results. This paper reports on experimental results obtained on EAST, where there are two ICRF antennas and two LH launchers. Among others diagnostics, the new reciprocating probe enabled to evidence the deleterious influence of ICRF power on LHWs coupling in L-mode plasmas. In areas connected with an active ICRF antenna, SOL potentials increase while densities tend to decrease, respectively enhancing impurities release and deteriorating LHWs coupling. This phenomenon has mostly been attributed to RF sheath; the one that forms on top of Plasma Facing Components (PFCs) and causes ExB density convections [3]. From those experiments it seems ICRF has a strong influence on magnetically connected areas, both in the near field - influencing ICRF waves coupling - and in farther locations such as in front of LH grills. Moreover, influence of ICRF on LH system was observed both in L and H modes. Those results are consistent with RF sheath rectification process. Concerning the influence of LHWs on ICRF coupling, nothing was observed in L-mode. Besides during H-mode experiments, LHWs have been identified as having a mitigating effect on ELMs [4], which on average lowers the pedestal, increasing edge densities to the profit of ICRF waves coupling.

Elastic parabolic equation solutions for oceanic T-wave generation and propagation from deep seismic sources.

PubMed

Frank, Scott D; Collis, Jon M; Odom, Robert I

2015-06-01

Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations.

On the exact solutions of high order wave equations of KdV type (I)

NASA Astrophysics Data System (ADS)

Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

2014-12-01

In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

Detection of sinkholes or anomalies using full seismic wave fields.

DOT National Transportation Integrated Search

2013-04-01

This research presents an application of two-dimensional (2-D) time-domain waveform tomography for detection of embedded sinkholes and anomalies. The measured seismic surface wave fields were inverted using a full waveform inversion (FWI) technique, ...

Simulation of cold magnetized plasmas with the 3D electromagnetic software CST Microwave Studio®

NASA Astrophysics Data System (ADS)

Louche, Fabrice; Křivská, Alena; Messiaen, André; Wauters, Tom

2017-10-01

Detailed designs of ICRF antennas were made possible by the development of sophisticated commercial 3D codes like CST Microwave Studio® (MWS). This program allows for very detailed geometries of the radiating structures, but was only considering simple materials like equivalent isotropic dielectrics to simulate the reflection and the refraction of RF waves at the vacuum/plasma interface. The code was nevertheless used intensively, notably for computing the coupling properties of the ITER ICRF antenna. Until recently it was not possible to simulate gyrotropic medias like magnetized plasmas, but recent improvements have allowed programming any material described by a general dielectric or/and diamagnetic tensor. A Visual Basic macro was developed to exploit this feature and was tested for the specific case of a monochromatic plane wave propagating longitudinally with respect to the magnetic field direction. For specific cases the exact solution can be expressed in 1D as the sum of two circularly polarized waves connected by a reflection coefficient that can be analytically computed. Solutions for stratified media can also be derived. This allows for a direct comparison with MWS results. The agreement is excellent but accurate simulations for realistic geometries require large memory resources that could significantly restrict the possibility of simulating cold plasmas to small-scale machines.

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

NASA Astrophysics Data System (ADS)

Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar

2018-03-01

We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.

Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions.

PubMed

Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail

2014-01-01

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

Effects of half-wave and full-wave power source on the anodic oxidation process on AZ91D magnesium alloy

NASA Astrophysics Data System (ADS)

Wang, Ximei; Zhu, Liqun; Li, Weiping; Liu, Huicong; Li, Yihong

2009-03-01

Anodic films have been prepared on the AZ91D magnesium alloys in 1 mol/L Na 2SiO 3 with 10 vol.% silica sol addition under the constant voltage of 60 V at room temperature by half-wave and full-wave power sources. The weight of the anodic films has been scaled by analytical balance, and the thickness has been measured by eddy current instrument. The surface morphologies, chemical composition and structure of the anodic films have been characterized by scanning electron microscopy (SEM), energy dispersion spectrometry (EDS), X-ray diffraction (XRD) and transmission electron microscopy (TEM). The results show that the thickness and weight of the anodic films formed by the two power sources both increase with the anodizing time, and the films anodized by full-wave power source grow faster than that by half-wave one. Furthermore, we have fitted polynomial to the scattered data of the weight and thickness in a least-squares sense with MATLAB, which could express the growth process of the anodic films sufficiently. The full-wave power source is inclined to accelerate the growth of the anodic films, and the half-wave one is mainly contributed to the uniformity and fineness of the films. The anodic film consists of crystalline Mg 2SiO 4 and amorphous SiO 2.

Approximation of traveling wave solutions in wall-bounded flows using resolvent modes

NASA Astrophysics Data System (ADS)

McKeon, Beverley; Graham, Michael; Moarref, Rashad; Park, Jae Sung; Sharma, Ati; Willis, Ashley

2014-11-01

Significant recent attention has been devoted to computing and understanding exact traveling wave solutions of the Navier-Stokes equations. These solutions can be interpreted as the state-space skeleton of turbulence and are attractive benchmarks for studying low-order models of wall turbulence. Here, we project such solutions onto the velocity response (or resolvent) modes supplied by the gain-based resolvent analysis outlined by McKeon & Sharma (JFM, 2010). We demonstrate that in both pipe (Pringle et al., Phil. Trans. R. Soc. A, 2009) and channel (Waleffe, JFM, 2001) flows, the solutions can be well-described by a small number of resolvent modes. Analysis of the nonlinear forcing modes sustaining these solutions reveals the importance of small amplitude forcing, consistent with the large amplifications admitted by the resolvent operator. We investigate the use of resolvent modes as computationally cheap ``seeds'' for the identification of further traveling wave solutions. The support of AFOSR under Grants FA9550-09-1-0701, FA9550-12-1-0469, FA9550-11-1-0094 and FA9550-14-1-0042 (program managers Rengasamy Ponnappan, Doug Smith and Gregg Abate) is gratefully acknowledged.

Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

NASA Astrophysics Data System (ADS)

Dutykh, Denys; Hoefer, Mark; Mitsotakis, Dimitrios

2018-04-01

Some effects of surface tension on fully nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order 4.

Full wave dc-to-dc converter using energy storage transformers

NASA Technical Reports Server (NTRS)

Moore, E. T.; Wilson, T. G.

1969-01-01

Full wave dc-to-dc converter, for an ion thrustor, uses energy storage transformers to provide a method of dc-to-dc conversion and regulation. The converter has a high degree of physical simplicity, is lightweight and has high efficiency.

Strip waves in vibrated shear-thickening wormlike micellar solutions

NASA Astrophysics Data System (ADS)

Epstein, T.; Deegan, R. D.

2010-06-01

We present an instability in vertically vibrated dilute wormlike micellar solutions. Above a critical driving acceleration the fluid forms elongated solitary domains of high amplitude waves. We model this instability using a Mathieu equation modified to account for the non-Newtonian character of the fluid. We find that our model successfully reproduces the observed transitions.

Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali; Roshid, Harun-Or-

2014-01-01

Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering. 05.45.Yv, 02.30.Jr, 02.30.Ik.

Distributed source model for the full-wave electromagnetic simulation of nonlinear terahertz generation.

PubMed

Fumeaux, Christophe; Lin, Hungyen; Serita, Kazunori; Withayachumnankul, Withawat; Kaufmann, Thomas; Tonouchi, Masayoshi; Abbott, Derek

2012-07-30

The process of terahertz generation through optical rectification in a nonlinear crystal is modeled using discretized equivalent current sources. The equivalent terahertz sources are distributed in the active volume and computed based on a separately modeled near-infrared pump beam. This approach can be used to define an appropriate excitation for full-wave electromagnetic numerical simulations of the generated terahertz radiation. This enables predictive modeling of the near-field interactions of the terahertz beam with micro-structured samples, e.g. in a near-field time-resolved microscopy system. The distributed source model is described in detail, and an implementation in a particular full-wave simulation tool is presented. The numerical results are then validated through a series of measurements on square apertures. The general principle can be applied to other nonlinear processes with possible implementation in any full-wave numerical electromagnetic solver.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition. 2; Inclusion of Exchange

NASA Technical Reports Server (NTRS)

Shertzer, Janine; Temkin, Aaron

2004-01-01

The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.

ICRF antenna-plasma interactions and its influence on W sputtering in ASDEX upgrade

NASA Astrophysics Data System (ADS)

ASDEX Upgrade Team Bobkov, Vl.; Braun, F.; Colas, L.; Dux, R.; Faugel, H.; Giannone, L.; Herrmann, A.; Kallenbach, A.; Müller, H. W.; Neu, R.; Noterdaeme, J.-M.; Pütterich, Th.; Siegl, G.; Wolfrum, E.

2011-08-01

Analysis of the W concentration during ICRF over AUG experimental campaigns confirms the critical role of W antenna limiters for the W content in plasma, though other structures connected to antennas along magnetic field lines cannot be neglected as W sources.Abrupt changes of spectroscopically measured W sputtering patterns are observed which correlate with step-wise changes of connection lengths at antenna limiters. Analysis of discharges with the reversed direction of toroidal magnetic field shows less W release compared to identical discharges with the normal direction. The lower W release is accompanied by lower intensity of fluctuations of reflected ICRF power in the 1-60 kHz range. The observations suggest that local magnetic geometry and density convection at the antennas are at least as important for the W sputtering as the distribution of RF near-fields at the antenna.Measurements of DC currents flowing through the antenna limiters show that the limiters at the active antenna collect predominantly negative DC currents whereas those distant from the active antenna collect predominantly positive DC currents. The latter decrease and become more negative when the intensity of the RF pickup measured at the limiters increases. The mutual compensation between the positive and negative currents can lead to lower values of the DC current than those expected from simplified theoretical models of the RF/DC circuit.

ICRF antenna-plasma interactions and its influence on W sputtering in ASDEX upgrade

NASA Astrophysics Data System (ADS)

Bobkov, Vl.; Braun, F.; Colas, L.; Dux, R.; Faugel, H.; Giannone, L.; Herrmann, A.; Kallenbach, A.; Müller, H. W.; Neu, R.; Noterdaeme, J.-M.; Pütterich, Th.; Siegl, G.; Wolfrum, E.; ASDEX Upgrade Team

2011-08-01

Analysis of the W concentration during ICRF over AUG experimental campaigns confirms the critical role of W antenna limiters for the W content in plasma, though other structures connected to antennas along magnetic field lines cannot be neglected as W sources. Abrupt changes of spectroscopically measured W sputtering patterns are observed which correlate with step-wise changes of connection lengths at antenna limiters. Analysis of discharges with the reversed direction of toroidal magnetic field shows less W release compared to identical discharges with the normal direction. The lower W release is accompanied by lower intensity of fluctuations of reflected ICRF power in the 1-60 kHz range. The observations suggest that local magnetic geometry and density convection at the antennas are at least as important for the W sputtering as the distribution of RF near-fields at the antenna. Measurements of DC currents flowing through the antenna limiters show that the limiters at the active antenna collect predominantly negative DC currents whereas those distant from the active antenna collect predominantly positive DC currents. The latter decrease and become more negative when the intensity of the RF pickup measured at the limiters increases. The mutual compensation between the positive and negative currents can lead to lower values of the DC current than those expected from simplified theoretical models of the RF/DC circuit.

Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation

NASA Astrophysics Data System (ADS)

Wen, Xiao-Yong; Zhang, Guoqiang

2018-01-01

Under investigation in this paper is the Kundu equation, which may be used to describe the propagation process of ultrashort optical pulses in nonlinear optics. The modulational instability of the plane-wave for the possible reason of the formation of the rogue wave (RW) is studied for the system. Based on our proposed generalized perturbation (n,N - n)-fold Darboux transformation (DT), some new higher-order implicit RW solutions in terms of determinants are obtained by means of the generalized perturbation (1,N - 1)-fold DT, when choosing different special parameters, these results will reduce to the RW solutions of the Kaup-Newell (KN) equation, Chen-Lee-Liu (CLL) equation and Gerjikov-Ivanov (GI) equation, respectively. The relevant wave structures are shown graphically, which display abundant interesting wave structures. The dynamical behaviors and propagation stability of the first-order and second-order RW solutions are discussed by using numerical simulations, the higher-order nonlinear terms for the Kundu equation have an impact on the propagation instability of the RW. The method can also be extended to find the higher-order RW or rational solutions of other integrable nonlinear equations.

Dispersive solitary wave solutions of Kadomtsev-Petviashvili and modified Kadomtsev-Petviashvili dynamical equations in unmagnetized dust plasma

NASA Astrophysics Data System (ADS)

Seadawy, A. R.; El-Rashidy, K.

2018-03-01

The Kadomtsev-Petviashvili (KP) and modified KP equations are two of the most universal models in nonlinear wave theory, which arises as a reduction of system with quadratic nonlinearity which admit weakly dispersive waves. The generalized extended tanh method and the F-expansion method are used to derive exact solitary waves solutions of KP and modified KP equations. The region of solutions are displayed graphically.

Traveling-Wave Solutions of the Kolmogorov-Petrovskii-Piskunov Equation

NASA Astrophysics Data System (ADS)

Pikulin, S. V.

2018-02-01

We consider quasi-stationary solutions of a problem without initial conditions for the Kolmogorov-Petrovskii-Piskunov (KPP) equation, which is a quasilinear parabolic one arising in the modeling of certain reaction-diffusion processes in the theory of combustion, mathematical biology, and other areas of natural sciences. A new efficiently numerically implementable analytical representation is constructed for self-similar plane traveling-wave solutions of the KPP equation with a special right-hand side. Sufficient conditions for an auxiliary function involved in this representation to be analytical for all values of its argument, including the endpoints, are obtained. Numerical results are obtained for model examples.

Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.

PubMed

Islam, S M Rayhanul; Khan, Kamruzzaman; Akbar, M Ali

2015-01-01

In this paper, we implement the exp(-Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq.

Shock wave emission from laser-induced cavitation bubbles in polymer solutions.

PubMed

Brujan, Emil-Alexandru

2008-09-01

The role of extensional viscosity on the acoustic emission from laser-induced cavitation bubbles in polymer solutions and near a rigid boundary is investigated by acoustic measurements. The polymer solutions consist of a 0.5% polyacrylamide (PAM) aqueous solution with a strong elastic component and a 0.5% carboxymethylcellulose (CMC) aqueous solution with a weak elastic component. A reduction of the maximum amplitude of the shock wave pressure and a prolongation of the oscillation period of the bubble were found in the elastic PAM solution. It might be caused by an increased resistance to extensional flow which is conferred upon the liquid by the polymer additive. In both polymer solutions, however, the shock pressure decays proportionally to r(-1) with increasing distance r from the emission centre.

Extending the ICRF into the Infrared: 2MASS - UCAC Astrometry

NASA Technical Reports Server (NTRS)

Zacharias, Norbert; McCallon, Howard L.; Kopan, Eugene; Cutri, Roc M.

2000-01-01

An external comparison between the infrared 2MASS and the optical UCAC positions was performed, both being on the same system, the ICRS. About 48 million sources in common were identified. Random errors of the 2MASS catalog positions are about 60 to 70 mas per coordinate for the Ks = 4 to 14 range, increasing to about 100 to 150 mas for saturated and very faint stars. Systematic position differences between the 2 catalogs are very small, about 5 to 10 mas as a function of magnitude and color, with somewhat larger errors as a function of right ascension and declination. The extension of the ICRF into the infrared has become a reality.

Full-waveform inversion of surface waves in exploration geophysics

NASA Astrophysics Data System (ADS)

Borisov, D.; Gao, F.; Williamson, P.; Tromp, J.

2017-12-01

Full-waveform inversion (FWI) is a data fitting approach to estimate high-resolution properties of the Earth from seismic data by minimizing the misfit between observed and calculated seismograms. In land seismics, the source on the ground generates high-amplitude surface waves, which generally represent most of the energy recorded by ground sensors. Although surface waves are widely used in global seismology and engineering studies, they are typically treated as noise within the seismic exploration community since they mask deeper reflections from the intervals of exploration interest. This is mainly due to the fact that surface waves decay exponentially with depth and for a typical frequency range (≈[5-50] Hz) sample only the very shallow part of the subsurface, but also because they are much more sensitive to S-wave than P-wave velocities. In this study, we invert surface waves in the hope of using them as additional information for updating the near surface. In a heterogeneous medium, the main challenge of surface wave inversion is associated with their dispersive character, which makes it difficult to define a starting model for conventional FWI which can avoid cycle-skipping. The standard approach to dealing with this is by inverting the dispersion curves in the Fourier (f-k) domain to generate locally 1-D models, typically for the shear wavespeeds only. However this requires that the near-surface zone be more or less horizontally invariant over a sufficient distance for the spatial Fourier transform to be applicable. In regions with significant topography, such as foothills, this is not the case, so we revert to the time-space domain, but aim to minimize the differences of envelopes in the early stages of the inversion to resolve the cycle-skipping issue. Once the model is good enough, we revert to the classic waveform-difference inversion. We first present a few synthetic examples. We show that classical FWI might be trapped in a local minimum even for

Full polarimetric millimetre wave radar for stand-off security screening

NASA Astrophysics Data System (ADS)

Blackhurst, Eddie; Salmon, Neil; Southgate, Matthew

2017-10-01

The development and measurements are described of a frequency modulated continuous wave (FMCW) mono-static millimetre wave full polarimetric radar, operating at k-band (18 to 26 GHz). The system has been designed to explore the feasibility of using full polarimetry for the detection of concealed weapons, and person borne improvised explosive devices (PBIED). The philosophy of this scheme is a means to extract the maximum information content from a target which is normally in the single spatial pixel (sometimes sub-pixel) configuration in stand-off (tens of metres) and crowd surveillance scenarios. The radar comprises a vector network analyser (VNA), an orthomode transducer and a conical horn antenna. A calibration strategy is discussed and demonstrated using a variety of known calibration targets with known reflective properties, including a flat metal plate, dihedral reflector, metal sphere, helix and dipole. The orthomode transducer is based on a high performance linear polarizer of the turnstile type with isolation better than - 35dB between orthogonal polarisations. The calibration enables the polarimetric Sinclair scattering matrix to be measured at each frequency for coherent polarimetry, and this can be extended using multiple measurements via the Kennaugh matrix to investigate incoherent full polarimetry.

Visco-elastic controlled-source full waveform inversion without surface waves

NASA Astrophysics Data System (ADS)

Paschke, Marco; Krause, Martin; Bleibinhaus, Florian

2016-04-01

We developed a frequency-domain visco-elastic full waveform inversion for onshore seismic experiments with topography. The forward modeling is based on a finite-difference time-domain algorithm by Robertsson that uses the image-method to ensure a stress-free condition at the surface. The time-domain data is Fourier-transformed at every point in the model space during the forward modeling for a given set of frequencies. The motivation for this approach is the reduced amount of memory when computing kernels, and the straightforward implementation of the multiscale approach. For the inversion, we calculate the Frechet derivative matrix explicitly, and we implement a Levenberg-Marquardt scheme that allows for computing the resolution matrix. To reduce the size of the Frechet derivative matrix, and to stabilize the inversion, an adapted inverse mesh is used. The node spacing is controlled by the velocity distribution and the chosen frequencies. To focus the inversion on body waves (P, P-coda, and S) we mute the surface waves from the data. Consistent spatiotemporal weighting factors are applied to the wavefields during the Fourier transform to obtain the corresponding kernels. We test our code with a synthetic study using the Marmousi model with arbitrary topography. This study also demonstrates the importance of topography and muting surface waves in controlled-source full waveform inversion.

Decay of Solutions of the Wave Equation in the Kerr Geometry

NASA Astrophysics Data System (ADS)

Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.

2006-06-01

We consider the Cauchy problem for the massless scalar wave equation in the Kerr geometry for smooth initial data compactly supported outside the event horizon. We prove that the solutions decay in time in L ∞ loc. The proof is based on a representation of the solution as an infinite sum over the angular momentum modes, each of which is an integral of the energy variable ω on the real line. This integral representation involves solutions of the radial and angular ODEs which arise in the separation of variables.

Stability of Planar Rarefaction Wave to 3D Full Compressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Li, Lin-an; Wang, Teng; Wang, Yi

2018-05-01

We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier-Stokes equations with the heat-conductivities in an infinite long flat nozzle domain {R × T^2} . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x 2 and x 3 and its interactions with the planar rarefaction wave in x 1 direction.

Higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Wu, Xiao-Yu; Sun, Yan

2018-02-01

Under investigation in this paper is the higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials which can be applied in the nonlinear optics, hydrodynamics, plasma physics and Bose-Einstein condensation. Based on the Kadomtsev-Petviashvili hierarchy reduction, we construct the Nth order rogue wave-like solutions in terms of the Gramian under the integrable constraint. With the help of the analytic and graphic analysis, we exhibit the first-, second- and third-order rogue wave-like solutions through the different dispersion, nonlinearity and linear potential coefficients. We find that only if the dispersion and nonlinearity coefficients are proportional to each other, heights of the background of those rogue waves maintain unchanged with time increasing. Due to the existence of complex parameters, such nonautonomous rogue waves in the higher-order cases have more complex features than those in the lower.

Excitation of ship waves by a submerged object: New solution to the classical problem

NASA Astrophysics Data System (ADS)

Arzhannikov, A. V.; Kotelnikov, I. A.

2016-08-01

We have proposed a new method for solving the problem of ship waves excited on the surface of a nonviscous liquid by a submerged object that moves at a variable speed. As a first application of this method, we have obtained a new solution to the classic problem of ship waves generated by a submerged ball that moves rectilinearly with constant velocity parallel to the equilibrium surface of the liquid. For this example, we have derived asymptotic expressions describing the vertical displacement of the liquid surface in the limit of small and large values of the Froude number. The exact solution is presented in the form of two terms, each of which is reduced to one-dimensional integrals. One term describes the "Bernoulli hump" and another term the "Kelvin wedge." As a second example, we considered vertical oscillation of the submerged ball. In this case, the solution leads to the calculation of one-dimensional integral and describes surface waves propagating from the epicenter above the ball.

Excitation of ship waves by a submerged object: New solution to the classical problem.

PubMed

Arzhannikov, A V; Kotelnikov, I A

2016-08-01

We have proposed a new method for solving the problem of ship waves excited on the surface of a nonviscous liquid by a submerged object that moves at a variable speed. As a first application of this method, we have obtained a new solution to the classic problem of ship waves generated by a submerged ball that moves rectilinearly with constant velocity parallel to the equilibrium surface of the liquid. For this example, we have derived asymptotic expressions describing the vertical displacement of the liquid surface in the limit of small and large values of the Froude number. The exact solution is presented in the form of two terms, each of which is reduced to one-dimensional integrals. One term describes the "Bernoulli hump" and another term the "Kelvin wedge." As a second example, we considered vertical oscillation of the submerged ball. In this case, the solution leads to the calculation of one-dimensional integral and describes surface waves propagating from the epicenter above the ball.

A predictive transport modeling code for ICRF-heated tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Phillips, C.K.; Hwang, D.Q.; Houlberg, W.

In this report, a detailed description of the physic included in the WHIST/RAZE package as well as a few illustrative examples of the capabilities of the package will be presented. An in depth analysis of ICRF heating experiments using WHIST/RAZE will be discussed in a forthcoming report. A general overview of philosophy behind the structure of the WHIST/RAZE package, a summary of the features of the WHIST code, and a description of the interface to the RAZE subroutines are presented in section 2 of this report. Details of the physics contained in the RAZE code are examined in section 3.more » Sample results from the package follow in section 4, with concluding remarks and a discussion of possible improvements to the package discussed in section 5.« less

A predictive transport modeling code for ICRF-heated tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Phillips, C.K.; Hwang, D.Q.; Houlberg, W.

1992-02-01

In this report, a detailed description of the physic included in the WHIST/RAZE package as well as a few illustrative examples of the capabilities of the package will be presented. An in depth analysis of ICRF heating experiments using WHIST/RAZE will be discussed in a forthcoming report. A general overview of philosophy behind the structure of the WHIST/RAZE package, a summary of the features of the WHIST code, and a description of the interface to the RAZE subroutines are presented in section 2 of this report. Details of the physics contained in the RAZE code are examined in section 3.more » Sample results from the package follow in section 4, with concluding remarks and a discussion of possible improvements to the package discussed in section 5.« less

Sonic wave separation of invertase from a dilute solution to generated droplets.

PubMed

Tanner, R D; Ko, S; Loha, V; Prokop, A

2000-01-01

It has previously been shown that a droplet fractionation process, simulated by shaking a separatory funnel containing a dilute protein solution, can generate droplets richer in protein than present in the original dilute solution. In this article, we describe an alternative method that can increase the amount of protein transferred to the droplets. The new method uses ultrasonic waves, enhanced by a bubble gas stream to create the droplets. The amount of protein in these droplets increases by about 50%. In this method, the top layer of the dilute protein solution (of the solution-air interface) becomes enriched in protein when air is bubbled into the solution. This concentrating procedure is called bubble fractionation. Once the protein has passed through the initial buildup, this enriched protein layer is transferred into droplets with the aid of a vacuum above the solution at the same time that ultrasonic waves are introduced. The droplets are then carried over to a condenser and coalesced. We found that this new method provides an easier way to remove the protein-enriched top layer of the dilute solution and generates more droplets within a shorter period than the separatory funnel droplet generation method. The added air creates the bubbles and carries the droplets, and the vacuum helps remove the effluent airstream from the condenser. The maximum partition coefficient, the ratio of the protein concentration in the droplets to that in the residual solution (approx 8.5), occurred at pH 5.0.

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

PubMed

Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

2014-01-01

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

Full long-term design response analysis of a wave energy converter

DOE PAGES

Coe, Ryan G.; Michelen, Carlos; Eckert-Gallup, Aubrey; ...

2017-09-21

Efficient design of wave energy converters requires an accurate understanding of expected loads and responses during the deployment lifetime of a device. A study has been conducted to better understand best-practices for prediction of design responses in a wave energy converter. A case-study was performed in which a simplified wave energy converter was analyzed to predict several important device design responses. The application and performance of a full long-term analysis, in which numerical simulations were used to predict the device response for a large number of distinct sea states, was studied. Environmental characterization and selection of sea states for thismore » analysis at the intended deployment site were performed using principle-components analysis. The full long-term analysis applied here was shown to be stable when implemented with a relatively low number of sea states and convergent with an increasing number of sea states. As the number of sea states utilized in the analysis was increased, predicted response levels did not change appreciably. Furthermore, uncertainty in the response levels was reduced as more sea states were utilized.« less

Full long-term design response analysis of a wave energy converter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coe, Ryan G.; Michelen, Carlos; Eckert-Gallup, Aubrey

Efficient design of wave energy converters requires an accurate understanding of expected loads and responses during the deployment lifetime of a device. A study has been conducted to better understand best-practices for prediction of design responses in a wave energy converter. A case-study was performed in which a simplified wave energy converter was analyzed to predict several important device design responses. The application and performance of a full long-term analysis, in which numerical simulations were used to predict the device response for a large number of distinct sea states, was studied. Environmental characterization and selection of sea states for thismore » analysis at the intended deployment site were performed using principle-components analysis. The full long-term analysis applied here was shown to be stable when implemented with a relatively low number of sea states and convergent with an increasing number of sea states. As the number of sea states utilized in the analysis was increased, predicted response levels did not change appreciably. Furthermore, uncertainty in the response levels was reduced as more sea states were utilized.« less

Spin waves in full-polarized state of Dzyaloshinskii-Moriya helimagnets: Small-angle neutron scattering study

NASA Astrophysics Data System (ADS)

Grigoriev, S. V.; Sukhanov, A. S.; Altynbaev, E. V.; Siegfried, S.-A.; Heinemann, A.; Kizhe, P.; Maleyev, S. V.

2015-12-01

We develop the technique to study the spin-wave dynamics of the full-polarized state of the Dzyaloshinskii-Moriya helimagnets by polarized small-angle neutron scattering. We have experimentally proven that the spin-waves dispersion in this state has the anisotropic form. We show that the neutron scattering image displays a circle with a certain radius which is centered at the momentum transfer corresponding to the helix wave vector in helimagnetic phase ks, which is oriented along the applied magnetic field H . The radius of this circle is directly related to the spin-wave stiffness of this system. This scattering depends on the neutron polarization showing the one-handed nature of the spin waves in Dzyaloshinskii-Moriya helimagnets in the full-polarized phase. We show that the spin-wave stiffness A for MnSi helimagnet decreased twice as the temperature increases from zero to the critical temperature Tc.

Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Ivanov, S. K.; Kamchatnov, A. M.; Congy, T.; Pavloff, N.

2017-12-01

We provide a classification of the possible flows of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single polarization mode (also denoted as "magnetic excitation") obeying a system of equations equivalent to the Landau-Lifshitz equation for an easy-plane ferromagnet. We present the full set of one-phase periodic solutions. The corresponding Whitham modulation equations are obtained together with formulas connecting their solutions with the Riemann invariants of the modulation equations. The problem is not genuinely nonlinear, and this results in a non-single-valued mapping of the solutions of the Whitham equations with physical wave patterns as well as the appearance of interesting elements—contact dispersive shock waves—that are absent in more standard, genuinely nonlinear situations. Our analytic results are confirmed by numerical simulations.

Voltage mode electronically tunable full-wave rectifier

NASA Astrophysics Data System (ADS)

Petrović, Predrag B.; Vesković, Milan; Đukić, Slobodan

2017-01-01

The paper presents a new realization of bipolar full-wave rectifier of input sinusoidal signals, employing one MO-CCCII (multiple output current controlled current conveyor), a zero-crossing detector (ZCD), and one resistor connected to fixed potential. The circuit provides the operating frequency up to 10 MHz with increased linearity and precision in processing of input voltage signal, with a very low harmonic distortion. The errors related to the signal processing and errors bound were investigated and provided in the paper. The PSpice simulations are depicted and agree well with the theoretical anticipation. The maximum power consumption of the converter is approximately 2.83 mW, at ±1.2 V supply voltages.

A Gauss-Newton full-waveform inversion in PML-truncated domains using scalar probing waves

NASA Astrophysics Data System (ADS)

Pakravan, Alireza; Kang, Jun Won; Newtson, Craig M.

2017-12-01

This study considers the characterization of subsurface shear wave velocity profiles in semi-infinite media using scalar waves. Using surficial responses caused by probing waves, a reconstruction of the material profile is sought using a Gauss-Newton full-waveform inversion method in a two-dimensional domain truncated by perfectly matched layer (PML) wave-absorbing boundaries. The PML is introduced to limit the semi-infinite extent of the half-space and to prevent reflections from the truncated boundaries. A hybrid unsplit-field PML is formulated in the inversion framework to enable more efficient wave simulations than with a fully mixed PML. The full-waveform inversion method is based on a constrained optimization framework that is implemented using Karush-Kuhn-Tucker (KKT) optimality conditions to minimize the objective functional augmented by PML-endowed wave equations via Lagrange multipliers. The KKT conditions consist of state, adjoint, and control problems, and are solved iteratively to update the shear wave velocity profile of the PML-truncated domain. Numerical examples show that the developed Gauss-Newton inversion method is accurate enough and more efficient than another inversion method. The algorithm's performance is demonstrated by the numerical examples including the case of noisy measurement responses and the case of reduced number of sources and receivers.

Numerical Study of Periodic Traveling Wave Solutions for the Predator-Prey Model with Landscape Features

NASA Astrophysics Data System (ADS)

Yun, Ana; Shin, Jaemin; Li, Yibao; Lee, Seunggyu; Kim, Junseok

We numerically investigate periodic traveling wave solutions for a diffusive predator-prey system with landscape features. The landscape features are modeled through the homogeneous Dirichlet boundary condition which is imposed at the edge of the obstacle domain. To effectively treat the Dirichlet boundary condition, we employ a robust and accurate numerical technique by using a boundary control function. We also propose a robust algorithm for calculating the numerical periodicity of the traveling wave solution. In numerical experiments, we show that periodic traveling waves which move out and away from the obstacle are effectively generated. We explain the formation of the traveling waves by comparing the wavelengths. The spatial asynchrony has been shown in quantitative detail for various obstacles. Furthermore, we apply our numerical technique to the complicated real landscape features.

Dynamic of solitary wave solutions in some nonlinear pseudoparabolic models and Dodd-Bullough-Mikhailov equation

NASA Astrophysics Data System (ADS)

Ilhan, O. A.; Bulut, H.; Sulaiman, T. A.; Baskonus, H. M.

2018-02-01

In this study, the modified exp ( - Φ (η )) -expansion function method is used in constructing some solitary wave solutions to the Oskolkov-Benjamin-Bona-Mahony-Burgers, one-dimensional Oskolkov equations and the Dodd-Bullough-Mikhailov equation. We successfully construct some singular solitons and singular periodic waves solutions with the hyperbolic, trigonometric and exponential function structures to these three nonlinear models. Under the choice of some suitable values of the parameters involved, we plot the 2D and 3D graphics to some of the obtained solutions in this study. All the obtained solutions in this study verify their corresponding equation. We perform all the computations in this study with the help of the Wolfram Mathematica software. The obtained solutions in this study may be helpful in explaining some practical physical problems.

SIDON: A simulator of radio-frequency networks. Application to WEST ICRF launchers

NASA Astrophysics Data System (ADS)

Helou, Walid; Dumortier, Pierre; Durodié, Frédéric; Goniche, Marc; Hillairet, Julien; Mollard, Patrick; Berger-By, Gilles; Bernard, Jean-Michel; Colas, Laurent; Lombard, Gilles; Maggiora, Riccardo; Magne, Roland; Milanesio, Daniele; Moreau, Didier

2015-12-01

SIDON (SImulator of raDiO-frequency Networks) is an in-house developed Radio-Frequency (RF) network solver that has been implemented to cross-validate the design of WEST ICRF launchers and simulate their impedance matching algorithm while considering all mutual couplings and asymmetries. In this paper, the authors illustrate the theory of SIDON as well as results of its calculations. The authors have built time-varying plasma scenarios (a sequence of launchers front-faces L-mode and H-mode Z-matrices), where at each time step (1 millisecond here), SIDON solves the RF network. At the same time, when activated, the impedance matching algorithm controls the matching elements (vacuum capacitors) and thus their corresponding S-matrices. Typically a 1-second pulse requires around 10 seconds of computational time on a desktop computer. These tasks can be hardly handled by commercial RF software. This innovative work allows identifying strategies for the launchers future operation while insuring the limitations on the currents, voltages and electric fields, matching and Load-Resilience, as well as the required straps voltage amplitude/phase balance. In this paper, a particular attention is paid to the simulation of the launchers behavior when arcs appear at several locations of their circuits using SIDON calculator. This latter work shall confirm or identify strategies for the arc detection using various RF electrical signals. One shall note that the use of such solvers in not limited to ICRF launchers simulations but can be employed, in principle, to any linear or linearized RF problem.

Some Interaction Solutions of a Reduced Generalised (3+1)-Dimensional Shallow Water Wave Equation for Lump Solutions and a Pair of Resonance Solitons

NASA Astrophysics Data System (ADS)

Wang, Yao; Chen, Mei-Dan; Li, Xian; Li, Biao

2017-05-01

Through Hirota bilinear transformation and symbolic computation with Maple, a class of lump solutions, rationally localised in all directions in the space, to a reduced generalised (3+1)-dimensional shallow water wave (SWW) equation are prensented. The resulting lump solutions all contain six parameters, two of which are free due to the translation invariance of the SWW equation and the other four of which must satisfy a nonzero determinant condition guaranteeing analyticity and rational localisation of the solutions. Then we derived the interaction solutions for lump solutions and one stripe soliton and the result shows that the particular lump solutions with specific values of the involved parameters will be drowned or swallowed by the stripe soliton. Furthermore, we extend this method to a more general combination of positive quadratic function and hyperbolic functions. Especially, it is interesting that a rogue wave is found to be aroused by the interaction between lump solutions and a pair of resonance stripe solitons. By choosing the values of the parameters, the dynamic properties of lump solutions, interaction solutions for lump solutions and one stripe soliton and interaction solutions for lump solutions and a pair of resonance solitons, are shown by dynamic graphs.

Three dimensional full-wave nonlinear acoustic simulations: Applications to ultrasound imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pinton, Gianmarco

Characterization of acoustic waves that propagate nonlinearly in an inhomogeneous medium has significant applications to diagnostic and therapeutic ultrasound. The generation of an ultrasound image of human tissue is based on the complex physics of acoustic wave propagation: diffraction, reflection, scattering, frequency dependent attenuation, and nonlinearity. The nonlinearity of wave propagation is used to the advantage of diagnostic scanners that use the harmonic components of the ultrasonic signal to improve the resolution and penetration of clinical scanners. One approach to simulating ultrasound images is to make approximations that can reduce the physics to systems that have a low computational cost.more » Here a maximalist approach is taken and the full three dimensional wave physics is simulated with finite differences. This paper demonstrates how finite difference simulations for the nonlinear acoustic wave equation can be used to generate physically realistic two and three dimensional ultrasound images anywhere in the body. A specific intercostal liver imaging scenario for two cases: with the ribs in place, and with the ribs removed. This configuration provides an imaging scenario that cannot be performed in vivo but that can test the influence of the ribs on image quality. Several imaging properties are studied, in particular the beamplots, the spatial coherence at the transducer surface, the distributed phase aberration, and the lesion detectability for imaging at the fundamental and harmonic frequencies. The results indicate, counterintuitively, that at the fundamental frequency the beamplot improves due to the apodization effect of the ribs but at the same time there is more degradation from reverberation clutter. At the harmonic frequency there is significantly less improvement in the beamplot and also significantly less degradation from reverberation. It is shown that even though simulating the full propagation physics is computationally

Refraction of dispersive shock waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khodorovskii, V. V.; Leszczyszyn, A. M.

2012-09-01

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave, often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of the defocusing nonlinear Schrödinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem.

Complexiton and solitary wave solutions of the coupled nonlinear Maccari’s system using two integration schemes

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Nuray, Elif

2018-01-01

In this paper, we consider a coupled nonlinear Maccari’s system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the solitary wave solutions. They are the modified F-Expansion and the generalized projective Riccati equation methods. Topological, non-topological, complexiton, singular and trigonometric function solutions are derived. A comparison between the results in this paper and the well-known results in the literature is also given. The derived structures of the obtained solutions offer a rich platform to study the nonlinear CNMS. Numerical simulation of the obtained solutions are presented with interesting figures showing the physical meaning of the solutions.

Source positions from VLBI combined solution

NASA Astrophysics Data System (ADS)

Bachmann, S.; Thaller, D.; Engelhardt, G.

2014-12-01

The IVS Combination Center at BKG is primarily responsible for combined Earth Orientation Parameter (EOP) products and the generation of a terrestrial reference frame based on VLBI observations (VTRF). The procedure is based on the combination of normal equations provided by six IVS Analysis Centers (AC). Since more and more ACs also provide source positions in the normal equations - beside EOPs and station coordinates - an estimation of these parameters is possible and should be investigated. In the past, the International Celestial Reference Frame (ICRF) was not generated as a combined solution from several individual solutions, but was based on a single solution provided by one AC. The presentation will give an overview on the combination strategy and the possibilities for combined source position determination. This includes comparisons with existing catalogs, quality estimation and possibilities of rigorous combination of EOP, TRF and CRF in one combination process.

The focusing effect of P-wave in the Moon's and Earth's low-velocity core. Analytical solution

NASA Astrophysics Data System (ADS)

Fatyanov, A. G.; Burmin, V. Yu

2018-04-01

The important aspect in the study of the structure of the interiors of planets is the question of the presence and state of core inside them. While for the Earth this task was solved long ago, the question of whether the core of the Moon is in a liquid or solid state up to the present is debatable up to present. If the core of the Moon is liquid, then the velocity of longitudinal waves in it should be lower than in the surrounding mantle. If the core is solid, then most likely, the velocity of longitudinal waves in it is higher than in the mantle. Numerical calculations of the wave field allow us to identify the criteria for drawing conclusions about the state of the lunar core. In this paper we consider the problem of constructing an analytical solution for wave fields in a layered sphere of arbitrary radius. A stable analytic solution is obtained for the wave fields of longitudinal waves in a three-layer sphere. Calculations of the total wave fields and rays for simplified models of the Earth and the Moon with real parameters are presented. The analytical solution and the ray pattern showed that the low-velocity cores of the Earth and the Moon possess the properties of a collecting lens. This leads to the emergence of a wave field focusing area. As a result, focused waves of considerable amplitude appear on the surface of the Earth and the Moon. In the Earth case, they appear before the first PKP-wave arrival. These are so-called "precursors", which continue in the subsequent arrivals of waves. At the same time, for the simplified model of the Earth, the maximum amplitude growth is observed in the 147-degree region. For the Moon model, the maximum amplitude growth is around 180°.

Overview of the new capabilities of TORIC-v6 and comparison with TORIC-v5

NASA Astrophysics Data System (ADS)

Bilato, R.; Brambilla, M.; Bertelli, N.

2016-10-01

Since its release, version 5 (v5) of the full-wave TORIC code, characterized by an optimized parallelized solver for its routinely use in TRANSP package, has been ameliorated in many technical issues, e.g. the plasma-vacuum transition and the full-spectrum antenna modeling. For the WPCD-benchmark cases a good agreement between the new version, v6, and v5 is found. The major improvement, however, has been done in interfacing TORIC-v6 with the Fokker-Planck SSFPQL solver to account for the back-reaction of ICRF and NBI heating on the wave propagation and absorption. Special algorithms have been developed for SSFPQL for the numerical precision at high pitch-angle resolution and to evaluate the generalized dispersion function directly from the numerical solution. Care has been spent in automatizing the non-linear loop between TORIC-v6 and SSFPQL. In v6 the description of wave absorption at high-harmonics has been revised and applied to DEMO. For high-harmonic regimes there is an ongoing activity on the comparison with AORSA.

Breather solutions of a fourth-order nonlinear Schrödinger equation in the degenerate, soliton, and rogue wave limits

NASA Astrophysics Data System (ADS)

Chowdury, Amdad; Krolikowski, Wieslaw; Akhmediev, N.

2017-10-01

We present one- and two-breather solutions of the fourth-order nonlinear Schrödinger equation. With several parameters to play with, the solution may take a variety of forms. We consider most of these cases including the general form and limiting cases when the modulation frequencies are 0 or coincide. The zero-frequency limit produces a combination of breather-soliton structures on a constant background. The case of equal modulation frequencies produces a degenerate solution that requires a special technique for deriving. A zero-frequency limit of this degenerate solution produces a rational second-order rogue wave solution with a stretching factor involved. Taking, in addition, the zero limit of the stretching factor transforms the second-order rogue waves into a soliton. Adding a differential shift in the degenerate solution results in structural changes in the wave profile. Moreover, the zero-frequency limit of the degenerate solution with differential shift results in a rogue wave triplet. The zero limit of the stretching factor in this solution, in turn, transforms the triplet into a singlet plus a low-amplitude soliton on the background. A large value of the differential shift parameter converts the triplet into a pure singlet.

Breather solutions of a fourth-order nonlinear Schrödinger equation in the degenerate, soliton, and rogue wave limits.

PubMed

Chowdury, Amdad; Krolikowski, Wieslaw; Akhmediev, N

2017-10-01

We present one- and two-breather solutions of the fourth-order nonlinear Schrödinger equation. With several parameters to play with, the solution may take a variety of forms. We consider most of these cases including the general form and limiting cases when the modulation frequencies are 0 or coincide. The zero-frequency limit produces a combination of breather-soliton structures on a constant background. The case of equal modulation frequencies produces a degenerate solution that requires a special technique for deriving. A zero-frequency limit of this degenerate solution produces a rational second-order rogue wave solution with a stretching factor involved. Taking, in addition, the zero limit of the stretching factor transforms the second-order rogue waves into a soliton. Adding a differential shift in the degenerate solution results in structural changes in the wave profile. Moreover, the zero-frequency limit of the degenerate solution with differential shift results in a rogue wave triplet. The zero limit of the stretching factor in this solution, in turn, transforms the triplet into a singlet plus a low-amplitude soliton on the background. A large value of the differential shift parameter converts the triplet into a pure singlet.

Modulation instability, Fermi-Pasta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation.

PubMed

Akhmediev, Nail; Ankiewicz, Adrian

2011-04-01

We study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times. These periodic solutions comprise a family of two-parameter solutions with an arbitrary background field and a frequency of initial perturbation. The solutions are recurrent, since they return the field state to the original constant background solution after the process of nonlinear evolution has passed. These solutions can be considered as a complete resolution of the Fermi-Pasta-Ulam paradox for the A-L system. One remarkable consequence of the recurrent evolution is the nonlinear phase shift gained by the constant background wave after the process. A particular case of this family is the rational solution of the first-order or fundamental rogue wave.

On the Periodic Solutions of the Five-Dimensional Lorenz Equation Modeling Coupled Rosby Waves and Gravity Waves

NASA Astrophysics Data System (ADS)

Carvalho, Tiago; Llibre, Jaume

2017-06-01

Lorenz studied the coupled Rosby waves and gravity waves using the differential system U˙ = -VW + bVZ,V˙ = UW - bUZ,Ẇ = -UV,Ẋ = -Z,Ż = bUV + X. This system has the two first integrals H1 = U2 + V2,H 2 = V2 + W2 + X2 + Z2. Our main result shows that in each invariant set {H1 = h1 > 0}∩{H2 = h2 > 0} there are at least four (resp., 2) periodic solutions of the differential system with b≠0 and h2 > h1 (resp., h2 < h1).

Traveling wave and exact solutions for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Mahak, Nadia

2018-06-01

The nonlinear Schrödinger equation (NLSE) with the aid of three order dispersion terms is investigated to find the exact solutions via the extended (G'/G2)-expansion method and the first integral method. Many exact traveling wave solutions, such as trigonometric, hyperbolic, rational, soliton and complex function solutions, are characterized with some free parameters of the problem studied. It is corroborated that the proposed techniques are manageable, straightforward and powerful tools to find the exact solutions of nonlinear partial differential equations (PDEs). Some figures are plotted to describe the propagation of traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions.

The existence of minimum speed of traveling wave solutions to a non-KPP isothermal diffusion system

NASA Astrophysics Data System (ADS)

Chen, Xinfu; Liu, Guirong; Qi, Yuanwei

2017-08-01

The reaction-diffusion system at =axx - abn ,bt = Dbxx + abn, where n ≥ 1 and D > 0, arises from many real-world chemical reactions. Whereas n = 1 is the KPP type nonlinearity, which is much studied and very important results obtained in literature not only in one dimensional spatial domains, but also multi-dimensional spaces, but n > 1 proves to be much harder. One of the interesting features of the system is the existence of traveling wave solutions. In particular, for the traveling wave solution a (x , t) = a (x - vt), b (x , t) = b (x - vt), where v > 0, if we fix lim x → - ∞ ⁡ (a , b) = (0 , 1) it was proved by many authors with different bounds v* (n , D) > 0 such that a traveling wave solution exists for any v ≥v* when n > 1. For the latest progress, see [7]. That is, the traveling wave problem exhibits the mono-stable phenomenon for traveling wave of scalar equation ut =uxx + f (u) with f (0) = f (1) = 0, f (u) > 0 in (0 , 1) and, u = 0 is unstable and u = 1 is stable. A natural and significant question is whether, like the scalar case, there exists a minimum speed. That is, whether there exists a minimum speed vmin > 0 such that traveling wave solution of speed v exists iff v ≥vmin? This is an open question, in spite of many works on traveling wave of the system in last thirty years. This is duo to the reason, unlike the KPP case, the minimum speed cannot be obtained through linear analysis at equilibrium points (a , b) = (0 , 1) and (a , b) = (1 , 0). In this work, we give an affirmative answer to this question.

Stability and instability of periodic travelling wave solutions for the critical Korteweg-de Vries and nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Angulo Pava, Jaime; Natali, Fábio M. Amorin

2009-04-01

In this paper we establish new results about the existence, stability, and instability of periodic travelling wave solutions related to the critical Korteweg-de Vries equation ut+5u4ux+u=0, and the critical nonlinear Schrödinger equation ivt+v+|v=0. The periodic travelling wave solutions obtained in our study tend to the classical solitary wave solutions in the infinite wavelength scenario. The stability approach is based on the theory developed by Angulo & Natali in [J. Angulo, F. Natali, Positivity properties of the Fourier transform and the stability of periodic travelling wave solutions, SIAM J. Math. Anal. 40 (2008) 1123-1151] for positive periodic travelling wave solutions associated to dispersive evolution equations of Korteweg-de Vries type. The instability approach is based on an extension to the periodic setting of arguments found in Bona & Souganidis & Strauss [J.L. Bona, P.E. Souganidis, W.A. Strauss, Stability and instability of solitary waves of Korteweg-de Vries type, Proc. Roy. Soc. London Ser. A 411 (1987) 395-412]. Regarding the critical Schrödinger equation stability/instability theories similar to the critical Korteweg-de Vries equation are obtained by using the classical Grillakis & Shatah & Strauss theory in [M. Grillakis, J. Shatah, W. Strauss, Stability theory of solitary waves in the presence of symmetry II, J. Funct. Anal. 94 (1990) 308-348; M. Grillakis, J. Shatah, W. Strauss, Stability theory of solitary waves in the presence of symmetry I, J. Funct. Anal. 74 (1987) 160-197]. The arguments presented in this investigation have prospects for the study of the stability of periodic travelling wave solutions of other nonlinear evolution equations.

Experimental pathways to understand and avoid high-Z impurity contamination from ICRF heating in tokamaks

NASA Astrophysics Data System (ADS)

Reinke, Matthew

2016-10-01

Recent results from Alcator C-Mod and JET demonstrate progress in understanding and mitigating core high-Z impurity contamination linked to ICRF heating in tokamaks with high-Z PFCs. Theory has identified two likely mechanisms: impurity sources due to sputtering enhanced by RF-rectified sheaths and greater cross-field SOL transport due to ExB convective cells. New experiments on Alcator C-Mod and JET demonstrate convective cell transport is likely a sub-dominant effect, despite directly observing ExB flows from rectified RF fields on C-Mod. Trace N2 introduced in the far SOL on field lines connected to and well away from an active ICRF antenna result in similar levels of core nitrogen, indicating local RF-driven transport is weak. This suggests the core high-Z density, nZ,core, is determined by sheath-induced sputtering and RF-independent SOL transport, allowing further reductions through antenna design. ICRF heating on C-Mod uses a unique, field aligned (FAA) and a pair of conventional, toroidally aligned (TAA) antennas. The FAA is designed to reduce rectified voltages relative to the TAA, and the impact of sheath-induced sputtering is explored by observing nZ,core while varying the TAA/FAA heating mix. A reduction of approximately 50% in core high-Z content is seen in L-modes when using the FAA and high-Z sources at the antenna limiter are effectively eliminated, indicating the remaining RF-driven source is away from the limiter. A drop in nZ,core may also be realized by locating the RF antenna on the inboard side where SOL transport aids impurity screening. New C-Mod experiments demonstrate up to a factor of 5 reduction in core nitrogen when N2 is injected on the high-field side as compared to low-field side impurity fueling. Varying the magnetic topology helps to elucidate the SOL transport physics responsible, laying a physics basis for inboard RF antenna placement. This work is supported by U.S. DOE Award DE-FC02-99ER54512, using Alcator C-Mod and carried out

Numerical solutions of acoustic wave propagation problems using Euler computations

NASA Technical Reports Server (NTRS)

Hariharan, S. I.

1984-01-01

This paper reports solution procedures for problems arising from the study of engine inlet wave propagation. The first problem is the study of sound waves radiated from cylindrical inlets. The second one is a quasi-one-dimensional problem to study the effect of nonlinearities and the third one is the study of nonlinearities in two dimensions. In all three problems Euler computations are done with a fourth-order explicit scheme. For the first problem results are shown in agreement with experimental data and for the second problem comparisons are made with an existing asymptotic theory. The third problem is part of an ongoing work and preliminary results are presented for this case.

Whistlers, Helicons, Lower Hybrid Waves: the Physics of RF Wave Absorption Without Cyclotron Resonances

NASA Astrophysics Data System (ADS)

Pinsker, R. I.

2014-10-01

In hot magnetized plasmas, two types of linear collisionless absorption processes are used to heat and drive noninductive current: absorption at ion or electron cyclotron resonances and their harmonics, and absorption by Landau damping and the transit-time-magnetic-pumping (TTMP) interactions. This tutorial discusses the latter process, i.e., parallel interactions between rf waves and electrons in which cyclotron resonance is not involved. Electron damping by the parallel interactions can be important in the ICRF, particularly in the higher harmonic region where competing ion cyclotron damping is weak, as well as in the Lower Hybrid Range of Frequencies (LHRF), which is in the neighborhood of the geometric mean of the ion and electron cyclotron frequencies. On the other hand, absorption by parallel processes is not significant in conventional ECRF schemes. Parallel interactions are especially important for the realization of high current drive efficiency with rf waves, and an application of particular recent interest is current drive with the whistler or helicon wave at high to very high (i.e., the LHRF) ion cyclotron harmonics. The scaling of absorption by parallel interactions with wave frequency is examined and the advantages and disadvantages of fast (helicons/whistlers) and slow (lower hybrid) waves in the LHRF in the context of reactor-grade tokamak plasmas are compared. In this frequency range, both wave modes can propagate in a significant fraction of the discharge volume; the ways in which the two waves can interact with each other are considered. The use of parallel interactions to heat and drive current in practice will be illustrated with examples from past experiments; also looking forward, this tutorial will provide an overview of potential applications in tokamak reactors. Supported by the US Department of Energy under DE-FC02-04ER54698.

Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids

NASA Astrophysics Data System (ADS)

Boué, Laurent; Dasgupta, Ratul; Laurie, Jason; L'Vov, Victor; Nazarenko, Sergey; Procaccia, Itamar

2011-08-01

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett.JTPLA20021-364010.1134/S002136401008014X 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.

Imaging of transient surface acoustic waves by full-field photorefractive interferometry.

PubMed

Xiong, Jichuan; Xu, Xiaodong; Glorieux, Christ; Matsuda, Osamu; Cheng, Liping

2015-05-01

A stroboscopic full-field imaging technique based on photorefractive interferometry for the visualization of rapidly changing surface displacement fields by using of a standard charge-coupled device (CCD) camera is presented. The photorefractive buildup of the space charge field during and after probe laser pulses is simulated numerically. The resulting anisotropic diffraction upon the refractive index grating and the interference between the polarization-rotated diffracted reference beam and the transmitted signal beam are modeled theoretically. The method is experimentally demonstrated by full-field imaging of the propagation of photoacoustically generated surface acoustic waves with a temporal resolution of nanoseconds. The surface acoustic wave propagation in a 23 mm × 17 mm area on an aluminum plate was visualized with 520 × 696 pixels of the CCD sensor, yielding a spatial resolution of 33 μm. The short pulse duration (8 ns) of the probe laser yields the capability of imaging SAWs with frequencies up to 60 MHz.

Optical soliton solutions, periodic wave solutions and complexitons of the cubic Schrödinger equation with a bounded potential

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Zou, Li

2018-01-01

In this paper, we consider the cubic Schrödinger equation with a bounded potential, which describes the propagation properties of optical soliton solutions. By employing an ansatz method, we precisely derive the bright and dark soliton solutions of the equation. Moreover, we obtain three classes of analytic periodic wave solutions expressed in terms of the Jacobi's elliptic functions including cn ,sn and dn functions. Finally, by using a tanh function method, its complexitons solutions are derived in a very natural way. It is hoped that our results can enrich the nonlinear dynamical behaviors of the cubic Schrödinger equation with a bounded potential.

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

OPTICAL SPECTRA OF CANDIDATE INTERNATIONAL CELESTIAL REFERENCE FRAME (ICRF) FLAT-SPECTRUM RADIO SOURCES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Titov, O.; Stanford, Laura M.; Johnston, Helen M.

2013-07-01

Continuing our program of spectroscopic observations of International Celestial Reference Frame (ICRF) sources, we present redshifts for 120 quasars and radio galaxies. Data were obtained with five telescopes: the 3.58 m European Southern Observatory New Technology Telescope, the two 8.2 m Gemini telescopes, the 2.5 m Nordic Optical Telescope (NOT), and the 6.0 m Big Azimuthal Telescope of the Special Astrophysical Observatory in Russia. The targets were selected from the International VLBI Service for Geodesy and Astrometry candidate International Celestial Reference Catalog which forms part of an observational very long baseline interferometry (VLBI) program to strengthen the celestial reference frame.more » We obtained spectra of the potential optical counterparts of more than 150 compact flat-spectrum radio sources, and measured redshifts of 120 emission-line objects, together with 19 BL Lac objects. These identifications add significantly to the precise radio-optical frame tie to be undertaken by Gaia, due to be launched in 2013, and to the existing data available for analyzing source proper motions over the celestial sphere. We show that the distribution of redshifts for ICRF sources is consistent with the much larger sample drawn from Faint Images of the Radio Sky at Twenty cm (FIRST) and Sloan Digital Sky Survey, implying that the ultra-compact VLBI sources are not distinguished from the overall radio-loud quasar population. In addition, we obtained NOT spectra for five radio sources from the FIRST and NRAO VLA Sky Survey catalogs, selected on the basis of their red colors, which yielded three quasars with z > 4.« less

Global paths of time-periodic solutions of the Benjamin-Ono equation connecting arbitrary traveling waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ambrose, David M.; Wilkening, Jon

2008-12-11

We classify all bifurcations from traveling waves to non-trivial time-periodic solutions of the Benjamin-Ono equation that are predicted by linearization. We use a spectrally accurate numerical continuation method to study several paths of non-trivial solutions beyond the realm of linear theory. These paths are found to either re-connect with a different traveling wave or to blow up. In the latter case, as the bifurcation parameter approaches a critical value, the amplitude of the initial condition grows without bound and the period approaches zero. We propose a conjecture that gives the mapping from one bifurcation to its counterpart on the othermore » side of the path of non-trivial solutions. By experimentation with data fitting, we identify the form of the exact solutions on the path connecting two traveling waves, which represents the Fourier coefficients of the solution as power sums of a finite number of particle positions whose elementary symmetric functions execute simple orbits in the complex plane (circles or epicycles). We then solve a system of algebraic equations to express the unknown constants in the new representation in terms of the mean, a spatial phase, a temporal phase, four integers (enumerating the bifurcation at each end of the path) and one additional bifurcation parameter. We also find examples of interior bifurcations from these paths of already non-trivial solutions, but we do not attempt to analyze their algebraic structure.« less

Propagation of large-amplitude waves on dielectric liquid sheets in a tangential electric field: exact solutions in three-dimensional geometry.

PubMed

Zubarev, Nikolay M; Zubareva, Olga V

2010-10-01

Nonlinear waves on sheets of dielectric liquid in the presence of an external tangential electric field are studied theoretically. It is shown that waves of arbitrary shape in three-dimensional geometry can propagate along (or against) the electric field direction without distortion, i.e., the equations of motion admit a wide class of exact traveling wave solutions. This unusual situation occurs for nonconducting ideal liquids with high dielectric constants in the case of a sufficiently strong field strength. Governing equations for evolution of plane symmetric waves on fluid sheets are derived using conformal variables. A dispersion relation for the evolution of small perturbations of the traveling wave solutions is obtained. It follows from this relation that, regardless of the wave shape, the amplitudes of small-scale perturbations do not increase with time and, hence, the traveling waves are stable. We also study the interaction of counterpropagating symmetric waves with small but finite amplitudes. The corresponding solution of the equations of motion describes the nonlinear superposition of the oppositely directed waves. The results obtained are applicable for the description of long waves on fluid sheets in a horizontal magnetic field.

New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing

NASA Astrophysics Data System (ADS)

Vinayagam, P. S.; Radha, R.; Al Khawaja, U.; Ling, Liming

2018-06-01

We investigate generalized nonlocal coupled nonlinear Schorödinger equation containing Self-Phase Modulation, Cross-Phase Modulation and four wave mixing involving nonlocal interaction. By means of Darboux transformation we obtained a family of exact breathers and solitons including the Peregrine soliton, Kuznetsov-Ma breather, Akhmediev breather along with all kinds of soliton-soliton and breather-soltion interactions. We analyze and emphasize the impact of the four-wave mixing on the nature and interaction of the solutions. We found that the presence of four wave mixing converts a two-soliton solution into an Akhmediev breather. In particular, the inclusion of four wave mixing results in the generation of a new solutions which is spatially and temporally periodic called "Soliton (Breather) lattice".

Dynamics of nonautonomous discrete rogue wave solutions for an Ablowitz-Musslimani equation with PT-symmetric potential.

PubMed

Yu, Fajun

2017-02-01

Starting from a discrete spectral problem, we derive a hierarchy of nonlinear discrete equations which include the Ablowitz-Ladik (AL) equation. We analytically study the discrete rogue-wave (DRW) solutions of AL equation with three free parameters. The trajectories of peaks and depressions of profiles for the first- and second-order DRWs are produced by means of analytical and numerical methods. In particular, we study the solutions with dispersion in parity-time ( PT) symmetric potential for Ablowitz-Musslimani equation. And we consider the non-autonomous DRW solutions, parameters controlling and their interactions with variable coefficients, and predict the long-living rogue wave solutions. Our results might provide useful information for potential applications of synthetic PT symmetric systems in nonlinear optics and condensed matter physics.

Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: Exact solutions and stability.

PubMed

Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A

2016-12-01

An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.

Dark solitons, breathers, and rogue wave solutions of the coupled generalized nonlinear Schrödinger equations.

PubMed

Priya, N Vishnu; Senthilvelan, M; Lakshmanan, M

2014-06-01

We construct dark-dark soliton, general breather (GB), Akhmediev breather (AB), Ma soliton (MS), and rogue wave (RW) solutions of a coupled generalized nonlinear Schrödinger (CGNLS) equation. While dark-dark solitons are captured in the defocusing regime of the CGNLS system, the other solutions, namely, GB, AB, MS, and RW, are identified in the focusing regime. We also analyze the structures of GB, AB, MS, and RW profiles with respect to the four-wave mixing parameter. We show that when we increase the value of the real part of the four-wave mixing parameter, the number of peaks in the breather profile increases and the width of each peak shrinks. Interestingly, the direction of this profile also changes due to this change. As far as the RW profile is concerned the width of the peak becomes very thin when we increase the value of this parameter. Further, we consider the RW solution as the starting point, derive AB, MS, and GB in the reverse direction, and show that the solutions obtained in both directions match each other. In the course of the reverse analysis we also demonstrate how to capture the RW solutions directly from AB and MS.

A note on free and forced Rossby wave solutions: The case of a straight coast and a channel

NASA Astrophysics Data System (ADS)

Graef, Federico

2017-03-01

The free Rossby wave (RW) solutions in an ocean with a straight coast when the offshore wavenumber of incident (l1) and reflected (l2) wave are equal or complex are discussed. If l1 = l2 the energy streams along the coast and a uniformly valid solution cannot be found; if l1,2 are complex it yields the sum of an exponentially decaying and growing (away from the coast) Rossby wave. The channel does not admit these solutions as free modes. If the wavenumber vectors of the RWs are perpendicular to the coast, the boundary condition of no normal flow is trivially satisfied and the value of the streamfunction does not need to vanish at the coast. A solution that satisfies Kelvin's theorem of time-independent circulation at the coast is proposed. The forced RW solutions when the ocean's forcing is a single Fourier component are studied. If the forcing is resonant, i.e. a free Rossby wave (RW), the linear response will depend critically on whether the wave carries energy perpendicular to the channel or not. In the first case, the amplitude of the response is linear in the direction normal to the channel, y, and in the second it has a parabolic profile in y. Examples of these solutions are shown for channels with parameters resembling the Mozambique Channel, the Tasman Sea, the Denmark Strait and the English Channel. The solutions for the single coast are unbounded, except when the forcing is a RW trapped against the coast. If the forcing is non-resonant, exponentially decaying or trapped RWs could be excited in the coast and both the exponentially ;decaying; and exponentially ;growing; RW could be excited in the channel.

Soliton solutions to the fifth-order Korteweg-de Vries equation and their applications to surface and internal water waves

NASA Astrophysics Data System (ADS)

Khusnutdinova, K. R.; Stepanyants, Y. A.; Tranter, M. R.

2018-02-01

We study solitary wave solutions of the fifth-order Korteweg-de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear dispersion, as well as two nonlinear dispersive terms. An exact solitary wave solution to this equation is derived, and the dependence of its amplitude, width, and speed on the parameters of the governing equation is studied. It is shown that the derived solution can represent either an embedded or regular soliton depending on the equation parameters. The nonlinear dispersive terms can drastically influence the existence of solitary waves, their nature (regular or embedded), profile, polarity, and stability with respect to small perturbations. We show, in particular, that in some cases embedded solitons can be stable even with respect to interactions with regular solitons. The results obtained are applicable to surface and internal waves in fluids, as well as to waves in other media (plasma, solid waveguides, elastic media with microstructure, etc.).

Detection of sinkholes or anomalies using full seismic wave fields : phase II.

DOT National Transportation Integrated Search

2016-08-01

A new 2-D Full Waveform Inversion (FWI) software code was developed to characterize layering and anomalies beneath the ground surface using seismic testing. The software is capable of assessing the shear and compression wave velocities (Vs and Vp) fo...

Numerical solutions of several reflected shock-wave flow fields with nonequilibrium chemical reactions

NASA Technical Reports Server (NTRS)

Hanson, R. K.; Presley, L. L.; Williams, E. V.

1972-01-01

The method of characteristics for a chemically reacting gas is used in the construction of the time-dependent, one-dimensional flow field resulting from the normal reflection of an incident shock wave at the end wall of a shock tube. Nonequilibrium chemical reactions are allowed behind both the incident and reflected shock waves. All the solutions are evaluated for oxygen, but the results are generally representative of any inviscid, nonconducting, and nonradiating diatomic gas. The solutions clearly show that: (1) both the incident- and reflected-shock chemical relaxation times are important in governing the time to attain steady state thermodynamic properties; and (2) adjacent to the end wall, an excess-entropy layer develops wherein the steady state values of all the thermodynamic variables except pressure differ significantly from their corresponding Rankine-Hugoniot equilibrium values.

Ion cyclotron emission from energetic fusion products in tokamak plasmas: A full-wave calculation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Batchelor, D.B.; Jaeger, E.F.; Colestock, P.L.

1989-06-01

A full-wave ion cyclotron resonant heating (ICRH) code has been modified to allow calculation of cyclotron emission from energetic ions in tokamaks. The immediate application is to fusion alpha particles in near-ignition devices. This permits detailed evaluation of proposed alpha particle diagnostics (Proceedings of the Thirteenth European Conference on Controlled Fusion and Plasma Heating, Schliersee, Federal Republic of Germany, 1986, edited by G. Briffod and M. Kaufmann (European Physical Society, Petit-Lancy, Switzerland, 1986), Part 1, Vol. 2, p. 37.) This full-wave approach automatically takes into account wall reflections, standing waves, and plasma absorption and overcomes the difficulties inherent in attemptingmore » to apply conventional geometrical optics to long wavelengths. By calculating the coherent radiation field caused by an ensemble of localized current sources (and retaining the phase information), the directivity of pickup antennas is correctly represented.« less

Impulsive spherical gravitational waves

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Nutku, Y.

2001-03-01

Penrose's identification with warp provides the general framework for constructing the continuous form of impulsive gravitational wave metrics. We present the two-component spinor formalism for the derivation of the full family of impulsive spherical gravitational wave metrics which brings out the power in identification with warp and leads to the simplest derivation of exact solutions. These solutions of the Einstein vacuum field equations are obtained by cutting Minkowski space into two pieces along a null cone and re-identifying them with warp which is given by an arbitrary nonlinear holomorphic transformation. Using two-component spinor techniques we construct a new metric describing an impulsive spherical gravitational wave where the vertex of the null cone lies on a worldline with constant acceleration.

Extending fullwave core ICRF simulation to SOL and antenna regions using FEM solver

NASA Astrophysics Data System (ADS)

Shiraiwa, S.; Wright, J. C.

2016-10-01

A full wave simulation approach to solve a driven RF waves problem including hot core, SOL plasmas and possibly antenna is presented. This approach allows for exploiting advantages of two different way of representing wave field, namely treating spatially dispersive hot conductivity in a spectral solver and handling complicated geometry in SOL/antenna region using an unstructured mesh. Here, we compute a mode set in each region with the RF electric field excitation on the connecting boundary between core and edge regions. A mode corresponding to antenna excitation is also computed. By requiring the continuity of tangential RF electric and magnetic fields, the solution is obtained as unique superposition of these modes. In this work, TORIC core spectral solver is modified to allow for mode excitation, and the edge region of diverted Alcator C-Mod plasma is modeled using COMSOL FEM package. The reconstructed RF field is similar in the core region to TORIC stand-alone simulation. However, it contains higher poloidal modes near the edge and captures a wave bounced and propagating in the poloidal direction near the vacuum-plasma boundary. These features could play an important role when the single power pass absorption is modest. This new capability will enable antenna coupling calculations with a realistic load plasma, including collisional damping in realistic SOL plasma and other loss mechanisms such as RF sheath rectification. USDoE Awards DE-FC02-99ER54512, DE-FC02-01ER54648.

Neutral axis determination of full size concrete structures using coda wave measurements

NASA Astrophysics Data System (ADS)

Jiang, Hanwan; Zhan, Hanyu; Zhuang, Chenxu; Jiang, Ruinian

2018-03-01

Coda waves experiencing multiple scattering behaviors are sensitive to weak changes occurring in media. In this paper, a typical four-point bending test with varied external loads is conducted on a 30-meter T-beam that is removed from a bridge after being in service for 15 years, and the coda wave signals are collected with a couple of sources-receivers pairs. Then the observed coda waves at different loads are compared to calculate their relative velocity variations, which are utilized as the parameter to distinct the compression and tensile zones as well as determine the neutral axis position. Without any prior knowledge of the concrete beam, the estimated axis position agrees well with the associated strain gage measurement results, and the zones bearing stress and tension behaviors are indicated. The presented work offers significant potential for Non-Destructive Testing and Evaluation of full-size concrete structures in future work.

Helicon Plasma Injector and Ion Cyclotron Acceleration Development in the VASIMR Experiment

NASA Technical Reports Server (NTRS)

Squire, Jared P.; Chang, Franklin R.; Jacobson, Verlin T.; McCaskill, Greg E.; Bengtson, Roger D.; Goulding, Richard H.

2000-01-01

In the Variable Specific Impulse Magnetoplasma Rocket (VASIMR) radio frequency (rf) waves both produce the plasma and then accelerate the ions. The plasma production is done by action of helicon waves. These waves are circular polarized waves in the direction of the electron gyromotion. The ion acceleration is performed by ion cyclotron resonant frequency (ICRF) acceleration. The Advanced Space Propulsion Laboratory (ASPL) is actively developing efficient helicon plasma production and ICRF acceleration. The VASIMR experimental device at the ASPL is called VX-10. It is configured to demonstrate the plasma production and acceleration at the 10kW level to support a space flight demonstration design. The VX-10 consists of three electromagnets integrated into a vacuum chamber that produce magnetic fields up to 0.5 Tesla. Magnetic field shaping is achieved by independent magnet current control and placement of the magnets. We have generated both helium and hydrogen high density (>10(exp 18) cu m) discharges with the helicon source. ICRF experiments are underway. This paper describes the VX-10 device, presents recent results and discusses future plans.

A forward-advancing wave expansion method for numerical solution of large-scale sound propagation problems

NASA Astrophysics Data System (ADS)

Rolla, L. Barrera; Rice, H. J.

2006-09-01

In this paper a "forward-advancing" field discretization method suitable for solving the Helmholtz equation in large-scale problems is proposed. The forward wave expansion method (FWEM) is derived from a highly efficient discretization procedure based on interpolation of wave functions known as the wave expansion method (WEM). The FWEM computes the propagated sound field by means of an exclusively forward advancing solution, neglecting the backscattered field. It is thus analogous to methods such as the (one way) parabolic equation method (PEM) (usually discretized using standard finite difference or finite element methods). These techniques do not require the inversion of large system matrices and thus enable the solution of large-scale acoustic problems where backscatter is not of interest. Calculations using FWEM are presented for two propagation problems and comparisons to data computed with analytical and theoretical solutions and show this forward approximation to be highly accurate. Examples of sound propagation over a screen in upwind and downwind refracting atmospheric conditions at low nodal spacings (0.2 per wavelength in the propagation direction) are also included to demonstrate the flexibility and efficiency of the method.

Exact solitary wave solution for higher order nonlinear Schrodinger equation using He's variational iteration method

NASA Astrophysics Data System (ADS)

Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet

2017-11-01

In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.

Full-wave Moment Tensor and Tomographic Inversions Based on 3D Strain Green Tensor

DTIC Science & Technology

2010-01-31

propagation in three-dimensional (3D) earth, linearizes the inverse problem by iteratively updating the earth model , and provides an accurate way to...self-consistent FD-SGT databases constructed from finite-difference simulations of wave propagation in full-wave tomographic models can be used to...determine the moment tensors within minutes after a seismic event, making it possible for real time monitoring using 3D models . 15. SUBJECT TERMS

Time-Domain Full-Wave Modeling of Nonlinear Air Breakdown in High-Power Microwave Devices and Systems

DTIC Science & Technology

2017-09-30

AFRL-RD-PS- AFRL-RD-PS- TR-2017-0047 TR-2017-0047 TIME -DOMAIN FULL-WAVE MODELING OF NONLINEAR AIR BREAKDOWN IN HIGH-POWER MICROWAVE...Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions...TITLE AND SUBTITLE Time -Domain Full-Wave Modeling of Nonlinear Air Breakdown in High-Power Microwave Devices and Systems 5a. CONTRACT NUMBER 5b

Travelling wave solutions of the homogeneous one-dimensional FREFLO model

NASA Astrophysics Data System (ADS)

Huang, B.; Hong, J. Y.; Jing, G. Q.; Niu, W.; Fang, L.

2018-01-01

Presently there is quite few analytical studies in traffic flows due to the non-linearity of the governing equations. In the present paper we introduce travelling wave solutions for the homogeneous one-dimensional FREFLO model, which are expressed in the form of series and describe the procedure that vehicles/pedestrians move with a negative velocity and decelerate until rest, then accelerate inversely to positive velocities. This method is expect to be extended to more complex situations in the future.

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

One-Dimensional Full Wave Simulation of Equatorial Magnetosonic Wave Propagation in an Inhomogeneous Magnetosphere

NASA Astrophysics Data System (ADS)

Liu, Xu; Chen, Lunjin; Yang, Lixia; Xia, Zhiyang; Malaspina, David M.

2018-01-01

The effect of the plasmapause on equatorially radially propagating fast magnetosonic (MS) waves in the Earth's dipole magnetic field is studied by using finite difference time domain method. We run 1-D simulation for three different density profiles: (1) no plasmapause, (2) with a plasmapause, and (3) with a plasmapause accompanied with fine-scale density irregularity. We find that (1) without plasmapause the radially inward propagating MS wave can reach ionosphere and continuously propagate to lower altitude if no damping mechanism is considered. The wave properties follow the cold plasma dispersion relation locally along its trajectory. (2) For simulation with a plasmapause with a scale length of 0.006 RE compared to wavelength, only a small fraction of the MS wave power is reflected by the plasmapause. WKB approximation is generally valid for such plasmapause. (3) The multiple fine-scale density irregularities near the outer edge of plasmapause can effectively block the MS wave propagation, resulting in a terminating boundary for MS waves near the plasmapause.

Signal-to-Noise Ratio Requirements for Half-Wave and Full-Wave Nonlinear Detectors with Arbitrary Power Laws, Sampling Rates, Input Spectra, and Filter Characteristics

DTIC Science & Technology

1986-06-10

system consisting of a sampler, a nonlinear rectifier, and a low-pass filter is evaluated generally , for arbitrary half-wave or full-wave v-th law...spectra, the possibility of using deliberate undersampling with no loss of performance is illustrated. The use of a half-wave rectifier generally ... some cases, significantly so. Programs for all procedures employed are presented so that investigation of additional cases or combinations of

Analysis of resonant fast ion distributions during combined ICRF and NBI heating with transients using neutron emission spectroscopy

NASA Astrophysics Data System (ADS)

Hellesen, C.; Mantsinen, M.; Conroy, S.; Ericsson, G.; Eriksson, J.; Kiptily, V. G.; Nabais, F.; Contributors, JET

2018-05-01

ICRF heating at the fundamental cyclotron frequency of a hydrogen minority ion species also gives rise to a partial power absorption by deuterium ions at their second harmonic resonance. This paper studies the deuterium distributions resulting from such 2nd harmonic heating at JET using neutron emission spectroscopy data from the time of flight spectrometer TOFOR. The fast deuterium distributions are obtained over the energy range 100 keV to 2 MeV. Specifically, we study how the fast deuterium distributions vary as ICRF heating is used alone as well as in combination with NBI heating. When comparing the different heating scenarios, we observed both a difference in the shapes of the distributions as well as in their absolute level. The differences are most pronounced below 0.5 MeV. Comparisons are made with corresponding distributions calculated with the code PION. We find a good agreement between the measured distributions and those calculated with PION, both in terms of their shapes as well as their amplitudes. However, we also identified a period with signs of an inverted fast ion distribution, which showed large disagreements between the modeled and measured results. Resonant interactions with tornado modes, i.e. core localized toroidal alfven eigenmodes (TAEs), are put forward as a possible explanation for the inverted distribution.

Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-12-01

In this study, we presented the problem formulations of models for internal solitary waves in a stratified shear flow with a free surface. The nonlinear higher order of extended KdV equations for the free surface displacement is generated. We derived the coefficients of the nonlinear higher-order extended KdV equation in terms of integrals of the modal function for the linear long-wave theory. The wave amplitude potential and the fluid pressure of the extended KdV equation in the form of solitary-wave solutions are deduced. We discussed and analyzed the stability of the obtained solutions and the movement role of the waves by making graphs of the exact solutions.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

NASA Technical Reports Server (NTRS)

Shertzer, J.; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

Automatic computation of the travelling wave solutions to nonlinear PDEs

NASA Astrophysics Data System (ADS)

Liang, Songxin; Jeffrey, David J.

2008-05-01

Various extensions of the tanh-function method and their implementations for finding explicit travelling wave solutions to nonlinear partial differential equations (PDEs) have been reported in the literature. However, some solutions are often missed by these packages. In this paper, a new algorithm and its implementation called TWS for solving single nonlinear PDEs are presented. TWS is implemented in MAPLE 10. It turns out that, for PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases. Program summaryProgram title:TWS Catalogue identifier:AEAM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAM_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:1250 No. of bytes in distributed program, including test data, etc.:78 101 Distribution format:tar.gz Programming language:Maple 10 Computer:A laptop with 1.6 GHz Pentium CPU Operating system:Windows XP Professional RAM:760 Mbytes Classification:5 Nature of problem:Finding the travelling wave solutions to single nonlinear PDEs. Solution method:Based on tanh-function method. Restrictions:The current version of this package can only deal with single autonomous PDEs or ODEs, not systems of PDEs or ODEs. However, the PDEs can have any finite number of independent space variables in addition to time t. Unusual features:For PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases. Additional comments:It is easy to use. Running time:Less than 20 seconds for most cases, between 20 to 100 seconds for some cases, over 100 seconds for few cases. References: [1] E.S. Cheb-Terrab, K. von

Two-dimensional solitary waves and periodic waves on coupled nonlinear electrical transmission lines

NASA Astrophysics Data System (ADS)

Wang, Heng; Zheng, Shuhua

2017-06-01

By using the dynamical system approach, the exact travelling wave solutions for a system of coupled nonlinear electrical transmission lines are studied. Based on this method, the bifurcations of phase portraits of a dynamical system are given. The two-dimensional solitary wave solutions and periodic wave solutions on coupled nonlinear transmission lines are obtained. With the aid of Maple, the numerical simulations are conducted for solitary wave solutions and periodic wave solutions to the model equation. The results presented in this paper improve upon previous studies.

RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anton, Luis; MartI, Jose M; Ibanez, Jose M

2010-05-01

We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, andmore » can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.« less

Monte-Carlo Orbit/Full Wave Simulation of Fast Alfvén Wave (FW) Damping on Resonant Ions in Tokamaks

NASA Astrophysics Data System (ADS)

Choi, M.; Chan, V. S.; Tang, V.; Bonoli, P.; Pinsker, R. I.; Wright, J.

2005-09-01

To simulate the resonant interaction of fast Alfvén wave (FW) heating and Coulomb collisions on energetic ions, including finite orbit effects, a Monte-Carlo code ORBIT-RF has been coupled with a 2D full wave code TORIC4. ORBIT-RF solves Hamiltonian guiding center drift equations to follow trajectories of test ions in 2D axisymmetric numerical magnetic equilibrium under Coulomb collisions and ion cyclotron radio frequency quasi-linear heating. Monte-Carlo operators for pitch-angle scattering and drag calculate the changes of test ions in velocity and pitch angle due to Coulomb collisions. A rf-induced random walk model describing fast ion stochastic interaction with FW reproduces quasi-linear diffusion in velocity space. FW fields and its wave numbers from TORIC are passed on to ORBIT-RF to calculate perpendicular rf kicks of resonant ions valid for arbitrary cyclotron harmonics. ORBIT-RF coupled with TORIC using a single dominant toroidal and poloidal wave number has demonstrated consistency of simulations with recent DIII-D FW experimental results for interaction between injected neutral-beam ions and FW, including measured neutron enhancement and enhanced high energy tail. Comparison with C-Mod fundamental heating discharges also yielded reasonable agreement.

Travelling-wave amplitudes as solutions of the phase-field crystal equation

NASA Astrophysics Data System (ADS)

Nizovtseva, I. G.; Galenko, P. K.

2018-01-01

The dynamics of the diffuse interface between liquid and solid states is analysed. The diffuse interface is considered as an envelope of atomic density amplitudes as predicted by the phase-field crystal model (Elder et al. 2004 Phys. Rev. E 70, 051605 (doi:10.1103/PhysRevE.70.051605); Elder et al. 2007 Phys. Rev. B 75, 064107 (doi:10.1103/PhysRevB.75.064107)). The propagation of crystalline amplitudes into metastable liquid is described by the hyperbolic equation of an extended Allen-Cahn type (Galenko & Jou 2005 Phys. Rev. E 71, 046125 (doi:10.1103/PhysRevE.71.046125)) for which the complete set of analytical travelling-wave solutions is obtained by the method (Malfliet & Hereman 1996 Phys. Scr. 15, 563-568 (doi:10.1088/0031-8949/54/6/003); Wazwaz 2004 Appl. Math. Comput. 154, 713-723 (doi:10.1016/S0096-3003(03)00745-8)). The general solution of travelling waves is based on the function of hyperbolic tangent. Together with its set of particular solutions, the general solution is analysed within an example of specific task about the crystal front invading metastable liquid (Galenko et al. 2015 Phys. D 308, 1-10 (doi:10.1016/j.physd.2015.06.002)). The influence of the driving force on the phase-field profile, amplitude velocity and correlation length is investigated for various relaxation times of the gradient flow. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.

Alfven Simple Waves

NASA Astrophysics Data System (ADS)

Webb, G. M.; Zank, G. P.; Burrows, R.

2009-12-01

Multi-dimensional Alfvén simple waves in magnetohydrodynamics (MHD) are investigated using Boillat's formalism. For simple wave solutions, all physical variables (the gas density, pressure, fluid velocity, entropy, and magnetic field induction in the MHD case) depend on a single phase function ǎrphi which is a function of the space and time variables. The simple wave ansatz requires that the wave normal and the normal speed of the wave front depend only on the phase function ǎrphi. This leads to an implicit equation for the phase function, and a generalisation of the concept of a plane wave. We obtain examples of Alfvén simple waves, based on the right eigenvector solutions for the Alfvén mode. The Alfvén mode solutions have six integrals, namely that the entropy, density, magnetic pressure and the group velocity (the sum of the Alfvén and fluid velocity) are constant throughout the wave. The eigen-equations require that the rate of change of the magnetic induction B with ǎrphi throughout the wave is perpendicular to both the wave normal n and B. Methods to construct simple wave solutions based on specifying either a solution ansatz for n(ǎrphi) or B(ǎrphi) are developed.

Twisted gravitational waves

NASA Astrophysics Data System (ADS)

Bini, Donato; Chicone, Carmen; Mashhoon, Bahram

2018-03-01

In general relativity (GR), linearized gravitational waves propagating in empty Minkowski spacetime along a fixed spatial direction have the property that the wave front is the Euclidean plane. Beyond the linear regime, exact plane waves in GR have been studied theoretically for a long time and many exact vacuum solutions of the gravitational field equations are known that represent plane gravitational waves. These have parallel rays and uniform wave fronts. It turns out, however, that GR also admits exact solutions representing gravitational waves propagating along a fixed direction that are nonplanar. The wave front is then nonuniform and the bundle of rays is twisted. We find a class of solutions representing nonplanar unidirectional gravitational waves and study some of the properties of these twisted waves.

Global smooth solutions of 3-D null-form wave equations in exterior domains with Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Jun, Li; Huicheng, Yin

2018-05-01

The paper is devoted to investigating long time behavior of smooth small data solutions to 3-D quasilinear wave equations outside of compact convex obstacles with Neumann boundary conditions. Concretely speaking, when the surface of a 3-D compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition, we prove that the smooth small data solution exists globally provided that the Neumann boundary condition on the exterior domain is given. One of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself. As an application of the main result, the global stability to 3-D static compressible Chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude.

Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. III: nonspherical Schwarzschild waves and singularities at null infinity

NASA Astrophysics Data System (ADS)

Frauendiener, Jörg; Hennig, Jörg

2018-03-01

We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Frauendiener and Hennig (2017 Class. Quantum Grav. 34 045005), to the case of general, nonsymmetric solutions. A key element of our approach is the modern standard representation of spacelike infinity as a cylinder. With a decomposition into spherical harmonics, we reduce the four-dimensional wave equation to a family of two-dimensional equations. These equations can be used to study the behaviour at the cylinder, where the solutions turn out to have, in general, logarithmic singularities at infinitely many orders. We derive regularity conditions that may be imposed on the initial data, in order to avoid the first singular terms. We then demonstrate that the fully pseudospectral time evolution scheme can be applied to this problem leading to a highly accurate numerical reconstruction of the nonsymmetric solutions. We are particularly interested in the behaviour of the solutions at future null infinity, and we numerically show that the singularities spread to null infinity from the critical set, where the cylinder approaches null infinity. The observed numerical behaviour is consistent with similar logarithmic singularities found analytically on the critical set. Finally, we demonstrate that even solutions with singularities at low orders can be obtained with high accuracy by virtue of a coordinate transformation that converts solutions with logarithmic singularities into smooth solutions.

THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

PubMed

Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

2013-01-01

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

Time-domain full-waveform inversion of Rayleigh and Love waves in presence of free-surface topography

NASA Astrophysics Data System (ADS)

Pan, Yudi; Gao, Lingli; Bohlen, Thomas

2018-05-01

Correct estimation of near-surface seismic-wave velocity when encountering lateral heterogeneity and free surface topography is one of the challenges to current shallow seismic. We propose to use time-domain full-waveform inversion (FWI) of surface waves, including both Rayleigh and Love waves, to solve this problem. We adopt a 2D time-domain finite-difference method with an improved vacuum formulation (IVF) to simulate shallow-seismic Rayleigh wave in presence of free-surface topography. We modify the IVF for SH-wave equation for the simulation of Love wave in presence of topographic free surface and prove its accuracy by benchmark tests. Checkboard model tests are performed in both cases when free-surface topography is included or neglected in FWI. Synthetic model containing a dipping planar free surface and lateral heterogeneity was then tested, in both cases of considering and neglecting free-surface topography. Both checkerboard and synthetic models show that Rayleigh- and Love-wave FWI have similar ability of reconstructing near-surface structures when free-surface topography is considered, while Love-wave FWI could reconstruct near-surface structures better than Rayleigh-wave when free-surface topography is neglected.

New exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in multi-temperature electron plasmas

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Tian, Yu; Zeng, Zhi-Fang

2017-10-01

In this paper, we aim to introduce a new form of the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation for the long waves of small amplitude with slow dependence on the transverse coordinate. By using the Hirota's bilinear form and the extended homoclinic test approach, new exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation are presented. Moreover, the properties and characteristics for these new exact periodic solitary-wave solutions are discussed with some figures.

Full Equations (FEQ) model for the solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures

USGS Publications Warehouse

Franz, Delbert D.; Melching, Charles S.

1997-01-01

The Full EQuations (FEQ) model is a computer program for solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures. A stream system that is simulated by application of FEQ is subdivided into stream reaches (branches), parts of the stream system for which complete information on flow and depth are not required (dummy branches), and level-pool reservoirs. These components are connected by special features; that is, hydraulic control structures, including junctions, bridges, culverts, dams, waterfalls, spillways, weirs, side weirs, and pumps. The principles of conservation of mass and conservation of momentum are used to calculate the flow and depth throughout the stream system resulting from known initial and boundary conditions by means of an implicit finite-difference approximation at fixed points (computational nodes). The hydraulic characteristics of (1) branches including top width, area, first moment of area with respect to the water surface, conveyance, and flux coefficients and (2) special features (relations between flow and headwater and (or) tail-water elevations, including the operation of variable-geometry structures) are stored in function tables calculated in the companion program, Full EQuations UTiLities (FEQUTL). Function tables containing other information used in unsteady-flow simulation (boundary conditions, tributary inflows or outflows, gate settings, correction factors, characteristics of dummy branches and level-pool reservoirs, and wind speed and direction) are prepared by the user as detailed in this report. In the iterative solution scheme for flow and depth throughout the stream system, an interpolation of the function tables corresponding to the computational nodes throughout the stream system is done in the model. FEQ can be applied in the simulation of a wide range of stream configurations (including loops), lateral-inflow conditions, and special features. The

Full-wave multiscale anisotropy tomography in Southern California

NASA Astrophysics Data System (ADS)

Lin, Yu-Pin; Zhao, Li; Hung, Shu-Huei

2014-12-01

Understanding the spatial variation of anisotropy in the upper mantle is important for characterizing the lithospheric deformation and mantle flow dynamics. In this study, we apply a full-wave approach to image the upper-mantle anisotropy in Southern California using 5954 SKS splitting data. Three-dimensional sensitivity kernels combined with a wavelet-based model parameterization are adopted in a multiscale inversion. Spatial resolution lengths are estimated based on a statistical resolution matrix approach, showing a finest resolution length of ~25 km in regions with densely distributed stations. The anisotropic model displays structural fabric in relation to surface geologic features such as the Salton Trough, the Transverse Ranges, and the San Andreas Fault. The depth variation of anisotropy does not suggest a lithosphere-asthenosphere decoupling. At long wavelengths, the fast directions of anisotropy are aligned with the absolute plate motion inside the Pacific and North American plates.

Experimental solution for scattered imaging of the interference of plasmonic and photonic mode waves launched by metal nano-slits.

PubMed

Li, Xing; Gao, Yaru; Jiang, Shuna; Ma, Li; Liu, Chunxiang; Cheng, Chuanfu

2015-02-09

Using an L-shaped metal nanoslit to generate waves of the pure photonic and plasmonic modes simultaneously, we perform an experimental solution for the scattered imaging of the interference of the two waves. From the fringe data of interference, the amplitudes and the wavevector components of the two waves are obtained. The initial phases of the two waves are obtained from the phase map reconstructed with the interference of the scattered image and the reference wave in the interferometer. The difference in the wavevector components gives rise to an additional phase delay. We introduce the scattering theory under Kirchhoff's approximation to metal slit regime and explain the wavevector difference reasonably. The solution of the quantities is a comprehensive reflection of excitation, scattering and interference of the two waves. By decomposing the polarized incident field with respect to the slit element, the scattered image produced by slit of arbitrary shape can be solved with the nanoscale Huygens-Fresnel principle. This is demonstrated by the experimental intensity pattern and phase map produced by a ring-slit and its consistency with the calculated results.

On the existence of solutions to a one-dimensional degenerate nonlinear wave equation

NASA Astrophysics Data System (ADS)

Hu, Yanbo

2018-07-01

This paper is concerned with the degenerate initial-boundary value problem to the one-dimensional nonlinear wave equation utt =((1 + u) aux) x which arises in a number of various physical contexts. The global existence of smooth solutions to the degenerate problem was established under relaxed conditions on the initial-boundary data by the characteristic decomposition method. Moreover, we show that the solution is uniformly C 1 , α continuous up to the degenerate boundary and the degenerate curve is C 1 , α continuous for α ∈ (0 , min ⁡ a/1+a, 1/1+a).

Exact time-dependent nonlinear dispersive wave solutions in compressible magnetized plasmas exhibiting collapse.

PubMed

Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans

2011-04-08

Compressional waves in a magnetized plasma of arbitrary resistivity are treated with the lagrangian fluid approach. An exact nonlinear solution with a nontrivial space and time dependence is obtained with boundary conditions as in Harris' current sheet. The solution shows competition among hydrodynamic convection, magnetic field diffusion, and dispersion. This results in a collapse of density and the magnetic field in the absence of dispersion. The dispersion effects arrest the collapse of density but not of the magnetic field. A possible application is in the early stage of magnetic star formation.

Guided solitary waves.

PubMed

Miles, J

1980-04-01

Transversely periodic solitary-wave solutions of the Boussinesq equations (which govern wave propagation in a weakly dispersive, weakly nonlinear physical system) are determined. The solutions for negative dispersion (e.g., gravity waves) are singular and therefore physically unacceptable. The solutions for positive dispersion (e.g., capillary waves or magnetosonic waves in a plasma) are physically acceptable except in a limited parametric interval, in which they are complex. The two end points of this interval are associated with (two different) resonant interactions among three basic solitary waves, two of which are two-dimensional complex conjugates and the third of which is one-dimensional and real.

Integrable aspects and rogue wave solution of Sasa-Satsuma equation with variable coefficients in the inhomogeneous fiber

NASA Astrophysics Data System (ADS)

Zhang, Yu-Ping; Yu, Lan; Wei, Guang-Mei

2018-02-01

Under investigation with symbolic computation in this paper, is a variable-coefficient Sasa-Satsuma equation (SSE) which can describe the ultra short pulses in optical fiber communications and propagation of deep ocean waves. By virtue of the extended Ablowitz-Kaup-Newell-Segur system, Lax pair for the model is directly constructed. Based on the obtained Lax pair, an auto-Bäcklund transformation is provided, then the explicit one-soliton solution is obtained. Meanwhile, an infinite number of conservation laws in explicit recursion forms are derived to indicate its integrability in the Liouville sense. Furthermore, exact explicit rogue wave (RW) solution is presented by use of a Darboux transformation. In addition to the double-peak structure and an analog of the Peregrine soliton, the RW can exhibit graphically an intriguing twisted rogue-wave (TRW) pair that involve four well-defined zero-amplitude points.

Study of the effects of corrugated wall structures due to blanket modules around ICRH antennas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumortier, Pierre; Louche, Fabrice; Messiaen, André

2014-02-12

In future fusion reactors, and in ITER, the first wall will be covered by blanket modules. These blanket modules, whose dimensions are of the order of the ICRF wavelengths, together with the clearance gaps between them will constitute a corrugated structure which will interact with the electromagnetic waves launched by ICRF antennas. The conditions in which the grooves constituted by the clearance gaps between the blanket modules can become resonant are studied. Simple analytical models and numerical simulations show that mushroom type structures (with larger gaps at the back than at the front) can bring down the resonance frequencies, whichmore » could lead to large voltages in the gaps between the blanket modules and perturb the RF properties of the antenna if they are in the ICRF operating range. The effect on the wave propagation along the wall structure, which is acting as a spatially periodic (toroidally and poloidally) corrugated structure, and hence constitutes a slow wave structure modifying the wall boundary condition, is examined.« less

Pseudo-incompressible, finite-amplitude gravity waves: wave trains and stability

NASA Astrophysics Data System (ADS)

Schlutow, Mark; Klein, Rupert

2017-04-01

Based on weak asymptotic WKB-like solutions for two-dimensional atmospheric gravity waves (GWs) traveling wave solutions (wave trains) are derived and analyzed with respect to stability. A systematic multiple-scale analysis using the ratio of the dominant wavelength and the scale height as a scale separation parameter is applied on the fully compressible Euler equations. A distinguished limit favorable for GWs close to static instability, reveals that pseudo-incompressible rather than Boussinesq theory applies. A spectral expansion including a mean flow, combined with the additional WKB assumption of slowly varying phases and amplitudes, is used to find general weak asymptotic solutions. This ansatz allows for arbitrarily strong, non-uniform stratification and holds even for finite-amplitude waves. It is deduced that wave trains as leading order solutions can only exist if either some non-uniform background stratification is given but the wave train propagates only horizontally or if the wave train velocity vector is given but the background is isothermal. For the first case, general analytical solutions are obtained that may be used to model mountain lee waves. For the second case with the additional assumption of horizontal periodicity, upward propagating wave train fronts were found. These wave train fronts modify the mean flow beyond the non-acceleration theorem. Stability analysis reveal that they are intrinsically modulationally unstable. The range of validity for the scale separation parameter was tested with fully nonlinear simulations. Even for large values an excellent agreement with the theory was found.

The extended Einstein-Maxwell-aether-axion model: Exact solutions for axionically controlled pp-wave aether modes

NASA Astrophysics Data System (ADS)

Balakin, Alexander B.

2018-03-01

The extended Einstein-Maxwell-aether-axion model describes internal interactions inside the system, which contains gravitational, electromagnetic fields, the dynamic unit vector field describing the velocity of an aether, and the pseudoscalar field associated with the axionic dark matter. The specific feature of this model is that the axion field controls the dynamics of the aether through the guiding functions incorporated into Jacobson’s constitutive tensor. Depending on the state of the axion field, these guiding functions can control and switch on or switch off the influence of acceleration, shear, vorticity and expansion of the aether flow on the state of physical system as a whole. We obtain new exact solutions, which possess the pp-wave symmetry, and indicate them by the term pp-wave aether modes in contrast to the pure pp-waves, which cannot propagate in this field conglomerate. These exact solutions describe a specific dynamic state of the pseudoscalar field, which corresponds to one of the minima of the axion potential and switches off the influence of shear and expansion of the aether flow; the model does not impose restrictions on Jacobson’s coupling constants and on the axion mass. Properties of these new exact solutions are discussed.

Determination of medium electrical properties through full-wave modelling of frequency domain reflectrometry data

NASA Astrophysics Data System (ADS)

André, Frédéric; Lambot, Sébastien

2015-04-01

Accurate knowledge of the shallow soil properties is of prime importance in agricultural, hydrological and environmental engineering. During the last decade, numerous geophysical techniques, either invasive or resorting to proximal or remote sensing, have been developed and applied for quantitative characterization of soil properties. Amongst them, time domain reflectrometry (TDR) and frequency domain reflectometry (FDR) are recognized as standard techniques for the determination of soil dielectric permittivity and electrical conductivity, based on the reflected electromagnetic waves from a probe inserted into the soil. TDR data were first commonly analyzed in the time domain using methods considering only a part of the waveform information. Later, advancements have led to the possibility of analyzing the TDR signal through full-wave inverse modeling either in the time or the frequency domains. A major advantage of FDR compared to TDR is the possibility to increase the bandwidth, thereby increasing the information content of the data and providing more detailed characterization of the medium. Amongst the recent works in this field, Minet et al. (2010) developed a modeling procedure for processing FDR data based on an exact solution of Maxwell's equations for wave propagation in one-dimensional multilayered media. In this approach, the probe head is decoupled from the medium and is fully described by characteristic transfer functions. The authors successfully validated the method for homogeneous sand subject to a range of water contents. In the present study, we further validated the modelling approach using reference liquids with well-characterized frequency-dependent electrical properties. In addition, the FDR model was coupled with a dielectric mixing model to investigate the ability of retrieving water content, pore water electrical conductivity and sand porosity from inversion of FDR data acquired in sand subject to different water content levels. Finally, the

Numerical solution of the full potential equation using a chimera grid approach

NASA Technical Reports Server (NTRS)

Holst, Terry L.

1995-01-01

A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

Stability of transition waves and positive entire solutions of Fisher-KPP equations with time and space dependence

NASA Astrophysics Data System (ADS)

Shen, Wenxian

2017-09-01

This paper is concerned with the stability of transition waves and strictly positive entire solutions of random and nonlocal dispersal evolution equations of Fisher-KPP type with general time and space dependence, including time and space periodic or almost periodic dependence as special cases. We first show the existence, uniqueness, and stability of strictly positive entire solutions of such equations. Next, we show the stability of uniformly continuous transition waves connecting the unique strictly positive entire solution and the trivial solution zero and satisfying certain decay property at the end close to the trivial solution zero (if it exists). The existence of transition waves has been studied in Liang and Zhao (2010 J. Funct. Anal. 259 857-903), Nadin (2009 J. Math. Pures Appl. 92 232-62), Nolen et al (2005 Dyn. PDE 2 1-24), Nolen and Xin (2005 Discrete Contin. Dyn. Syst. 13 1217-34) and Weinberger (2002 J. Math. Biol. 45 511-48) for random dispersal Fisher-KPP equations with time and space periodic dependence, in Nadin and Rossi (2012 J. Math. Pures Appl. 98 633-53), Nadin and Rossi (2015 Anal. PDE 8 1351-77), Nadin and Rossi (2017 Arch. Ration. Mech. Anal. 223 1239-67), Shen (2010 Trans. Am. Math. Soc. 362 5125-68), Shen (2011 J. Dynam. Differ. Equ. 23 1-44), Shen (2011 J. Appl. Anal. Comput. 1 69-93), Tao et al (2014 Nonlinearity 27 2409-16) and Zlatoš (2012 J. Math. Pures Appl. 98 89-102) for random dispersal Fisher-KPP equations with quite general time and/or space dependence, and in Coville et al (2013 Ann. Inst. Henri Poincare 30 179-223), Rawal et al (2015 Discrete Contin. Dyn. Syst. 35 1609-40) and Shen and Zhang (2012 Comm. Appl. Nonlinear Anal. 19 73-101) for nonlocal dispersal Fisher-KPP equations with time and/or space periodic dependence. The stability result established in this paper implies that the transition waves obtained in many of the above mentioned papers are asymptotically stable for well-fitted perturbation. Up to the author�

Whistler Observations on DEMETER Compared with Full Electromagnetic Wave Simulations

NASA Astrophysics Data System (ADS)

Compston, A. J.; Cohen, M.; Lehtinen, N. G.; Inan, U.; Linscott, I.; Said, R.; Parrot, M.

2014-12-01

Terrestrial Very Low Frequency (VLF) electromagnetic radiation, which strongly impacts the Van Allen radiation belt electron dynamics, is injected across the ionosphere into the Earth's plasmasphere from two primary sources: man-made VLF transmitters and lightning discharges. Numerical models of trans-ionospheric propagation of such waves remain unvalidated, and early models may have overestimated the absorption, hindering a comprehensive understanding of the global impact of VLF waves in the loss of radiation belt electrons. In an attempt to remedy the problem of a lack of accurate trans-ionospheric propagation models, we have used a full electromagnetic wave method (FWM) numerical code to simulate the propagation of lightning-generated whistlers into the magnetosphere and compared the results with whistlers observed on the DEMETER satellite and paired with lightning stroke data from the National Lightning Detection Network (NLDN). We have identified over 20,000 whistlers occuring in 14 different passes of DEMETER over the central United States during the summer of 2009, and 14,000 of those occured within the 2000 km x 2000 km simulation grid we used. As shown in the attached figure, which shows a histogram of the ratio of the simulated whistler energy to the measured whistler energy for the 14,000 whistlers we compared, the simulation tends to slightly underestimate the total whistler energy injected by about 5 dB. However, the simulation underestimates the DEMETER measurements more as one gets further from the source lightning stroke, so since the signal to noise ratio of more distant whistlers will be smaller, possibly additive noise in the DEMETER measurements (which of course is not accounted for in the model) may explain some of the observed discrepancy.

The Riemann problem for the relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation

NASA Astrophysics Data System (ADS)

Shao, Zhiqiang

2018-04-01

The relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation is studied. The Riemann problem is solved constructively. The delta shock wave arises in the Riemann solutions, provided that the initial data satisfy some certain conditions, although the system is strictly hyperbolic and the first and third characteristic fields are genuinely nonlinear, while the second one is linearly degenerate. There are five kinds of Riemann solutions, in which four only consist of a shock wave and a centered rarefaction wave or two shock waves or two centered rarefaction waves, and a contact discontinuity between the constant states (precisely speaking, the solutions consist in general of three waves), and the other involves delta shocks on which both the rest mass density and the proper energy density simultaneously contain the Dirac delta function. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, we establish the existence and uniqueness of solutions involving delta shocks for the Riemann problem.

Full Waveform Modelling for Subsurface Characterization with Converted-Wave Seismic Reflection

NASA Astrophysics Data System (ADS)

Triyoso, Wahyu; Oktariena, Madaniya; Sinaga, Edycakra; Syaifuddin, Firman

2017-04-01

While a large number of reservoirs have been explored using P-waves seismic data, P-wave seismic survey ceases to provide adequate result in seismically and geologically challenging areas, like gas cloud, shallow drilling hazards, strong multiples, highly fractured, anisotropy. Most of these reservoir problems can be addressed using P and PS seismic data combination. Multicomponent seismic survey records both P-wave and S-wave unlike conventional survey that only records compressional P-wave. Under certain conditions, conventional energy source can be used to record P and PS data using the fact that compressional wave energy partly converts into shear waves at the reflector. Shear component can be recorded using down going P-wave and upcoming S-wave by placing a horizontal component geophone on the ocean floor. A synthetic model is created based on real data to analyze the effect of gas cloud existence to PP and PS wave reflections which has a similar characteristic to Sub-Volcanic imaging. The challenge within the multicomponent seismic is the different travel time between P-wave and S-wave, therefore the converted-wave seismic data should be processed with different approach. This research will provide a method to determine an optimum converted point known as Common Conversion Point (CCP) that can solve the Asymmetrical Conversion Point of PS data. The value of γ (Vp/Vs) is essential to estimate the right CCP that will be used in converted-wave seismic processing. This research will also continue to the advanced processing method of converted-wave seismic by applying Joint Inversion to PP&PS seismic. Joint Inversion is a simultaneous model-based inversion that estimates the P&S-wave impedance which are consistent with the PP&PS amplitude data. The result reveals a more complex structure mirrored in PS data below the gas cloud area. Through estimated γ section resulted from Joint Inversion, we receive a better imaging improvement below gas cloud area tribute to

Global existence of solutions for semilinear damped wave equation in 2-D exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

We consider a mixed problem of a damped wave equation utt-Δ u+ ut=| u| p in the two dimensional exterior domain case. Small global in time solutions can be constructed in the case when the power p on the nonlinear term | u| p satisfies p ∗=2solution in the exterior domain. A new device developed in Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions

NASA Astrophysics Data System (ADS)

Khajehtourian, Romik

Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium. The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium. In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The

Some new exact solitary wave solutions of the van der Waals model arising in nature

NASA Astrophysics Data System (ADS)

Bibi, Sadaf; Ahmed, Naveed; Khan, Umar; Mohyud-Din, Syed Tauseef

2018-06-01

This work proposes two well-known methods, namely, Exponential rational function method (ERFM) and Generalized Kudryashov method (GKM) to seek new exact solutions of the van der Waals normal form for the fluidized granular matter, linked with natural phenomena and industrial applications. New soliton solutions such as kink, periodic and solitary wave solutions are established coupled with 2D and 3D graphical patterns for clarity of physical features. Our comparison reveals that the said methods excel several existing methods. The worked-out solutions show that the suggested methods are simple and reliable as compared to many other approaches which tackle nonlinear equations stemming from applied sciences.

Exact solutions for the source-excited cylindrical electromagnetic waves in a nonlinear nondispersive medium.

PubMed

Es'kin, V A; Kudrin, A V; Petrov, E Yu

2011-06-01

The behavior of electromagnetic fields in nonlinear media has been a topical problem since the discovery of materials with a nonlinearity of electromagnetic properties. The problem of finding exact solutions for the source-excited nonlinear waves in curvilinear coordinates has been regarded as unsolvable for a long time. In this work, we present the first solution of this type for a cylindrically symmetric field excited by a pulsed current filament in a nondispersive medium that is simultaneously inhomogeneous and nonlinear. Assuming that the medium has a power-law permittivity profile in the linear regime and lacks a center of inversion, we derive an exact solution for the electromagnetic field excited by a current filament in such a medium and discuss the properties of this solution.

Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

NASA Astrophysics Data System (ADS)

Vitanov, Nikolay K.

2011-03-01

We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

Scattering of acoustic evanescent waves by circular cylinders: Partial wave series solution

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2002-05-01

Evanescent acoustical waves occur in a variety of situations such as when sound is incident on a fluid interface beyond the critical angle and when flexural waves on a plate are subsonic with respect to the surrounding fluid. The scattering by circular cylinders at normal incidence was calculated to give insight into the consequences on the scattering of the evanescence of the incident wave. To analyze the scattering, it is necessary to express the incident wave using a modified expansion involving cylindrical functions. For plane evanescent waves, the expansion becomes a double summation with products of modified and ordinary Bessel functions. The resulting modified series is found for the scattering by a fluid cylinder in an unbounded medium. The perfectly soft and rigid cases are also examined. Unlike the case of an ordinary incident wave, the counterpropagating partial waves of the same angular order have unequal magnitudes when the incident wave is evanescent. This is a consequence of the exponential dependence of the incident wave amplitude on the transverse coordinate. The associated exponential dependence of the scattering on the location of a scatterer was previously demonstrated [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 93, 1192-1195 (1993)].

Development of a GPU-Accelerated 3-D Full-Wave Code for Electromagnetic Wave Propagation in a Cold Plasma

NASA Astrophysics Data System (ADS)

Woodbury, D.; Kubota, S.; Johnson, I.

2014-10-01

Computer simulations of electromagnetic wave propagation in magnetized plasmas are an important tool for both plasma heating and diagnostics. For active millimeter-wave and microwave diagnostics, accurately modeling the evolution of the beam parameters for launched, reflected or scattered waves in a toroidal plasma requires that calculations be done using the full 3-D geometry. Previously, we reported on the application of GPGPU (General-Purpose computing on Graphics Processing Units) to a 3-D vacuum Maxwell code using the FDTD (Finite-Difference Time-Domain) method. Tests were done for Gaussian beam propagation with a hard source antenna, utilizing the parallel processing capabilities of the NVIDIA K20M. In the current study, we have modified the 3-D code to include a soft source antenna and an induced current density based on the cold plasma approximation. Results from Gaussian beam propagation in an inhomogeneous anisotropic plasma, along with comparisons to ray- and beam-tracing calculations will be presented. Additional enhancements, such as advanced coding techniques for improved speedup, will also be investigated. Supported by U.S. DoE Grant DE-FG02-99-ER54527 and in part by the U.S. DoE, Office of Science, WDTS under the Science Undergraduate Laboratory Internship program.

Full Wave Parallel Code for Modeling RF Fields in Hot Plasmas

NASA Astrophysics Data System (ADS)

Spencer, Joseph; Svidzinski, Vladimir; Evstatiev, Evstati; Galkin, Sergei; Kim, Jin-Soo

2015-11-01

FAR-TECH, Inc. is developing a suite of full wave RF codes in hot plasmas. It is based on a formulation in configuration space with grid adaptation capability. The conductivity kernel (which includes a nonlocal dielectric response) is calculated by integrating the linearized Vlasov equation along unperturbed test particle orbits. For Tokamak applications a 2-D version of the code is being developed. Progress of this work will be reported. This suite of codes has the following advantages over existing spectral codes: 1) It utilizes the localized nature of plasma dielectric response to the RF field and calculates this response numerically without approximations. 2) It uses an adaptive grid to better resolve resonances in plasma and antenna structures. 3) It uses an efficient sparse matrix solver to solve the formulated linear equations. The linear wave equation is formulated using two approaches: for cold plasmas the local cold plasma dielectric tensor is used (resolving resonances by particle collisions), while for hot plasmas the conductivity kernel is calculated. Work is supported by the U.S. DOE SBIR program.

Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

DOE PAGES

Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; ...

2015-07-10

Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes themore » rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide

Full-duplex radio-over-fiber system with tunable millimeter-wave signal generation and wavelength reuse for upstream signal.

PubMed

Wang, Yiqun; Pei, Li; Li, Jing; Li, Yueqin

2017-06-10

A full-duplex radio-over-fiber system is proposed, which provides both the generation of a millimeter-wave (mm-wave) signal with tunable frequency multiplication factors (FMFs) and wavelength reuse for uplink data. A dual-driving Mach-Zehnder modulator and a phase modulator are cascaded to form an optical frequency comb. An acousto-optic tunable filter based on a uniform fiber Bragg grating (FBG-AOTF) is employed to select three target optical sidebands. Two symmetrical sidebands are chosen to generate mm waves with tunable FMFs up to 16, which can be adjusted by changing the frequency of the applied acoustic wave. The optical carrier is reused at the base station for uplink connection. FBG-AOTFs driven by two acoustic wave signals are experimentally fabricated and further applied in the proposed scheme. Results of the research indicate that the 2-Gbit/s data can be successfully transmitted over a 25-km single-mode fiber for bidirectional full-duplex channels with power penalty of less than 2.6 dB. The feasibility of the proposed scheme is verified by detailed simulations and partial experiments.

Investigation of the reconstruction accuracy of guided wave tomography using full waveform inversion

NASA Astrophysics Data System (ADS)

Rao, Jing; Ratassepp, Madis; Fan, Zheng

2017-07-01

Guided wave tomography is a promising tool to accurately determine the remaining wall thicknesses of corrosion damages, which are among the major concerns for many industries. Full Waveform Inversion (FWI) algorithm is an attractive guided wave tomography method, which uses a numerical forward model to predict the waveform of guided waves when propagating through corrosion defects, and an inverse model to reconstruct the thickness map from the ultrasonic signals captured by transducers around the defect. This paper discusses the reconstruction accuracy of the FWI algorithm on plate-like structures by using simulations as well as experiments. It was shown that this algorithm can obtain a resolution of around 0.7 wavelengths for defects with smooth depth variations from the acoustic modeling data, and about 1.5-2 wavelengths from the elastic modeling data. Further analysis showed that the reconstruction accuracy is also dependent on the shape of the defect. It was demonstrated that the algorithm maintains the accuracy in the case of multiple defects compared to conventional algorithms based on Born approximation.

Study of travelling wave solutions for some special-type nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Song, Junquan; Hu, Lan; Shen, Shoufeng; Ma, Wen-Xiu

2018-07-01

The tanh-function expansion method has been improved and used to construct travelling wave solutions of the form U={\\sum }j=0n{a}j{\\tanh }jξ for some special-type nonlinear evolution equations, which have a variety of physical applications. The positive integer n can be determined by balancing the highest order linear term with the nonlinear term in the evolution equations. We improve the tanh-function expansion method with n = 0 by introducing a new transform U=-W\\prime (ξ )/{W}2. A nonlinear wave equation with source terms, and mKdV-type equations, are considered in order to show the effectiveness of the improved scheme. We also propose the tanh-function expansion method of implicit function form, and apply it to a Harry Dym-type equation as an example.

Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Simbanefayi, Innocent; Khalique, Chaudry Masood

2018-03-01

In this work we study the Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the two-way propagation of waves. Using Lie symmetry method together with Jacobi elliptic function expansion and Kudryashov methods we construct its travelling wave solutions. Also, we derive conservation laws of the KdV-BBM equation using the variational derivative approach. In this method, we begin by computing second-order multipliers for the KdV-BBM equation followed by a derivation of the respective conservation laws for each multiplier.

Interaction Solutions for Lump-line Solitons and Lump-kink Waves of the Dimensionally Reduced Generalised KP Equation

NASA Astrophysics Data System (ADS)

Ahmed, Iftikhar

2017-09-01

In this work, we investigate dimensionally reduced generalised Kadomtsev-Petviashvili equation, which can describe many nonlinear phenomena in fluid dynamics. Based on the bilinear formalism, direct Maple symbolic computations are used with an ansätz function to construct three classes of interaction solutions between lump and line solitons. Furthermore, the dynamics of interaction phenomena is explained with 3D plots and 2D contour plots. For the first class of interaction solutions, lump appeared at t=0, and there was a normal interaction between lump and line solitons at t=1, 2, 5, and 10. For the second class of interaction solutions, lump appeared from one side of line soliton at t=0, but it started moving downward at t=1, 2, and 5. Finally, at t=10, this lump was completely swallowed by other side. By contrast, for the third class of interaction solutions, lump appeared from one side of line soliton at t=0, but it started moving upward at t=1, 2, and 5. Finally, at t=10, this lump was completely swallowed by other side. Furthermore, interaction solutions between lump solutions and kink wave are also investigated. These results might be helpful to understand the propagation processes for nonlinear waves in fluid mechanics.

Full Waveform Inversion of Diving & Reflected Waves based on Scale Separation for Velocity and Impedance Imaging

NASA Astrophysics Data System (ADS)

Brossier, Romain; Zhou, Wei; Operto, Stéphane; Virieux, Jean

2015-04-01

Full Waveform Inversion (FWI) is an appealing method for quantitative high-resolution subsurface imaging (Virieux et al., 2009). For crustal-scales exploration from surface seismic, FWI generally succeeds in recovering a broadband of wavenumbers in the shallow part of the targeted medium taking advantage of the broad scattering-angle provided by both reflected and diving waves. In contrast, deeper targets are often only illuminated by short-spread reflections, which favor the reconstruction of the short wavelengths at the expense of the longer ones, leading to a possible notch in the intermediate part of the wavenumber spectrum. To update the velocity macromodel from reflection data, image-domain strategies (e.g., Symes & Carazzone, 1991) aim to maximize a semblance criterion in the migrated domain. Alternatively, recent data-domain strategies (e.g., Xu et al., 2012, Ma & Hale, 2013, Brossier et al., 2014), called Reflection FWI (RFWI), inspired by Chavent et al. (1994), rely on a scale separation between the velocity macromodel and prior knowledge of the reflectivity to emphasize the transmission regime in the sensitivity kernel of the inversion. However, all these strategies focus on reflected waves only, discarding the low-wavenumber information carried out by diving waves. With the current development of very long-offset and wide-azimuth acquisitions, a significant part of the recorded energy is provided by diving waves and subcritical reflections, and high-resolution tomographic methods should take advantage of all types of waves. In this presentation, we will first review the issues of classical FWI when applied to reflected waves and how RFWI is able to retrieve the long wavelength of the model. We then propose a unified formulation of FWI (Zhou et al., 2014) to update the low wavenumbers of the velocity model by the joint inversion of diving and reflected arrivals, while the impedance model is updated thanks to reflected wave only. An alternate inversion of

Global solutions and finite time blow-up for fourth order nonlinear damped wave equation

NASA Astrophysics Data System (ADS)

Xu, Runzhang; Wang, Xingchang; Yang, Yanbing; Chen, Shaohua

2018-06-01

In this paper, we study the initial boundary value problem and global well-posedness for a class of fourth order wave equations with a nonlinear damping term and a nonlinear source term, which was introduced to describe the dynamics of a suspension bridge. The global existence, decay estimate, and blow-up of solution at both subcritical (E(0) < d) and critical (E(0) = d) initial energy levels are obtained. Moreover, we prove the blow-up in finite time of solution at the supercritical initial energy level (E(0) > 0).

WKB solution 4×4 for electromagnetic waves in a planar magnetically anisotropic inhomogeneous layer

NASA Astrophysics Data System (ADS)

Moiseeva, Natalya Michailovna; Moiseev, Anton Vladimirovich

2018-04-01

In the paper, an oblique incidence of a plane electromagnetic wave on a planar magnetically anisotropic inhomogeneous layer is considered. We consider the case when all the components of the magnetic permeability tensor are non zero and vary with distance from the interface of media. The WKB method gives a matrix 4 × 4 solution for the projections of the electromagnetic wave fields during its propagation. The dependence of the cross-polarized components on the orientation of the anisotropic medium relative to the plane of incidence of the medium is analyzed.

New solitary wave solutions of the time-fractional Cahn-Allen equation via the improved (G'/G)-expansion method

NASA Astrophysics Data System (ADS)

Batool, Fiza; Akram, Ghazala

2018-05-01

An improved (G'/G)-expansion method is proposed for extracting more general solitary wave solutions of the nonlinear fractional Cahn-Allen equation. The temporal fractional derivative is taken in the sense of Jumarie's fractional derivative. The results of this article are generalized and extended version of previously reported solutions.

Fast solution of elliptic partial differential equations using linear combinations of plane waves.

PubMed

Pérez-Jordá, José M

2016-02-01

Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

Rogue waves and lump solutions for a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid mechanics

NASA Astrophysics Data System (ADS)

Wu, Xiao-Yu; Tian, Bo; Chai, Han-Peng; Sun, Yan

2017-08-01

Under investigation in this letter is a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves propagating in a fluid. Employing the Hirota method and symbolic computation, we obtain the lump, breather-wave and rogue-wave solutions under certain constraints. We graphically study the lump waves with the influence of the parameters h1, h3 and h5 which are all the real constants: When h1 increases, amplitude of the lump wave increases, and location of the peak moves; when h3 increases, lump wave’s amplitude decreases, but location of the peak keeps unchanged; when h5 changes, lump wave’s peak location moves, but amplitude keeps unchanged. Breather waves and rogue waves are displayed: Rogue waves emerge when the periods of the breather waves go to the infinity.

Full wave modulator-demodulator amplifier apparatus. [for generating rectified output signal

NASA Technical Reports Server (NTRS)

Black, J. M. (Inventor)

1974-01-01

A full-wave modulator-demodulator apparatus is described including an operational amplifier having a first input terminal coupled to a circuit input terminal, and a second input terminal alternately coupled to the circuit input terminal. A circuit is ground by a switching circuit responsive to a phase reference signal and the operational amplifier is alternately switched between a non-inverting mode and an inverting mode. The switching circuit includes three field-effect transistors operatively associated to provide the desired switching function in response to an alternating reference signal of the same frequency as an AC input signal applied to the circuit input terminal.

Alfvén simple waves

NASA Astrophysics Data System (ADS)

Webb, G. M.; Zank, G. P.; Burrows, R. H.; Ratkiewicz, R. E.

2011-02-01

Multi-dimensional Alfvén simple waves in magnetohydrodynamics (MHD) are investigated using Boillat's formalism. For simple wave solutions, all physical variables (the gas density, pressure, fluid velocity, entropy, and magnetic field induction in the MHD case) depend on a single phase function ϕ, which is a function of the space and time variables. The simple wave ansatz requires that the wave normal and the normal speed of the wave front depend only on the phase function ϕ. This leads to an implicit equation for the phase function and a generalization of the concept of a plane wave. We obtain examples of Alfvén simple waves, based on the right eigenvector solutions for the Alfvén mode. The Alfvén mode solutions have six integrals, namely that the entropy, density, magnetic pressure, and the group velocity (the sum of the Alfvén and fluid velocity) are constant throughout the wave. The eigenequations require that the rate of change of the magnetic induction B with ϕ throughout the wave is perpendicular to both the wave normal n and B. Methods to construct simple wave solutions based on specifying either a solution ansatz for n(ϕ) or B(ϕ) are developed.

Mixed lump-kink and rogue wave-kink solutions for a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation in fluid mechanics

NASA Astrophysics Data System (ADS)

Hu, Cong-Cong; Tian, Bo; Wu, Xiao-Yu; Yuan, Yu-Qiang; Du, Zhong

2018-02-01

Under investigation is a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves in a fluid. Via the Hirota method and symbolic computation, we obtain the mixed lump-kink and mixed rogue wave-kink solutions. Through the mixed lump-kink solutions, we observe three different phenomena between a lump and one kink. For the fusion phenomenon, a lump and a kink are merged with the lump's energy transferring into the kink gradually, until the lump merges into the kink completely. Fission phenomenon displays that a lump separates from a kink. The last phenomenon shows that a lump travels together with a kink with their amplitudes unchanged. In addition, we graphically study the interaction between a rogue wave and a pair of the kinks. It can be observed that the rogue wave arises from one kink and disappears into the other kink. At certain time, the amplitude of the rogue wave reaches the maximum.

Full wave characterization of microstrip open end discontinuities patterned on anisotropic substrates using potential theory

NASA Technical Reports Server (NTRS)

Toncich, S. S.; Collin, R. E.; Bhasin, K. B.

1993-01-01

A technique for a full wave characterization of microstrip open end discontinuities fabricated on uniaxial anisotropic substrates using potential theory is presented. The substrate to be analyzed is enclosed in a cutoff waveguide, with the anisotropic axis aligned perpendicular to the air-dielectric interface. A full description of the sources on the microstrip line is included with edge conditions built in. Extention to other discontinuities is discussed.

Full-wave Nonlinear Inverse Scattering for Acoustic and Electromagnetic Breast Imaging

NASA Astrophysics Data System (ADS)

Haynes, Mark Spencer

Acoustic and electromagnetic full-wave nonlinear inverse scattering techniques are explored in both theory and experiment with the ultimate aim of noninvasively mapping the material properties of the breast. There is evidence that benign and malignant breast tissue have different acoustic and electrical properties and imaging these properties directly could provide higher quality images with better diagnostic certainty. In this dissertation, acoustic and electromagnetic inverse scattering algorithms are first developed and validated in simulation. The forward solvers and optimization cost functions are modified from traditional forms in order to handle the large or lossy imaging scenes present in ultrasonic and microwave breast imaging. An antenna model is then presented, modified, and experimentally validated for microwave S-parameter measurements. Using the antenna model, a new electromagnetic volume integral equation is derived in order to link the material properties of the inverse scattering algorithms to microwave S-parameters measurements allowing direct comparison of model predictions and measurements in the imaging algorithms. This volume integral equation is validated with several experiments and used as the basis of a free-space inverse scattering experiment, where images of the dielectric properties of plastic objects are formed without the use of calibration targets. These efforts are used as the foundation of a solution and formulation for the numerical characterization of a microwave near-field cavity-based breast imaging system. The system is constructed and imaging results of simple targets are given. Finally, the same techniques are used to explore a new self-characterization method for commercial ultrasound probes. The method is used to calibrate an ultrasound inverse scattering experiment and imaging results of simple targets are presented. This work has demonstrated the feasibility of quantitative microwave inverse scattering by way of a self

Global multiresolution models of surface wave propagation: comparing equivalently regularized Born and ray theoretical solutions

NASA Astrophysics Data System (ADS)

Boschi, Lapo

2006-10-01

I invert a large set of teleseismic phase-anomaly observations, to derive tomographic maps of fundamental-mode surface wave phase velocity, first via ray theory, then accounting for finite-frequency effects through scattering theory, in the far-field approximation and neglecting mode coupling. I make use of a multiple-resolution pixel parametrization which, in the assumption of sufficient data coverage, should be adequate to represent strongly oscillatory Fréchet kernels. The parametrization is finer over North America, a region particularly well covered by the data. For each surface-wave mode where phase-anomaly observations are available, I derive a wide spectrum of plausible, differently damped solutions; I then conduct a trade-off analysis, and select as optimal solution model the one associated with the point of maximum curvature on the trade-off curve. I repeat this exercise in both theoretical frameworks, to find that selected scattering and ray theoretical phase-velocity maps are coincident in pattern, and differ only slightly in amplitude.

True amplitude wave equation migration arising from true amplitude one-way wave equations

NASA Astrophysics Data System (ADS)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

Characterization and Mitigation of ICRF Antenna - Plasma Edge Interaction

NASA Astrophysics Data System (ADS)

Hong, Rongjie; Tynan, George; Wukitch, Steve; Lin, Yijun; Terry, Jim; Chilenski, M.; Golfinopoulos, T.; Hubbard, A.; Mumgaard, R. T.; Perkins, R.; Reinke, M. L.; Alcator C-Mod Team

2017-10-01

Recent experiments reveal that RF-induced potentials (VRF) in the SOL and impurity source at the antenna can be reduced to background levels via optimizing the power ratio between the inner and outer current straps, Pcent /Pout . Experiments indicate the antenna impurity source reduction for the field aligned antenna is due to geometrical alignment rather than electrical symmetry. Additional experiments performed without an optimized Pcent /Pout showed that VRF and the associated convection cells do not influence the impurity penetration or core impurity confinement. These results suggest the core impurity contamination associated with ICRF heating is dominated by an increased impurity source rather than a change in impurity transport. Further, the convective cell strength was expected to scale inversely with B-field. The observed poloidal velocity (measure of convective cell strength), however, decreased less than expected. In addition, the measured maximum VRF increased and penetrated farther into the SOL at higher B-field and plasma current. Results also suggest VRF is strongly influenced by the SOL plasma parameters rather than by RF parameters. Work supported by the U.S. DoE, Office of Science, Office of Fusion Energy Sciences, User Facility Alcator C-Mod under DE-FC02-99ER54512 and DE-SC 0010720.

Rigorous asymptotics of traveling-wave solutions to the thin-film equation and Tanner’s law

NASA Astrophysics Data System (ADS)

Giacomelli, Lorenzo; Gnann, Manuel V.; Otto, Felix

2016-09-01

We are interested in traveling-wave solutions to the thin-film equation with zero microscopic contact angle (in the sense of complete wetting without precursor) and inhomogeneous mobility {{h}3}+{λ3-n}{{h}n} , where h, λ, and n\\in ≤ft(\\frac{3}{2},\\frac{7}{3}\\right) denote film height, slip parameter, and mobility exponent, respectively. Existence and uniqueness of these solutions have been established by Maria Chiricotto and the first of the authors in previous work under the assumption of sub-quadratic growth as h\\to ∞ . In the present work we investigate the asymptotics of solutions as h\\searrow 0 (the contact-line region) and h\\to ∞ . As h\\searrow 0 we observe, to leading order, the same asymptotics as for traveling waves or source-type self-similar solutions to the thin-film equation with homogeneous mobility h n and we additionally characterize corrections to this law. Moreover, as h\\to ∞ we identify, to leading order, the logarithmic Tanner profile, i.e. the solution to the corresponding unperturbed problem with λ =0 that determines the apparent macroscopic contact angle. Besides higher-order terms, corrections turn out to affect the asymptotic law as h\\to ∞ only by setting the length scale in the logarithmic Tanner profile. Moreover, we prove that both the correction and the length scale depend smoothly on n. Hence, in line with the common philosophy, the precise modeling of liquid-solid interactions (within our model, the mobility exponent) does not affect the qualitative macroscopic properties of the film.

Fast wave experiments in LAPD: RF sheaths, convective cells and density modifications

NASA Astrophysics Data System (ADS)

Carter, T. A.; van Compernolle, B.; Martin, M.; Gekelman, W.; Pribyl, P.; van Eester, D.; Crombe, K.; Perkins, R.; Lau, C.; Martin, E.; Caughman, J.; Tripathi, S. K. P.; Vincena, S.

2017-10-01

An overview is presented of recent work on ICRF physics at the Large Plasma Device (LAPD) at UCLA. The LAPD has typical plasma parameters ne 1012 -1013 cm-3, Te 1 - 10 eV and B 1000 G. A new high-power ( 150 kW) RF system and fast wave antenna have been developed for LAPD. The source runs at a frequency of 2.4 MHz, corresponding to 1 - 7fci , depending on plasma parameters. Evidence of rectified RF sheaths is seen in large increases ( 10Te) in the plasma potential on field lines connected to the antenna. The rectified potential scales linearly with antenna current. The rectified RF sheaths set up convective cells of local E × B flows, measured indirectly by potential measurements, and measured directly with Mach probes. At high antenna powers substantial modifications of the density profile were observed. The plasma density profile initially exhibits transient low frequency oscillations (10 kHz). The amplitude of the fast wave fields in the core plasma is modulated at the same low frequency, suggesting fast wave coupling is affected by the density rearrangement. Work performed at the Basic Plasma Science Facility, supported jointly by the National Science Foundation and the Department of Energy.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

NASA Technical Reports Server (NTRS)

Shertzer, Janine; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

Wave Impact on a Wall: Comparison of Experiments with Similarity Solutions

NASA Astrophysics Data System (ADS)

Wang, A.; Duncan, J. H.; Lathrop, D. P.

2014-11-01

The impact of a steep water wave on a fixed partially submerged cube is studied with experiments and theory. The temporal evolution of the water surface profile upstream of the front face of the cube in its center plane is measured with a cinematic laser-induced fluorescence technique using frame rates up to 4,500 Hz. For a small range of cube positions, the surface profiles are found to form a nearly circular arc with upward curvature between the front face of the cube and a point just downstream of the wave crest. As the crest approaches the cube, the effective radius of this portion of the profile decreases rapidly. At the same time, the portion of the profile that is upstream of the crest approaches a straight line with a downward slope of about 15°. As the wave impact continues, the circular arc shrinks to zero radius with very high acceleration and a sudden transition to a high-speed vertical jet occurs. This flow singularity is modeled with a power-law scaling in time, which is used to create a time-independent system of equations of motion. The scaled governing equations are solved numerically and the similarly scaled measured free surface shapes, are favorably compared with the solutions. The support of the Office of Naval Research is gratefully acknowledged.

Solitary traveling wave solutions of pressure equation of bubbly liquids with examination for viscosity and heat transfer

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-03-01

In this research, we investigate one of the most popular model in nature and also industrial which is the pressure equation of bubbly liquids with examination for viscosity and heat transfer which has many application in nature and engineering. Understanding the physical meaning of exact and solitary traveling wave solutions for this equation gives the researchers in this field a great clear vision of the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer and also dynamics of contrast agents in the blood flow at ultrasonic researches. To achieve our goal, we apply three different methods which are extended tanh-function method, extended simple equation method and a new auxiliary equation method on this equation. We obtained exact and solitary traveling wave solutions and we also discuss the similarity and difference between these three method and make a comparison between results that we obtained with another results that obtained with the different researchers using different methods. All of these results and discussion explained the fact that our new auxiliary equation method is considered to be the most general, powerful and the most result-oriented. These kinds of solutions and discussion allow for the understanding of the phenomenon and its intrinsic properties as well as the ease of way of application and its applicability to other phenomena.

Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain

NASA Astrophysics Data System (ADS)

Ryo, Ikehata

Uniform energy and L2 decay of solutions for linear wave equations with localized dissipation will be given. In order to derive the L2-decay property of the solution, a useful device whose idea comes from Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) is used. In fact, we shall show that the L2-norm and the total energy of solutions, respectively, decay like O(1/ t) and O(1/ t2) as t→+∞ for a kind of the weighted initial data.

Full Waveform 2.5D Teleseismic Surface Wave Tomography with Application to the Tien Shan

NASA Astrophysics Data System (ADS)

Roecker, S. W.; Priestley, K. F.; Baker, B. I.

2011-12-01

We adapt the 2.5D spectral domain finite difference waveform tomography algorithm of Roecker et al. (2010) to permit the analysis of teleseismically recorded surface waves. The teleseismic body wave technique of generating synthetic waveforms by specifying an analytic solution for a background wavefield in a 1D model and solving for a scattered field excited by this background is equally applicable to surface waves. We use the locked mode approach of Gomberg and Masters (1988) to calculate the background Greens functions at each point of the finite difference (FD) grid. Because of the much greater concentration of energy at the surface, we adopt the cell-based FD operators of Min et al. (2004) to calculate the free surface boundary conditions, and the generalized stretching function of Komatitch and Martin (2007) to improve the absorption in the PML. We use this algorithm to analyze broad band seismograms of events in Sumatra recorded by the MANAS array in the Tien Shan. Our results show that the upper mantle beneath much of the central Tien Shan has shear wavespeeds at least 10% lower than the lithosphere beneath the Tarim basin to the south or the Kazach shield to the north. At the same time, there appears to be a remnant lithospheric lid beneath the Kyrgyz range in the north, an observation consistent with previous receiver function studies in this area.

Controllable parabolic-cylinder optical rogue wave.

PubMed

Zhong, Wei-Ping; Chen, Lang; Belić, Milivoj; Petrović, Nikola

2014-10-01

We demonstrate controllable parabolic-cylinder optical rogue waves in certain inhomogeneous media. An analytical rogue wave solution of the generalized nonlinear Schrödinger equation with spatially modulated coefficients and an external potential in the form of modulated quadratic potential is obtained by the similarity transformation. Numerical simulations are performed for comparison with the analytical solutions and to confirm the stability of the rogue wave solution obtained. These optical rogue waves are built by the products of parabolic-cylinder functions and the basic rogue wave solution of the standard nonlinear Schrödinger equation. Such rogue waves may appear in different forms, as the hump and paw profiles.

Development of full wave code for modeling RF fields in hot non-uniform plasmas

NASA Astrophysics Data System (ADS)

Zhao, Liangji; Svidzinski, Vladimir; Spencer, Andrew; Kim, Jin-Soo

2016-10-01

FAR-TECH, Inc. is developing a full wave RF modeling code to model RF fields in fusion devices and in general plasma applications. As an important component of the code, an adaptive meshless technique is introduced to solve the wave equations, which allows resolving plasma resonances efficiently and adapting to the complexity of antenna geometry and device boundary. The computational points are generated using either a point elimination method or a force balancing method based on the monitor function, which is calculated by solving the cold plasma dispersion equation locally. Another part of the code is the conductivity kernel calculation, used for modeling the nonlocal hot plasma dielectric response. The conductivity kernel is calculated on a coarse grid of test points and then interpolated linearly onto the computational points. All the components of the code are parallelized using MPI and OpenMP libraries to optimize the execution speed and memory. The algorithm and the results of our numerical approach to solving 2-D wave equations in a tokamak geometry will be presented. Work is supported by the U.S. DOE SBIR program.

On the decay of solutions to the 2D Neumann exterior problem for the wave equation

NASA Astrophysics Data System (ADS)

Secchi, Paolo; Shibata, Yoshihiro

We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition and study the asymptotic behavior of the solution for large times. For possible application we are interested to show a decay estimate which does not involve weighted norms of the initial data. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.

Focusing Leaky Waves: A Class of Electromagnetic Localized Waves with Complex Spectra

NASA Astrophysics Data System (ADS)

Fuscaldo, Walter; Comite, Davide; Boesso, Alessandro; Baccarelli, Paolo; Burghignoli, Paolo; Galli, Alessandro

2018-05-01

Localized waves, i.e., the wide class of limited-diffraction, limited-dispersion solutions to the wave equation are generally characterized by real wave numbers. We consider the role played by localized waves with generally complex "leaky" wave numbers. First, the impact of the imaginary part of the wave number (i.e., the leakage constant) on the diffractive (spatial broadening) features of monochromatic localized solutions (i.e., beams) is rigorously evaluated. Then general conditions are derived to show that only a restricted class of spectra (either real or complex) allows for generating a causal localized wave. It turns out that backward leaky waves fall into this category. On this ground, several criteria for the systematic design of wideband radiators, namely, periodic radial waveguides based on backward leaky waves, are established in the framework of leaky-wave theory. An effective design method is proposed to minimize the frequency dispersion of the proposed class of devices and the impact of the "leakage" on the dispersive (temporal broadening) features of polychromatic localized solutions (i.e., pulses) is accounted for. Numerical results corroborate the concept, clearly highlighting the advantages and limitations of the leaky-wave approach for the generation of localized pulses at millimeter-wave frequencies, where energy focusing is in high demand in modern applications.

Full skin quantitative optical coherence elastography achieved by combining vibration and surface acoustic wave methods

NASA Astrophysics Data System (ADS)

Li, Chunhui; Guan, Guangying; Huang, Zhihong; Wang, Ruikang K.; Nabi, Ghulam

2015-03-01

By combining with the phase sensitive optical coherence tomography (PhS-OCT), vibration and surface acoustic wave (SAW) methods have been reported to provide elastography of skin tissue respectively. However, neither of these two methods can provide the elastography in full skin depth in current systems. This paper presents a feasibility study on an optical coherence elastography method which combines both vibration and SAW in order to give the quantitative mechanical properties of skin tissue with full depth range, including epidermis, dermis and subcutaneous fat. Experiments are carried out on layered tissue mimicking phantoms and in vivo human forearm and palm skin. A ring actuator generates vibration while a line actuator were used to excited SAWs. A PhS-OCT system is employed to provide the ultrahigh sensitive measurement of the generated waves. The experimental results demonstrate that by the combination of vibration and SAW method the full skin bulk mechanical properties can be quantitatively measured and further the elastography can be obtained with a sensing depth from ~0mm to ~4mm. This method is promising to apply in clinics where the quantitative elasticity of localized skin diseases is needed to aid the diagnosis and treatment.

Analytical solutions of Landau (1+1)-dimensional hydrodynamics

DOE PAGES

Wong, Cheuk-Yin; Sen, Abhisek; Gerhard, Jochen; ...

2014-12-17

To help guide our intuition, summarize important features, and point out essential elements, we review the analytical solutions of Landau (1+1)-dimensional hydrodynamics and exhibit the full evolution of the dynamics from the very beginning to subsequent times. Special emphasis is placed on the matching and the interplay between the Khalatnikov solution and the Riemann simple wave solution at the earliest times and in the edge regions at later times.

A class of traveling wave solutions for space-time fractional biological population model in mathematical physics

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Batool, Fiza

2017-10-01

The (G'/G)-expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G)-expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.

The effects of the Asselin time filter on numerical solutions to the linearized shallow-water wave equations

NASA Technical Reports Server (NTRS)

Schlesinger, R. E.; Johnson, D. R.; Uccellini, L. W.

1983-01-01

In the present investigation, a one-dimensional linearized analysis is used to determine the effect of Asselin's (1972) time filter on both the computational stability and phase error of numerical solutions for the shallow water wave equations, in cases with diffusion but without rotation. An attempt has been made to establish the approximate optimal values of the filtering parameter nu for each of the 'lagged', Dufort-Frankel, and Crank-Nicholson diffusion schemes, suppressing the computational wave mode without materially altering the physical wave mode. It is determined that in the presence of diffusion, the optimum filter length depends on whether waves are undergoing significant propagation. When moderate propagation is present, with or without diffusion, the Asselin filter has little effect on the spatial phase lag of the physical mode for the leapfrog advection scheme of the three diffusion schemes considered.

ORNL diagnostic and modeling development for LAPD ICRF experiments

NASA Astrophysics Data System (ADS)

Isler, R. C.; Caughman, J. B. O.; Lau, C.; Martin, E. H.; Perkins, R. J.; Compernolle, B. Van; Vincena, S.; Tripathi, S. K. P.; Gekelman, W.

2017-10-01

PPPL, UCLA, and ORNL scientists have recently collaborated on a three week ICRF campaign at the upgraded LAPD device to study near field-plasma interactions associated with a single strap antenna driven at 2.38 MHz with 100 kW of RF power. This poster highlights ORNL involvement through implementation of the following diagnostics: an optical emission probe to measure neutral density, a retarding field energy analyzer to measure fast ions, phase locked imaging to measure line integrated RF-driven optical emission fluctuations, and an RF compensated triple Langmuir probe to measure density and temperature. To interpret the results of the experimental campaign a 3D cold plasma finite element model with realistic antenna and vacuum vessel geometry was developed in COMSOL. A summary of these results will be discussed. Highlights include a proof of principle localized and spatially resolved measurement of the neutral density, a strong increase in RF-driven optical emission fluctuations directly in front of the RF antenna strap, a shift in fast ion energies near the plasma edge, and qualitative agreement between the COMSOL cold plasma model with the various diagnostics. Funded by the DOE OFES (DE-AC05-00OR22725, DE-AC02-09CH11466, and DE-FC02-07ER54918) and the Univ. of California (12-LR-237124).

Lorentz-Abraham-Dirac versus Landau-Lifshitz radiation friction force in the ultrarelativistic electron interaction with electromagnetic wave (exact solutions).

PubMed

Bulanov, Sergei V; Esirkepov, Timur Zh; Kando, Masaki; Koga, James K; Bulanov, Stepan S

2011-11-01

When the parameters of electron-extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crucially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possesses unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency. For this, a class of the exact solutions to the nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.

Evaluation of truncation error and adaptive grid generation for the transonic full potential flow calculations

NASA Technical Reports Server (NTRS)

Nakamura, S.

1983-01-01

The effects of truncation error on the numerical solution of transonic flows using the full potential equation are studied. The effects of adapting grid point distributions to various solution aspects including shock waves is also discussed. A conclusion is that a rapid change of grid spacing is damaging to the accuracy of the flow solution. Therefore, in a solution adaptive grid application an optimal grid is obtained as a tradeoff between the amount of grid refinement and the rate of grid stretching.

RF sheaths for arbitrary B field angles

NASA Astrophysics Data System (ADS)

D'Ippolito, Daniel; Myra, James

2014-10-01

RF sheaths occur in tokamaks when ICRF waves encounter conducting boundaries and accelerate electrons out of the plasma. Sheath effects reduce the efficiency of ICRF heating, cause RF-specific impurity influxes from the edge plasma, and increase the plasma-facing component damage. The rf sheath potential is sensitive to the angle between the B field and the wall, the ion mobility and the ion magnetization. Here, we obtain a numerical solution of the non-neutral rf sheath and magnetic pre-sheath equations (for arbitrary values of these parameters) and attempt to infer the parametric dependences of the Child-Langmuir law. This extends previous work on the magnetized, immobile ion regime. An important question is how the rf sheath voltage distributes itself between sheath and pre-sheath for various B field angles. This will show how generally previous estimates of the rf sheath voltage and capacitance were reasonable, and to improve the RF sheath BC. Work supported by US DOE grants DE-FC02-05ER54823 and DE-FG02-97ER54392.

Analytical solution of the problem of a shock wave in the collapsing gas in Lagrangian coordinates

NASA Astrophysics Data System (ADS)

Kuropatenko, V. F.; Shestakovskaya, E. S.

2016-10-01

It is proposed the exact solution of the problem of a convergent shock wave and gas dynamic compression in a spherical vessel with an impermeable wall in Lagrangian coordinates. At the initial time the speed of cold ideal gas is equal to zero, and a negative velocity is set on boundary of the sphere. When t > t0 the shock wave spreads from this point into the gas. The boundary of the sphere will move under the certain law correlated with the motion of the shock wave. The trajectories of the gas particles in Lagrangian coordinates are straight lines. The equations determining the structure of the gas flow between the shock front and gas border have been found as a function of time and Lagrangian coordinate. The dependence of the entropy on the velocity of the shock wave has been found too. For Lagrangian coordinates the problem is first solved. It is fundamentally different from previously known formulations of the problem of the self-convergence of the self-similar shock wave to the center of symmetry and its reflection from the center, which was built up for the infinite area in Euler coordinates.

Rapid decay of nonlinear whistler waves in two dimensions: Full particle simulation

NASA Astrophysics Data System (ADS)

Umeda, Takayuki; Saito, Shinji; Nariyuki, Yasuhiro

2017-05-01

The decay of a nonlinear, short-wavelength, and monochromatic electromagnetic whistler wave is investigated by utilizing a two-dimensional (2D) fully relativistic electromagnetic particle-in-cell code. The simulation is performed under a low-beta condition in which the plasma pressure is much lower than the magnetic pressure. It has been shown that the nonlinear (large-amplitude) parent whistler wave decays through the parametric instability in a one-dimensional (1D) system. The present study shows that there is another channel for the decay of the parent whistler wave in 2D, which is much faster than in the timescale of the parametric decay in 1D. The parent whistler wave decays into two sideband daughter whistlers propagating obliquely with respect to the ambient magnetic field with a frequency close to the parent wave and two quasi-perpendicular electromagnetic modes with a frequency close to zero via a 2D decay instability. The two sideband daughter oblique whistlers also enhance a nonlinear longitudinal electrostatic wave via a three-wave interaction as a secondary process.

Radio structure effects on the optical and radio representations of the ICRF

NASA Astrophysics Data System (ADS)

Andrei, A. H.; da Silva Neto, D. N.; Assafin, M.; Vieira Martins, R.

Silva Neto et al. (2002) show that comparing the ICRF Ext.1 sources standard radio position (Ma et al. 1998) against their optical counterpart position (Zacharias et al. 1999, Monet et al., 1998), a systematic pattern appears, which depends on the radio structure index (Fey and Charlot, 2000). The optical to radio offsets produce a distribution suggestive of a coincidence of the optical and radio centroids worse for the radio extended than for the radio compact sources. On average, the coincidence between the optical and radio centroids is found 7.9±1.1 mas smaller for the compact than for the extended sources. Such an effect is reasonably large, and certainly much too large to be due to errors on the VLBI radio position. On the other hand, it is too small to be accounted to the errors on the optical position, which moreover should be independent from the radio stucture. Thus, other than a true pattern of centroids non-coincidence, the remaining explanation is of a hazard result. This paper summarizes the several statistical tests used to discard the hazard explanation.

Fingering patterns in Hele-Shaw flows are density shock wave solutions of dispersionless KdV hierarchy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Teodorescu, Razvan; Lee, S - Y; Wiegmann, P

We investigate the hydrodynamics of a Hele-Shaw flow as the free boundary evolves from smooth initial conditions into a generic cusp singularity (of local geometry type x{sup 3} {approx} y{sup 2}), and then into a density shock wave. This novel solution preserves the integrability of the dynamics and, unlike all the weak solutions proposed previously, is not underdetermined. The evolution of the shock is such that the net vorticity remains zero, as before the critical time, and the shock can be interpreted as a singular line distribution of fluid deficit.

On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks

NASA Astrophysics Data System (ADS)

Santucci, F.; Santini, P. M.

2016-10-01

We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.

Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves

USGS Publications Warehouse

Xia, J.; Miller, R.D.; Park, C.B.

1999-01-01

The shear-wave (S-wave) velocity of near-surface materials (soil, rocks, pavement) and its effect on seismic-wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Rayleigh-wave phase velocity of a layered-earth model is a function of frequency and four groups of earth properties: P-wave velocity, S-wave velocity, density, and thickness of layers. Analysis of the Jacobian matrix provides a measure of dispersion-curve sensitivity to earth properties. S-wave velocities are the dominant influence on a dispersion curve in a high-frequency range (>5 Hz) followed by layer thickness. An iterative solution technique to the weighted equation proved very effective in the high-frequency range when using the Levenberg-Marquardt and singular-value decomposition techniques. Convergence of the weighted solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method. Synthetic examples demonstrated calculation efficiency and stability of inverse procedures. We verify our method using borehole S-wave velocity measurements.Iterative solutions to the weighted equation by the Levenberg-Marquardt and singular-value decomposition techniques are derived to estimate near-surface shear-wave velocity. Synthetic and real examples demonstrate the calculation efficiency and stability of the inverse procedure. The inverse results of the real example are verified by borehole S-wave velocity measurements.

Rapid Regional Centroid Solutions

NASA Astrophysics Data System (ADS)

Wei, S.; Zhan, Z.; Luo, Y.; Ni, S.; Chen, Y.; Helmberger, D. V.

2009-12-01

The 2008 Wells Nevada Earthquake was recorded by 164 broadband USArray stations within a distance of 550km (5 degrees) with all azimuths uniformly sampled. To establish the source parameters, we applied the Cut and Paste (CAP) code to all the stations to obtain a mechanism (strike/dip/rake=35/41/-85) at a depth of 9km and Mw=5.9. Surface wave shifts range from -8s to 8s which are in good agreement with ambient seismic noise (ASN) predictions. Here we use this data set to test the accuracy of the number of stations needed to obtain adequate solutions (position of the compressional and tension axis) for mechanism. The stations were chosen at random where combinations of Pnl and surface waves were used to establish mechanism and depth. If the event is bracketed by two stations, we obtain an accurate magnitude with good solutions about 80% of the trials. Complete solutions from four stations or Pnl from 10 stations prove reliable in nearly all situations. We also explore the use of this dataset in locating the event using a combination of surface wave travel times and/or the full waveform inversion (CAPloc) that uses the CAP shifts to refine locations. If the mechanism is known (fixed) only a few stations is needed to locate an event to within 5km if date is available at less than 150km. In contrast, surface wave travel times (calibrated to within one second) produce amazing accurate locations with only 6 stations reasonably distributed. It appears this approach is easily automated as suggested by Scrivner and Helmberger (1995) who discussed travel times of Pnl and surface waves and the evolving of source accuracy as the various phases arrive.

Lorentz-Abraham-Dirac versus Landau-Lifshitz radiation friction force in the ultrarelativistic electron interaction with electromagnetic wave (exact solutions)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bulanov, Sergei V.; Esirkepov, Timur Zh.; Kando, Masaki

2011-11-15

When the parameters of electron-extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crucially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possesses unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency. For this, a class of the exact solutions to themore » nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.« less

A post-processing method to simulate the generalized RF sheath boundary condition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Myra, James R.; Kohno, Haruhiko

For applications of ICRF power in fusion devices, control of RF sheath interactions is of great importance. A sheath boundary condition (SBC) was previously developed to provide an effective surface impedance for the interaction of the RF sheath with the waves. The SBC enables the surface power flux and rectified potential energy available for sputtering to be calculated. For legacy codes which cannot easily implement the SBC, or to speed convergence in codes which do implement it, we consider here an approximate method to simulate SBCs by post-processing results obtained using other, e.g. conducting wall, boundary conditions. The basic approximationmore » is that the modifications resulting from the generalized SBC are driven by a fixed incoming wave which could be either a fast wave or a slow wave. Finally, the method is illustrated in slab geometry and compared with exact numerical solutions; it is shown to work very well.« less

A post-processing method to simulate the generalized RF sheath boundary condition

DOE PAGES

Myra, James R.; Kohno, Haruhiko

2017-10-23

For applications of ICRF power in fusion devices, control of RF sheath interactions is of great importance. A sheath boundary condition (SBC) was previously developed to provide an effective surface impedance for the interaction of the RF sheath with the waves. The SBC enables the surface power flux and rectified potential energy available for sputtering to be calculated. For legacy codes which cannot easily implement the SBC, or to speed convergence in codes which do implement it, we consider here an approximate method to simulate SBCs by post-processing results obtained using other, e.g. conducting wall, boundary conditions. The basic approximationmore » is that the modifications resulting from the generalized SBC are driven by a fixed incoming wave which could be either a fast wave or a slow wave. Finally, the method is illustrated in slab geometry and compared with exact numerical solutions; it is shown to work very well.« less

Analysis and Design of a Novel W-band SPST Switch by Employing Full-Wave EM Simulator

NASA Astrophysics Data System (ADS)

Xu, Zhengbin; Guo, Jian; Qian, Cheng; Dou, Wenbin

2011-12-01

In this paper, a W-band single pole single throw (SPST) switch based on a novel PIN diode model is presented. The PIN diode is modeled using a full-wave electromagnetic (EM) simulator and its parasitic parameters under both forward and reverse bias states are described by a T-network. By this approach, the measurement-based model, which is usually a must for high performance switch design, is no longer necessary. A compensation structure is optimized to obtain a high isolation of the switch. Accordingly, a W-band SPST switch is designed using a full wave EM simulator. Measurement results agree very well with simulated ones. Our measurements show that the developed switch has less than 1.5 dB insertion loss under the `on' state from 88 GHz to 98 GHz. Isolation greater than 30 dB over 2 GHz bandwidth and greater than 20 dB over 5 GHz bandwidth can be achieved at the center frequency of 94 GHz under the `off' state.

An exact solution to the relativistic equation of motion of a charged particle driven by a linearly polarized electromagnetic wave

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1988-01-01

An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..

Improved distorted wave theory with the localized virial conditions

NASA Astrophysics Data System (ADS)

Hahn, Y. K.; Zerrad, E.

2009-12-01

The distorted wave theory is operationally improved to treat the full collision amplitude, such that the corrections to the distorted wave Born amplitude can be systematically calculated. The localized virial conditions provide the tools necessary to test the quality of successive approximations at each stage and to optimize the solution. The details of the theoretical procedure are explained in concrete terms using a collisional ionization model and variational trial functions. For the first time, adjustable parameters associated with an approximate scattering solution can be fully determined by the theory. A small number of linear parameters are introduced to examine the convergence property and the effectiveness of the new approach.

Analytical model for vibration prediction of two parallel tunnels in a full-space

NASA Astrophysics Data System (ADS)

He, Chao; Zhou, Shunhua; Guo, Peijun; Di, Honggui; Zhang, Xiaohui

2018-06-01

This paper presents a three-dimensional analytical model for the prediction of ground vibrations from two parallel tunnels embedded in a full-space. The two tunnels are modelled as cylindrical shells of infinite length, and the surrounding soil is modelled as a full-space with two cylindrical cavities. A virtual interface is introduced to divide the soil into the right layer and the left layer. By transforming the cylindrical waves into the plane waves, the solution of wave propagation in the full-space with two cylindrical cavities is obtained. The transformations from the plane waves to cylindrical waves are then used to satisfy the boundary conditions on the tunnel-soil interfaces. The proposed model provides a highly efficient tool to predict the ground vibration induced by the underground railway, which accounts for the dynamic interaction between neighbouring tunnels. Analysis of the vibration fields produced over a range of frequencies and soil properties is conducted. When the distance between the two tunnels is smaller than three times the tunnel diameter, the interaction between neighbouring tunnels is highly significant, at times in the order of 20 dB. It is necessary to consider the interaction between neighbouring tunnels for the prediction of ground vibrations induced underground railways.

Periodic waves in fiber Bragg gratings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chow, K. W.; Merhasin, Ilya M.; Malomed, Boris A.

2008-02-15

We construct two families of exact periodic solutions to the standard model of fiber Bragg grating (FBG) with Kerr nonlinearity. The solutions are named ''sn'' and ''cn'' waves, according to the elliptic functions used in their analytical representation. The sn wave exists only inside the FBG's spectral bandgap, while waves of the cn type may only exist at negative frequencies ({omega}<0), both inside and outside the bandgap. In the long-wave limit, the sn and cn families recover, respectively, the ordinary gap solitons, and (unstable) antidark and dark solitons. Stability of the periodic solutions is checked by direct numerical simulations and,more » in the case of the sn family, also through the calculation of instability growth rates for small perturbations. Although, rigorously speaking, all periodic solutions are unstable, a subfamily of practically stable sn waves, with a sufficiently large spatial period and {omega}>0, is identified. However, the sn waves with {omega}<0, as well as all cn solutions, are strongly unstable.« less

Prediction of the bottomonium D-wave spectrum from full lattice QCD.

PubMed

Daldrop, J O; Davies, C T H; Dowdall, R J

2012-03-09

We calculate the full spectrum of D-wave states in the Υ system in lattice QCD for the first time, by using an improved version of nonrelativistic QCD on coarse and fine "second-generation" gluon field configurations from the MILC Collaboration that include the effect of up, down, strange, and charm quarks in the sea. By taking the 2S-1S splitting to set the lattice spacing, we determine the (3)D2-1S splitting to 2.3% and find agreement with experiment. Our prediction of the fine structure relative to the (3)D2 gives the (3)D3 at 10.181(5) GeV and the (3)D1 at 10.147(6) GeV. We also discuss the overlap of (3)D1 operators with (3)S1 states.

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Efficient calculation of full waveform time domain inversion for electromagnetic problem using fictitious wave domain method and cascade decimation decomposition

NASA Astrophysics Data System (ADS)

Imamura, N.; Schultz, A.

2016-12-01

Recently, a full waveform time domain inverse solution has been developed for the magnetotelluric (MT) and controlled-source electromagnetic (CSEM) methods. The ultimate goal of this approach is to obtain a computationally tractable direct waveform joint inversion to solve simultaneously for source fields and earth conductivity structure in three and four dimensions. This is desirable on several grounds, including the improved spatial resolving power expected from use of a multitude of source illuminations, the ability to operate in areas of high levels of source signal spatial complexity, and non-stationarity. This goal would not be obtainable if one were to adopt the pure time domain solution for the inverse problem. This is particularly true for the case of MT surveys, since an enormous number of degrees of freedom are required to represent the observed MT waveforms across a large frequency bandwidth. This means that for the forward simulation, the smallest time steps should be finer than that required to represent the highest frequency, while the number of time steps should also cover the lowest frequency. This leads to a sensitivity matrix that is computationally burdensome to solve a model update. We have implemented a code that addresses this situation through the use of cascade decimation decomposition to reduce the size of the sensitivity matrix substantially, through quasi-equivalent time domain decomposition. We also use a fictitious wave domain method to speed up computation time of the forward simulation in the time domain. By combining these refinements, we have developed a full waveform joint source field/earth conductivity inverse modeling method. We found that cascade decimation speeds computations of the sensitivity matrices dramatically, keeping the solution close to that of the undecimated case. For example, for a model discretized into 2.6x105 cells, we obtain model updates in less than 1 hour on a 4U rack-mounted workgroup Linux server, which

Higher-order rational solitons and rogue-like wave solutions of the (2 + 1)-dimensional nonlinear fluid mechanics equations

NASA Astrophysics Data System (ADS)

Wen, Xiao-Yong; Yan, Zhenya

2017-02-01

The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N - 1) -fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a ≠ 0) into higher-order rational solitons (a = 0) in (x, t)-space with y = const . These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.

Dynamics of lumps and dark-dark solitons in the multi-component long-wave-short-wave resonance interaction system.

PubMed

Rao, Jiguang; Porsezian, Kuppuswamy; He, Jingsong; Kanna, Thambithurai

2018-01-01

General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave-short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviours of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission. It is shown that the fundamental (simplest) semi-rational solutions can exhibit fission of a dark soliton into a lump and a dark soliton or fusion of one lump and one dark soliton into a dark soliton. The non-fundamental semi-rational solutions are further classified into three subclasses: higher-order, multi- and mixed-type semi-rational solutions. The higher-order semi-rational solutions show the process of annihilation (production) of two or more lumps into (from) one dark soliton. The multi-semi-rational solutions describe N ( N ≥2) lumps annihilating into or producing from N -dark solitons. The mixed-type semi-rational solutions are a hybrid of higher-order semi-rational solutions and multi-semi-rational solutions. For the mixed-type semi-rational solutions, we demonstrate an interesting dynamical behaviour that is characterized by partial suppression or creation of lumps from the dark solitons.

Dynamics of lumps and dark-dark solitons in the multi-component long-wave-short-wave resonance interaction system

NASA Astrophysics Data System (ADS)

Rao, Jiguang; Porsezian, Kuppuswamy; He, Jingsong; Kanna, Thambithurai

2018-01-01

General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave-short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviours of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission. It is shown that the fundamental (simplest) semi-rational solutions can exhibit fission of a dark soliton into a lump and a dark soliton or fusion of one lump and one dark soliton into a dark soliton. The non-fundamental semi-rational solutions are further classified into three subclasses: higher-order, multi- and mixed-type semi-rational solutions. The higher-order semi-rational solutions show the process of annihilation (production) of two or more lumps into (from) one dark soliton. The multi-semi-rational solutions describe N(N≥2) lumps annihilating into or producing from N-dark solitons. The mixed-type semi-rational solutions are a hybrid of higher-order semi-rational solutions and multi-semi-rational solutions. For the mixed-type semi-rational solutions, we demonstrate an interesting dynamical behaviour that is characterized by partial suppression or creation of lumps from the dark solitons.

Optimal solution of full fuzzy transportation problems using total integral ranking

NASA Astrophysics Data System (ADS)

Sam’an, M.; Farikhin; Hariyanto, S.; Surarso, B.

2018-03-01

Full fuzzy transportation problem (FFTP) is a transportation problem where transport costs, demand, supply and decision variables are expressed in form of fuzzy numbers. To solve fuzzy transportation problem, fuzzy number parameter must be converted to a crisp number called defuzzyfication method. In this new total integral ranking method with fuzzy numbers from conversion of trapezoidal fuzzy numbers to hexagonal fuzzy numbers obtained result of consistency defuzzyfication on symmetrical fuzzy hexagonal and non symmetrical type 2 numbers with fuzzy triangular numbers. To calculate of optimum solution FTP used fuzzy transportation algorithm with least cost method. From this optimum solution, it is found that use of fuzzy number form total integral ranking with index of optimism gives different optimum value. In addition, total integral ranking value using hexagonal fuzzy numbers has an optimal value better than the total integral ranking value using trapezoidal fuzzy numbers.

Solution of steady and unsteady transonic-vortex flows using Euler and full-potential equations

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Chuang, Andrew H.; Hu, Hong

1989-01-01

Two methods are presented for inviscid transonic flows: unsteady Euler equations in a rotating frame of reference for transonic-vortex flows and integral solution of full-potential equation with and without embedded Euler domains for transonic airfoil flows. The computational results covered: steady and unsteady conical vortex flows; 3-D steady transonic vortex flow; and transonic airfoil flows. The results are in good agreement with other computational results and experimental data. The rotating frame of reference solution is potentially efficient as compared with the space fixed reference formulation with dynamic gridding. The integral equation solution with embedded Euler domain is computationally efficient and as accurate as the Euler equations.

Full-duplex bidirectional transmission of 10-Gb/s millimeter-wave QPSK signal in E-band optical wireless link.

PubMed

Fang, Yuan; Yu, Jianjun; Chi, Nan; Xiao, Jiangnan

2014-01-27

We experimentally demonstrated full-duplex bidirectional transmission of 10-Gb/s millimeter-wave (mm-wave) quadrature phase shift keying (QPSK) signal in E-band (71-76 GHz and 81-86 GHz) optical wireless link. Single-mode fibers (SMF) are connected at both sides of the antenna for uplink and downlink which realize 40-km SMF and 2-m wireless link for bidirectional transmission simultaneously. We utilized multi-level modulation format and coherent detection in such E-band optical wireless link for the first time. Mm-wave QPSK signal is generated by photonic technique to increase spectrum efficiency and received signal is coherently detected to improve receiver sensitivity. After the coherent detection, digital signal processing is utilized to compensate impairments of devices and transmission link.

Spherical shock waves in general relativity

NASA Astrophysics Data System (ADS)

Nutku, Y.

1991-11-01

We present the metric appropriate to a spherical shock wave in the framework of general relativity. This is a Petrov type-N vacuum solution of the Einstein field equations where the metric is continuous across the shock and the Riemann tensor suffers a step-function discontinuity. Spherical gravitational waves are described by type-N Robinson-Trautman metrics. However, for shock waves the Robinson-Trautman solutions are unacceptable because the metric becomes discontinuous in the Robinson-Trautman coordinate system. Other coordinate systems that have so far been introduced for describing Robinson-Trautman solutions also suffer from the same defect. We shall present the C0-form of the metric appropriate to spherical shock waves using Penrose's approach of identification with warp. Further extensions of Penrose's method yield accelerating, as well as coupled electromagnetic-gravitational shock-wave solutions.

A phase space approach to wave propagation with dispersion.

PubMed

Ben-Benjamin, Jonathan S; Cohen, Leon; Loughlin, Patrick J

2015-08-01

A phase space approximation method for linear dispersive wave propagation with arbitrary initial conditions is developed. The results expand on a previous approximation in terms of the Wigner distribution of a single mode. In contrast to this previously considered single-mode case, the approximation presented here is for the full wave and is obtained by a different approach. This solution requires one to obtain (i) the initial modal functions from the given initial wave, and (ii) the initial cross-Wigner distribution between different modal functions. The full wave is the sum of modal functions. The approximation is obtained for general linear wave equations by transforming the equations to phase space, and then solving in the new domain. It is shown that each modal function of the wave satisfies a Schrödinger-type equation where the equivalent "Hamiltonian" operator is the dispersion relation corresponding to the mode and where the wavenumber is replaced by the wavenumber operator. Application to the beam equation is considered to illustrate the approach.

CMS-Wave

DTIC Science & Technology

2014-10-27

a phase-averaged spectral wind-wave generation and transformation model and its interface in the Surface-water Modeling System (SMS). Ambrose...applications of the Boussinesq (BOUSS-2D) wave model that provides more rigorous calculations for design and performance optimization of integrated...navigation systems . Together these wave models provide reliable predictions on regional and local spatial domains and cost-effective engineering solutions

Wave turbulence

NASA Astrophysics Data System (ADS)

Nazarenko, Sergey

2015-07-01

Wave turbulence is the statistical mechanics of random waves with a broadband spectrum interacting via non-linearity. To understand its difference from non-random well-tuned coherent waves, one could compare the sound of thunder to a piece of classical music. Wave turbulence is surprisingly common and important in a great variety of physical settings, starting with the most familiar ocean waves to waves at quantum scales or to much longer waves in astrophysics. We will provide a basic overview of the wave turbulence ideas, approaches and main results emphasising the physics of the phenomena and using qualitative descriptions avoiding, whenever possible, involved mathematical derivations. In particular, dimensional analysis will be used for obtaining the key scaling solutions in wave turbulence - Kolmogorov-Zakharov (KZ) spectra.

Colliding impulsive gravitational waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nutku, Y.; Halil, M.

1977-11-28

We formulate the problem of colliding plane gravitational waves with two polarizations as the harmonic mappings of Riemannian manifolds and construct an exact solution of the vacuum Einstein field equations describing the interaction of colliding impulsive gravitational waves which in the limit of collinear polarization reduces to the solution of Khan and Penrose.

Use of .sup.3 He.sup.30 + ICRF minority heating to simulate alpha particle heating

DOEpatents

Post, Jr., Douglass E.; Hwang, David Q.; Hovey, Jane

1986-04-22

Neutron activation due to high levels of neutron production in a first heated deuterium-tritium plasma is substantially reduced by using Ion Cyclotron Resonance Frequency (ICRF) heating of energetic .sup.3 He.sup.++ ions in a second deuterium-.sup.3 He.sup.++ plasma which exhibit an energy distribution and density similar to that of alpha particles in fusion reactor experiments to simulate fusion alpha particle heating in the first plasma. The majority of the fast .sup.3 He.sup.++ ions and their slowing down spectrum can be studied using either a modulated hydrogen beam source for producing excited states of He.sup.+ in combination with spectrometers or double charge exchange with a high energy neutral lithium beam and charged particle detectors at the plasma edge. The maintenance problems thus associated with neutron activation are substantially reduced permitting energetic alpha particle behavior to be studied in near term large fusion experiments.

Mathieu Progressive Waves

NASA Astrophysics Data System (ADS)

Andrei, B. Utkin

2011-10-01

A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal curvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.

Evidence of Non-Coincidence between Radio and Optical Positions of ICRF Sources.

NASA Astrophysics Data System (ADS)

Andrei, A. H.; da Silva, D. N.; Assafin, M.; Vieira Martins, R.

2003-11-01

Silva Neto et al. (SNAAVM: 2002) show that comparing the ICRF Ext1 sources standard radio position (Ma et al., 1998) against their optical counterpart position(ZZHJVW: Zacharias et al., 1999; USNO A2.0: Monet et al., 1998), a systematic pattern appears, which depends on the radio structure index (Fey and Charlot, 2000). The optical to radio offsets produce a distribution suggestive of a coincidence of the optical and radio centroids worse for the radio extended than for the radio compact sources. On average, the coincidence between the optical and radio centroids is found 7.9 +/- 1.1 mas smaller for the compact than for the extended sources. Such an effect is reasonably large, and certainly much too large to be due to errors on the VLBI radio position. On the other hand, it is too small to be accounted to the errors on the optical position, which moreover should be independent from the radio structure. Thus, other than a true pattern of centroids non-coincidence, the remaining explanation is of a hazard result. This paper summarizes the several statistical tests used to discard the hazard explanation.

An efficient flexible-order model for 3D nonlinear water waves

NASA Astrophysics Data System (ADS)

Engsig-Karup, A. P.; Bingham, H. B.; Lindberg, O.

2009-04-01

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.

Repetitive extracorporeal shock wave applications are superior in inducing angiogenesis after full thickness burn compared to single application.

PubMed

Goertz, O; von der Lohe, L; Lauer, H; Khosrawipour, T; Ring, A; Daigeler, A; Lehnhardt, M; Kolbenschlag, J

2014-11-01

Burn wounds remain a challenge due to subsequent wound infection and septicemia, which can be prevented by acceleration of wound healing. The aim of the study was to analyze microcirculation and leukocyte endothelium interaction with particular focus on angiogenesis after full-thickness burn using three different repetitions of low energy shock waves. Full-thickness burns were inflicted to the ears of hairless mice (n=44; area: 1.6±0.05 mm2 (mean±SEM)). Mice were randomized into four groups: the control group received a burn injury but no shock waves; group A received ESWA (0.03 mJ/mm2) on day one after burn injury; group B received shock waves on day one and day three after burn injury; group C ESWA on day one, three and seven after burn injury. Intravital fluorescent microscopy was used to assess microcirculatory parameters, angiogenesis and leukocyte interaction. Values were obtained before burn (baseline value) immediately after and on days 1, 3, 7 and 12 after burn. Shock-wave treated groups showed significantly accelerated angiogenesis compared to the control group. The non-perfused area (NPA) is regarded as a parameter for angiogenesis and showed the following data on day 12 2.7±0.4% (group A, p=0.001), 1.4±0.5% (group B, p<0.001), 1.0±0.3% (group C, p<0.001), 6.1±0.9% (control group). Edema formation is positively correlated with the number of shock wave applications: day 12: group A: 173.2±9.8%, group B: 184.2±6.6%, group C: 201.1±6.9%, p=0.009 vs. control: 162.3±8.7% (all data: mean±SEM). According to our data shock waves positively impact the wound healing process following burn injury. Angiogenesis showed significantly improved activity after shock wave application. In all three treatment groups angiogenesis was higher compared to the control group. Within the ESWA groups, double applications showed better results than single application and three applications showed better results than single or double applications. Copyright © 2014

Spherical shock waves in general relativity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nutku, Y.

1991-11-15

We present the metric appropriate to a spherical shock wave in the framework of general relativity. This is a Petrov type-{ital N} vacuum solution of the Einstein field equations where the metric is continuous across the shock and the Riemann tensor suffers a step-function discontinuity. Spherical gravitational waves are described by type-{ital N} Robinson-Trautman metrics. However, for shock waves the Robinson-Trautman solutions are unacceptable because the metric becomes discontinuous in the Robinson-Trautman coordinate system. Other coordinate systems that have so far been introduced for describing Robinson-Trautman solutions also suffer from the same defect. We shall present the {ital C}{sup 0}-formmore » of the metric appropriate to spherical shock waves using Penrose's approach of identification with warp. Further extensions of Penrose's method yield accelerating, as well as coupled electromagnetic-gravitational shock-wave solutions.« less

Wave equations in conformal gravity

NASA Astrophysics Data System (ADS)

Du, Juan-Juan; Wang, Xue-Jing; He, You-Biao; Yang, Si-Jiang; Li, Zhong-Heng

2018-05-01

We study the wave equation governing massless fields of all spins (s = 0, 1 2, 1, 3 2 and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes.

Spatiotemporal optical dark X solitary waves.

PubMed

Baronio, Fabio; Chen, Shihua; Onorato, Miguel; Trillo, Stefano; Wabnitz, Stefan; Kodama, Yuji

2016-12-01

We introduce spatiotemporal optical dark X solitary waves of the (2+1)D hyperbolic nonlinear Schrödinger equation (NLSE), which rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between the NLSE and a well-known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary waves may propagate for long distances (tens of nonlinear lengths) before they eventually break up, owing to the modulation instability of the continuous wave background. This finding opens a novel path for the excitation and control of X solitary waves in nonlinear optics.

PML solution of longitudinal wave propagation in heterogeneous media

NASA Astrophysics Data System (ADS)

Farzanian, M.; Arbabi, Freydoon; Pak, Ronald

2016-06-01

This paper describes the development of a model for unbounded heterogeneous domains with radiation damping produced by an unphysical wave absorbing layer. The Perfectly Matched Layer (PML) approach is used along with a displacement-based finite element. The heterogeneous model is validated using the closed-form solution of a benchmark problem: a free rod with two-part modulus subjected to a specified time history. Both elastically supported and unsupported semi-infinite rods with different degrees of inhomogeneity and loading are considered. Numerical results illustrate the effects of inhomogeneity on the response and are compared with those for equivalent homogeneous domains. The effects of characteristic features of the inhomogeneous problem, presence of local maxima and cut-off frequency are determined. A degenerate case of a homogeneous semi-infinite rod on elastic foundations is produced by tending the magnitude of the foundation stiffness to zero. The response of the latter is compared with that of a free rod. The importance of proper selection of the PML parameters to highly accurate and efficient results is demonstrated by example problems.

Rational Solutions and Lump Solutions of the Potential YTSF Equation

NASA Astrophysics Data System (ADS)

Sun, Hong-Qian; Chen, Ai-Hua

2017-07-01

By using of the bilinear form, rational solutions and lump solutions of the potential Yu-Toda-Sasa-Fukuyama (YTSF) equation are derived. Dynamics of the fundamental lump solution, n1-order lump solutions, and N-lump solutions are studied for some special cases. We also find some interaction behaviours of solitary waves and one lump of rational solutions.

New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.

Shape optimization of solid-air porous phononic crystal slabs with widest full 3D bandgap for in-plane acoustic waves

NASA Astrophysics Data System (ADS)

D'Alessandro, Luca; Bahr, Bichoy; Daniel, Luca; Weinstein, Dana; Ardito, Raffaele

2017-09-01

The use of Phononic Crystals (PnCs) as smart materials in structures and microstructures is growing due to their tunable dynamical properties and to the wide range of possible applications. PnCs are periodic structures that exhibit elastic wave scattering for a certain band of frequencies (called bandgap), depending on the geometric and material properties of the fundamental unit cell of the crystal. PnCs slabs can be represented by plane-extruded structures composed of a single material with periodic perforations. Such a configuration is very interesting, especially in Micro Electro-Mechanical Systems industry, due to the easy fabrication procedure. A lot of topologies can be found in the literature for PnCs with square-symmetric unit cell that exhibit complete 2D bandgaps; however, due to the application demand, it is desirable to find the best topologies in order to guarantee full bandgaps referred to in-plane wave propagation in the complete 3D structure. In this work, by means of a novel and fast implementation of the Bidirectional Evolutionary Structural Optimization technique, shape optimization is conducted on the hole shape obtaining several topologies, also with non-square-symmetric unit cell, endowed with complete 3D full bandgaps for in-plane waves. Model order reduction technique is adopted to reduce the computational time in the wave dispersion analysis. The 3D features of the PnC unit cell endowed with the widest full bandgap are then completely analyzed, paying attention to engineering design issues.

Asymmetric Rogue Waves, Breather-to-Soliton Conversion, and Nonlinear Wave Interactions in the Hirota-Maxwell-Bloch System

NASA Astrophysics Data System (ADS)

Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan

2016-02-01

We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.

Fast wave power flow along SOL field lines in NSTX

NASA Astrophysics Data System (ADS)

Perkins, R. J.; Bell, R. E.; Diallo, A.; Gerhardt, S.; Hosea, J. C.; Jaworski, M. A.; Leblanc, B. P.; Kramer, G. J.; Phillips, C. K.; Roquemore, L.; Taylor, G.; Wilson, J. R.; Ahn, J.-W.; Gray, T. K.; Green, D. L.; McLean, A.; Maingi, R.; Ryan, P. M.; Jaeger, E. F.; Sabbagh, S.