zbMATH — the first resource for mathematics

Stable explicit coupling of the yee scheme with a linear current model in fluctuating magnetized plasmas. (English) Zbl 1349.76563
Summary: This work analyzes the stability of the Yee scheme for non-stationary Maxwell’s equations coupled with a linear current model with density fluctuations. We show that the usual procedure may yield unstable scheme for physical situations that correspond to strongly magnetized plasmas in X-mode (TE) polarization. We propose to use first order clustered discretization of the vectorial product that gives back a stable coupling. We validate the schemes on some test cases representative of direct numerical simulations of X-mode in a magnetic fusion plasma including turbulence.

76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
82D10 Statistical mechanics of plasmas
Full Text: DOI
[1] Bohner, M. U., Simulation of microwave propagation in a fusion plasma, (January 2011), Institut für Plasmaforschung, University of Stuttgart, Master Thesis
[2] Branbilla, M., Kinetic theory of plasma waves - homogeneous plasmas, International Series of Monographs on Physics, (1998), Clarendon Press
[3] Chen, F. F.; White, R. B., Amplification and absorption of electromagnetic waves in overdense plasmas, (Yamanaka, C., Laser Interaction with Matter, Series of Selected Papers in Physics, (1984), Phys. Soc. Japan), 16, 565-587, (1974), Anthologized
[4] Cooke, S. J.; Botton, M.; Antonsen, T. M.; Levush, B., A leapfrog formulation of the 3D ADI-FDTD algorithm, Int. J. Numer. Model., 22, 187-200, (2009) · Zbl 1158.78335
[5] Cummer, S. A., An analysis of new and existing FDTD methods for isotropic cold plasma and a method for improving their accuracy, IEEE Trans. Antennas Propag., 45, 392-400, (1997)
[6] da Silva, F.; Heuraux, S.; Manso, M., Studies on O-mode reflectometry spectra simulations with velocity shear layer, Nucl. Fusion, 46, 9, S816-S823, (2006)
[7] da Silva, F.; Heuraux, S.; Gusakov, E.; Popov, A., A numerical study of forward- and back-scattering signatures on Doppler reflectometry signals, IEEE Trans. Plasma Sci., 38, 2144-2148, (2010)
[8] da Silva, F.; Heuraux, S.; Manso, M., Developments on reflectometry simulations for fusion plasmas: applications to ITER position reflectometry, J. Plasma Phys., 72, 1205, (2006)
[9] F. da Silva, S. Heuraux, T. Ribeiro, B. Scott, Development of a 2D full-wave JE-FDTD Maxwell X-mode code for reflectometry simulation, Lisbon, 2009, IRW9.
[10] Del Pino, S.; Després, B.; Havé, P.; Jourdren, H.; Piserchia, P. F., 3D finite volume simulation of acoustic waves in the Earth atmosphere, Comput. Fluids, 38, 4, 765-777, (2009) · Zbl 1242.76160
[11] Després, B.; Imbert-Gérard, L. M.; Weder, R., Hybrid resonance of Maxwell’s equations in slab geometry, J. Math. Pures Appl., 101, 5, 623-659, (May 2014) · Zbl 1296.35182
[12] Desroziers, S.; Nataf, F.; Sentis, R., Simulation of laser propagation in a plasma with a frequency wave equation, J. Comput. Phys., 227, 4, 2610-2625, (1 February 2008) · Zbl 1132.76040
[13] Dumont, R. J.; Phillips, C. K.; Smithe, D. N., Effects of non-Maxwellian species on ion cyclotron waves propagation and absorption in magnetically confined plasmas, Phys. Plasmas, 12, 042508, (2005)
[14] Heh, D. Y.; Tan, E. L., FDTD modeling for dispersive media using matrix exponential method, IEEE Microw. Wirel. Compon. Lett., 19, 53-55, (2009)
[15] Huang, S.; Li, F., FDTD implementation for magnetoplasma medium using exponential time differencing, IEEE Microw. Wirel. Compon. Lett., 15, 183-185, (2005)
[16] Lee, Joo Hwa; Kalluri, Dikshitulu K., Three-dimensional FDTD simulation of electromagnetic wave transformation in a dynamic inhomogeneous magnetized plasma, IEEE Antennas Wirel. Propag. Lett., 47, 1146-1151, (1999)
[17] Jandieri, G. V.; Ishimaru, A.; Mchedlishvili, N. F.; Takidze, I. G., Spatial power spectrum of multiple scattered ordinary and extraordinary waves in magnetized plasma with electron density fluctuations, Prog. Electromagn. Res. M, 25, 87-100, (2012)
[18] Kohn, A.; Jacquot, J.; Bongard, M. W.; Gallian, S.; Hinson, E. T.; Volpe, F. A., Full-wave modeling of the O-X mode conversion in the pegasus toroidal experiment
[19] Liang, D.; Yuan, Q., The spatial fourth-order energy-conserved S-FDTD scheme for Maxwell’s equations, J. Comput. Phys., 243, 344-364, (2013) · Zbl 1349.78094
[20] Liu, S.; Liu, Sh., Runge-Kutta exponential time differencing FDTD method for anisotropic magnetized plasma, IEEE Antennas Wirel. Propag. Lett., 7, 306-309, (2008)
[21] Peysson, Y.; Decker, J.; Morini, L.; Coda, S., RF current drive and plasma fluctuations, Plasma Phys. Control. Fusion, 53, 124028, (2011)
[22] Popov, A. Yu., Anomalous reflection of electromagnetic waves at O-X mode conversion in 2D inhomogeneous turbulent plasma, Plasma Phys. Control. Fusion, 57, 025010, (2015)
[23] Smithe, D. N., Finite-difference time-domain simulation of fusion plasmas at radiofrequency time scales, Phys. Plasmas, 14, 056104, (2007)
[24] Stix, T. H., The theory of plasma waves, Advanced Physics Monograph Series, (1962), McGraw-Hill · Zbl 0116.22302
[25] G. Swanson, Plasma waves, IOP series in plasma physics, 2003.
[26] Sysoeva, E. V.; Gusakov, E. Z.; da Silva, F.; Heuraux, S.; Popov, A. Yu., ECRH beam broadening in the edge turbulent plasma of fusion machines, Nucl. Fusion, 55, 033016, (2015)
[27] Tan, E. L., Fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain methods, IEEE Trans. Antennas Propag., 56, 170-177, (2008) · Zbl 1369.78833
[28] Terrasse, I.; Abboud, T., Modélisation des phénomènes de propagation d’ondes, master lecture notes of ENSTA high school
[29] Tierens, W., Finite element and finite difference based approaches for the time-domain simulation of plasma-wave interactions, (2013), Gent University, PhD thesis
[30] Tierens, W.; De Zutter, D., An unconditionally stable time-domain discretization on Cartesian meshes for the simulation of nonuniform magnetized cold plasma, J. Comput. Phys., 231, 5144-5156, (2012) · Zbl 1334.76093
[31] Tsironis, C.; Peeters, A. G.; Isliker, H.; Strintzi, D.; Chatziantonaki, I.; Vlahos, L., Electron-cyclotron wave scattering by edge density fluctuations in ITER, Phys. Plasmas, 16, 112510, (2009)
[32] Xu, L.; Yuan, N., FDTD formulations for scattering from 3-D anisotropic magnetized plasma objects, IEEE Antennas Wirel. Propag. Lett., 5, 335-338, (2006)
[33] Yee, K. S., Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Antennas Propag., 14, 802-808, (1966)
[34] Yu, Y.; Simpson, J., An EJ collocated 3-D FDTD model of electromagnetic wave propagation in magnetized cold plasma, IEEE Trans. Antennas Propag., 58, 469-478, (2010) · Zbl 1369.78855
[35] Zheng, F.; Chen, Z.; Zhang, J., Toward the development of a three dimensional unconditionally stable finite-different time-domain method, IEEE Trans. Microw. Theory Tech., 48, 1550-1558, (2000)
[36] Zweben, S. J.; Maqueda, R. J.; Stotler, D. P., High-speed imaging of edge turbulence in NSTX, Nucl. Fusion, 44, 134-153, (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.