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Plasma waves as a benchmark problem

Part of: PLA The Vlasov Equation

Published online by Cambridge University Press:  23 February 2017

Patrick Kilian Open the ORCID record for Patrick Kilian [Opens in a new window] ,
Patricio A. Muñoz ,
Cedric Schreiner  and
Felix Spanier
Patrick Kilian*
Affiliation:
Centre for Space Research, North-West University, Potchefstroom 2520, South Africa
Patricio A. Muñoz
Affiliation:
Max-Planck-Institute for Solar System Research, Göttingen 37077, Germany
Cedric Schreiner
Affiliation:
Centre for Space Research, North-West University, Potchefstroom 2520, South Africa Lehrstuhl für Astronomie, Julius-Maximilians-Universität, Würzburg 97074, Germany
Felix Spanier
Affiliation:
Centre for Space Research, North-West University, Potchefstroom 2520, South Africa
*
†Email address for correspondence: 28233530@nwu.ac.za
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Abstract

A large number of wave modes exist in a magnetized plasma. Their properties are determined by the interaction of particles and waves. In a simulation code, the correct treatment of field quantities and particle behaviour is essential to correctly reproduce the wave properties. Consequently, plasma waves provide test problems that cover a large fraction of the simulation code. The large number of possible wave modes and the freedom to choose parameters make the selection of test problems time consuming and comparison between different codes difficult. This paper therefore aims to provide a selection of test problems, based on different wave modes and with well-defined parameter values, that is accessible to a large number of simulation codes to allow for easy benchmarking and cross-validation. Example results are provided for a number of plasma models. For all plasma models and wave modes that are used in the test problems, a mathematical description is provided to clarify notation and avoid possible misunderstanding in naming.

Keywords

magnetized plasmasplasma wavesspace plasma physics
Type
Tutorial
Information
Journal of Plasma Physics , Volume 83 , Issue 1 , February 2017 , 707830101
Copyright
© Cambridge University Press 2017 

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References

Bernstein, I. B. 1958 Waves in a plasma in a magnetic field. Phys. Rev. 109, 10–21.CrossRefGoogle Scholar
Birdsall, C. K. & Langdon, A. B. 2005 Plasma Physics Via Computer Simulation, 1st edn. Taylor and Francis.Google Scholar
Birn, J., Drake, J. F., Shay, M. A., Rogers, B. N., Denton, R. E., Hesse, M., Kuznetsova, M., Ma, Z. W., Bhattacharjee, A., Otto, A. et al. 2001 Geospace environmental modeling (GEM) magnetic reconnection challenge. J. Geophys. Res. 106 (A3), 3715–3719.Google Scholar
Bittencourt, J. A. 2004 Fundamentals of Plasma Physics, 3rd edn. Springer.Google Scholar
Bulanov, S. V., Pegoraro, F. & Sakharov, A. S. 1992 Magnetic reconnection in electron magnetohydrodynamics. Phys. Fluids B 4 (8), 2499–2508.CrossRefGoogle Scholar
Chen, L., Thorne, R. M., Shprits, Y. & Ni, B. 2013 An improved dispersion relation for parallel propagating electromagnetic waves in warm plasmas: application to electron scattering. J. Geophys. Res. 118 (5), 2185–2195.CrossRefGoogle Scholar
Darwin, C. G. 1920 The dynamical motions of charged particles. Phil. Mag. 39, 537.CrossRefGoogle Scholar
Dawson, J. M. 1961 On landau damping. Phys. Fluids 4 (7), 869–874.Google Scholar
Decyk, V. K.2011 Description of spectral particle-in-cell codes in the upic framework. Presentation at ISSS-10.Google Scholar
Dimits, A. M., Bateman, G., Beer, M. A., Cohen, B. I., Dorland, W., Hammett, G. W., Kim, C., Kinsey, J. E., Kotschenreuther, M., Kritz, A. H. et al. 2000 Comparisons and physics basis of tokamak transport models and turbulence simulations. Phys. Plasmas 7 (3), 969–983.CrossRefGoogle Scholar
Esirkepov, T. Zh. 2001 Exact charge conservation scheme for particle-in-cell simulation with an arbitrary form-factor. Comput. Phys. Commun. 135 (2), 144–153.Google Scholar
Falchetto, G. L., Scott, B. D., Angelino, P., Bottino, A., Dannert, T., Grandgirard, V., Janhunen, S., Jenko, F., Jolliet, S., Kndl, A. M. et al. 2008 The European turbulence code benchmarking effort: turbulence driven by thermal gradients in magnetically confined plasmas. Plasma Phys. Control. Fusion 50 (12), 124015.Google Scholar
Fried, B. D. & Conte, S. D.(Eds) 1961 The Plasma Dispersion Function. Academic.Google Scholar
Görler, T., Tronko, N., Hornsby, W. A., Bottino, A., Kleiber, R., Norscini, C., Grandgirard, V., Jenko, F. & Sonnendrücker, E. 2016 Intercode comparison of gyrokinetic global electromagnetic modes. Phys. Plasmas 23 (7), 072503.Google Scholar
Jackson, J. D. 1975 Classical Electrodynamics, 2nd edn. Wiley.Google Scholar
Jain, N., Das, A., Kaw, P. & Sengupta, S. 2003 Nonlinear electron magnetohydrodynamic simulations of sausage-like instability of current channels. Phys. Plasmas 10 (1), 29–36.CrossRefGoogle Scholar
Kilian, P., Burkart, T. & Spanier, F. 2012 The influence of the mass ratio on particle acceleration by the filamentation instability. In High Performance Computing in Science and Engineering ’11 (ed. Nagel, W. E., Krner, D. B. & Resch, M. M.), pp. 5–13. Springer.Google Scholar
Koskinen, H. E. J. 2011 Physics of Space Storms from the Solar Surface the Earth. Springer.Google Scholar
Krause, T. B., Apte, A. & Morrison, P. J. 2007 A unified approach to the Darwin approximation. Phys. Plasmas 14 (10), 102112.Google Scholar
Landau, L. 1946 On the vibrations of the electronic plasma. J. Expl Theor. Phys. 16 (7), 574–586.Google Scholar
Maxwell, J. C. 1865 A dynamical theory of the electromagnetic field. Phil. Trans. R. Soc. Lond. 155 (1), 459–513.Google Scholar
Muñoz, P. A., Jain, N., Kilian, P. & Büchner, J.2016 A new hybrid code (CHIEF) implementing the inertial electron fluid equation without approximation. Comput. Phys. Commun. (submitted), arXiv:1612.03818.Google Scholar
Nunn, D. 1993 A novel technique for the numerical simulation of hot collision-free plasma; Vlasov hybrid simulation. J. Comput. Phys. 108 (1), 180–196.CrossRefGoogle Scholar
Roennmark, K.1982 Waves in homogeneous, anisotropic multicomponent plasmas (WHAMP). Tech. Rep., Kiruna Geophysical Insitute.Google Scholar
Schreiner, C., Kilian, P. & Spanier, F. 2017 Recovering the damping rates of cyclotron damped plasma waves from simulation data. Commun. Comput. Phys. 21 (4), 947–980 (in press).Google Scholar
Shaikh, D. 2009 Theory and simulations of whistler wave propagation. J. Plasma Phys. 75, 117–132.CrossRefGoogle Scholar
Sitenko, A. G. 1967 Electromagnetic Fluctuations in Plasma. Academic.Google Scholar
Stix, T. H. 1962 The Theory of Plasma Waves. McGraw-Hill.Google Scholar
Swanson, D. G. 2003 Plasma Waves, 2nd edn. Taylor and Francis.Google Scholar
Vlasov, A. A. 1938 On high-frequency properties of electron gas. J. Expl Theor. Phys. 8 (3), 291–318.Google Scholar
Yee, K. 1966 Numerical solution of inital boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 14 (3), 302–307.Google Scholar