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Normal-mode-based theory of collisionless plasma waves

Published online by Cambridge University Press:  03 July 2019

J. J. Ramos
J. J. Ramos*
Affiliation:
Equipo de propulsión espacial y plasmas (EP2), Universidad Carlos III de Madrid, E-28911 Leganés, Spain
*
†Email address for correspondence: jeramos@ing.uc3m.es
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Abstract

The Van Kampen normal-mode method is applied in a comprehensive study of the linear wave perturbations of a homogeneous, magnetized and finite-temperature plasma, described by the collisionless Vlasov–Maxwell system in its non-relativistic version. The analysis considers a stable, Maxwellian background, but is otherwise completely general in that it allows for arbitrary wave propagation direction relative to the equilibrium magnetic field, multiple plasma species and general polarization states of the perturbed electromagnetic fields. A convenient formulation is introduced whereby the generator of the time advance is a Hermitian operator, analogous to the Hamiltonian in the Schrödinger equation of quantum mechanics. This guarantees a real frequency spectrum and complete bases of normal modes. Expansions in these normal-mode bases yield immediately the solutions of initial-value problems for general initial conditions. With standard initial conditions and propagation direction parallel to the equilibrium magnetic field, all the familiar results obtained following Landau’s Laplace transform approach are recovered. Considering such parallel propagation, the present work shows also explicitly and provides an example of how to construct special initial conditions that result in different, damped but otherwise arbitrarily prescribed time variations of the macroscopic variables. The known dispersion relations for perpendicular propagation are also recovered.

Keywords

plasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 85 , Issue 4 , August 2019 , 905850401
Copyright
© Cambridge University Press 2019 

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References

Belmont, G., Mottez, F., Chust, T. & Hess, S. 2008 Existence of non-Landau solutions for Langmuir waves. Phys. Plasmas 15, 052310.Google Scholar
Bernstein, I. B. 1958 Waves in a plasma in a magnetic field. Phys. Rev. 109, 10.Google Scholar
Bers, A. 2016 Plasma Physics and Fusion Plasma Electrodynamics. Oxford University Press.Google Scholar
Brambilla, M. 1998 Kinetic Theory of Plasma Waves: Homogeneous Plasmas. Clarendon Press.Google Scholar
Case, K. M. 1959 Plasma oscillations. Ann. Phys. 7, 349.Google Scholar
Felderhof, N. G. 1963a Theory of transverse waves in Vlasov plasmas. I. No external fields; isotropic equilibrium. Physica 29, 293.Google Scholar
Felderhof, N. G. 1963b Theory of transverse waves in Vlasov plasmas. II. External magnetic field; anisotropic equilibrium. Physica 29, 317.Google Scholar
Fried, B. D. & Conte, S. D. 1961 The Plasma Dispersion Function. Academic Press.Google Scholar
Goldston, R. J. & Rutherford, P. H. 2000 Introduction to Plasma Physics. Taylor and Francis.Google Scholar
Hazeltine, R. D. & Waelbroeck, F. L. 2004 The Framework of Plasma Physics. Westview Press.Google Scholar
Ignatov, A. M. 2017 Electromagnetic Van Kampen waves. Plasma Phys. Rep. 43, 29.Google Scholar
Krall, N. A. & Trivelpiece, A. N. 1973 Principles of Plasma Physics. McGraw-Hill.Google Scholar
Lambert, A. J. D., Best, R. W. B. & Sluijter, F. W. 1982 Van Kampen and Case formalism applied to linear and weakly nonlinear initial value problems in unmagnetized plasma. Contrib. Plasma Phys. 22, 101.Google Scholar
Landau, L. 1946 On the vibrations of the electronic plasma. J. Phys. (USSR) 10, 25.Google Scholar
Lifshitz, E. M. & Pitaevskii, L. P. 1981 Physical Kinetics. Pergamon Press.Google Scholar
McCune, J. E. 1966 Three-dimensional normal modes in a magnetized Vlasov plasma. Phys. Fluids 9, 1788.Google Scholar
Pecseli, H. L. 2012 Waves and Oscillations in Plasmas. Taylor and Francis.Google Scholar
Pradhan, T. 1957 Plasma oscillations in a steady magnetic field: circularly polarized electromagnetic modes. Phys. Rev. 107, 1222.Google Scholar
Ramos, J. J. 2017 Longitudinal sound waves in a collisionless, quasineutral plasma. J. Plasma Phys. 83, 725830601.Google Scholar
Ramos, J. J. & White, R. L. 2018 Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism. Phys. Plasmas 25, 034501.Google Scholar
Stix, T. H. 1962 The Theory of Plasma Waves. McGraw-Hill.Google Scholar
Van Kampen, N. G. 1955 On the theory of stationary waves in plasmas. Physica 21, 949.Google Scholar
Van Kampen, N. G. & Felderhof, B. U. 1967 Theoretical Methods in Plasma Physics. North Holland.Google Scholar
Watanabe, Y. 1968 Theory of Vlasov plasma oscillation in a magnetic field. J. Phys. Soc. Japan 25, 250.Google Scholar
Weitzner, H. 1963 Plasma oscillations and Landau damping. Phys. Fluids 6, 1123.Google Scholar