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Longitudinal sound waves in a collisionless, quasineutral plasma

Part of: Professor Francesco Pegoraro

Published online by Cambridge University Press:  29 November 2017

J. J. Ramos
J. J. Ramos*
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: ramos@psfc.mit.edu
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Abstract

The time evolution of slow sound waves in a homogeneous, collisionless and quasineutral plasma, in particular their Landau damping, is investigated using the kinetic-magnetohydrodynamics formulation of Ramos (J. Plasma Phys. vol. 81, 2015 p. 905810325; vol. 82, 2016 p. 905820607). In this approach, the electric field is eliminated from a closed, hybrid fluid-kinetic system that ensures automatically the fulfilment of the charge neutrality condition. Considering the time dependence of a spatial-Fourier-mode linear perturbation with wavevector parallel to the equilibrium magnetic field, this can be cast as a second-order self-adjoint problem with a continuum spectrum of real and positive squared frequencies. Therefore, a conventional resolution of the identity with a continuum basis of singular normal modes is guaranteed, which simplifies significantly a Van Kampen-like treatment of the Landau damping. The explicit form of such singular normal modes is obtained, along with their orthogonality relations. These are used to derive the damped time evolution of the fluid moments of solutions of initial-value problems, for the most general kinds of initial conditions. The non-zero parallel electric field is not used explicitly in this analysis, but it is calculated from any given solution after the later has been obtained.

Keywords

plasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 6 , December 2017 , 725830601
Copyright
© Cambridge University Press 2017 

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References

Barnes, A. 1966 Collisionless damping of hydromagnetic waves. Phys. Fluids 8, 1483.CrossRefGoogle Scholar
Bernstein, I. B., Greene, J. M. & Kruskal, M. D. 1957 Exact nonlinear plasma oscillations. Phys. Rev. 108, 546.CrossRefGoogle Scholar
Bers, A. 2016 Plasma Physics and Fusion Plasma Electrodynamics. Oxford University Press.CrossRefGoogle Scholar
Case, K. M. 1959 Plasma oscillations. Ann. Phys. 7, 349.CrossRefGoogle Scholar
Chandrasekhar, S., Kaufman, A. N. & Watson, K. M. 1957 Properties of an ionized gas of low density in a magnetic field III. Ann. Phys. 2, 435.CrossRefGoogle 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
Kovrizhnykh, L. M. 1960 Oscillations of an electron–ion plasma. Sov. Phys. JETP 10, 1198.Google Scholar
Krall, N. A. & Trivelpiece, A. N. 1973 Principles of Plasma Physics. McGraw-Hill.CrossRefGoogle Scholar
Kruskal, M. D. & Oberman, C. R. 1958 On the stability of plasma in static equilibrium. Phys. Fluids 1, 275.CrossRefGoogle Scholar
Kurlsrud, R. 1962 General stability theory in plasma physics. In Proc. Int. School of Physics Enrico Fermi, Varenna, Italy. Course XXV (ed. Rosenbluth, M. N.), Advanced Plasma Theory. North Holland.Google Scholar
Kutsenko, A. B. & Stepanov 1960 Instability of plasma with anisotropic distribution of ion and electron velocities. Sov. Phys. JETP 11, 1323.Google Scholar
Landau, L. 1946 On the vibrations of the electronic plasma. J.  Phys. (USSR) 10, 25.Google Scholar
Ramos, J. J. 2015 On the normal-mode frequency spectrum of kinetic magnetohydrodynamics. J. Plasma Phys. 81, 905810325.CrossRefGoogle Scholar
Ramos, J. J. 2016 On stability criteria for kinetic magnetohydrodynamics. J. Plasma Phys. 82, 905820607.CrossRefGoogle Scholar
Rosenbluth, M. N. & Rostoker, N. 1959 Theoretical structure of plasma equations. Phys. Fluids 2, 23.CrossRefGoogle 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.CrossRefGoogle Scholar