New approach for the study of linear Vlasov stability of inhomogeneous systems

Camporeale, Enrico; Delzanno, Gian Luca; Lapenta, Giovanni; Daughton, William

doi:doi:10.1063/1.2345358

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A comparison of ultrarelativistic electron- and positron-bunch propagation in plasmas

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Electron plasmas: Confinement and mode structure in a small aspect ratio toroidal experiment

Toroidal electron plasmas have remained less explored due to their poor confinement properties. Their equilibrium, stability, and confinement properties are therefore not entirely understood and continue to remain a topic of intense ongoing research. Large aspect-ratio theory suggests poor confinement in toroidal devices can be overcome by the application of a radial electric field; this has been verified successfully in some of the recent experiments. In the present paper, we report the longes...

This paper presents an alternative technique for solving the linearized Vlasov-Maxwell set of equations, in which the velocity dependence of the perturbed distribution function is described by means of an infinite series of orthogonal functions, chosen as Hermite polynomials. The orthogonality properties of such functions allow us to decompose the Vlasov equation into a set of infinite coupled linear equations. With a suitable truncation relation, the problem is transformed in an eigenvalue problem. This technique is based on solid but easy concepts, not attempting to evaluate the integration over the unperturbed trajectories and can be applied to any equilibrium. Although the solutions are approximate, because they neglect contributions of higher order coefficients of the series, the physical meaning of the low-order coefficients is clear. Furthermore the accuracy of the solution, which depends on the number of terms taken into account in the Hermite series, appears to be merely a problem of computational power. The method has been tested for a 1D Harris equilibrium, known to give rise to several instabilities like tearing, drift kink, and lower hybrid. The results are shown in agreement with those obtained by Daughton with a traditional technique based on the integration over unperturbed orbits.

Article Outline

INTRODUCTION
MATHEMATICAL METHOD
FREE PARAMETERS
RESULTS
1. Drift kink instability
2. Lower hybrid drift instability
3. Tearing instability
CONCLUSION

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KEYWORDS and PACS

Keywords

Vlasov equation, Maxwell equations, plasma kinetic theory, plasma transport processes, tearing instability, kink instability, plasma hybrid waves, integration, eigenvalues and eigenfunctions

PACS

52.35.Py

Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.25.Dg

Plasma kinetic equations
52.25.Fi

Transport properties
52.35.Hr

Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.20.Dq

Particle orbits
02.60.Jh

Numerical differentiation and integration

ARTICLE DATA

Digital Object Identifier

http://dx.doi.org/10.1063/1.2345358

PUBLICATION DATA

ISSN

1070-664X (print)

1089-7674 (online)

Publisher

$abstract.society.value is a Member of CrossRef

American Institute of Physics

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