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Longitudinal Ion Oscillations in a Hot Plasma

### Abstract

Linearized, longitudinal waves in a hot plasma include, besides the familiar electron plasma oscillations, in which the frequency ω is of order ω_{ p } = (4π*ne* ^{2}/*m*)^{½}, also ion plasma oscillations with ω ≈ ω_{ p }(*m/M*)^{½}. The properties of the latter are explored using a Vlasov equation description of the plasma. For equal ion and electron temperatures, *T*_{e} = T_{i} , there exists a discrete sequence of ion oscillations, but all are strongly damped, i.e., have ‐Im ω/Re ω ⪞ 0.5, and hence are not likely to be observable. The ratio Im ω/Re ω can be made to approach zero (facilitating detection of the waves) by either increasing *T*_{e}/T_{i} or by producing a current flow in the plasma. In the latter case, Im ω can even be made positive (corresponding to growing waves), the current required for this being smaller the larger the value of *T*_{e}/T_{i} . This growing wave is just the familiar two‐stream instability which is thus seen to be an unstable ion oscillation. It is also noteworthy that the ion oscillations, which for small *k* have the properties usually associated with an acoustic wave (longitudinal polarization, ω ∝ *k*), are obtained using a formalism which is sometimes designated as ``collisionless.''

© 1961 The American Institute of Physics

Received 21 July 1960
Published online 09 December 2004

/content/aip/journal/pof1/4/1/10.1063/1.1706174

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4.Since collision times may be very small on a macroscopic scale and still long compared to it is reasonable to suppose, in the context of an initial value problem, that the plasma has come to equilibrium (and hence has Maxwellian distribution) with a small initial perturbation whose development in time we study. In the generation of a plasma, energy may be given preferentially to one species; for times short compared to the interchange of energy between electrons and ions we may approximately describe the situation by assigning different temperatures to the two species.

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