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 ωp = (4πne2/m)½, also ion plasma oscillations with ω ≈ ωp(m/M)½. The properties of the latter are explored using a Vlasov equation description of the plasma. For equal ion and electron temperatures, Te = Ti, 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 Te/Ti 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 Te/Ti. 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.''

Electrodynamics in a very thin current sheet leading to magnetic reconnection

“…We had already noted that the wavelength λ z ∼8λ do and k z λ do ∼0.7. Such wave numbers for the dominant modes are comparable with the wave numbers expected for the Buneman and ion acoustic instabilities given by k y ∼ω po /V de when electron drift velocity V de ∼V teo (Fried and Gould, 1961). We note from Figs.…”

Physical consequences of the inclusion of anomalous resistivity in the dynamics of 2D magnetic reconnection

“…When T e ∼ = T i , a different streaming instability will occur when v dr ∼ ξ, where ξ = k B T e /m e is the mean thermal speed of electrons, leading to the excitation of electron plasma waves (Fried & Gould 1961). In essence, following a heuristic argument by Buneman (1958), we expect the effective collision time to be reduced from the kinetic value to the much smaller value 2 π/ω pe , where ω pe is the electron plasma frequency, enhancing the resistivity accordingly.…”

Analysis of Dispersion and Damping of Ion Waves in Plasma

“…It may be emphasized that the limiting value V x and (3) are also found as simplified solutions of a kinetic treatment as given by Fried et al [11] with the same assumptions T { < T e and v in = 0.…”