Damping of transversal plasma-electron oscillations and waves in low-collision electron-ion plasmas

TL;DR

This paper applies a novel Laplace transform method to analyze transversal plasma-electron oscillations in low-collision plasmas, revealing two wave branches and deriving damping expressions for low-velocity electron waves.

Contribution

It introduces a new application of the Laplace transform to find asymptotic solutions of Vlasov equations, identifying damping mechanisms for electron waves in low-collision plasmas.

Findings

Identifies high-frequency and low-velocity electron wave branches.

Derives damping rates for low-velocity electron waves.

Shows transformation of non-damping to damping waves through iterative methods.

Abstract

Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is here applied to consider transversal oscillations and waves in low-collision quasi-neutral (n_i \simeq n_e) Maxwellian electron-ion plasmas. We obtain two branches of electron waves: the ubiquitous one of high-frequency and high-velocity oscillations and the unusual low-velocity one. Taking into account Coulomb collisions in the limit m_e << m_i, \bar{v_i} << \bar{v_e}, and T_e m_e << T_i m_i results in expressions for transversal plasma-electron oscillation/wave decrements with a damping of the low-velocity electron branch \sim n_i^{1/3}/\bar{v}_e^{4/3}, where n_i is the ion density and \bar{v}_e is the mean electron velocity. It ought to rehabilitate Vlasov principal value prescription for relevant integrals, but to supplement it with representation of an asymptotical solution as a sum of exponents (not a single one). "Non-damping" kinematical waves in low-collision plasma transform in the damping ones at reasonably chosen iteration process.