Analysis of transient and asymptotic behavior in relativistic Landau damping

Abstract

Relativistic electrostatic oscillations in a collisionless nonmagnetized plasma are considered. An integral form of the Vlasov–Poisson problem is solved numerically and both the transient and the asymptotic behavior of the electric field are calculated in a very accurate way. The existence of a critical value for the wave number, under which no Landau damping occurs, has been verified, and the asymptotic behavior of the oscillations in the one-dimensional kinetic model has been evaluated. Some errors have been found in previously published analytical expressions. A new expression is proposed and verified numerically. An analytical expression of the asymptotic behavior for full three-dimensional kinetic model is deduced and numerically tested.

Relativistic Landau damping of longitudinal waves in isotropic pair plasmas

“…This agrees with the analysis of [6] and the numerical simulations of [9]. Notice that there is always a physically real solution for S, though as a → ∞, S → 0 from the asymptotic expansion of Eq.…”

“…These were proposed (in electronion plasmas) by Buti [2] and presented in more detail by Lerche [3]. Further exploration and modelling by Schlickeiser [6] and Schlickeiser and Kneller [7] revealed more properties, with a measure of numerical verification by Sartori and Coppa [9]. The particle-wave resonance condition essential for classical Landau damping is modified by the presence of the Lorentz factor…”

“…Subsequent detailed analysis by Buti [2] and Lerche [3] produced additional mathematical insight into the rich physics of the phenomenon. Collisionless damping has become important in a wider context (see the reviews by Ryutov [4] and Ivanov [5]) and other recent works [6][7][8][9][10] show that progress in understanding, and modelling, this topic is still being made, albeit in classical electronion plasmas. For example, experimental measurements of classical linear collisionless damping [11] show quantitative agreement with Landau's treatment for low-energy electron-ion plasmas.…”

Study on longitudinal dispersion relation in one-dimensional relativistic plasma: Linear theory and Vlasov simulation

“…Considerable works have been contributed to this subject over the past few decades, [15][16][17][18][19][20][21][22][23][24][25][26][27][28] mainly focusing on theoretical analysis by linearizing relativistic Vlasov equation as well as the coupled field equations. New findings not appearing in the nonrelativistic limit are explored.…”

“…For example, there exists electron plasma wave mode free from Landau damping, referred to as superluminal mode. 18,20,28 Some of the theoretic work is also extended to investigate detailed relativistic physics, such as the acceleration issue in solar wind electrons. 10 Vlasov simulations provide a kinetic description of the evolution of a collisionless plasma in the phase (position and momentum) space.…”