Generalized Theory of Landau Damping

TL;DR

This paper presents a generalized theoretical framework for Landau damping in plasma, deriving exact solutions that reveal discrete spectra of wave frequencies and dispersion curves, validated by mathematical experiments.

Contribution

It introduces a new regularization principle for singular integrals, leading to an exact solution and revealing discrete spectra in Landau damping.

Findings

Existence of discrete frequency spectrum

Discrete dispersion curves identified

Analytical results match mathematical experiments

Abstract

Collisionless damping of electrical waves in plasma is investigated in the frame of the classical formulation of the problem. The new principle of regularization of the singular integral is used. The exact solution of the corresponding dispersion equation is obtained. The results of calculations lead to existence of discrete spectrum of frequencies and discrete spectrum of dispersion curves. Analytical results are in good coincidence with results of direct mathematical experiments. Key words: Foundations of the theory of transport processes and statistical physics; Boltzmann physical kinetics; damping of plasma waves, linear theory of wave`s propagation PACS: 67.55.Fa, 67.55.Hc