1997/06/28 by В. Н. Сошников, V. N. Soshnikov, Soshnikov, V. N. · 1 citation
Chemistry · Engineering · Physics and Astronomy · #Electrostatics and Colloid Interactions #FOS: Physical sciences #Magneto-Optical Properties and Applications #Plasma Physics (physics.plasm-ph) #Surface and Thin Film Phenomena #physics.plasm-ph
paper · pdf · doi:10.48550/arxiv.physics/9706041
8 pages, uses revtex.sty[prb,aps]
openalex publication_date 1997/06/28 · arxiv created 1997/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new and effective method to find plasma oscillatory and wave modes. It implies searching a pair of poles of two-dimensional (in coordinate x and time t) Laplace transform of self-consistent plasma electric field E(x,t) → Ep1p2, where p1 ≡ -i ω, p2 ≡ i k are Laplace transform parameters, that is determining a pair of zeros of the following equation \frac1Ep1p2 = 0 . This kind of conditional equation for searching double poles of Ep1p2 we call ``general dispersion equation'', so far as it is used to find the pair values (ω(n), k(n)), n=1, 2, ... . It differs basically from the classic dispersion equation εl(ω,k) = 0 (and is not its generalization), where εl is longitudinal dielectric susceptibility, its analytical formula being derived according to Landau analytical continuation. In distinction to εl, which is completely plasma characteristic, the function Ep1p2 is defined by initial and boundary conditions and allows one to find all the variety of asymptotical plasma modes for each concrete plasma problem. In this paper we demonstrate some possibilities of applying this method to the simplest cases of collisionless ion-electron plasma and to electron plasma with collisions described by a collision-relaxation term -νf(1).