Twisting in One Dimensional Periodic Vlasov-Poisson System

TL;DR

This paper demonstrates the occurrence of twisting and filamentation phenomena near stable steady states in a one-dimensional periodic Vlasov-Poisson system, highlighting growth in the electron distribution's gradient over time.

Contribution

It establishes the existence of stable steady states and proves the development of twisting and filamentation in the system, advancing understanding of plasma dynamics.

Findings

Growth in the L1 norm of the gradient over time

Existence of stable steady states for certain ion densities

Filamentation phenomena near stable states

Abstract

We prove that twisting and filamentation occur near a family of stable steady states for one dimensional periodic Vlasov-Poisson system, describing the electron dynamics under a fixed ion background. More precisely, we establish the growth in time of the L1 norm of the gradient for the electron distribution function and the corresponding flow map in the phase space. To support this result, we prove existence results of stable steady states for a class of ion densities on the torus.