Linear and Nonlinear Landau Damping using Particle-in-Cell Simulation

Abstract

I present the effect of finite amplitude, which was ignored in Landau’s linearized theory and a transition criterion between linear and nonlinear Landau damping. To adjust the finite amplitude of wave and the initial trapped electron flux J_xT0, we used Particle-in-Cell simulation that can uniquely modulate these parameters. The finite amplitude of wave potential and kinetic energies were predicted

these matched the simulation exactly. Oscillation and damping rates in Landau damping agreed remarkably well with those of theory and differed substantially from theory beyond a certain range of amplitude.Either large amplitude or large J_xT0 increased degree of damping

this increase diminished the transportation of trapped electrons.More accurate description of linear Landau damping coupled withthe finite amplitude effect was possible. Although previous theories predict nonlinear waves in large amplitude, we did not observe the expected nonlinear wave because of diminished J_xT0 under some conditions.