Nonlinear Weibel waves

Abstract

We found nonlinear stationary Weibel waves for bi-Maxwellian electron distribution function with small and moderate temperature anisotropy, α = T⊥/T∥ − 1 < 1. We showed that at small phase velocities ω/k Weibel waves are almost linear with the dispersive law ω2 = ak2 − bk4 at which the waves exist in a finite range of wave numbers, 0 < k < kmax = (a/b)1/2 = α1/2ωpe/c, where linear growth rate exists. Here ωpe is the electronic plasma frequency and c is the speed of light. At larger phase velocities, ω/k ≃ (ω/k)max = α1/2(T∥/m)1/2 Weibel waves become nonlinear having the form of cnoidal waves and solitons. We also found the magnitude of the magnetic field in the saturated stage, B ≃ α1/2(8πnT∥)1/2.