Nonlinear Effects in the Weibel Instability

Abstract

Using the particle-in-cell code, we performed numerical simulations of the Weibel instability in plasmas with a two-temperature Maxwellian distribution function. We found harmonics in the power spectrum of the Weibel-generated turbulent magnetic field, which permitted us to measure directly the magnitude of the nonlinear effects. It is shown that by the time of the instability saturation the nonlinear effects are insignificant in the case of a large initial anisotropy and are vanishing in the case of a small initial anisotropy, so that the nonlinearity is not the reason why the magnetic field stops to increase. The asymptotic form of the power spectrum of the magnetic field in the region of small scales is determined. It is demonstrated that the nonlinearity is essential for the generation of a large-scale magnetic field and therefore plays a crucial role at the stage of the magnetic field decay. Astrophysical applications of the obtained results are discussed.