The nonlinear evolution of the Weibel instability driven by the anisotropy of the electron distribution function in a collisionless plasma is investigated in a spatially one-dimensional configuration with a Vlasov code in a two-dimensional velocity space. It is found that the electromagnetic fields generated by this instability cause a strong deformation of the electron distribution function in phase space, corresponding to highly filamented magnetic vortices. Eventually, these deformations lead to the generation of short wavelength Langmuir modes that form highly localized electrostatic structures corresponding to jumps of the electrostatic potential.

The transition between non resonant (Weibel-type) and resonant (whistler) instabilities is investigated numerically in plasma configurations with an ambient magnetic field of increasing amplitudes. The Vlasov-Maxwell system is solved in a configuration where the fields have three components but depend only on one coordinate and on time. The nonlinear evolution of these instabilities is shown to lead to the excitation of electromagnetic and electrostatic modes at the first few harmonics of the plasma frequency and, in the case of a large ambient magnetic field, to a long-wavelength, spatial modulation of the amplitude of the magnetic field generated by the whistler instability.

In this paper, we investigate nonrelativistic, kinetic, linear phase of the filamentation instability when an external magnetic field is present in the direction of the counterstreaming electron beams using Vlasov simulations in 1D-3V space. We first investigate the growth rate of instability. In the linear growth regime, our results correspond to the previous conclusions that with the increase in strength of the ambient magnetic field, there is a suppression of instability. Interestingly, we established that at a critical/threshold magnetic field, Vlasov simulations and particlein-cell (PIC) simulations differ in their instability behaviour. At this particular magnetic field, there is a complete suppression of the growth of instability in Vlasov results compared to PIC simulations, where a strong growth of instability is shown. It is believed that thermal noise in the PIC leads to the growth. However, Vlasov simulations show wave-wave coupling which stabilises the modes. In this work, our focus is to demonstrate the difference in this behaviour and to thoroughly analyse the spectra and wave generation for the same.

Kinetic numerical simulations of the evolution of the Weibel instability during the full nonlinear regime are presented. The formation of strong distortions in the electron distribution function resulting in formation of strong peaks in it and their influence on the resulting electrostatic waves are shown.