• Weibel instability
• Vlasov simulations
• nonlinear evolution
• low frequency modulations
• multiple harmonics
• electrostatic coherent structures
• electron temperature anisotropy
• double layers
• collisionless plasma
• whistler instability
• whistler oscillitons

Plasma instabilities play an important role in astrophysics in general and space plasmas in particular. Weibel and whistler instabilities in particular have attracted much attention in the recent years, due to their capability of generating a magnetic field from essentially any kind of initial noise. We investigate the different physical mechanisms that can accompany the generation of magnetic fields in a collisionless plasma regime, i.e., under conditions that are very far from thermodynamic equilibrium. These instabilities have been vigorously studied using linear theory. However, in a high frequency, collisionless plasma, kinetic effects modify the nonlinear behavior of the plasma. Analytically, the study of the nonlinear evolution of such instabilities is not easy. Our aim is to study the nonlinear evolution of these instabilities using computer simulations.


A bi-Maxwellian distribution function with electron temperature anisotropy is considered as an initial state leading to the generation of magnetic fields. It is found that the Weibel instability causes a violent deformation of the electron distribution function in phase space combined with mixing processes, leading to the generation of short wavelength Langmuir modes. This results in the formation of highly localized electrostatic structures which are of interest in space plasmas.


The transition between non resonant (Weibel-type) and resonant (whistler) instabilities is also investigated in plasma configurations with an ambient magnetic field of increasing amplitudes. 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. At large ambient magnetic field we find a low frequency long wavelength modulation of the whistler wave spectrum that we interpret in terms of the self-consistent interaction between the perturbed magnetic field and the low frequency electron and proton density modulations. The magnetic modulations that we observe are reminiscent of the so called ``whistler oscillitons'' that arise under the condition that the mode phase velocity coincides with its group velocity.