Vlasov simulations of self generated strong magnetic fields in plasmas and laser-plasma interaction

A new formulation based on Hamiltonian reduction technique using the invariance of generalized canonical momentum is introduced for the study of relativistic Weibel-type instability. An example of application is given for the current filamentation instability resulting from the propagation of two counter-streaming electron beams in the relativistic regime of the instability. This model presents a double advantage. From an analytical point of view, the method is exact and standard fluid dispersion relations for Weibel or filamentation instabilies can be recovered. From a numerical point of view, the method allows a drastic reduction of the computational time. A 1D multi-stream Vlasov-Maxwell code is developed using such dynamical invariants in the perpendicular momentum space. Numerical comparison with a full Vlasov-Maxwell system has also been carried out to show the efficiency of this reduction technique.