An important challenge in plasma physics is to determine whether ionized gases can be confined by strong magnetic fields. After properly formulating the model, this question leads to a penalized version of the Relativistic Vlasov Maxwell system, marked by the role of a singular factor ε −1 corresponding to the inverse of a cyclotron frequency. Stationary (equilibrium) solutions to this system are well understood, but it is not clear how perturbations from equilibrium could lead to destabilization of the plasma (the plasma explodes releasing uncontrollable energy).

In this talk, and in the case of neutral, cold, and dilute plasmas (like in the Earth's magnetosphere), I will show that smooth solutions corresponding to perturbations of equilibria exist on a uniform time interval [0,T]. Then, I will discuss how to further extend these results to hot plasmas for well prepared initial data.

These are joint works with C. Cheverry and D. Preissl.