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This article is devoted to the kinetic description in phase space ofmagnetically confined plasmas. It addresses the problem of stability nearequilibria of the Relativistic Vlasov Maxwell system. We work under theGlassey-Strauss compactly supported momentum assumption on the density function$f(t,\cdot)$. Magnetically confined plasmas are characterized by the presenceof a strong external magnetic field $ x \mapsto \epsilon^{-1} \mathbf{B}_e(x)$,where $\epsilon$ is a small parameter related to the inverse gyrofrequency ofelectrons. In comparison, the self consistent internal electromagnetic fields$(E,B) $ are supposed to be small. In the non-magnetized setting, local $ C^1$-solutions do exist but do not exclude the possibility of blow up in finitetime for large data. Consequently, in the strongly magnetized case, since $\epsilon^{-1} $ is large, standard results predict that the lifetime$T_\epsilon$ of solutions may shrink to zero when $ \epsilon $ goes to $ 0 $.In this article, through field straightening, and a time averaging procedure weshow a uniform lower bound ($0<T<T_\epsilon$) on the lifetime of solutions anduniform Sup-Norm estimates. A bootstrap argument allows us to show $f$ remainsat a distance $\epsilon$ from the linearized system, while the internal fieldscan differ by order 1 for well prepared initial data.

Uniform Lifetime for Classical Solutions to the Hot, Magnetized, Relativistic Vlasov Maxwell System