On the Spitzer-Härm Regime and Nonlocal Approximations: Modeling, Analysis, and Numerical Simulations

This paper is devoted to the derivation of the Spitzer–Härm limit from the coupled system of PDEs describing the evolution of charged particles and electromagnetic fields. We identify a relevant asymptotic regime which leads to a non linear diffusion equation for the electron temperature. Then, we discuss some intermediate models, which remain of hydrodynamic nature but involve a nonlocal coupling through integral or pseudo-differential operators. In particular, we exhibit important mathematical properties of the so–called Schurtz-Nicoläı model like the well-posedness and the maximum principle. We also design numerical schemes for the non local models and analyze their consistency and stability properties.