The incompressible limit of the Euler-Maxwell two-fluid system

TL;DR

This paper proves the existence of modulation equations for the incompressible limit of the Euler-Maxwell two-fluid system, linking it to extended magnetohydrodynamics and enabling better understanding of plasma phenomena.

Contribution

It adapts the filtering unitary group method to establish well-posedness of asymptotic equations for the EMTF system, connecting them to XMHD.

Findings

Solutions of the asymptotic equations correspond to those of incompressible XMHD

Provides a new mathematical foundation for plasma phenomena analysis

Simplifies access to turbulence, Hall effects, and magnetic reconnection studies

Abstract

In this text, the filtering unitary group method developed, among others, by S. Schochet is adapted to prove the existence and well-posedness of modulation equations describing the incompressible limit of the Euler-Maxwell Two-Fluid (EMTF) system. The reduced model captures up to the ion and electron skin depths the long-time behavior of solutions near a constant neutral background with non-zero densities. In the prepared case, the solutions of our asymptotic equations are in one-to-one correspondence with those of incompressible eXtended MagnetoHyDrodynamics (XMHD), hence providing a new basis to the XMHD framework which is currently being studied by physicists through Hamiltonian methods, see P.J. Morrison et al. By this way, we can give a simplified access to many plasma phenomena such as (a form of two-fluid) turbulence, Hall and inertial effects, as well as collisionless magnetic reconnection.