Limit model for the Vlasov–Maxwell system with strong magnetic fields via gyroaveraging

Abstract

This paper deals with the Vlasov–Maxwell system in the case of a strong magnetic field. After a physically motivated nondimensionalization of the original system, a Hilbert expansion is employed around a small parameter given as the product of the characteristic time scale and the gyrofrequency. From this, necessary conditions on the solvability of the reduced system are derived. An important aspect is the reduction of the six-dimensional phase space to five dimensions. In addition to the discussion of the partial differential equations, also initial and boundary conditions both for the full system and the limit model are studied.