A novel method to construct stationary solutions of the Vlasov-Maxwell system : the relativistic case

摘要

A method to derive stationary solutions of the relativistic Vlasov-Maxwellsystem is explored. In the non-relativistic case, a method using the Hermitepolynomial series to describe the deviation from the Maxwell-Boltzmanndistribution is found to be successful in deriving a few stationary solutionsincluding two dimensional one. Instead of the Hermite polynomial series, twospecial orthogonal polynomial series, which are appropriate to expand thedeviation from the Maxwell-J\"uttner distribution, are introduced in thispaper. By applying this method, a new two-dimensional equilibrium is derived,which may provide an initial setup for investigations of three-dimensionalrelativistic collisionless reconnection of magnetic fields.