Eur. Phys. J. D (2014) 68: 175
https://doi.org/10.1140/epjd/e2014-50007-9

Regular Article

Tokamak-like Vlasov equilibria^*

¹ Max-Planck-Institut für Plasmaphysik, Euratom Association, 85748 Garching bei München, Germany
² Department of Physics, University of Ioannina, Association Euratom-Hellenic Republic, 451 10 Ioannina, Greece

^a e-mail: gthroum@cc.uoi.gr

Received: 2 January 2014
Received in final form: 27 February 2014
Published online: 27 June 2014

Abstract

Vlasov equilibria of axisymmetric plasmas with vacuum toroidal magnetic field can be reduced, up to a selection of ions and electrons distributions functions, to a Grad-Shafranov-like equation. Quasineutrality narrow the choice of the distributions functions. In contrast to two-dimensional translationally symmetric equilibria whose electron distribution function consists of a displaced Maxwellian, some toroidal equilibria need deformed Maxwellians. In order to be able to carry through the calculations, the two cases considered here are produced by means of either a Heaviside step function or an exponential function. The resulting Grad-Shafranov-like equations are established explicitly.