Equilibrium configurations of Vlasov plasmas carrying a current component along an external magnetic field

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Abstract
A class of equilibrium configurations of Vlasov plasmas carrying a current component along an external magnetic field is presented. The present slab model contains the diamagnetic current jy, and the field-aligned current jz for arbitrary βc (= particle pressure/magnetic pressure of the applied constant field). For fixed βc and field-aligned current, our model admits a family of equilibrium solutions in which the diamagnetic currents range from zero to a maximum value. The amount of diamagnetic current flowing in a machine depends on the width of the machine, the field-aligned current and other plasma parameters. The Helmholtz free energy of the system is calculated under the constraints that the total number of particles and the field-aligned current are conserved. The least unstable equilibrium configuration in a machine is obtained by minimizing the free energy under the stated constraints among all equilibria whose plasma widths do not exceed the width of the machine.