Abstract
The generalized Helmholtz equations of relativistic multifluid plasmas can be integrated for axisymmetric equilibria in close analogy to the magnetic flux conservation law in ideal magnetohydrodynamics [J. D. Bekenstein and E. Oron, Phys. Rev. D 18, 1809 (1978)]. The results are, for each fluid component, two flux functions and a potential equation for the poloidal stream function. Amp\`ere's equation for the four-potential ${A}_{\ensuremath{\nu}}$ is reduced to two coupled equations for the time-like and the toroidal component. So we have altogether four potential equations for a two-component plasma; they can be derived from a variational principle.
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