Existence and uniqueness of the pressure profile p(A) of a current-carrying quasineutral equilibrium plasma

It is proved that the nonlinear integral equation (quasineutrality condition) for the electrostatic potential φ of an isothermal quasineutral current-carrying equilibrium plasma with translational invariance has a solution φ(A) determined uniquely up to an arbitrary additive constant, where A is the magnetic flux function. This implies the existence and uniqueness of the pressure profile p(A). The existence proof is constructive, which implies its potential usefulness for the practical computation of current-carrying plasma equilibria.