Representations of currents and magnetic fields in isotropic magnetohydrostatic plasma

Abstract

We develop the theory describing electric currents in magnetized plasma for the case of static equilibrium with isotropic pressure. The current density is determined by pressure balance and charge conservation. We show that the current density can be expressed as the sum of the current density determined by plasma pressure gradients, Jp = c▽F × ▽P, and the force‐free current density, Jf = gB, where F = ∫ ds/B is the flux tube volume per unit flux measured from a surface at which the normal component of Jp vanishes, P is the scalar pressure, and g is a field line constant. The expression explicitly satisfies charge conservation, and its perpendicular component is the usual perpendicular current density. In the absence of force‐free currents, J is a curl; in this case it is possible to introduce a magnetic scalar potential, ψ, that satisfies the equation ▽²ψ = −4π▽ · P▽F; the magnetic field can then be determined from B = −▽ψ −4πP▽F.