Exponential Taylor states in circular cylinders

Abstract

Solutions to the Woltjer–Taylor relaxed plasma equation ∇×B=μB, with μ a constant, inside an infinitely long, circular cylinder with magnetically impermeable walls and no net axial magnetic flux, are obtained for complex k, where modal spatial dependence is exp i(mθ−kz). Complex k yields the continuum of externally driven states between μ=0 (currentless) and the finite ‖μ‖ free-states. The continuum states are related to formation of plasma from magnetized electrode sources.