Toroidal flow-caused change in magnetic topology of equilibrium eigenstates

Abstract

Equilibrium eigenstates of an axisymmetric magnetically confined plasma with toroidal flow are investigated by means of exact solutions of the ideal magnetohydrodynamic equations. The study includes “compressible” flows with constant temperature T(ψ), but varying density on magnetic surfaces and incompressible ones with constant density ϱ(ψ), but varying temperature thereon [the function ψ(R,z) is the poloidal magnetic flux function with (R,z,ϕ) cylindrical coordinates]. These variations are necessary for the existence of tokamak steady states with flow. The “compressible” and incompressible solutions are associated with the ansatz ω2∕T∝M0=const and d(ϱω2)∕dψ=Aψ, respectively, where ω(ψ) is the rotation frequency. In both cases eigenfunctions of the form ψln=Zl(z)Rn(R) (l,n=1,2,…) describe configurations with l×n magnetic axes. A connection between multitoroidal configurations and reversed magnetic shear is also identified. Owing to the flow, the respective eigenvalues can be considered in two alternative...