Toroidal flow-caused change in magnetic topology of equilibrium eigenstates

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 ω 2 ∕ T ∝ M 0 = const and d ( ϱ ω 2 ) ∕ d ψ = A ψ , respectively, where ω ( ψ ) is the rotation frequency. In both cases eigenfunctions of the form ψ ℓ n = Z ℓ ( z ) R n ( 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 ways: either as flow eigenvalues, M 0 ℓ and A ℓ , which depend on a pressure parameter P 0 or as pressure eigenvalues P 0 ℓ , which depend on the flow parameters, M 0 or A . In the context of the latter consideration when the flow parameters are varied continuously there are transition points, ( M 0 ) m and A m ( m = 1 , 2 , … ) , at which an additional magnetic axis is formed. This flow-caused change in magnetic topology is possible solely in the presence of toroidicity because in the limit of infinite aspect ratio the axial flow does not appear in the equilibrium equation. Also, the lower the aspect ratio the smaller ( M 0 ) m and A m . In addition, the effects of the flow and the aspect ratio on the Shafranov shift are evaluated along with the variations of density and temperature on magnetic surfaces.