
Physics 1999
Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flowsDOI: 10.1017/S0022377899008041 Abstract: A recent study on axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas {\bf 5}, 2378 (1998)] is extended to the generic case of helically symmetric equilibria with incompressible flows. It is shown that the equilibrium states of the system under consideration are governed by an elliptic partial differential equation for the helical magnetic flux function $\psi$ containing five surface quantities along with a relation for the pressure. The above mentioned equation can be transformed to one possessing differential part identical in form to the corresponding static equilibrium equation, which is amenable to several classes of analytic solutions. In particular, equilibria with electric fields perpendicular to the magnetic surfaces and nonconstantMachnumber flows are constructed. Unlike the case in axisymmetric equilibria with isothermal magnetic surfaces, helically symmetric $T=T(\psi)$ equilibria are overdetermined, i.e., in this case the equilibrium equations reduce to a set of eight ordinary differential equations with seven surface quantities. In addition, it is proved the nonexistence of incompressible helically symmetric equilibria with (a) purely helical flows (b) nonparallel flows with isothermal magnetic surfaces and the magnetic field modulus being a surface quantity (omnigenous equilibria).
