Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flows

A recent study on axisymmetric ideal magnetohydrodynamic equilibria with in compressible flows [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas 5, 2 378 (1998)] is extended to the generic case: of helically symmetric equilib ria with incompressible flows. It is shown that the equilibrium states of t he system under consideration are governed by an elliptic pal tial differen tial equation for the helical magnetic flux function psi containing five su rface quantities along with a relation for the pressure. The above-mentione d equation can be transformed to one possessing a differential part identic al in form to the corresponding static equilibrium equation, which is amena ble to several classes of analytical solutions. In particular equilibria wi th electric fields perpendicular to time magnetic surfaces and non-constant -Mach-number flows are constructed. Unlike the case in axisymmetric equilib ria with isothermal magnetic surfaces, helically symmetric T = T(psi) equil ibria are overdetermined, i.e. in this case the equilibrium equations reduc e to a set of eight ordinary differential equations with seven surface quan tities. In addition, the non-existence is proved of incompressible helicall y symmetric equilibria with (a) purely helical flows and (b) non-parallel f lows with isothermal magnetic surfaces and with the magnetic field modulus a surface quantity (omnigenous equilibria).