Some stationary solutions of two-fluid magnetohydrodynamic equations

Some stationary solutions of two-fluid magnetohydrodynamic equations are constructed using generalized helicity invariants. Solutions corresponding to the Z pinch, Bennett pinch, θ pinch, etc., are constructed. The Z-pinch-like solution is identical to Weibel's solution [Phys. Fluids 2, 52 (1959)], while the Bennett-pinch-like solution contains nonuniform axial drifts. By constructing the same solutions from the Vlasov--Maxwell system of equations, it is shown that the results obtained here are consistent with those of Mahajan [Phys. Fluids B 1, 43 (1989)]. Similarly, new θ-pinch-like solutions are constructed and the relation of these to earlier work is discussed