Magnetohydrodynamic equilibrium with helicoidal symmetry

Abstract

We studied MHD equilibrium applying to the particular case of helicoidal coordinates, a formalism that leads to a differential equation for the magnetic flux ψ for equilibrium with an unknown variable in general curvilinear coordinates. The different possible equilibrium types may be defined with the knowledge of p=p(ψ) (pressure) and B_γ=B(ψ) (covariant component <γ> of the magnetic field). we solved this equation in the following cases: i) In the vacuum p=0; J=0 (J is the current density). ii) Force free cases, J is parallel to B. iii) p is linear function of ψ.