Spheromak as a minimum dissipation non force-free state

The principle of minimum dissipation together with the constraint of global magnetic helicity leads to the Euler-Lagrange equation ∇ x ∇ x ∇ x B = ΛB for a closed system containing magnetized plasma. The spheromak configuration emerges as a solution of this equation on using analytically continued Chandrasekhar Kendall eigenfunctions in the complex domain and assuming conducting boundary conditions B·n = 0 and j x n = 0 at the boundary. The solutions differ significantly from the minimum energy state of Taylor as exhibited by a finite pressure gradient in the axisymmetric state. The value of β has been calculated in the z = 0 plane and is found to be about 40%. For values of Λ, higher than the value corresponding to minimum dissipation state, double humped spatial behaviour of j·B/B2 and hollow pressure profiles are exhibited. These results show a good agreement with those obtained by solving nonlinear Grad-Shafranov equation containing pressure. (author)