Jump conditions in transonic equilibria

In the present paper, the numerical calculation of transonic equilibria, first introduced with the FLOW code in Guazzotto [Phys. Plasmas 11, 604 (2004)], is critically reviewed. In particular, the necessity and effect of imposing explicit jump conditions at the transonic discontinuity are investigated. It is found that standard (low- β, large aspect ratio) transonic equilibria satisfy the correct jump condition with very good approximation even if the jump condition is not explicitly imposed. On the other hand, it is also found that high- β, low aspect ratio equilibria require the correct jump condition to be explicitly imposed. Various numerical approaches are described to modify FLOW to include the jump condition. It is proved that the new methods converge to the correct solution even in extreme cases of very large β, while they agree with the results obtained with the old implementation of FLOW in lower- β equilibria.