Adiabatic plasma equilibrium and application to a reconnection problem

The evolution of many plasma systems is adiabatic, i.e., plasma entropy is conserved in each magnetic flux tube. An apparently surprising result found recently from simulations of a forced magnetic reconnection problem (the 'Newton Challenge' [J. Birn et al., Phys. Plasmas 13, 092117 (2006)]) is that even in the presence of a dissipative process such as reconnection, the entropy within a flux tube can still be approximately conserved, due to the strong localization of the dissipation. To address plasma equilibrium with such adiabatic constraints, a novel code has been developed that computes equilibria with entropy profile as input, using the alternating dimension method [H. Grad et al., Proc. Natl. Acad. Sci. USA 72, 3789 (1975)]. The code alternates between solving the two-dimensional (2D) Grad-Shafranov equation to obtain the field configuration (flux function A) from the pressure profile P(A) and a 1D ordinary differential equation that uses the entropy conservation to derive the pressure function P(A) from a flux surface average. As a particular application, the code is used to compute equilibria relevant to the Newton Challenge, with a grid reflecting the reconnected state topology (with an X and an O point). The equilibria found agree very well with late stages of magnetohydrodynamic simulations of the Newton Challenge. This agreement not only validates the new code, but also proves that the final state approached by the reconnection simulations is indeed an equilibrium quasiadiabatically connected with the initial state. The results also show a significant release of magnetic energy through reconnection. Finally, other potential applications of the new code, especially to adiabatic evolution of space plasmas, are discussed