Asymptotics of the Riemann–Hilbert Problem for a Magnetic Reconnection Model in Plasma

Abstract

For the Riemann–Hilbert problem in a singularly deformed domain, an asymptotic expansion is found that corresponds to the limit transition from Somov’s magnetic reconnection model to Syrovatskii’s one as the relative shock front length $$\varrho $$ tends to zero. It is shown that this passage to the limit corresponding to $$\varrho \to 0$$ is performed with the preservation of the reverse current region, while the parameter determining magnetic field refraction on shock waves grows as $${{\varrho }^{{ - 1/2}}}$$ . Moreover, the correction term to the Syrovatskii field has the order of $$\rho $$ and decreases in an inverse proportion to the distance from the current configuration.