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.

中文翻译：

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等离子体中磁重联模型的Riemann-Hilbert问题的渐近性

摘要

对于奇异变形域中的Riemann–Hilbert问题，当相对冲击前沿长度\（\ varrho \）趋于零时，发现了一个渐进扩展，它对应于从索莫夫的磁重连接模型到Syrovatskii的极限过渡。结果表明，在保留反向电流区域的情况下，进行到对应于\（\ varrho \ to 0 \）的极限的传递，而确定冲击波的磁场折射的参数随\（{{\ varrho} ^ {{--1/2}}} \）。此外，对Syrovatskii字段的校正项的阶数为\（\ rho \），并且与距当前配置的距离成反比减小。