Multiple X line reconnection: 1. A criterion for the transition from a single X line to a multiple X line reconnection

Abstract

In an earlier paper we suggested that the multiple X line reconnection process may occur at the dayside magnetopause and lead to the occurrence of flux transfer events. In a series of papers we shall examine in detail various aspects of the multiple X line reconnection processes. In the present paper, the first of the series, we attempt to obtain a criterion for the transition from the classical single X line reconnection to the multiple X line reconnection based on a two‐dimensional simulation model. It is found that the development of tearing instability in the diffusion region of the reconnection configuration may lead to the formation of magnetic islands and hence to the occurrence of multiple X line reconnection. The criterion for the tearing instability is found to be l/δ > 7 coth (8/S0.5), where S is the Lundquist number based on the width of the diffusion region, l is the half‐length, and δ the half‐width of the diffusion region. Furthermore, a formula is obtained for the dependence of the ratio l/δ on the system length Lz, the imposed reconnection rate R0, and the resistivity η. The ratio l/δ is found to increase with an increasing system length Lz, an increasing imposed reconnection rate R0, and a decreasing resistivity η. Therefore the multiple X line reconnection process tends to occur when the system length is long, the reconnection rate is high, or the resistivity is small.