Nonlinear ballooning instability in the near‐Earth magnetotail: Growth, structure, and possible role in substorms

To examine the scenario that the onset of a substorm can be triggered by ballooning instabilities in the near‐Earth magnetotail, we have performed three‐dimensional direct magnetohydrodynamic simulations of the nonlinear evolution of the ideal ballooning instability in two types of analytic Grad‐Shafranov equilibria of the magnetotail. The nonlinear growth and spatial structure (in both real and spectral spaces) of the instability are obtained for both classes of equilibria, and its observable consequences are explored. In particular, the linearly unstable ballooning mode is demonstrated to grow exponentially in the early nonlinear phase, and it starts to slow down or saturate in the intermediate nonlinear phase. The intermediate nonlinear phase is characterized by the formation of fine‐scale patterns determined by the dominant k y mode and spatially discontinuous structures that tend to accumulate at the stagnation point of the sheared flow profile spontaneously generated by the instability. It is proposed that, unlike the predictions of a theory of explosive nonlinear growth, the nonlinear ballooning instability, by itself, cannot produce a current disruption. However, the possibility remains open that the ballooning instability, when coupled to current‐driven instabilities and nonideal mechanisms such as reconnection and turbulent transport, may produce current sheet disruption in the near‐Earth magnetotail.