MHD intermediate shocks in coronal mass ejections

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Abstract
We consider a simplified model of coronal mass ejections in which at least a portion of the interaction with the background corona involves a shock wave and examine the allowable shock solutions and their compressive signatures. The MHD shock‐jump equations have a maximum of three possible types of solutions with an entropy rise for fixed values of the physical variables (slow, intermediate, and fast shocks). However, one of the three solution classes (the intermediate shock) is widely believed to not occur in nature and is regarded as nonevolutionary or extraneous. Without the intermediate shock, there is no multiplicity of solutions in that only one shock (or none) can occur for given physical values. We consider all three potential shock types and show, solely on the basis of the shock‐jump equations, that intermediate shocks must exist along some segment of the shock front for certain parametric regimes and for conditions that probably occur in some coronal mass ejections. Intermediate shocks arise as a result of cross‐flow interactions in our study; that is, allowable shock solutions at certain locations in the flow field dictate that intermediate shocks occur in adjacent (perpendicular to the flow velocity) regions. Consequently, the flow must be treated as, at least, a two‐dimensional problem. Numerical simulations of the nonlinear, time‐dependent MHD equations in two dimensions verify the formation of intermediate shocks as predicted from arguments based on analytic theory.