Thin filament simulations for Earth's plasma sheet: Tests of validity of the quasi-static convection approximation

The main goal of this paper is to estimate the errors involved in applying a quasi‐static convection model such as the Rice Convection Model (RCM) or its equilibrium version (RCM‐E), which neglect inertial currents, to treat the injection of fresh particles into the inner magnetosphere in a substorm expansion phase. The approach is based on the idea that the dipolarization process involves earthward motion of a bubble that consists of flux tubes that have lower values of the entropy parameter than the surrounding medium. Our tests center on comparing MHD simulations with RCM‐ and RCM‐E‐like quasi‐static approximations, for cases where the bubble is considered to be a thin ideal‐MHD filament. Those quasi‐static solutions miss the interchange oscillations that are often a feature of the MHD results. RCM and, to a lesser extent, RCM‐E calculations tend to overestimate the westward electric field at the ionospheric footprint of the bubble and underestimate its duration. However, both get the time integral of the E × B drift velocity right as well as the net energization of the particles in the filament. The quasi‐static approximation is most accurate if its computed value of the braking time of the bubble's earthward motion is long compared to the period of the relevant interchange oscillation. Comparison of MHD filament simulations of interchange instability with corresponding RCM calculations suggests a similar validity criterion. For plasma sheet conditions, the quasi‐static approximation is typically best if the background medium has lowβ, worst if it consists of highly stretched field lines. Key Points Quasi‐static models do not describe interchange oscillations Quasi‐static models are accurate on time scales long compared to inertial times Quasi‐static models tend to overestimate auroral electric fields in substorms