Accurate geomagnetic field models are crucial to the study of radiation belt phenomena. We quantitatively examine the accuracy of several external models widely in use via the Office National d'Etudes et de Recherche Aérospatiales‐Département Environnement Spatial (ONERA‐DESP) libraries. We study 2 years characterized by very different space weather conditions, 1996 and 2003. The year 1996, at solar minimum, exhibited many high‐speed streams and a few corotating interaction regions but was generally quiet. In contrast, 2003 included the Halloween storm, one of the most intense geomagnetic storms on record caused by a coronal mass ejection. The performance of each model, as measured by prediction efficiency and skill score, is evaluated as a function of magnetospheric conditions (reflected by the geomagnetic index Kp) and magnetic local time (MLT). Not surprisingly, the newer models tend to perform better and interesting comparisons arise between the performances of the models during different periods of the solar cycle and across different Kp and MLT values. For Kp < 4, most models show similar performance, but for higher values, there are large differences between newer and older model performance. As a function of MLT, noticeable dips in the performance of older models are observed near dawn. These dips are suspected to be effects of field‐aligned and partial ring currents that are not fully incorporated into the models, but their exact nature is unknown.

We calculate the quasi-stationary structure of a radiating shock wave propagating through a spherically symmetric shell of cold gas by solving the time-dependent equations of radiation hydrodynamics on an adaptive grid. We show that this code successfully resolves the shock wave in both the subcritical and supercritical cases and, for the first time, we have reproduced all the expected features -including the optically thin temperature spike at a supercritical shock front -without invoking analytic jump conditions at the discontinuity. We solve the full moment equations for the radiation flux and energy density, but the shock wave structure can also be reproduced if the radiation flux is assumed to be proportional to the gradient of the energy density (the diffusion approximation), as long as the radiation energy density is determined by the appropriate radiative transfer moment equation.We find that Zel'dovich and Raizer's analytic solution for the shock wave structure accurately describes a subcritical shock but it underestimates the gas temperature, pressure, and the radiation flux in the gas ahead of a supercritical shock. We argue that this discrepancy is a consequence of neglecting terms which are second order in the minimum shock compression ratio [η 1 = (γ − 1)/(γ + 1), where γ is the adiabatic index] and the inaccurate treatment of radiative transfer near the discontinuity. In addition, we verify that the maximum temperature of the gas immediately behind the shock is given by T + = 4T 1 /(γ + 1), where T 1 is the gas temperature far behind the shock.

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