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Approximate analytic solutions exist for particle motion in a one‐dimensional current sheet with a constant normal magnetic field component. These solutions are tested against precise numerical calculations, and a range of validity of the analytic solutions is inferred. For example, in the geomagnetic tail neutral sheet, for a dawn‐dusk electric field of 0.1–1 mV/m, lobe field of 10–40 nT, and sheet thickness of 1000 km, the analytic solutions serve as a good predictor of particle motion when the normal magnetic field component is less than 3 or 4 nT. By using the analytic solutions, initial distribution functions are mapped into final (accelerated) distributions, and the analytic mappings are compared with numerical mappings.
Speiser et al. (Sun,) studied this question.