We investigate single charged particle dynamics in the Earth's magnetotail using a simple, scale free magnetic field model which is explicitly time dependent, with a corresponding induction electric field. The time-dependent Hamiltonian of particle motion in the simple model describes a system of two coupled oscillators which is driven. When the (time-dependent) ratio of the oscillation frequencies is different from unity, the motion is regular, but if it approaches unity at some point on the trajectory, the motion becomes chaotic. A parametric &agr; is found which characterizes the adiabaticity of the system, and the transition time for behavior in the system is given by &agr;t→1. The condition &agr;t≈1 is equivalent to &kgr;≈1 in the static parabolic field model discussed by previous authors (Buchner and Zelenyi, 1989). The explicit time dependence produces two possible classes of motion, ordered by &agr;. If the reversal is thick and is folding slowly, so that &agr;≪1, the motion is a transition in behavior, from regular &mgr; conserving the chaotic ''cucumberlike'' trajectories, when t≈1/&agr;. If on the other hand, the reversal is thin and folds quickly, so that &agr;≫1, the particles execute regular ''ring type'' trajectories once t>1/&agr;.

Simple estimates of presubstorm magnetotail parameters indicate that electrons in a slowly thinning (15-min time scale), thick (1RE) sheet have &agr;≪1, whereas protons in a thin (several hundreds of kilometers) sheet which thins on a 5-min time scale have &agr;≫1. Hence the behavior of the particles, and by implication, the field reversal which they support, will depend upon the adiabaticity of the system &agr;, as well as the ''chaotization'' parameter &agr;t; this is shown only to be the case in a model which is explicitly time dependent and which includes the induction electric field. ¿ American Geophysical Union 1993