A quasi‐thermodynamic model is presented for the relaxation of magnetotail plasmas during substorms, followed by quiet times. It is proposed that the plasma relaxes to a state of low‐potential energy subject to a small number of global constraints. The constraints are exactly preserved by all ideal motions and, approximately, by a wide class of nonideal motions of the plasma undergoing magnetic reconnection. A variational principle which minimizes the free energy predicts the relaxed state. Exact, two‐dimensional solutions of the relaxed state are obtained. A universal feature of the exact solutions is a chain of magnetic islands along the tail axis. Sufficient conditions for the stability of relaxed states are obtained from the second variation of the free‐energy functional.
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A. Bhattacharjee (1987) studied this question.
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