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 principal which minimizes the free energy 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. ¿American Geophysical Union 1987