Self-organized states in sustained toroidal pinches

Toroidal pinches sustained longer than the resistive decay time of the conf iguration will self-organize into a state characterized by relatively weak magnetic fluctuations compared to those responsible for the initial relaxat ion. The time-averaged field profiles are not adequately described by Taylo r's theory, because the plasma is in a driven-dissipative state where the g lobal magnetic flux and helicity are not inherently constrained. It is prop osed here that the time-averaged fields should attain a state of minimum ma gnetic energy under the constraint of constant Ohmic energy dissipation rat e. This theory relates the field profiles to the resistivity profile eta(r) . In particular, it predicts that j/B --> 0 at the boundary if eta -->infin ity there, in agreement with experiment and physical intuition. The theory also predicts the pressure profile. (C) 2000 American Institute of Physics. [S1070- 664X(00)00410-9].