Relaxed, minimum dissipation states, for a flux core spheromak sustained by helicity injection

Minimum dissipation states of a flux core spheromak sustained by helicity injection are presented. Helicity balance is used as a constraint and the resistivity is considered to be non-uniform. Two types of relaxed states are found: one has a central core formed by the flux that links the electrodes surrounded by a toroidal region of closed flux surfaces and the other has the open flux wrapped around the closed flux surfaces. The analysis includes two important features: a self-consistent calculation of the magnetic flux through the electrodes and a resistivity which depends upon the poloidal flux. Non-uniform resistivity effects can be very important because of the qualitative and quantitative changes they produce in the safety factor profile.