The minimum dissipation state for tokamaks

The principle of minimum dissipation rate subject to helicity and energy balance is applied to tokamaks with an arbitrary aspect ratio. We solved the resulting Euler-Lagrange equations analytically and numerically. It is found that for low and general aspect ratio tokamaks, there exists different typical minimum dissipation state, corresponding to the typical experimental current profile respectively. It is also found that there exist different types of relaxed states in different regions of the parameter space for a selected device. Three forms of current profile are presented under different experimental conditions for a low aspect ratio tokamak like NSTX. The first peaks in the edge region of the high field side similar as the typical experimental form. The second peaks in the central region on the equatorial plane. The third may have a hole or reverse in the central part. E0/ηB0 is the key parameter in determining the final relaxed state; both the second and the third states could be obtained violently by increasing it to be above a critical value. (author)