Relaxed states for Ohmically driven tokamaks with an arbitrary aspect ratio

Abstract

The relaxed state of plasma in Ohmically driven tokamaks with an arbitrary aspect ratio is explored using the principle of minimum dissipation rate subject to the helicity and the energy balance. The resulting Euler–Lagrange equations are solved analytically and numerically. The self-consistent solutions of whole Euler–Lagrange equations as well as both helicity and energy balance equations are obtained numerically for the given parameters and boundary conditions. It is found that for low and general aspect ratio tokamaks, there exist different typical minimum dissipation states, corresponding respectively to different typical current profiles observed in experiments. It is also found that there exist different types of relaxed states in the different regions of the parameter space for a selected device. Each current profile mode is achieved by adjusting controllable parameters such as plasma resistivity, boundary toroidal magnetic field or boundary electric field. The results show that there exists a key parameter E0/ηB0 in determining the final relaxed states. The typical minimum dissipation state may evolve to other forms of states abruptly by increasing E0/ηB0 to be above a critical value. Three forms of current profile are presented for the low aspect ratio National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)]. The first form peaks in the edge of the high field side similar to 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 region. Both the second and third states could be obtained by increasing E0/ηB0 to be above the critical value.