Radial electric field structure between electrodes separated by a finite distance in tokamak plasmas

Various types of peaked structure in the radial electric field are predicted theoretically in edge biasing experiments using electrodes. A nonlinear diffusion equation is employed to describe the radial electric field, and is solved in the region bounded by electrodes. Structures with multiple peaks are allowed when the distance between electrodes is finite. The minimum value for the distance between electrodes is obtained. The distance between electrodes, the externally driven current and the applied voltage determine the number of solutions. Multiple transitions and hysteresis are predicted from the relationship between the voltage and the current.