Toroidal equilibrium analysis of an axi-symmetric plasma

For controls and stability analysis of an axi-symmetric toroidal plasma, such as a tokamak and a reversed field pinch, the authors have developed the code solving Grad-Shafranov (GS) equation as a free boundary condition including external poloidal coil currents. A FEM algorithm of this code is fundamentally based on the one proposed by Semenzato, et.al. and they choose the next hybrid type functional for the GS equations to adjust boundaries of elements where difference interpolation functions are used, such as two node semi-infinite element. Using the flux function I(ψ) = rBt of a toroidal field proposed by M. Suzuki, et.al., the authors analyzed a toroidal equilibrium of a reversed field pinch configuration including finite pressure gradient and external poloidal coil currents. A typical example of an equilibrium of R/a = 4, β = 0.1, F = -0.25 and θ = 1.8 is shown. Calculated results of the toroidal effect on F - Θ curve and a RFP equilibrium with a poloidal divertor will be presented