Numerical calculation of free boundary equilibrium via meshfree method and its application in Alborz tokamak

Abstract

In the present study, the calculation of free boundary axisymmetric tokamak equilibrium has been presented via the meshfree numerical method. This method of calculation has not been used previously for free boundary condition. As a practical application of the proposed numerical method two approaches of Alborz plasma equilibrium calculations were taken into account. First, the design of the poloidal field coil system has been carried out with consideration of the limiter. Second, the calculation has been developed by considering the divertor configuration. Considering the absence of analytical solution for free boundary condition, the validity of the code was examined by three different methods. The convergence of this method was checked by error calculation. Also the mathematical numerical correctness and accuracy were investigated by a comparison with the finite difference method and the uniqueness of a solution was confirmed by the independence on variations of the computational domain. The decrement trend in errors behavior was observed and the error for near circular configuration was reached less than 1e−4 in a few iterations. Moreover, the minimum Root Mean Squared (RMS) error achieved by the MLS method was 5.4826e−6 that correspond to the divertor configuration. The good results obtained from the verification process prove that the methodology applied here is reliable for tokamak equilibrium calculations and can be used as an effective tool in future studies.