A Finite Element Versus Analytical Approach to the Solution of the Current Diffusion Equation in Tokamaks

Abstract

This paper deals with two efficient approaches for solving the current diffusion equation (CDE), which governs current diffusion through the conductive plasma inside a tokamak and compares them to CRONOS tokamak simulation suite, as well. Namely, CDE is solved via the finite-element method (FEM) and an analytical technique, respectively, and the obtained results are subsequently compared with the solution obtained from the state-of-the-art CRONOS suite with finite-difference calculations. The FEM solution is carried out featuring the use of linear and Hermite type shape functions, respectively, while the analytical solution is obtained by applying certain approximations to the CDE. The tradeoff between different approaches has been undertaken. Thus, the results obtained via the FEM approach (with Hermite basis function, in particular) show very good agreement with the CRONOS results, while also providing the stability of the solution. On the other hand, the results obtained via the analytical solution clearly demonstrate a good agreement with the numerical results in the edge region, which makes it very useful for various applications, e.g., for benchmarking purposes.