Title:

Determining the Equilibrium State of a High-Temperature Plasma in a Magnetic Confinement Nuclear Fusion Reactor

Magnetic confinement fusion has long been seen as the “Holy Grail” for clean, renewable energy. With a number of tokamaks coming online in the next decade (SPARC, ITER, and NSTX-U, to name a few), finding good equilibrium solutions for axisymmetric plasmas is a necessary step in both tokamak design and subsequent stability analysis. The Grad-Shafranov equation is a 2D ideal magnetohydrodynamic (MHD) equilibrium equation that can match the toroidal shape of tokamak plasmas. First, we wrote a modified successive over-relaxation Poisson solver that can compute analytical solutions to the Grad-Shafranov equation and the Shafranov shift with accuracy. Next, we applied additional methods from the literature to generate equilibrium solutions that better account for the additional poloidal field coils and Ohmic heating solenoids of modern tokamaks [1, 2]. These methods include adding a Picard iteration to update the source function, critical point analysis, and use of the Green’s function for an axisymmetric current source. References [1] J. Johnson, H. Dalhed, J. Greene, R. Grimm, Y. Hsieh, S. Jardin, J. Manickam, M. Okabayashi, R. Storer, A. Todd, D. Voss, and K. Weimer, “Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria”, Journal of Computational Physics 32, 212–234 (1979). [2] S. Jardin, Computational Methods in Plasma Physics (CRC Press, 2010).

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