Schematic of magnetic geometry showing ideal MHD barriers , and the relaxed plasma regions .
Pressure profile used for demonstrating the limit of MRXMHD. The continuous curve is the pressure profile in Eq. (41) which is used with VMEC, and the stepped profile is the N = 16 approximation used with SPEC.
Comparison of magnetic surfaces: zero-pressure ( ); the SPEC interfaces are shown in thin lines (upper and lower half) and the VMEC surfaces are shown in thick lines (upper half only).
Comparison of magnetic surfaces: high-pressure ( ); the SPEC interfaces are shown in thin lines (upper and lower half) and the VMEC surfaces are shown in thick lines (upper half only).
Convergence: the error (Δ) between the continuous pressure (VMEC) and stepped pressure (SPEC) solutions are shown as a function of the number of plasma regions N for the s = 1/4 SPEC interface. The dotted line shows the zero-beta case ( ), and the solid line shows the high-beta case ( ). The grey line has a slope −2, the expected rate of convergence. These simulations were run on a single 3 GHz Intel Xeon 5450 CPU with the longest (the N = 128 case) taking 10.1 min using 20 poloidal Fourier harmonics and 768 fifth-order polynomial finite elements in the radial direction.
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