Abstract
In order to investigate finite beta effects on the toroidal field ripple in a tokamak, three-dimensional free-boundary magnetohydrodynamics (MHD) equilibria are studied for a tokamak configuration that has an aspect ratio of 3.5 and an almost circular cross-section. Equilibria that are consistent with the non-axisymmetric external magnetic field are obtained by the VMEC code with a prescribed safety factor profile. To study tokamak configurations with a free-boundary constraint, we modify the boundary condition to specify the plasma position and size in the VMEC code. From the equilibria obtained, the change of the toroidal field ripple due to the finite pressure is calculated and the three-dimensional MHD effect on the ripple is estimated. In a finite pressure equilibrium, the toroidal ripple is changed by the equilibrium plasma current. The influence of the purely three-dimensional MHD effect on the toroidal field ripple is not large but the ripple is also changed by the variation of the axisymmetric component in finite pressure equilibria. In a medium-beta equilibrium, high energy particle confinement changes significantly due to the variation of the ripple well depth along the field line, because of the Shafranov shift, the change of the magnetic field line pitch due to the Pfirsch–Schlüter current, and the above mentioned finite pressure effect on the field ripple.
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