Finite beta effects on MHD equilibria and energetic ion losses in a rippled tokamak

The efficiency of energetic ion confinement is reduced by ripple fields, which are mainly generated by the finite number of toroidal field coils in a tokamak reactor. Finite beta effects alter magnetic field structures and energetic ion orbits. Finite beta effects on magnetohydrodynamic (MHD) equilibria have been thoroughly researched. However, it is not known how finite beta effects affect energetic ion losses. To investigate this, the MHD equilibrium was calculated using the VMEC code. Finite beta effects on the ripple ratio were accurately investigated and it was found that the non-axisymmetric poloidal field generated by the plasma current could not be ignored. The guiding centre orbit equation was solved to clarify physical considerations of finite beta effects on the energetic ion losses. The energetic ion orbits were found to be strongly affected by the diamagnetic effect. By performing calculations for energetic ions with the same initial position, it was found that the diamagnetic effect produced two opposing effects: it reduced particle loss due to the closed |B| contour and it increased particle loss due to the high curvature of the |B| contour

The Finite Beta Effects on the Toroidal Field Ripple in a Tokamak Plasma

The efficiency of energetic ion confinement is reduced in a tokamak plasma by the non-axisymmetric field, namely the ripple field. The ripple field is produced by a finite number of toroidal field coils. It is affected by the non-axisymmetric finite beta effect. The three-dimensional MHD equilibrium calculation code VMEC is used to analyze the non-axisymmetric finite beta effect in a ripple tokamak. In the VMEC code, the flux coordinates are used, so the calculation region is limited to the area of plasma. To calculate the orbit outside the plasma, we develop a field calculation code, which is based on the Biot-Savart law. The details of the method and results are described in this paper