Analytical formula for pellet fuel source density in toroidal plasma configurations based on an areal deposition model

Abstract

An analytical formula for the fuel source density η F (Ψ) over a magnetic flux surface Ψ following pellet injection is derived. During pellet motion the ablated and ionized fuel will be initially deposited nearby the pellet, prior to subsequent homogenization within the magnetic flux surfaces. Here in our research, it is assumed that the deposition area projected normal to the magnetic field is on the order of the cross-sectional area of the ionized ablation column whose axis is aligned with the magnetic field. Previous pellet deposition codes [1] employed a point source deposition approximation, which overpredicts the surface-averaged density, particularly when the obliquity between the pellet trajectory and the flux surface normal approaches 90 degrees. A key finding of this study is that as the obliquity approaches 90 degrees, grazing trajectory, the areal model predicts a well behaved η F and removes the unphysical divergence stemming from the point model. To illustrate the difference exhibited between areal and point models for near grazing trajectories, we considered vertical pellet injection into a CFETR-like tokamak with a negative triangularity plasma cross section using a pellet ablation/deposition module.