Neutral-beam injection into a tokamak, part I: fast-ion spatial distribution for tangential injection

Abstract

The production processes and spatial distribution of fast ions resulting from tangential injection of a diffuse neutral beam into a tokamak are discussed. The spatial distribution of fast ions for various injection trajectories and absorption mean free paths are calculated and discussed in detail. Maximum beam absorption for a parabolic density profile is shown to occur for injection roughly halfway between the inner wall of the torus and the magnetic axis; however, since this maximum is near unity and only weakly dependent on the injection trajectory, this is not the most important possible optimization. Since the drift orbit surface area over which the fast ions are distributed is roughly proportional to the distance from the magnetic axis, the fast ion density is found to be strongly peaked at the magnetic axis for present experiments where the absorption mean free path λ is comparable to the plasma radius a. This geometric peaking effect is strong enough to overcome the exponential beam attenuation and cause the fast-ion density and consequent beam energy deposition to be peaked at the plasma centre as long as λ0 ≳ a/4. Charge exchange of the fast ions with neutrals in the plasma can deplete the fast-ion population, particularly near the plasma edge. When charge exchange is an important loss mechanism, beam injection nearly tangent to the magnetic axis is found to maximize the beam effectiveness in heating.