Doppler-shifted neutral beam line shape and beam transmission

Analysis of Doppler-shifted Balmer-α line emission from the Tokamak Fusion Test Reactor's (TFTR) neutral beam injection systems has revealed that the line shape, which is a direct measure of the velocity distribution function, is well approximated by the sum of two Gaussians, or, alternatively, by a Lorentzian. For the sum of two Gaussians, the wide-divergence part of the distribution contains 40% of the beam power and has a divergence five times that of the narrow part. Assuming a narrow 1/e-divergence of 1.3 degree (based on fits to the beam shape on the calorimeter), the wide part has a divergence of 6.9 degree. The entire line shape is also well approximated by a Lorentzian with a half-maximum divergence of 0.9 degree. Up to now, most fusion neutral beam modelers have assumed a single Gaussian velocity distribution, at the extraction plane, in each direction perpendicular to beam propagation. This predicts a beam transmission efficiency from the ion source to the calorimeter of 97%. Waterflow calorimetry data, however, yield a transmission efficiency of ∼75%, a value in rough agreement with predictions of the two Gaussian or Lorentzian models presented here. The broad wing of the two Gaussian distribution also accurately predicts the loss in the neutralizer. An additional factor in determining the power density at the surface of beam absorbers is the angle at which the particles arrive. Angles are different for particles emitted from different locations on the ion source. To treat this situation, the average angle of incidence is calculated. For beam loss at the exit of the neutralizer, the average angle of incidence is 2.2 degree, rather than the 4.95 degree subtended by the center of the ion source. This average angle of incidence is found to be a function of beam divergence