Numerical model for electron cyclotron heating profiles in stellarator geometry

Abstract

A model is described which scales electron cyclotron heating (ECH) profiles derived from ray tracing over a range of plasma beta. The model includes terms that incorporate the magnetic geometry and the local dependence on density and temperature. With this model, a heating profile generated from ray tracing is calculated once for a given magnetic field and used to predict new heating profiles for arbitrary beta without any need for further ray tracing. One immediate application is the use of the predicted profiles as input to time dependent transport codes so that the contribution of the heating term can be updated as often as desired, with essentially no computational cost. The present level of sophistication permits realistic prediction of heating profiles (agreement of 20% between the integrated power predicted from ray tracing and the scaling model) over several orders of magnitude in plasma beta. Since temperature and density dependence is incorporated in the model, sensitivity to different profile shapes can also be predicted. This model is applied to the laborious calculation of the rays that scatter from the vacuum chamber walls of the Advanced Toroidal Facility (ATF) device. The calculations are done for the second harmonic extraordinary mode, but the model is immediately applicable to other heating scenarios, such as the fundamental ordinary mode. Also presented is a method for calculating the effect of multiple wall reflections which removes the need for complicated and expensive calculations to trace the rays through numerous reflections.