TCABR tokamak rotation profile reconstruction

Abstract

From observations of the radiative emission of the plasma column, which can be considered symmetrically cylindrical and optically transparent, it is possible to obtain information about the radial distribution of this radiation (Abel's problem). The study of the radial profile of quantities, such as ionic temperature, the spatial distribution of impurities, and density, are of great interest to plasma physics because they provide us with information about localized phenomena. There are numerous computational methods to solve the Abel problem. A very old method, but very illustrative of the problems that arise when trying to solve an equation like Abel's, is called Pearce's numerical method. It consists of dividing the plasma column cross-section into concentric rings, and the emissivity µ(r) is considered constant inside each ring that is limited by the radii RK and rk1, where: (RK rk1 ) = r0/m; m represents the number of rings. The question naturally arises: which of the numerous existing methods is the most suitable for obtaining the radial distribution of plasma emissivity? It can be said with certainty that all methods are both good and bad. The problem lies in the fact that the Abel equation belongs to a class of mathematical problems called ill-conditioned where a small fluctuation in the input data produces a large fluctuation in the output data. Thus, for the same value in RK we can find the functions µ1(RK) and µ2(RK) which are both very different, but both satisfy the initial conditions of the problem. In this research project, we intend to use the Pearce method to write a routine that allows us to study the influence of the noise level in obtaining the emissivity profiles. It is also intended to investigate some methods used to obtain the emissivity profile and write a routine that allows us to reconstruct the spatial profile of plasma rotation velocity in the tokamak TCABR. (AU)