Abstract
In tokamak nuclear fusion reactors, one of the main issues is to know the total emission of radiation, which is mandatory to understand the plasma physics and is very useful to monitor and control the plasma evolution. This radiation can be measured by means of a bolometer system that consists in a certain number of elements sensitive to the integral of the radiation along straight lines crossing the plasma. By placing the sensors in such a way to have families of crossing lines, sophisticated tomographic inversion algorithms allow to reconstruct the radiation tomography in the 2D poloidal cross-section of the plasma. In tokamaks, the number of projection cameras is often quite limited resulting in an inversion mathematic problem very ill conditioned so that, usually, it is solved by means of a grid-based, iterative constrained optimization procedure, whose convergence time is not suitable for the real time requirements. In this paper, to illustrate the method, an assumption not valid in general is made on the correlation among the grid elements, based on the statistical distribution of the radiation emissivity over a set of tomographic reconstructions, performed off-line. Then, a regularization procedure is carried out, which merge highly correlated grid elements providing a squared coefficients matrix with an enough low condition number. This matrix, which is inverted offline once for all, can be multiplied by the actual bolometer measures returning the tomographic reconstruction, with calculations suitable for real time application. The proposed algorithm is applied, in this paper, to a synthetic case study.
Highlights
The tokamak is an experimental machine designed to exploit the energy from controlled fusion reaction [1]
The undetermined nature of the problem is usually compensated by minimizing a functional, which represents the a priori knowledge of the system under study. The drawback of these approaches is that the functional depends on the measures, and it cannot be optimized offline. This could represent a serious limit in monitoring the nuclear fusion reactors, where a timely intervention is necessary to react to phenomena with very rapid evolution, such as in case of disruption
The tomographic reconstruction, providing a 2-D image of the plasma radiation, is very useful to monitor the chain of events during a discharge, distinguishing different phenomena, such as impurity transport and accumulation into the plasma, plasma heating and even disruptions [25]
Summary
The tokamak is an experimental machine designed to exploit the energy from controlled fusion reaction [1]. Solving the linear system in (2) is referred to as the tomographic reconstruction problem, i.e., reconstructing the 2D plasma emissivity distribution in the poloidal tokamak cross-section starting from an often limited number of line-integrated, noisy, measures of the plasma radiation. In [24,25] the Maximum Likelihood method was implemented for the bolometer tomography at JET, where the likelihood probability density function was assumed to follow the error statistics of the experimental data In this case as well, the a priori information states the smoothness along the magnetic surfaces, given by the plasma equilibrium. A regularization procedure is performed, which merge highly correlated grid elements providing a resulting matrix with an enough low condition number In such a way, solution of Equation (2) can be obtained in real time allowing to monitor the discharge evolution.
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