ECRH and Electron Heat Transport in Tokamaks

摘要

It has been shown that the solution of the simplified transport equation in a finite cylinder is a Fourier-Bessel series. This series represents in fact a decomposition of the heat source in eigenmodes, which are characterized by the Bessel functions of order 0. The physical interpretation of the eigenmodes is the following: when the heat source is given by a Bessel function of order 0, the temperature profile has exactly the same form as the source at every time. At the beginning of the power injection, the effectiveness of the temperature response is the same for each eigenmode, and the response in temperature, having the same form as the source, is local. Conversely, in the later phase of the evolution, the effectiveness of the temperature response for each eigenmode is different: the higher the order, the lower the effectiveness. In this case the response in temperature appears as non-local. It can be concluded that the profile resilience mainly results from two effects: the first one is that the lower order eigenmodes are more favored than the higher order; the second one (volume effect) is that the central source (ohmic heating) is favored with respect to the off-axis source (ECRH) in the contribution to the temperature profile shape. We emphasize that the resilience effect on the temperature profile is a basic and natural property of the diffusion equation in cylindrical geometry. All additional effects, as the heat pinch, critical gradient, etc, can reinforce this resilience. Finally, this analytical solution has been used with success for the determination of the transport coefficient and the polarization of the EC waves during ECRH experiments in the Tore Supra tokamak.