Neural networks for fast soft X-ray tomographic inversions in tokamaks

摘要

1.The tomographic inversion problem Reconstructing the local plasma emissivity in the soft X-ray (SXR) range 0.1-20 keV can be very useful to access crucial information on particle transport, magnetohydrodynamic activity or impurity content in tokamaks. In particular, radiative cooling of heavy impurities like tungsten (W) could be detrimental for the plasma core performances of ITER and developing robust and fast SXR diagnostics is an essential issue to monitor the impurities and to prevent their central accumulation. 2D tomography is the usual method to access the local SXR emissivity of the plasma in a poloidal cross-section of the tokamak from lineintegrated measurements of two or more pinhole cameras. In the Line-of-Sight (LoS) approximation, the m_j measurements of the j-th detector (in W.m~(-2)) looking at the plasma through the camera aperture is given by the following line integral, after spatial discretization of the plasma 2D emissivity field in N_p pixels: {formula} where ε_i is the plasma emissivity (in W.m~(-3)) in the i-th pixel filtered by the spectral response of the diagnostic, the transfer matrix element T_(ji) contains the length (in m) of the j-th LoS in the i-th pixel and ξ_j denotes systematic and statistical error such as electronic noise in the m_j measurements. This mathematically ill-posed and quite challenging problem is traditionally solved using the Tikhonov regularization, by adding a priori information on the emissivity distribution, which typically imposes smoothness of the reconstructed profile. The solution of Eq. 1 is then: {formula} where H is a regularization operator and the parameter λ acts as a balance between overfitting of the measurements and over-smoothing of the solution. The minimum Fisher information (MFI) method is the most commonly used in current European tokamaks like TCV [1], ASDEX Upgrade [2] or WEST [3]. Although significant progress is made on Tikhonov regularization methods to shorten the inversion time [4]