Efficient way to find maximum a posteriori of nonnegative gaussian process tomography for plasma radiation during SPI induced disruption experiments

Shattered pellet injector (SPI) is designed to protect tokamaks from disruptions by dissipating stored plasma energy prompted by the injected pellets. KSTAR is equipped with two SPIs which allow us to study how differently the stored plasma energy is dissipated for different combinations of various pellet types and the relative injection times. For this purpose, reconstructing distribution of radiative power loss in space and time caused by the pellets is important. Total radiative power loss at a poloidal section is obtained by a tomographic reconstruction using the fast bolometer made of poloidal filtered AXUV detector arrays. Using the Gaussian process prior, reconstruction can be performed even with fewer number of lines of sight compared to the number of pixels, but the result shows negative radiation power for an asymmetric radiation distribution by the pellets. More accurate results could be obtained with the nonnegative prior and the Gibbs sampler, but it becomes computationally expensive when we have to deal with more than 1000 frames in each experiment. By introducing a more efficient method of calculating the maximum a posteriori for the truncated multivariate normal distribution, we are able to check the total radiation power results immediately after each experiment.