Because of the vast memory requirements in multidimensional electromagnetic wave propagation calculations and in the postprocessing of the data, we employ massively parallel processing (MPP) techniques on the Cray massively parallel supercomputer T3D located at the National Energy Research Supercomputer Center, NERSC.
Calculations of the scattered field due to density fluctuations in 2 and 3 dimensions are performed with our LLNL collaborator Dr. Bedros Afeyan's SOFTSTEP code (see Theory and Simulation of the Temporal Evolution of Fluctuation Reflectometry Signals, Sherwood Fusion Theory Conference, 1995). SOFTSTEP utilitizes the Split Operator Fast Fourier Transform (FFT) technique to solve sets of Slow-Temporal-Envelope Parabolic partial differential equations. By averaging over the electromagnetic timescale, the resulting equations which are solved by SOFTSTEP track the space-time evolution of the scattered field on the timescale of the evolution of the fluctuations without being taxed by the burden of tracking the typically thousand-fold faster microwave period. For a given fluctuation spectrum, SOFTSTEP calculations produce the amplitude and phase of the scattered signal at any desired observation point. This is the direct problem in fluctuation reflectometry.
A major challenge in the postprocessing of SOFTSTEP simulations involves the reconstruction of the fluctuation spectrum that gave rise to the computed scattered field. This is the inverse problem in fluctuation reflectometry. Our approach is to use holographic techniques to calculate interference patterns between scattered signals at various locations in the observation plane. By computing the coherence properties and correlations between various moments of these field distributions, we can obtain valuable information on the wavelength spectrum and location of the fluctuations.
The various massively parallel postprocessing routines we have developed are a crucial part of our experimental efforts to reconstruct density fluctuations from our reflectometry data. These multipurpose tools are an integral part of UCD's plasma diagnostics program.
