Bill M. Day, Jr.
Supervisor: David L. Hwang
Building 661, Room 13, L-794
Lawrence Livermore National Laboratory
Livermore, California 94550
Investigation into the creation, behavior, and stability of ionized gases becomes ever more important as advances are made in the confinement and control of fusion-grade plasmas. The Davis Diverted Torus, a relatively small research tokamak (a donut-shaped fusion vessel designed to confine plasma with strong magnetic fields), operates to better understand the underlying principles which govern plasma generation, energy injection, and control issues.
One proposed way of fueling such a device involves injecting hot "rings" of plasma into the tokamak using a compact torus electromagnetically accelerated injection system (see Figure 1). To properly run experiments to determine the viability of such a system, a method is needed whereby one may accurately ascertain what amount of plasma is being injected and how much energy it contains. Such a system requires the detection of radiation emitted by the ionizing plasma, organization and storage of the volumes of measured emissivities, and finally computerized reconstruction of the data to produce useful images of temperature, ion density, etc.1 J. J. Engbrecht worked to develop the vacuum ultraviolet (VUV) detector array design and D. B. Sinars designed and prototyped a high-speed analog-to-digital converter (ADC) for data transmission and storage, while I focused on programming a simulation of the proposed geometry to find out which reconstruction algorithm would give the quickest, most accurate results with the least number of detector arrays possible (thus minimizing hardware cost). Please see Figure 2 for a schematic of the diagnostic equipment.
After familiarizing myself with the workings of the available Absoft Fortran 77 Compiler and Macintosh Programmers Workshop and reviewing the image processing and computerized tomography literature, I coded an additive routine known as "simple backprojection." This method reconstructs on an imposed x-y grid. It requires that conversions be made between the x-y grid and the index notation which describes the hardware geometry (where 1,1,1 would indicate the first detector array, first detector, and first step out this detector's direction). The method gives very crude results and was quickly discarded as insufficient for the desired reconstruction, but it did give some preliminary hints as to how many arrays of detectors might be needed for a more precise reconstruction.
I next considered a far more advanced method, the maximum entropy method (MENT). As implemented, it is based heavily upon the work of the Experimental Test Accelerator Group at LLNL and B. A. Jacoby's extant Fortran code2,3. The method seems ideal in that it assumes no prior knowledge, except that the Second Law of Thermodynamics applies, i.e. that natural systems move towards the most disorderly, and therefore probable, state consistent with the line-averaged radiation measurements. The length of code required for this reconstruction is easily ten times that of the backprojection, yet the results can be seen to be much better in its many successful applications in the scientific and medical fields.
Unfortunately, the complexity of the geometry has required very tedious development and debugging cycles, and as of now I have not achieved a stable, converging MENT simulation. However, preliminary results from backprojection simulations indicate that three or four detector arrays, with approximately sixteen detectors each, will provide adequate resolution in the reconstructed image. This relatively small number of detector arrays (which, taken together with their ADC's comprise the majority of the diagnostic system's expense) should allow for fairly fine reconstruction of temperatures, densities and impurity content of the generated plasmas.
