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10E503-3 Roche et al.
Rev. Sci. Instrum. 83, 10E503 (2012)
FIG. 3. Simulation with Gaussian input. Top left: Input image. Then from left to right, top to bottom: successive iterations of the algorithm. Notice how the iterative weighting recovers not only the shape, but the peak height of the input.
FIG. 5. Reconstructed density profiles during FRC equilibrium at 1 μs time steps. The units of both axes are centimeters. The white lines represent the 16 collimated lines of sight. The red arcs represent the position of the magnetic null at the depicted time slices.1
factors. Inverting the data at 1 μs intervals yields 2D images of the reconstruction area as shown in Fig. 5. The data pre- sented are typical during FRC equilibrium. The FRC is very stable during this 20–30 μs time window.
V. SUMMARY AND DISCUSSION
The design of a new tomographic apparatus was de- scribed. Its analysis methodology was explained and verified. Reconstruction of experimental data show the emissivity pro- file as a function of time for an FRC. Further analysis of these data show they represent the impurity density profile. This information has led to the preliminary calculation of the plasma’s diffusion coefficient of 10–103 m2/s.
1L. C. Steinhauer, Phys. Plasmas 18, 070501 (2011).
2 H. Gota, N. Bolte, B. Deng, D. Gupta, V. Kiyashko, K. Knapp, R. Mendoza,
M. Morehouse, T. Roche, and F. Wessel, Rev. Sci. Instrum. 81, 10D512
(2010).
3D. Gupta, N. Bolte, H. Gota, R. Hayashi, V. Kiyashko, P. Marsili, M.
Morehouse, S. Primavera, T. Roche, and F. Wessel, Rev. Sci. Instrum. 81,
10D730 (2009).
4M. Slepchenkov, M. Morehouse, V. Kiyashko, F. Wessel, N. Rostoker, N.
Bolte, and T. Roche, in 2011 IEEE/NPSS 24th Symposium on Fusion Engi-
neering (SOFE) (2011), pp. 1–5.
5Z. Pietrzyk, G. Vlases, R. Brooks, K. Hahn, and R. Raman, Nucl. Fusion
27, 1478 (1987).
6W. Pierce, R. Maqueda, R. Brooks, and R. Farengo, Nucl. Fusion 33, 117
(1993).
7M. Anton, H. Weisen, M. J. Dutch, W. vonderLinden, F. Buhlmann,
R. Chavan, B. Marletaz, P. Marmillod, and P. Paris, Plasma Phys. ControlledFusion38,1849(1996).
This leads us to the system of equations to be solved, ( T˜ T ∗ T˜ + H ( n ) ) ∗ g ( n + 1 ) = T˜ T ∗ ˜f ,
( 7 )
where we have set all of the ∂φ/∂gi = 0. A more complete derivation of these equations is available in Anton et al.7 The number of iterations that must be performed was determined by looking at successive reconstructions of simulated input data as shown in Fig. 3. The reconstructions converged after 4 iterations.
IV. EXPERIMENTAL DATA
Raw signals from a typical shot are displayed in Fig. 4. The signals have been adjusted by their associated calibration
FIG.4. SignalsfromPMTspreinversion.