Inversion Techniques in the Soft-X-Ray Tomography of Fusion Plasmas: Toward Real-Time Applications

REFERENCES

• L. C. INGESSON, B. ALPER, B. J. PETERSON, and J.-C. VALLET, “Tomography Diagnostics: Bolometry and Soft X-Ray Detection,” Fusion Sci. Technol., 53, 528 (2008).
   Web of Science ®Google Scholar
• M. B. McGARRY et al., “Multicolor SXR Tomography on MST,” presented at American Physical Society 50th Annual Meeting of Division of Plasma Physics, Dallas, Texas, November 17–21, 2008; http://plasma.physics.wisc.edu/uploadedfiles/talk/apsdpp08McGarry532.pdf (current as of Mar. 15, 2010).
   Google Scholar
• L. GABELLIERI et al., “A Simplified Automatic Method to Infer Information About Impurity Content and Spatial Distribution in Tokamak Plasmas,” Europhysical Conference Abstracts: 36th Conf. Plasma Physics, Sofia, Bulgaria, June 29–July 3, 2009, Vol. 33E, p. P4.201, European Physical Society (2009).
   Google Scholar
• A. INCE-CUSHMAN et al., “Spatially Resolved High Resolution X-Ray Spectroscopy for Magnetically Confined Fusion Plasmas,” Rev. Sci. Instrum., 79, 10E302 (2008).
   Web of Science ®Google Scholar
• S. YAMAGUCHI, H. IGAMI, H. TANAKA, and T. MAEKAWA, “Three-Dimensional Observation of an Helical Hot Structure During a Sawtooth Crash in the WT-3 Tokamak,” Phys. Rev. Lett., 93, 045005 (2004).
   PubMed Web of Science ®Google Scholar
• J. P. QIAN et al., “Equilibrium Reconstruction of Plasma Profiles Based on Soft X-Ray Imaging in DIII-D,” Nucl. Fusion, 49, 025003 (2009).
   Google Scholar
• A. MURARI et al., “‘Burning Plasma’ Diagnostics for the Physics of JET and ITER,” Plasma Phys. Control. Fusion, 47, B249 (2005).
   Google Scholar
• Yu. V. GOTT and M. M. STEPANENKO, “Vacuum Photo-diode Detectors for Soft X-Ray ITER Plasma Tomography,” Rev. Sci. Instrum., 76, 073506 (2005).
   Google Scholar
• D. PACELLA and D. MAZON, “Soft X-Ray Diagnostics and Treatments for Future Real Time Applications,” AIP Conf. Proc., 988, 405 (2008).
   Google Scholar
• A. MURARI et al., “Development of Real-Time Diagnostics and Feedback Algorithms for JET in View of the Next Step,” Plasma Phys. Control. Fusion, 47, 3, 395 (2005).
   Google Scholar
• G. T. HERMAN, Fundamentals of Computerized Tomography, Springer-Verlag London Limited (2009).
   Google Scholar
• V. WEINZETTL et al., “Design of Multi-Range Tomographic System for Transport Studies in Tokamak Plasmas,” Nucl. Instrum. Methods Phys. Rev. A (2010)(to be published); doi: 10.1016/j.nima.2010.04.010.
   Google Scholar
• L. C. INGESSON et al., “Soft X Ray Tomography During ELMs and Impurity Injection in JET,” Nucl. Fusion, 38, 1675 (1998).
   Web of Science ®Google Scholar
• A. M. CORMACK, “Representation of a Function by Its Line Integrals, with Some Radiological Applications. II,” J. Appl. Phys., 35, 2908 (1964).
   Web of Science ®Google Scholar
• L. WANG and R. S. GRANETZ, “An Analytical Expression for the Radon Transform of Bessel Basis Functions in Tomography,” Rev. Sci. Instrum., 62, 1115 (1991).
   Google Scholar
• G. BONHEURE et al., “ANovel Method for Trace Tritium Transport Studies,” Nucl. Fusion, 49, 8, 085025 (2009).
   Google Scholar
• K. ERTL et al., “Maximum Entropy Based Reconstruction of Soft X Ray Emissivity Profiles in W7-AS,” Nucl. Fusion, 36, 1477 (1996).
   Google Scholar
• J. KIM and W. CHOE, “Fast Singular Value Decomposition Combined Maximum Entropy Method for Plasma Tomography,” Rev. Sci. Instrum., 77, 023506 (2006).
   Google Scholar
• P. C. HANSEN, “Numerical Tools for Analysis and Solution of Fredholm Integral Equations of the First Kind,” Inverse Problems, 8, 849 (1992).
   Web of Science ®Google Scholar
• G. C. FEHMERS, L. P. J. KAMP, and F. W. SLUIJTER, “An Algorithm for Quadratic Optimization with One Quadratic Constraint and Bounds on the Variables,” Inverse Problems, 14, 893 (1998).
   Web of Science ®Google Scholar
• M. ANTON et al., “X-Ray Tomography on the TCV Tokamak,” Plasma Phys. Control. Fusion, 38, 1849 (1996).
   Google Scholar
• G. DEMETER, “Tomography Using Neural Networks,” Rev. Sci. Instrum., 68, 1438 (1997).
   Google Scholar
• T. CRACIUNESCU et al., “A Comparison of Four Reconstruction Methods for JET Neutron and Gamma Tomography,” Nucl. Inst. Methods Phys. Res. A, 605, 3, 374 (2009).
   Google Scholar
• J. KIM, S. H. LEE, and W. CHOE, “Comparison of the Three Tokamak Plasma Tomography Methods for High Spatial Resolution and Fast Calculation,” Rev. Sci. Instrum., 77, 10F513 (2006).
   Google Scholar
• A. K. CHATTOPADHYAY, A. ANAND, and C. V. S. RAO, “Tomography for SST-1 Tokamak with Pixel Method,” Rev. Sci. Instrum, 76, 063502 (2005).
   Google Scholar
• S. KÁLVIN and L. C. INGESSON, “Performance Analysis of ITER Tomographic Systems,” AIP Conf. Proc., 988, 485 (2008).
   Google Scholar
• J. MLYNAR et al., “Investigation of the Consistency of Magnetic and Soft X-Ray Plasma Position Measurements on TCV by Means of a Rapid Tomographic Inversion Algorithm,” Plasma Phys. Control. Fusion, 45, 2, 169 (2003).
   Google Scholar
• Yu. N. DNESTROVSKIJ, E. S. LYADINA, and P. V. SAVRUKHIN, “The Space-Time Tomographic Problem of Plasma Diagnostics,” Sov. J. Plasma Phys., 18, 107 (1992).
   Google Scholar
• E. S. LYADINA et al., “A Space-Time Tomography Algorithm for the Five-Camera Soft X-Ray Diagnostic at RTP,” Europhysics Conference Abstracts: 20th Conf. Controlled Fusion and Plasma Physics, Lisbon, Portugal, July 26–30, 1993, Vol. 17C, Part III, p. 1151, European Physical Society (1993).
   Google Scholar
• T. CRACIUNESCU etal., “The Maximum Likelihood Reconstruction Method for JET Neutron Tomography,” Nucl. Instrum. Methods Phys. Res. A, 595, 623 (2008).
   Google Scholar
• N. TERASAKI et al., “Linear Algebraic Algorithms for High Speed and Stable Reconstruction of Plasma Image,” Fusion Eng. Des., 34–35, 801 (1997).
   Google Scholar
• J. R. BAKER, T. F. BUDINGER, and R. H. HUESMAN, “Generalized Approach to Inverse Problems in Tomography: Image Reconstruction for Spatially Variant Systems Using Natural Pixels,” Crit. Rev. Biomed. Eng., 20, 47 (1992).
   Google Scholar
• G. FUCHS, Y. MIURA, and M. MORI, “Soft X-Ray Tomography on Tokamaks Using Flux Coordinates,” Plasma Phys. Control. Fusion, 36, 307 (1994).
   Google Scholar
• R. S. GRANETZ and M. C. BORRÁS, “Is X-Ray Emissivity Constant on Magnetic Flux Surfaces?” Fusion Eng. Des., 34-35, 153 (1997).
   Google Scholar
• C. P. TANZI, H. J. DE BLANK, and A. J. H. DONNÉ, “A New Approach to Internal Disruption Analysis with the Five-Camera Soft-X-Ray Diagnostic on RTP,” Rev. Sci. Instrum., 66, 537 (1995).
   Google Scholar
• E. RONCHI et al., “Neural Networks Based Neutron Emissivity Tomography at JET with Real-Time Capabilities,” Nucl. Instrum. Methods Phys. Res. A, 613, 295 (2010).
   Google Scholar
• H. THOMSEN et al., “Application of Neural Networks for Fast Tomographic Inversion on Wendelstein 7-X,” Europhysics Conference Abstracts: 35th Conf. Plasma Physics, Crete, Greece, June 9–13, 2008, Vol. 32D, p. P-1.065, European Physical Society (2008).
   Google Scholar
• O. BARANA et al., “Neural Networks for Real Time Determination of Radiated Power in JET,” Rev. Sci. Instrum., 73, 2038 (2002).
   Google Scholar
• E. VAN DER GOOT, A. W. EDWARDS, and J. HOLM, “Real Time Application of Transputers for Soft X-Ray Tomography in Nuclear Fusion Research,” Proc. 1st Int. Conf. Applications of Transputers, Liverpool, United Kingdom, August 23–25, 1989, p. 306, IOS (1990).
   Google Scholar
• J. MLYNAR, B. P. DUVAL, J. HORACEK, and J. B. LISTER, “Present and Perspective Roles of Soft X-Ray Tomography in Tokamak Plasma Position Measurements,” Fusion Eng. Des., 66–68, 905 (2003).
   Google Scholar
• P. J. CARVALHO et al., “Real-Time Plasma Control Based on the ISTTOK Tomography Diagnostic,” Rev. Sci. Instrum., 79, 10, 10F329 (2008).
   Google Scholar