Potential of a Bayesian integrated determination of the ion effective charge via Bremsstrahlung and charge exchange spectroscopy in Tokamak plasmas

IEEE Transactions on Plasma Science

Volumn 38, Issue 11 PART 2, 2010, Pages 3168-3196

  Verdoolaege, Geert ^a   Fischer, Rainer ^b   Van Oost, Guido ^a  

^a GHENT UNIVERSITY   (Belgium)

^b MAX PLANCK INSTITUT FÜR PLASMAPHYSIK   (Germany)

Author keywords

Bayesian probability theory (BPT); integrated data analysis (IDA); ion effective charge; tokamak plasmas

Indexed keywords

BAYESIAN; BAYESIAN PROBABILITY THEORY; CHARGE EXCHANGE SPECTROSCOPY; DATA CONSISTENCY; DATA SETS; EFFECTIVE CHARGE; ERROR BARS; EXPERIMENTAL DETERMINATION; FUSION PLASMAS; IMPURITY CONCENTRATION; IMPURITY TRANSPORT; INTEGRATED APPROACH; INTEGRATED DATA; OPERATIONAL SCENARIO; PROBABILISTIC MODELS; RIGOROUS ANALYSIS; STANDING PROBLEMS; STATISTICAL UNCERTAINTY; SYSTEMATIC DEVIATION; THERMONUCLEAR BURNS; TIME SLICE; TOKAMAK PLASMAS; UNCERTAINTY SOURCES;

BAYESIAN NETWORKS; CHARGE TRANSFER; DATA REDUCTION; ERROR ANALYSIS; FUSION REACTORS; ION EXCHANGE; IONS; MAGNETOPLASMA; PLASMA THEORY; PROBABILITY DENSITY FUNCTION; SPECTRUM ANALYSIS; SYSTEMATIC ERRORS;

UNCERTAINTY ANALYSIS;

EID: 78349283973     PISSN: 00933813     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPS.2010.2071884     Document Type: Article

References (57)

1. I. Hutchinson, Principles of Plasma Diagnostics, 2nd ed. Cambridge, U. K.: Cambridge Univ. Press, 2002.
2. R. Fischer, A. Dinklage, and E. Pasch, "Bayesian modelling of fusion diagnostics, " Plasma Phys. Control. Fusion, vol. 45, no. 7, pp. 1095-1111, Jul. 2003.
3. S. Arshad, J. G. Cordey, D. C. McDonald, J. Farthing, E. Joffrin, M. von Hellermann, C. M. Roach, and J. Svensson, "Chapter 11: Data validation, analysis, and applications for fusion plasmas, " Fusion Sci. Technol., vol. 53, no. 2, pp. 667-698, Feb. 2008.
4. R. Fischer, C. Wendland, A. Dinklage, S. Gori, and V. Dose, "Thomson scattering analysis with the Bayesian probability theory, " Plasma Phys. Control. Fusion, vol. 44, no. 8, pp. 1501-1519, Aug. 2002. (Pubitemid 34974938)
5. R. Fischer and A. Dinklage, "Integrated data analysis of fusion diagnostics by means of the Bayesian probability theory, " Rev. Sci. Instrum., vol. 75, no. 10, pp. 4237-4239, Oct. 2004.
6. A. Dinklage, R. Fischer, and J. Svensson, "Topics and methods for data validation by means of Bayesian probability theory, " Fusion Sci. Technol., vol. 46, no. 2, pp. 355-364, Sep. 2004.
7. G. Verdoolaege, "Bayesian integrated determination of the ion effective charge via bremsstrahlung and charge exchange spectroscopy in tokamak plasmas, " Ph. D. dissertation, Ghent Univ., Ghent, Belgium, 2006.
8. eff in the TEXTOR tokamak from bremsstrahlung and CX impurity density measurements, " in Bayesian Inference and Maximum Entropy Methods in Science and Engineering. Melville, NY: AIP, 2006, ser. AIP Conference Proceedings, pp. 541-548.
9. K. Kadota, M. Otsuka, and J. Fujita, "Space-and time-resolved study of impurities by visible spectroscopy in the high-density regime of JIPP T-II tokamak plasma, " Nucl. Fusion, vol. 20, no. 2, pp. 209-212, 1980.
10. eff from visible bremsstrahlung measurements on TEXTOR, " Rev. Sci. Instrum., vol. 77, no. 10, p. 10F310, Oct. 2006.
11. eff on TEXTOR, " LPP - Royal Military Academy, Brussels, Belgium, Tech. Rep. 92, 1990.
12. M. Krychowiak, R. König, and T. Klinger, "Bayesian analysis of the effective charge from spectroscopic bremsstrahlung measurements in fusion plasmas, " J. Appl. Phys., vol. 96, no. 9, pp. 4784-4792, Nov. 2004.
13. eff from spectroscopic bremsstrahlung measurements at ASDEX Upgrade and JET, " Rev. Sci. Instrum., vol. 75, no. 10, pp. 4097-4099, Oct. 2004.
14. I. Hutchinson, Principles of Plasma Diagnostics, 2nd ed. Cambridge, U. K.: Cambridge Univ. Press, 2002, ch. 5.
15. A. Boileau, M. von Hellermann, L. Horton, J. Spence, and H. Summers, "The deduction of low-Z ion temperature and densities in the JET tokamak using charge exchange recombination spectroscopy, " Plasma Phys. Control. Fusion, vol. 31, no. 5, pp. 779-804, May 1989.
16. M. von Hellermann and H. Summers, Active Beam Spectroscopy at JET. London, U. K.: Elsevier, 1993, p. 135.
17. M. von Hellermann, W. Mandl, H. Summers, H. Weisen, A. Boileau, P. Morgan, H. Morsi, R. Koenig, M. Stamp, and R. Wolf, "Visible Charge Exchange Spectroscopy at JET, " Rev. Sci. Instrum., vol. 61, no. 11, pp. 3479-3486, Nov. 1990.
18. C. Negus, C. Giroud, A. Meigs, K.-D. Zastrow, and D. Hillis, "Enhanced core charge exchange recombination spectroscopy system on Joint European Torus, " Rev. Sci. Instrum., vol. 77, no. 10, p. 10F102, Oct. 2006.
19. A. Boileau, M. von Hellermann, L. Horton, H. Summers, and P. Morgan, "Analysis of low-Z impurity behavior in jet by charge-exchange spectroscopy measurements, " Nucl. Fusion, vol. 29, no. 9, pp. 1449-1458, 1989.
20. H. Weisen, M. von Hellermann, A. Boileau, L. Horton, W. Mandl, and H. Summers, "Charge exchange spectroscopy measurements of ion temperature and toroidal rotation in JET, " Nucl. Fusion, vol. 29, no. 12, pp. 2187-2197, 1989. (Pubitemid 20624957)
21. M. Tunklev, P. Breger, K. Günther, M. von Hellermann, R. König, M. O'Mullane, and K.-D. Zastrow, "Modelling of passive charge exchange emission and neutral background density deduction in JET, " Plasma Phys. Control. Fusion, vol. 41, no. 8, pp. 985-1004, Aug. 1999.
22. M. von Hellermann, "A charge exchange analysis package for ITER, " in Proc. 3rd Workshop Fusion Data Process., Validation Anal., Cadarache, France, 2004.
23. M. von Hellermann, private communication, 2006.
24. eff (0) to edge radiation, " in Proc. Int. Conf. Plasma Phys., Innsbruck, Austria, 1992, vol. II, pp. 1147-1149.
25. eff profile measurements in the Tore Supra tokamak and their mitigation, " Rev. Sci. Instrum., vol. 76, no. 8, p. 083501, Aug. 2005.
26. T. Bayes, "An essay towards solving a problem in the doctrine of chances, " Phil. Trans. R. Soc. London, vol. 53, pp. 370-418, 1763.
27. P. Laplace, Théorie Analytique des Probabilités, 1st ed. Paris, France: Courcier, 1812.
28. R. Cox, "Probability, frequency and reasonable expectation, " Amer. J. Phys., vol. 14, no. 1, pp. 1-13, Jan. 1946.
29. E. Jaynes, Probability Theory: The Logic of Science. Cambridge, U. K.: Cambridge Univ. Press, 2003.
30. D. Sivia, Data Analysis: A Bayesian Tutorial. New York: Oxford Univ. Press, 1996.
31. T. Loredo, "From Laplace to supernova SN 1987A, " in Maximum Entropy and Bayesian Methods. Dordrecht, The Netherlands: Kluwer, 1990, pp. 81-142.
32. A. Gelman, J. Carlin, H. Stern, and D. Rubin, Bayesian Data Analysis, 2nd ed. Boca Raton, FL: Chapman & Hall/CRC, 2004.
33. D. MacKay, "Bayesian interpolation, " Neural Comput., vol. 4, no. 3, pp. 415-447, May 1992.
34. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equations of state calculations by fast computing machines, " J. Chem. Phys., vol. 21, no. 6, pp. 1087-1092, Jun. 1953.
35. W. Hastings, "Monte Carlo sampling methods using Markov chains and their applications, " Biometrika, vol. 57, no. 1, pp. 97-109, Apr. 1970.
36. A. Gelfand and A. Smith, "Sampling based approaches to calculating marginal densities, " J. Amer. Stat. Assoc., vol. 85, no. 410, pp. 398-409, Jun. 1990.
37. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, " IEEE Trans. Pattern Anal. Mach. Intell., vol. 6, no. 6, pp. 721-741, Nov. 1984.
38. A. Gelman, "Iterative and non-iterative simulation algorithms, " Comput. Sci. Statist., vol. 24, pp. 433-438, 1992.
39. L. Tierney, "Markov chains for exploring posterior distributions, " Ann. Statist., vol. 22, no. 4, pp. 1701-1728, Dec. 1994.
40. C. Robert and G. Casella, Monte Carlo Statistical Methods, 2nd ed. New York: Springer-Verlag, 2004.
41. R. Neal, Probabilistic inference Using Markov Chain Monte Carlo Methods, 1993. [Online]. Available: http://omega.albany.edu:8008/neal.pdf
42. W. Gilks, S. Richardson, and D. Spiegelhalter, Monte Carlo Statistical Methods. London, U. K.: Chapman & Hall, 1996.
43. D. Gamerman, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. London, U. K.: Chapman & Hall, 1997.
44. P. Gregory, Bayesian Logical Data Analysis for the Physical Sciences. Cambridge, U. K.: Cambridge Univ. Press, 2005.
45. J. Svensson, A. Dinklage, J. Geiger, A. Werner, and R. Fischer, "Integrating diagnostic data analysis for W7-AS using Bayesian graphical models, " Rev. Sci. Instrum., vol. 75, no. 10, pp. 4219-4221, Oct. 2004.
46. R. Fischer, E. Wolfrum, and J. Schweinzer, "Probabilistic lithium beam data analysis, " Plasma Phys. Control. Fusion, vol. 50, no. 8, p. 085009, Aug. 2008.
47. R. Fischer, E. Wolfrum, and J. Schweinzer, "Probabilistic lithium beam data analysis, " in Proc. 34th EPS Conf. Plasma Phys., Warsaw, Poland, 2007.
48. R. Fischer, E. Wolfrum, W. Suttrop, and A. Kallenbach, "Integrated density profile analysis in ASDEX Upgrade H-modes, " in Proc. 35th EPS Conf. Plasma Phys., Hersonissos, Greece, 2008.
49. S. Kullback, Information Theory and Statistics. New York: Dover, 1968.
50. H. Dreier, A. Dinklage, R. Fischer, M. Hirsch, P. Kornejew, and E. Pasch, "Design of diagnostics: Case studies for Wendelstein 7-X, " Fusion Sci. Technol., vol. 50, no. 2, pp. 262-267, Aug. 2006.
51. G. Matthews, S. Allen, N. Asakura, J. Goetz, H. Guo, A. Kallenbach, B. Lipschultz, K. McCormick, M. Stamp, U. Samm, P. C. Stangeby, K.-H. Steuer, A. Taroni, B. Unterberg, and P. West, "Scaling radiative plasmas to ITER, " J. Nucl. Mater., vol. 241-243, pp. 450-455, Feb. 1997.
52. G. Telesca, U. Samm, B. Unterberg, R. Koch, A. Messiaen, and G. Van Oost, "Radiated power and ionic effective charge during neon injection experiments on TEXTOR, " Nucl. Fusion, vol. 36, no. 3, pp. 347-358, Mar. 1996.
53. G. Roberts, A. Gelman, and W. Gilks, "Weak convergence and optimal scaling of random walk Metropolis algorithms, " Ann. Appl. Probab., vol. 7, no. 1, pp. 110-120, Feb. 1997.
54. M. Chen and Q. Shao, "Monte Carlo estimation of Bayesian credible and HPD intervals, " J. Comput. Graph. Statist., vol. 8, no. 1, pp. 69-92, Mar. 1999.
55. P. Sen and J. Singer, Large Sample Methods in Statistics. New York: Chapman & Hall, 1994.
56. A. Donné, A. E. Costley, R. Barnsley, H. Bindslev, R. Boivin, G. Conway, R. Fisher, R. Giannella, H. Hartfuss, M. G. von Hellermann, E. Hodgson, L. C. Ingesson, K. Itami, D. Johnson, Y. Kawano, T. Kondoh, A. Krasilnikov, Y. Kusama, A. Litnovsky, P. Lotte, P. Nielsen, T. Nishitani, F. Orsitto, B. J. Peterson, G. Razdobarin, J. Sanchez, M. Sasao, T. Sugie, G. Vayakis, V. Voitsenya, K. Vukolov, C. Walker, and K. Young, "Chapter 7: Diagnostics, " Nucl. Fusion, vol. 47, no. 6, pp. S337-S384, Jun. 2007.
57. K. Young, "Chapter 1: Plasma measurements: An overview of requirements and status, " Fusion Sci. Technol., vol. 53, no. 2, pp. 281-303, Feb. 2008.