Gyrokinetic calculations of heat fluxes in the T-10 tokamak ohmic discharge

Cover Page

Cite item

Full Text

Abstract

The results of the first gyrokinetic calculations of anomalous heat fluxes in the T-10 tokamak plasma obtained for typical conditions of a discharge No. 71568 with ohmic heating are presented. The calculations have been performed at the Kurchatov Institute Supercomputer Center. The experimentally measured electron density and temperature profiles, ion temperature profiles with a large gradient leading to the so-called ion temperature gradient (ITG) turbulence, and also the profiles of carbon and oxygen impurity densities measured using the charge exchange recombination spectroscopy (CXRS) active diagnostics are used as input data. The “experimental” electron and ion heat fluxes are estimated from the heat balance condition using the ASTRA transport code. The analytical dependence of heat fluxes on the effective plasma charge is presented. Gyrokinetic calculations of anomalous electron and ion heat fluxes are performed for the T-10 tokamak for the first time. The well-known gyrokinetic GENE code is used in the so-called linear and nonlinear approximation with fixed density and temperature gradients taking into account the influence of carbon and oxygen impurities. A linear dependence of heat fluxes on the effective plasma charge is found, and the sensitivity of the results to input parameter errors is investigated. The results of gyrokinetic calculations for the T-10 tokamak are compared with the results obtained for facilities with similar input parameters. A comparison is made of gyrokinetic calculations of heat fluxes performed using the GENE code with the results of calculations by the CONTRA-T code, intended for the self-consistent simulation of low-frequency turbulence and transport processes in tokamaks with a large aspect ratio. Good agreement obtained in the work between the results of transport calculations using the ASTRA, GENE, and CONTRA-T codes based on various transport models for the ohmic discharge of the T-10 tokamak with a circular cross section, provides grounds for the further simulation of transport processes in plasma with additional heating and a more complex cross section shape of the plasma column.

Full Text

Restricted Access

About the authors

M. Yu. Isaev

National Research Centre “Kurchatov Institute”

Author for correspondence.
Email: isaev_my@nrcki.ru
Russian Federation, Moscow

O. Anuaruly

Al-Farabi Kazakh National University

Email: isaev_my@nrcki.ru
Kazakhstan, Almaty

A. Yu. Kuyanov

National Research Centre “Kurchatov Institute”

Email: isaev_my@nrcki.ru
Russian Federation, Moscow

D. V. Smirnov

National Research Centre “Kurchatov Institute”

Email: isaev_my@nrcki.ru
Russian Federation, Moscow

References

  1. Hinton F.L. and Hazeltine R.D. // Review of Modern Physics. 1976. V. 48. No. 2, P. 239.
  2. Yushmanov P.N., Takizuka T., Riedel K.S., Kardaun O.J., Cordey J.G., Kaye S.M. and Post D.E. // Nucl. Fusion. 1990. V. 30, No. 10. P. 1999.
  3. Vershkov V.A., Sarychev D.V., Notkin G.E., Shelukhin D.A., Buldakov M.A., Dnestrovskij Yu.N., Grashin S.A., Kirneva N.A., Krupin V.A., Klyuchnikov L.A., Melnikov A.V., Neudatchin S.V., Nurgaliev M.R., Pavlov Yu.D., Savrukhin P.V. and T-10 team. // Nucl. Fusion. 2017. V. 57. P. 102017.
  4. Dimits A.M., Bateman G., Beer M.A., Cohen B.I., Dorland W., Hammett G.W., Kim C., Kinsey J.E., Kotschenreuther M., Kritz A.H., Lao L.L., Mandrekas J., Nevins W.M., Parker S.E., Redd A.J., Shumaker D.E., Sydora R., and Weiland J. // Physics of Plasmas. 2000. V. 7. P. 969.
  5. Jenko F., Dorland W. and Kotschenreuther M. // Physics of Plasmas. 2000. N. 7. P. 1904.
  6. Lapillone X., Brunner S., Dannert T., Jolliet S., Matinoni A., Villard L., Goerler T., Jenko F., and Merz F. // Physics of Plasmas. 2009. V. 16. P. 032308.
  7. Citrin J., Arnichand H., Bernardo J., Bourdelle C., Garbet X., Jenko F., Hacquin S., Pueschel M.J., and Sabot R. // Plasma Phys. Cont. Fusion. 2017. V. 59. P. 064010.
  8. Creely A.J., Goerler T., Conway G.D., Freethy S.J., Howard N.T., Schneider P.A., W hite A.E., Will ensdorfer M. and The ASDEX Upgrade Team. // Nucl. Fusion. 2018. V. 58. P. 126001.
  9. Citrin J., Jenko F., Mantica P., Toss D., Bourdelle C., Dumont R., Garcia J., Haverkort J.W., Hogeweij G.M.D., Johnson T., Pueschel M.J. and JET-EFDA contributors. // Nucl.Fusion. 2014. V. 54. P. 023008.
  10. Klyuchnikov L.A., Krupin V.A., Nurgaliev M.R., Korobov K.V., Nemets A.R., Dnestrovskij A.Yu., Tugarinov S.N., Serov S.V., Naumenko N.N. // Rev. Sci. Instrum. 2016. V. 87. P. 053506.
  11. Pereverzev G.V., Yushmanov P.N. Preprint IPP. 2002. 5/98.
  12. Vershkov V.A., Buldakov M.A., Subbotin G.F., Shelukhin D.A., Melnikov A.V., Eliseev L.G., Kharchev N.K., Khabanov P.O., Drabinskiy M.A., Sergeev D.S., Myalton T.B., Trukhin V. M., Gorshkov A.V., Belbas I.S., Asadulin G.M. // Nucl. Fusion. 2019. V. 59. P. 066021.
  13. Nurgaliev M.R., Krupin V.A., Klyuchnikov L.A., Nemets A.R., Zemtsov I.A., Dnestrovskiy A.Yu., Borschegovskiy A.A., Kislov A.Ya., Sarychev D.V., Solovev N.A., Trukhin V.M., Pimenov I., Sergeev D.S., Myalton T.B., Tugarinov S.N., Naumenko N.N. // Proc. 46 th EPS Conference on Plasma Physics, Milan, Italy, P5.1078, July 2019.
  14. Krupin V.A., Nurgaliev M.R., Nemets A.R., Zemtsov I.A., Khabanov P. O., Drabinskiy M.A., Lysenko S.E., Melnikov A.V., Myalton T.B., Sergeev D.S., Solovev N.A., Sarychev D.V., Ryjakov D.V., Tugarinov S.N., Naumenko N.N. // Phys. Plasmas. 2022. V. 29. P. 062508.
  15. Houlberg W.A., Shaing K.C., Hirshman S.P., Zarnstorff M.C. // Phys. Plasmas. 1997. V. 4. P. 3230.
  16. Krupin V.A., Klyuchnikov L.A., Nurgaliev M.R., Nemets A.R., Zemtsov I.A., Dnestrovskiy A.Yu., Grashin S.A., Kislov A.Ya., Myalton T.B., Sarychev D.V., Sergeev D.S., Solovev N.A. and Trukhin V.M. // Plasma Phys. Control. Fusion. 2020. V. 62. P. 025019.
  17. Hirshman S.P., Hawryluk R.J. and Birge B. // Nucl. Fusion. 1977. V. 17. P. 611.
  18. Dux R. / Preprint IPP. 2006. 10/30.
  19. Spitzer L., Harm R. // Phys. Review. 1953. V. 89. No. 5, P. 977.
  20. Sauter O., Angioni C. and Lin-Liu Y. R. // Physics of Plasmas. 1999. V. 6. P. 2834.
  21. Hey J. D., Lie Y. T., Rusbüldt D., Hintz E. // Contributions to Plasma Physics. 1994. V. 34. No. 6. P. 725.
  22. Брагинский С. И. Вопросы теории плазмы / Под ред. M. A. Леонтовича. М.: Госатомиздат. 1963. Вып. 1. С. 183.
  23. Huba J.D. NRL Plasma Formulary.2011. ht tp: //wwwppd.nrl.navy.mil/nrlformulary .
  24. http: //genecode.org
  25. http: //computing.kiae.ru
  26. Balay S., Buschelman K., Eijlhout V., Gropp W.D., Kaushik D., Knepley M.G., McInnes L.C., Smith B.F. and Honh Zhang. // PETSc User Manual, 2004. ANL-95/11 – Rev.2.1.5.
  27. Miller R.L., Chu M.S., Greene J.M., Lin-Liu Y.R., Waltz R.E. // Phys. of Plasmas, 1998. V. 5. P. 973.
  28. Peeters A.G., Angioni C., Apostoliceanu M., Jenko F., Ryter F. // Phys. Of Plasmas. 2005. V. 12. P. 022505.
  29. Isaev M.Y., Anuaruly О., Brunner S., Goerler Т., Nurgaliev М.R., Pueschel M.J., Smirnov D.V., Teslyuk A.B. // Proc. XLIX Zvenigorod International Conference on Plasma Physics and Controlled Fusion, Zvenigorod, Russia, 20.3.2022. P. 20.
  30. Vershkov V.A., Buldakov M.A., Subbotin G.F., Shelukhin D.A., Melnikov A.V., Eliseev L.G., Kharchev N.K., Khabanov P.O., Drabinskiy M.A., Sergeev D.S., Myalton T.B., Trukhin V.M., Gorshkov A.V., Belbas I.S. and Asadulin G.M. // Nucl. Fusion. 2019. V. 59. P. 066021.
  31. Пастухов В.П., Смирнов Д.В., Чудин Н.В. // Физика плазмы. 2023. Т. 49. № 7. C. 609.
  32. Pastukhov V. P., Chudin N.V., Smirnov D.V. // Plasma Physics and Controlled Fusion, 2011, 53, 054015.
  33. Пастухов В.П., Кирнева Н.А., Смирнов Д.В. // Физика плазмы 2019. Т. 45. № 12. С. 1072.
  34. Isaev M.Y., Leonov V.M., Medvedev S.Y. // Fusion Science and Technol. 2019. V. 75. P. 218.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Radial profiles of the 71568 discharge calculated using the ASTRA code: a) electron and deuteron densities; b) electron and ion temperatures; c) carbon and oxygen ion densities; d) effective plasma charge and stability margin.

Download (285KB)
Indexing metadata
3. Fig. 2. Radial profiles of the 71568 discharge calculated using the ASTRA code: a) specific (per unit volume) power of ohmic heating, power of Coulomb interaction; b) radiation losses and recharge losses.

Download (120KB)
Indexing metadata
4. Fig. 3. Radial profiles of the 71568 discharge calculated using the ASTRA code: a) thermal fluxes of electrons (upper curve) and ions (lower curve); b) convective losses of electrons (upper curve) and ions (lower curve).

Download (169KB)
Indexing metadata
5. Fig. 4. Dependence of the Spitzer conductivity on the effective plasma charge (black line) and the power function (circles).

Download (53KB)
Indexing metadata
6. Fig. 5. Electron and ion heat fluxes at the average plasma radius depending on the relative concentration of carbon and oxygen ions, obtained using the ASTRA code (without the STRAHL module) for discharge T-10#71568.

Download (158KB)
Indexing metadata
7. Fig. 6. The GENE coordinate system (X, Y, Z) located on the field line (thick solid line) on an element of the magnetic surface with an average radius r / a = 0.5 of the T-10 tokamak.

Download (45KB)
Indexing metadata
8. Fig. 7. Normalized growth rate (circles) and frequency (squares) as a function of wave number k y ρ s calculated using the GENE code in the linear approximation for the T 10#71568 discharge with a two-component model at R / L n = 5.0, Z eff = 1.0. The frequencies of the ITG modes are positive, and the TEM modes are negative.

Download (75KB)
Indexing metadata
9. Fig. 8. Maximum normalized growth increment (circles) and frequency (squares) as a function of normalized temperature gradient calculated using GENE code for T-10 discharge #71568 with two-component plasma model at R/L n = 5.0, Z eff = 1.0. The region with R/L Ti < 5 is marked as TEM (T rapped Electron M ode), the region with R/L Ti > 5 is marked as ITG. Frequencies of ITG modes are positive, TEM modes are negative.

Download (69KB)
Indexing metadata
10. Fig. 9. Maximum growth increment as a function of the normalized ion temperature gradient calculated using the GENE code for the T-10 discharge #71568 with the four-component plasma model at Zeff = 1.6, for R/L n = 2.0 (circles), R/L n = 4.5 (squares), R/L n = 5.0 (crosses).

Download (63KB)
Indexing metadata
11. Fig. 10. Normalized frequency versus normalized ion temperature gradient calculated using GENE code for T-10 discharge #71568 with four-component plasma model at Zeff = 1.6 for R/L n = 2.0 (circles), R/L n = 4.5 (squares), R/L n = 5.0 (crosses). Frequencies of ITG modes are positive, TEM modes are negative.

Download (61KB)
Indexing metadata
12. Fig. 11. Normalized increments as a function of the effective plasma charge Z eff, calculated using the GENE code for the T -10 discharge #71568 with the four-component plasma model at k y ρ s = 0.15 (circles), k y ρ s = 0.20 (squares), k y ρ s = 0.30 (crosses), k y ρ s = 0.40 (diamonds).

Download (62KB)
Indexing metadata
13. Fig. 12. Normalized increments as a function of the temperature ratio T e / T i, calculated using the GENE code for the T -10 discharge #71568 with the four-component plasma model at ky ρ s = 0.15 (circles), ky ρ s = 0.20 (squares), ky ρ s = 0.30 (crosses), ky ρ s = 0.40 (diamonds).

Download (76KB)
Indexing metadata
14. Fig. 13. Electron (circles) and ion (crosses) heat fluxes < Q > V ´ ‚ at the average plasma radius, r / a = 0.50, depending on the normalized ion temperature gradient R / L Ti, calculated using the GENE code for the two-component discharge plasma model T -10#71568 at R / L Te = 7.2, R / L ni = R / L ne = 4.5.

Download (49KB)
Indexing metadata
15. Fig. 14. Electron (circles) and ion (crosses) heat fluxes < Q > V ´ ‚ at the average plasma radius, r / a = 0.50, depending on the normalized electron temperature gradient R / L Te, calculated using the GENE code for a two-component discharge plasma T 10#71568 in the nonlinear approximation at R / L Ti = 6.4, R / L ne = R / L ni = 4.5.

Download (49KB)
Indexing metadata
16. Fig. 15. Nonlinear evolution of thermal fluxes of electrons (circles) and ions (crosses), calculated using the GENE code for a two-component plasma discharge T -10#71568 at an average plasma radius r / a = 0.50 at R / L n = 4.5, R / L Ti = 6.4, R / L Te = 7.2.

Download (117KB)
Indexing metadata
17. Fig. 16. Nonlinear evolution of thermal fluxes of electrons (circles) and ions (crosses), calculated using the GENE code for a four-component plasma discharge T 10#71568 at an average plasma radius r / a = 0.50 at R / L n = 4.5, R / L Ti = 5.8, R / L Te = 7.5.

Download (86KB)
Indexing metadata
18. Fig. 17. Distribution of fluctuations of the normalized electron density in the plane perpendicular to the field line, calculated using the GENE code for the T-10#71568 discharge.

Download (273KB)
Indexing metadata
19. Fig. 18. Radial dependences of time-averaged heat fluxes in electrons (black solid line) and ions (gray dotted line) for Z eff = 1.7, obtained using the CONTRA-T code.

Download (50KB)
Indexing metadata
20. Fig. 19. Time evolutions of thermal fluxes of electrons (black curve) and ions (gray curve), obtained using the CONTRA-T code for the average plasma radius at Z eff = 1.7.

Download (108KB)
Indexing metadata
21. Fig. 20. Heat fluxes as a function of the effective plasma charge Z eff calculated for the T10#71568 discharge using the ASTRA code (without the STRAHL auxiliary module) for electrons (hollow circles), ions (crosses), using the gyrokinetic code GENE using a two-component model for electrons (asterisks) and for ions (hollow squares) at the mean plasma radius at R / L n = 4.5, R / L Ti = 6.4, R / L Te = 7.2. The heat fluxes obtained using the ASTRA/STRAHL code from Fig. 3a at the mean plasma radius r / a = 0.5 are shown by diamonds for electrons and triangles for ions. The heat fluxes obtained using the CONTRA-T code at the mean plasma radius r / a = 0.5 are shown by solid squares for electrons and solid circles for ions.

Download (57KB)
Indexing metadata

Copyright (c) 2024 Russian Academy of Sciences