Skip to main content
SpringerLink
Log in

Development of Rapid Simulation Code for NBI Heating Analysis in LHD

  • Original Research
  • Published:
Journal of Fusion Energy Aims and scope Submit manuscript

Abstract

We develop a rapid simulation code for neutral beam injection (NBI) heating analysis, FIT3D-RC, to evaluate the power deposition in NBI-heated plasmas of the Large Helical Device (LHD). This code evaluates the beam ion birth profile using the Gaussian process regression (GPR) model applied to precomputation results by the Monte Carlo simulation and calculates the power deposition profile by NBI heating based on the simple analytical solution of the Fokker-Planck equation. We apply this code to the NBI heating in LHD and compare the results with the conventional code (conv-FIT3D). We obtain good agreement in the power deposition profiles calculated by FIT3D-RC and that by conv-FIT3D. Furthermore, the calculation time is significantly reduced compared to the previously available codes. FIT3D-RC is expected to be used for the high-speed analysis and prediction of NBI-heated plasmas.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. J. Wesson, Tokamaks, 4th edn. (Oxford University Press, Oxford, 2011)

    MATH  Google Scholar 

  2. Y. Takeiri, T. Morisaki, M. Osakabe, M. Yokoyama, S. Sakakibara, H. Takahashi, Y. Nakamura, T. Oishi, G. Motojima, S. Murakami et al., Extension of the operational regime of the lhd towards a deuterium experiment. Nuclear Fusion 57(10), 102023 (2017). https://doi.org/10.1088/1741-4326/aa7fc2

    Article  ADS  Google Scholar 

  3. K. Tani, M. Azumi, H. Kishimoto, S. Tamura, Effect of toroidal field ripple on fast ion behavior in a tokamak. J. Phys. Soc. Japan 50(5), 1726–1737 (1981). https://doi.org/10.1143/JPSJ.50.1726

    Article  ADS  Google Scholar 

  4. R.J. Goldston, D. McCune, H. Towner, S. Davis, R. Hawryluk, G. Schmidt, New techniques for calculating heat and particle source rates due to neutral beam injection in axisymmetric tokamaks. J. Comput. Phys. 43(1), 61–78 (1981). https://doi.org/10.1016/0021-9991(81)90111-X

    Article  ADS  MATH  Google Scholar 

  5. M. Weiland, R. Bilato, R. Dux, B. Geiger, A. Lebschy, F. Felici, R. Fischer, M. Rittich, E.M. Van Zeeland, E.M. Team et al., Rabbit Real-time simulation of the nbi fast-ion distribution. Nuclear Fusion 58(8), 082032 (2018). https://doi.org/10.1088/1741-4326/aabf0f

    Article  ADS  Google Scholar 

  6. S. Murakami, N. Nakajima, M. Okamoto, Finite beta effects on the icrf and nbi heating in the large helical device. Trans. Fusion Technol. 27, 256 (1995)

    Article  Google Scholar 

  7. S. Murakami, A. Fukuyama, T. Akutsu, N. Nakajima, V. Chan, M. Choi, S. Chiu, L. Lao, V. Kasilov, T. Mutoh et al., A global simulation study of icrf heating in the lhd. Nuclear fusion 46(7), 425 (2006). https://doi.org/10.1088/0029-5515/46/7/S05

    Article  Google Scholar 

  8. H. Lee, K. Ida, M. Osakabe, M. Yokoyama, C. Suzuki, K. Nagaoka, R. Seki, M. Yoshinuma, N. Tamura, Group, L.E., et al., Dynamic transport study of heat and momentum transport in a plasma with improved ion confinement in the large helical device. Plasma Phys. Controlled Fusion 55(1), 014011 (2012). https://doi.org/10.1088/0741-3335/55/1/014011

  9. M. Yokoyama, R. Seki, C. Suzuki, M. Sato, M. Emoto, S. Murakami, M. Osakabe, T.I. Tsujimura, Y. Yoshimura, T. Ido et al., Extended capability of the integrated transport analysis suite, task3d-a, for lhd experiment. Nuclear Fusion 57(12), 126016 (2017). https://doi.org/10.1088/1741-4326/aa800a

    Article  ADS  Google Scholar 

  10. M. Honda, S. Satake, Y. Suzuki, G. Matsunaga, K. Shinohara, M. Yoshida, A. Matsuyama, S. Ide, H. Urano, Experimental analyses and predictive simulations of toroidal rotation driven by the neoclassical toroidal viscosity in rippled tokamaks. Nuclear Fusion 54(11), 114005 (2014). https://doi.org/10.1088/0029-5515/54/11/114005

    Article  ADS  Google Scholar 

  11. H. Yamaguchi, S. Murakami, Simulation study of nbi heating in the time-evolving and multi-ion-species plasmas of lhd. Nuclear Fusion 56(2), 026003 (2015). https://doi.org/10.1088/0029-5515/56/2/026003

    Article  ADS  Google Scholar 

  12. Y. Morishita, S. Murakami, K. Likin, D.T. Anderson, Simulation study of neutral beam injection heating in the hsx plasma. Plasma Fusion Res 14, 3403152 (2019). https://doi.org/10.1585/pfr.14.3403152

    Article  ADS  Google Scholar 

  13. K. Ogawa, M. Isobe, T. Nishitani, S. Murakami, R. Seki, H. Nuga, S. Kamio, Y. Fujiwara, H. Yamaguchi, Y. Saito et al., Energetic ion confinement studies using comprehensive neutron diagnostics in the large helical device. Nuclear Fusion 59(7), 076017 (2019). https://doi.org/10.1088/1741-4326/ab14bc

    Article  ADS  Google Scholar 

  14. H. Takahashi, K. Nagaoka, K. Mukai, M. Yokoyama, S. Murakami, S. Ohdachi, T. Bando, Y. Narushima, H. Nakano, M. Osakabe et al., Realization of high t i plasmas and confinement characteristics of itb plasmas in the lhd deuterium experiments. Nuclear Fusion 58(10), 106028 (2018). https://doi.org/10.1088/1741-4326/aad87e

    Article  ADS  Google Scholar 

  15. S. Murakami, H. Yamaguchi, A. Sakai, A. Wakasa, A. Fukuyama, K. Nagaoka, H. Takahashi, H. Nakano, M. Osakabe, K. Ida et al., Integrated transport simulations of high ion temperature plasmas of lhd. Plasma Phys. Controlled Fusion 57(5), 054009 (2015). https://doi.org/10.1088/0741-3335/57/5/054009

    Article  ADS  Google Scholar 

  16. R. Seki, K. Ogawa, M. Isobe, M. Yokoyama, S. Murakami, H. Nuga, S. Kamio, Y. Fujiwara, M. Osakabe, L.E. Group et al., Evaluation of neutron emission rate with fit3d-dd code in large helical device. Plasma Fusion Res. 14, 3402126 (2019). https://doi.org/10.1585/pfr.14.3402126

  17. M. Yokoyama, C. Suzuki, R. Seki, M. Osakabe, M. Yoshinuma, M. Sato, A. Wakasa, S. Murakami, A. Fukuyama, Y. Suzuki et al., Development of integrated transport analysis suite for lhd plasmas towards transport model validation and increased predictability. Plasma Fusion Res. 8, 2403016 (2013). https://doi.org/10.1585/pfr.8.2403016

    Article  ADS  Google Scholar 

  18. Y. Morishita, S. Murakami, M. Yokoyama, G. Ueno, Data assimilation system based on integrated transport simulation of large helical device plasma. Nuclear Fusion 60(5), 056001 (2020). https://doi.org/10.1088/1741-4326/ab7596

    Article  ADS  Google Scholar 

  19. Y. Morishita, S. Murakami, M. Yokoyama, G. Ueno, Application of the ensemble kalman smoother to turbulent transport analysis in lhd plasma. Plasma Fusion Res. 16, 2403016 (2021). https://doi.org/10.1585/pfr.16.2403016

    Article  ADS  Google Scholar 

  20. C.M. Bishop, Pattern Recognition and Machine Learning (Springer, New York, 2007)

    MATH  Google Scholar 

  21. H. Nuga, R. Seki, K. Ogawa, S. Kamio, Y. Fujiwara, M. Osakabe, M. Isobe, T. Nishitani, M. Yokoyama, L.E. Group, et al., Analysis of energetic particle confinement in lhd using neutron measurement and simulation codes. Plasma Fusion Res. 14, 3402075 (2019). doi: https://doi.org/10.1585/pfr.14.3402075

  22. M.F. Møller, A scaled conjugate gradient algorithm for fast supervised learning. Neural Netw. 6(4), 525–533 (1993). https://doi.org/10.1016/S0893-6080(05)80056-5

    Article  Google Scholar 

  23. J.D. Gaffey, Energetic ion distribution resulting from neutral beam injection in tokamaks. J. Plasma Phys. 16(2), 149–169 (1976). https://doi.org/10.1017/S0022377800020134

    Article  ADS  Google Scholar 

  24. S. Hirshman, P. Merkel et al., Three-dimensional free boundary calculations using a spectral green’s function method. Computer Phys. Commun. 43(1), 143–155 (1986). https://doi.org/10.1016/0010-4655(86)90058-5

Download references

Acknowledgements

The authors acknowledge LHD Experiment Group for sharing the LHD experiment data. This work has been supported by the NIFS Collaborative Research Program (NIFS14KNTT025 and NIFS20KLPT007), ISM Cooperative Research Program (2019-ISMCRP-2027 and 2020-ISMCRP-2026), QST Research Collaboration for Fusion DEMO, and JSPS KAKENHI Grant Number JP21J14260.

Author information

Authors and Affiliations

  1. Department of Nuclear Engineering, Kyoto University, Kyoto daigaku katsura, Nishikyo, Kyoto, Kyoto, 615-8540, Japan

    Yuya Morishita & Sadayoshi Murakami

  2. National Institute for Fusion Science, National Institutes of Natural Sciences, 322-6 Oroshi-cho, Toki, Gifu, 509-5292, Japan

    Masayuki Yokoyama, Ryosuke Seki, Hideo Nuga & Masaki Osakabe

  3. The Graduate University for Advanced Studies, SOKENDAI, 322-6 Oroshi-cho, Toki, Gifu, 509-5292, Japan

    Masayuki Yokoyama, Ryosuke Seki & Masaki Osakabe

  4. The Graduate University for Advanced Studies, SOKENDAI, 10-3 Midori-cho, Tachikawa, Tokyo, 190-0014, Japan

    Genta Ueno

  5. The Institute of Statistical Mathematics, Research Organization of Information and Systems, 10-3 Midori-cho, Tachikawa, Tokyo, 190-0014, Japan

    Genta Ueno

  6. The Joint Support-Center for Data Science Research, Research Organization of Information and Systems, 10-3 Midori-cho, Tachikawa, Tokyo, 190-0014, Japan

    Genta Ueno

Authors
  1. Yuya Morishita
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sadayoshi Murakami
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Masayuki Yokoyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ryosuke Seki
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hideo Nuga
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Masaki Osakabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Genta Ueno
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors listed contributed sufficiently to the project to be included as authors.

Corresponding author

Correspondence to Yuya Morishita.

Ethics declarations

Funding

This work was supported by JSPS KAKENHI Grant Number JP21J14260.

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Availability of data and materials

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The simulation codes (written in Fortran) employed in this study are available from the corresponding author upon reasonable request.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Morishita, Y., Murakami, S., Yokoyama, M. et al. Development of Rapid Simulation Code for NBI Heating Analysis in LHD. J Fusion Energ 41, 1 (2022). https://doi.org/10.1007/s10894-021-00313-5

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10894-021-00313-5

Keywords

Search

Navigation