Plasma and Fusion Research

Volume 19, 1403026 (2024)

Regular Articles


Two-Dimensional Axisymmetric Finite Element Simulation of Lower Hybrid Wave with an Iterative Scheme
Fumiya ADACHI, Naoto TSUJII, Akira EJIRI, Kouji SHINOHARA, Seowon JANG, Yi PENG, Kotaro IWASAKI, Yu-Ting LIN, Zhengnan JIANG, Yiming TIAN, Yangguang JIANG, Shengyu WANG, Yijin XIONG and Masaru YOSHIDA
University of Tokyo, Kashiwa 277-0882, Japan
(Received 27 October 2023 / Accepted 25 June 2024 / Published 23 July 2024)

Abstract

Simulating waves in hot plasmas in configuration space is a difficult problem because of the non-local property of the plasma response, which makes the wave equation an integro-differential one. In this research, we conducted an axisymmetric hot plasma full wave simulation at the lower hybrid frequency range with the finite element method. Kinetic effects were introduced in the direction parallel to the magnetic field. We implemented the code so that it can handle an arbitrary velocity distribution function to introduce electron kinetics. An iterative method was utilized to introduce the non-local hot plasma contribution, which is more memory efficient than direct solving. The hot plasma perturbed current density was iteratively calculated in our scheme. For the present simulation, we used the plasma equilibrium obtained by the experiment with the TST-2 spherical tokamak, which is located at the University of Tokyo. The simulation with the realistic profiles successfully converged. The electron heating power deposition profile was estimated for the obtained electric field solutions.


Keywords

lower hybrid wave, full wave simulation, finite element method

DOI: 10.1585/pfr.19.1403026


References

  • [1] M. Brambilla and T. Krücken, Nucl. Fusion 28, 1813 (1988).
  • [2] E.F. Jaeger, L.A. Berry, E. D’Azvedo, D.B. Batchelor et al., Phys. Plasmas 8, 1573 (2001).
  • [3] S. Shiraiwa, S. Ide, S. Itoh, O. Mitarai et al., Phys. Rev. Lett. 92, 035001 (2004).
  • [4] V.V. Dyachenko, O.N. Shcherbinin, E.Z. Gusakov, V.K. Gusev et al., Nucl. Fusion 55, 113001 (2015).
  • [5] P.T. Bonoli, J. Ko, R. Parker, A.E. Schmidt et al., Phys. Plasmas 15, 0561117 (2008).
  • [6] O. Meneghini, S. Shiraiwa and R. Parker, Phys. Plasmas 16, 090701 (2009).
  • [7] D. Green and L. Berry, Comput. Phys. Commun. 185, 736 (2014).
  • [8] P. Vallejos, T. Hellsten and T. Johnson, J. Phys. Conf. Ser. 1125, 012020 (2018).
  • [9] J.E. Drummond, R.A. Gerwin and B.G. Springer, J. Nucl. Energy, Part C Plasma Phys. 2, 98 (1961).
  • [10] T. Stix, Waves in Plasmas (American Institute of Physics, New York, 1992).
  • [11] H. Walker and P. Ni, SIAM J. Numer. Anal. 49, 1715 (2011).
  • [12] COMSOL Multiphysics, www.comsol.com, COMSOL AB, Stockholm, Sweden.
  • [13] MATLAB, www.mathworks.com, The MathWorks Inc., Natick, MA, USA.
  • [14] C. Lau, L.A. Berry, E.F. Jaeger and N. Bertelli, Plasma Phys. Control. Fusion 61, 045008 (2019).
  • [15] T. Shinya, Y. Takase, S. Yajima, C. Moeller et al., Nucl. Fusion 57, 036006 (2017).
  • [16] S. Yajima, Y. Takase, Y. Tajiri, Y. Takei et al., Nucl. Fusion 59, 066004 (2019).
  • [17] Y. Ko, N. Tsujii, A. Ejiri, O. Watanabe et al., Nucl. Fusion 63, 126015 (2023).
  • [18] L.L. Lao, H. St. John, R.D. Stambaugh, A.G. Kellman et al., Nucl. Fusion 25, 1611 (1985).
  • [19] R.W. Harvey and M.G. McCoy, Proc. IAEA TCM on Advances in Sim. and Modelling of Thermonuclear Plasmas, 489 (1992).
  • [20] A.P. Smirnov, R.W. Harvey and K. Kupfer, Bull. Am. Phys. Soc. 39, 1626 (1994).
  • [21] P.T. Bonoli and E. Ott, Phys. Fluids 25, 359 (1982).