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Title: The two-dimensional kinetic ballooning theory for ion temperature gradient mode in tokamak

Abstract

The two-dimensional (2D) kinetic ballooning theory is developed for the ion temperature gradient mode in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The ballooning transform converts the basic 2D linear gyro-kinetic equation into two equations: (1) the lowest order equation (ballooning equation) is an integral equation essentially the same as that reported by Dong et al., [Phys. Fluids B 4, 1867 (1992)] but has an undetermined Floquet phase variable, (2) the higher order equation for the rapid phase envelope is an ordinary differential equation in the same form as the 2D ballooning theory in a fluid model [Xie et al., Phys. Plasmas 23, 042514 (2016)]. The system is numerically solved by an iterative approach to obtain the (phase independent) eigen-value. The new results are compared here to the two earlier theories. We find a strongly modified up-down asymmetric mode structure, and non-trivial modifications to the eigen-value.

Authors:
ORCiD logo [1];  [2];  [3]; ORCiD logo [4];  [4];  [5]
+ Show Author Affiliations
  1. Sichuan Univ. of Science and Engineering, Zigong (China). Dept. of Physics
  2. Chinese Academy of Sciences (CAS), Hefei (China). Center for Magnetic Fusion Theory
  3. Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies
  4. Southwestern Inst. of Physics, Chengdu (China)
  5. Univ. of Science and Technology of China, Hefei (China). Dept. of Modern Physics
Publication Date:
Research Org.:
Univ. of Texas, Austin, TX (United States); Sichuan Univ. of Science and Engineering, Zigong (China); Chinese Academy of Sciences (CAS), Hefei (China); Univ. of Science and Technology of China, Hefei (China); Southwestern Institute of Physics, Chengdu (China)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES); Key Research Program of Frontier Sciences CAS (China); National Magnetic Confinement Fusion Energy Research Project (China); National Natural Science Foundation of China (NSFC); Foundation of Sichuan Univ. of Science and Engineering (China); Scientific Research Fund of the Sichuan Provincial Education Dept. (China)
OSTI Identifier:
1523476
Alternate Identifier(s):
OSTI ID: 1394010
Grant/Contract Number:  
FG02-04ER54742; QYZDB-SSWSYS004; 2015GB104004; 2015GB111003; 2013GB112009; 11575185; 11575186; 2016RCL21; 17ZA0281
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 10; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; integral transforms; plasma confinement; integral equations; spectral methods; tokamaks; functional equations; Newtonian mechanics; weight function; order theory; turbulence simulations

Citation Formats

Xie, T., Zhang, Y. Z., Mahajan, S. M., Hu, S. L., He, Hongda, and Liu, Z. Y. The two-dimensional kinetic ballooning theory for ion temperature gradient mode in tokamak. United States: N. p., 2017. Web. doi:10.1063/1.5003652.
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Xie, T., Zhang, Y. Z., Mahajan, S. M., Hu, S. L., He, Hongda, & Liu, Z. Y. The two-dimensional kinetic ballooning theory for ion temperature gradient mode in tokamak. United States. https://doi.org/10.1063/1.5003652
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Xie, T., Zhang, Y. Z., Mahajan, S. M., Hu, S. L., He, Hongda, and Liu, Z. Y. Fri . "The two-dimensional kinetic ballooning theory for ion temperature gradient mode in tokamak". United States. https://doi.org/10.1063/1.5003652. https://www.osti.gov/servlets/purl/1523476.
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@article{osti_1523476,
title = {The two-dimensional kinetic ballooning theory for ion temperature gradient mode in tokamak},
author = {Xie, T. and Zhang, Y. Z. and Mahajan, S. M. and Hu, S. L. and He, Hongda and Liu, Z. Y.},
abstractNote = {The two-dimensional (2D) kinetic ballooning theory is developed for the ion temperature gradient mode in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The ballooning transform converts the basic 2D linear gyro-kinetic equation into two equations: (1) the lowest order equation (ballooning equation) is an integral equation essentially the same as that reported by Dong et al., [Phys. Fluids B 4, 1867 (1992)] but has an undetermined Floquet phase variable, (2) the higher order equation for the rapid phase envelope is an ordinary differential equation in the same form as the 2D ballooning theory in a fluid model [Xie et al., Phys. Plasmas 23, 042514 (2016)]. The system is numerically solved by an iterative approach to obtain the (phase independent) eigen-value. The new results are compared here to the two earlier theories. We find a strongly modified up-down asymmetric mode structure, and non-trivial modifications to the eigen-value.},
doi = {10.1063/1.5003652},
journal = {Physics of Plasmas},
number = 10,
volume = 24,
place = {United States},
year = {Fri Sep 22 00:00:00 EDT 2017},
month = {Fri Sep 22 00:00:00 EDT 2017}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5003652
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Cited by: 2 works
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Figures / Tables:

FIG. 1 FIG. 1: The real (blue line) and imaginary (red line) parts of ballooning wave functions χ(k,λ) versus k for (a) λ = 0; (b) λ = π/4; (c) λ = π/2; (d) λ = -π/2. The physical parameters are kθρs0 = -0.53, ŝ = 1, q0 = 2, ηi0 =more » ηe0 = 3.5, Ln0/R = 0.12, and n = -53.« less
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Works referenced in this record:

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    Works referencing / citing this record:

    A theory of self-organized zonal flow with fine radial structure in tokamak
    journal, December 2017

    • Zhang, Y. Z.; Liu, Z. Y.; Xie, T.
    • Physics of Plasmas, Vol. 24, Issue 12
    • DOI: 10.1063/1.4995302

    The two-dimensional kinetic ballooning theory for trapped electron mode in tokamak
    journal, February 2019

    • Xie, T.; Zhang, Y. Z.; Mahajan, S. M.
    • Physics of Plasmas, Vol. 26, Issue 2
    • DOI: 10.1063/1.5048538
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      Figures / Tables found in this record:

      FIG. 1 (p. 5)figure
      Table I (p. 5)table
      FIG. 2 (p. 6)figure
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      FIG. 4 (p. 8)figure
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