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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]
  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 Inst. of Physics, Chengdu (China)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24); Key Research Program of Frontier Sciences CAS (China); National Magnetic Confinement Fusion Energy Research Project (China); National Natural Science Foundation of China (NNSFC); 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.
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. doi:10.1063/1.5003652.
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. doi:10.1063/1.5003652. https://www.osti.gov/servlets/purl/1523476.
@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 = {2017},
month = {9}
}

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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:

Two‐dimensional aspects of toroidal drift waves in the ballooning representation
journal, September 1992

  • Zhang, Y. Z.; Mahajan, S. M.; Zhang, X. D.
  • Physics of Fluids B: Plasma Physics, Vol. 4, Issue 9
  • DOI: 10.1063/1.860143

Structure of short-wavelength drift modes and transport in a toroidal plasma
journal, February 1996

  • Taylor, J. B.; Wilson, H. R.; Connor, J. W.
  • Plasma Physics and Controlled Fusion, Vol. 38, Issue 2
  • DOI: 10.1088/0741-3335/38/2/009

The Reynolds stress induced by weakly up-down asymmetric ion temperature gradient mode
journal, October 2016

  • Xie, T.; Zhang, Y. Z.; Mahajan, S. M.
  • Physics of Plasmas, Vol. 23, Issue 10
  • DOI: 10.1063/1.4966241

Ion internal transport barrier in neutral beam heated plasmas on HL-2A
journal, April 2016


The global version of the gyrokinetic turbulence code GENE
journal, August 2011

  • Görler, T.; Lapillonne, X.; Brunner, S.
  • Journal of Computational Physics, Vol. 230, Issue 18
  • DOI: 10.1016/j.jcp.2011.05.034

Structure of micro-instabilities in tokamak plasmas: Stiff transport or plasma eruptions?
journal, January 2014

  • Dickinson, D.; Roach, C. M.; Skipp, J. M.
  • Physics of Plasmas, Vol. 21, Issue 1
  • DOI: 10.1063/1.4861628

Ion temperature‐gradient‐driven modes and anomalous ion transport in tokamaks
journal, May 1989

  • Romanelli, F.
  • Physics of Fluids B: Plasma Physics, Vol. 1, Issue 5
  • DOI: 10.1063/1.859023

On broken ballooning symmetry
journal, July 1991


Electron temperature gradient driven turbulence
journal, May 2000

  • Jenko, F.; Dorland, W.; Kotschenreuther, M.
  • Physics of Plasmas, Vol. 7, Issue 5
  • DOI: 10.1063/1.874014

Linearized gyro-kinetics
journal, July 1978


Shear, Periodicity, and Plasma Ballooning Modes
journal, February 1978


Toroidal kinetic η i ‐mode study in high‐temperature plasmas
journal, March 1992

  • Dong, J. Q.; Horton, W.; Kim, J. Y.
  • Physics of Fluids B: Plasma Physics, Vol. 4, Issue 7
  • DOI: 10.1063/1.860040

The unified ballooning theory with weak up-down asymmetric mode structure and the numerical studies
journal, April 2016

  • Xie, T.; Qin, H.; Zhang, Y. Z.
  • Physics of Plasmas, Vol. 23, Issue 4
  • DOI: 10.1063/1.4947556

    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.