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:
-
- Sichuan Univ. of Science and Engineering, Zigong (China). Dept. of Physics
- Chinese Academy of Sciences (CAS), Hefei (China). Center for Magnetic Fusion Theory
- Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies
- Southwestern Inst. of Physics, Chengdu (China)
- 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.
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
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.
@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}
}
Web of Science
Figures / Tables:
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
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
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
Ion internal transport barrier in neutral beam heated plasmas on HL-2A
journal, April 2016
- Yu, D. L.; Wei, Y. L.; Liu, L.
- Nuclear Fusion, Vol. 56, Issue 5
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
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
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
Introduction to Numerical Analysis
book, January 2002
- Stoer, J.; Bulirsch, R.
- Texts in Applied Mathematics
On broken ballooning symmetry
journal, July 1991
- Zhang, Y. Z.; Mahajan, S. M.
- Physics Letters A, Vol. 157, Issue 2-3
Electron temperature gradient driven turbulence
journal, May 2000
- Jenko, F.; Dorland, W.; Kotschenreuther, M.
- Physics of Plasmas, Vol. 7, Issue 5
Shear, Periodicity, and Plasma Ballooning Modes
journal, February 1978
- Connor, J. W.; Hastie, R. J.; Taylor, J. B.
- Physical Review Letters, Vol. 40, Issue 6
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
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
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
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
Figures / Tables found in this record: