The two-dimensional kinetic ballooning theory for trapped electron mode in tokamak

Xie, T.; Zhang, Y. Z.; Mahajan, S. M.; Wu, F.; He, Hongda; Liu, Z. Y.

doi:10.1063/1.5048538

Title: The two-dimensional kinetic ballooning theory for trapped electron mode in tokamak

Abstract

The two-dimensional (2D) kinetic theory for a collisionless trapped electron mode is developed based on the Fourier-ballooning transform in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The system consists of two equations: the ballooning (integral) equation with a parameterized Floquet phase and a second order differential equation for the distribution of the Floquet phase. The coupled equations are, then, numerically solved as an eigenvalue problem yielding the 2D mode structure (in real space) as well as the global (phase-independent) eigenvalue for an L-mode parameter set. The 2D mode structure exhibits apparent radial-poloidal asymmetry; due to the poloidal coupling, the radial correlation length is found to be, at least, twice as large as the poloidal one. The global (phase-independent) eigenvalue of the mode differs considerably from the conventional local (phase-dependent) estimate. Finally, this paper shares many technical aspects with a published paper that works out the 2D kinetic theory for the ion temperature gradient mode [Xie et al., Phys. Plasmas 24, 102506 (2017)]

Authors:

^[1]; Zhang, Y. Z. ^[2];

^[3]; Wu, F. ^[1]; He, Hongda ^[4]; Liu, Z. Y. ^[5]

Sichuan Univ. of Science & Engineering (China)
Chinese Academy of Sciences (CAS), Beijing (China)
Univ. of Texas, Austin, TX (United States)
Southwestern Inst. of Physics, Sichuan (China)
Univ. of Science and Technology of China, Hefei, Anhui (China)

Publication Date:: Mon Feb 04 00:00:00 EST 2019

Research Org.:: Univ. of Texas, Austin, TX (United States)

Sponsoring Org.:: USDOE Office of Science (SC); Foundation of Sichuan Univ. of Science and Engineering; Sichuan Provincial Education Department

OSTI Identifier:: 1609567

Grant/Contract Number:: FG02-04ER54742; 2016RCL21; 17ZA0281

Resource Type:: Accepted Manuscript

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 26; Journal Issue: 2; Journal ID: ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; physics

Citation Formats


                    Xie, T., Zhang, Y. Z., Mahajan, S. M., Wu, F., He, Hongda, and Liu, Z. Y. The two-dimensional kinetic ballooning theory for trapped electron mode in tokamak.  United States: N. p., 2019. 
Web.  doi:10.1063/1.5048538.

Copy to clipboard


                    Xie, T., Zhang, Y. Z., Mahajan, S. M., Wu, F., He, Hongda, & Liu, Z. Y. The two-dimensional kinetic ballooning theory for trapped electron mode in tokamak.  United States.  https://doi.org/10.1063/1.5048538

Copy to clipboard


                    Xie, T., Zhang, Y. Z., Mahajan, S. M., Wu, F., He, Hongda, and Liu, Z. Y. Mon .  
"The two-dimensional kinetic ballooning theory for trapped electron mode in tokamak".  United States.  https://doi.org/10.1063/1.5048538.  https://www.osti.gov/servlets/purl/1609567.

Copy to clipboard


                    
@article{osti_1609567,

  title        = {The two-dimensional kinetic ballooning theory for trapped electron mode in tokamak},

  author       = {Xie, T. and Zhang, Y. Z. and Mahajan, S. M. and Wu, F. and He, Hongda and Liu, Z. Y.},

  abstractNote = {The two-dimensional (2D) kinetic theory for a collisionless trapped electron mode is developed based on the Fourier-ballooning transform in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The system consists of two equations: the ballooning (integral) equation with a parameterized Floquet phase and a second order differential equation for the distribution of the Floquet phase. The coupled equations are, then, numerically solved as an eigenvalue problem yielding the 2D mode structure (in real space) as well as the global (phase-independent) eigenvalue for an L-mode parameter set. The 2D mode structure exhibits apparent radial-poloidal asymmetry; due to the poloidal coupling, the radial correlation length is found to be, at least, twice as large as the poloidal one. The global (phase-independent) eigenvalue of the mode differs considerably from the conventional local (phase-dependent) estimate. Finally, this paper shares many technical aspects with a published paper that works out the 2D kinetic theory for the ion temperature gradient mode [Xie et al., Phys. Plasmas 24, 102506 (2017)]},

  doi          = {10.1063/1.5048538},

  journal      = {Physics of Plasmas},

  number       = 2,

  volume       = 26,

  place        = {United States},

  year         = {Mon Feb 04 00:00:00 EST 2019},

  month        = {Mon Feb 04 00:00:00 EST 2019}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1063/1.5048538

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 2 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in 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

Microinstability theory in tokamaks
journal, August 1978

Tang, W. M.
Nuclear Fusion, Vol. 18, Issue 8
DOI: 10.1088/0029-5515/18/8/006

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

Ballooning-mode theory of trapped-electron instabilities in tokamaks
journal, March 1981

Cheng, C. Z.; Chen, L.
Nuclear Fusion, Vol. 21, Issue 3
DOI: 10.1088/0029-5515/21/3/009

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

The two-dimensional kinetic ballooning theory for ion temperature gradient mode in tokamak
journal, October 2017

Xie, T.; Zhang, Y. Z.; Mahajan, S. M.
Physics of Plasmas, Vol. 24, Issue 10
DOI: 10.1063/1.5003652

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

Isotope effects of trapped electron modes in the presence of impurities in tokamak plasmas
journal, March 2016

Shen, Yong; Dong, J. Q.; Sun, A. P.
Plasma Physics and Controlled Fusion, Vol. 58, Issue 4
DOI: 10.1088/0741-3335/58/4/045028

Coupling of ion temperature gradient and trapped electron modes in the presence of impurities in tokamak plasmas
journal, May 2014

Du, Huarong; Wang, Zheng-Xiong; Dong, J. Q.
Physics of Plasmas, Vol. 21, Issue 5
DOI: 10.1063/1.4875342

On broken ballooning symmetry
journal, July 1991

Zhang, Y. Z.; Mahajan, S. M.
Physics Letters A, Vol. 157, Issue 2-3
DOI: 10.1016/0375-9601(91)90085-M

Linearized gyro-kinetics
journal, July 1978

Catto, P. J.
Plasma Physics, Vol. 20, Issue 7
DOI: 10.1088/0032-1028/20/7/011

Short wavelength trapped electron modes in tokamak plasmas
journal, April 2016

Zhang, N.; Gong, X. Y.; Dong, J. Q.
Physics of Plasmas, Vol. 23, Issue 4
DOI: 10.1063/1.4945638

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
DOI: 10.1103/PhysRevLett.40.396

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

General theory of kinetic ballooning modes
journal, January 1980

Frieman, E. A.; Rewoldt, G.; Tang, W. M.
Physics of Fluids, Vol. 23, Issue 9
DOI: 10.1063/1.863201

Kinetic-ballooning-mode theory in general geometry
journal, November 1980

Tang, W. M.; Connor, J. W.; Hastie, R. J.
Nuclear Fusion, Vol. 20, Issue 11
DOI: 10.1088/0029-5515/20/11/011

Electromagnetic kinetic toroidal eigenmodes for general magnetohydrodynamic equilibria
journal, January 1982

Rewoldt, G.
Physics of Fluids, Vol. 25, Issue 3
DOI: 10.1063/1.863760

A review of zonal flow experiments
journal, December 2008

Fujisawa, Akihide
Nuclear Fusion, Vol. 49, Issue 1
DOI: 10.1088/0029-5515/49/1/013001

Introduction to Numerical Analysis
journal, July 1970

O., J. M.; Froberg, Carl-Erik
Mathematics of Computation, Vol. 24, Issue 111
DOI: 10.2307/2004853

Survey of theories of anomalous transport
journal, May 1994

Conner, J. W.; Wilson, H. R.
Plasma Physics and Controlled Fusion, Vol. 36, Issue 5
DOI: 10.1088/0741-3335/36/5/002

Toroidal microinstability studies of high‐temperature tokamaks
journal, January 1990

Rewoldt, G.; Tang, W. M.
Physics of Fluids B: Plasma Physics, Vol. 2, Issue 2
DOI: 10.1063/1.859320

Generalised ballooning theory of two-dimensional tokamak modes
journal, December 2017

Abdoul, P. A.; Dickinson, D.; Roach, C. M.
Plasma Physics and Controlled Fusion, Vol. 60, Issue 2
DOI: 10.1088/1361-6587/aa9352

Zonal flows in plasma—a review
journal, April 2005

Diamond, P. H.; Itoh, S-I; Itoh, K.
Plasma Physics and Controlled Fusion, Vol. 47, Issue 5
DOI: 10.1088/0741-3335/47/5/R01

Introduction to Numerical Analysis
book, January 2002

Stoer, J.; Bulirsch, R.
Texts in Applied Mathematics
DOI: 10.1007/978-0-387-21738-3

Coupling of η _i and trapped electron modes in plasmas with negative magnetic shear
journal, March 1997

Dong, J. Q.; Mahajan, S. M.; Horton, W.
Physics of Plasmas, Vol. 4, Issue 3
DOI: 10.1063/1.872169

"Absolute Universal Instability" Is Not Universal
journal, January 1978

Tsang, K. T.; Catto, P. J.; Whitson, J. C.
Physical Review Letters, Vol. 40, Issue 5
DOI: 10.1103/PhysRevLett.40.327

Are Drift-Wave Eigenmodes Unstable?
journal, January 1978

Ross, David W.; Mahajan, Swadesh M.
Physical Review Letters, Vol. 40, Issue 5
DOI: 10.1103/PhysRevLett.40.324

Universal Eigenmode in a Strongly Sheared Magnetic Field
journal, August 1969

Pearlstein, L. D.; Berk, H. L.
Physical Review Letters, Vol. 23, Issue 5
DOI: 10.1103/PhysRevLett.23.220

Collisional effects on kinetic electromagnetic modes and associated quasilinear transport
journal, January 1987

Rewoldt, G.; Tang, W. M.; Hastie, R. J.
Physics of Fluids, Vol. 30, Issue 3
DOI: 10.1063/1.866332

Trapped electron stabilization of ballooning modes in low aspect ratio toroidal plasmas
journal, October 2004

Cheng, C. Z.; Gorelenkov, N. N.
Physics of Plasmas, Vol. 11, Issue 10
DOI: 10.1063/1.1783313

Structure of Micro-instabilities in Tokamak Plasmas: Stiff Transport or Plasma Eruptions?
text, January 2014

Dickinson, D.; Roach, C. M.; Skipp, J. M.
arXiv
DOI: 10.48550/arxiv.1409.1380

Generalised ballooning theory of two dimensional tokamak modes
text, January 2017

Abdoul, P. A.; Dickinson, D.; Roach, C. M.
arXiv
DOI: 10.48550/arxiv.1710.04717

Similar Records in DOE PAGES and OSTI.GOV collections:

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

Journal Article Xie, T. ; Zhang, Y. Z. ; Mahajan, S. M. ; ... - Physics of Plasmas

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 modelmore »« less
Cited by 2
https://doi.org/10.1063/1.5003652

Full Text Available
A theory of self-organized zonal flow with fine radial structure in tokamak

Journal Article Zhang, Y. Z. ; Liu, Z. Y. ; Xie, T. ; ... - Physics of Plasmas

The (low frequency) zonal flow-ion temperature gradient (ITG) wave system, constructed on Braginskii's fluid model in tokamak, is shown here to be a reaction-diffusion-advection system; it is derived by making use of a multiple spatiotemporal scale technique and two-dimensional (2D) ballooning theory. For real regular group velocities of ITG waves, two distinct temporal processes, sharing a very similar meso-scale radial structure, are identified in the nonlinear self-organized stage. The stationary and quasi-stationary structures reflect a particular feature of the poloidal group velocity. The equation set posed to be an initial value problem is numerically solved for JET low mode parameters;more »« less
Cited by 5
https://doi.org/10.1063/1.4995302

Full Text Available
Ballooning theory of the second kind-two dimensional tokamak modes

Journal Article Xie, T ; Wang, A K ; Zhang, Y Z ; ... - Physics of Plasmas

The 2-D ballooning transform, devised to study local high toroidal number (n) fluctuations in axisymmetric toroidal system (like tokamaks), yields a well-defined partial differential equation for the linear eigenmodes. In this paper, such a ballooning equation of the second kind is set up for ion temperature gradient driven modes pertinent to a 2-D non-dissipative fluid plasma; the resulting partial differential equation is numerically solved, to calculate the global eigenvalues, and the 2-D mode structure is presented graphically along with analytical companions. The radial localization of the mode results from translational symmetry breaking for growing modes and is a vivid manifestationmore »« less
https://doi.org/10.1063/1.4731724
The unified ballooning theory with weak up-down asymmetric mode structure and the numerical studies

Journal Article Xie, T., E-mail: xietao@ustc.edu.cn ; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026 ; Qin, H. ; ... - Physics of Plasmas

A unified ballooning theory, constructed on the basis of two special theories [Zhang et al., Phys. Fluids B 4, 2729 (1992); Y. Z. Zhang and T. Xie, Nucl. Fusion Plasma Phys. 33, 193 (2013)], shows that a weak up-down asymmetric mode structure is normally formed in an up-down symmetric equilibrium; the weak up-down asymmetry in mode structure is the manifestation of non-trivial higher order effects beyond the standard ballooning equation. It is shown that the asymmetric mode may have even higher growth rate than symmetric modes. The salient features of the theory are illustrated by investigating a fluid model formore »« less
https://doi.org/10.1063/1.4947556
Global gyrokinetic stability of collisionless microtearing modes in large aspect ratio tokamaks

Journal Article Swamy, Aditya K. ; Ganesh, R., E-mail: ganesh@ipr.res.in ; Chowdhury, J. ; ... - Physics of Plasmas

Linear full radius gyrokinetic calculations show the existence of unstable microtearing modes (MTMs) in purely collisionless, high temperature, large aspect ratio tokamak plasmas. The present study takes into account fully gyrokinetic highly passing ions and electrons. The global 2-D structures of the collisionless mode with full radius coupling of the poloidal modes is obtained and compared with another electromagnetic mode, namely, the Alfvén Ion Temperature Gradient (AITG) mode (or Kinetic Ballooning Mode, KBM) for the same equilibrium profile. Several important characteristics of the modes are brought out and compared, such as a clear signature in the symmetry properties of themore »« less
https://doi.org/10.1063/1.4893314

Similar Records

Title: The two-dimensional kinetic ballooning theory for trapped electron mode in tokamak

Abstract

Citation Formats

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

Microinstability theory in tokamaks journal, August 1978

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

Ballooning-mode theory of trapped-electron instabilities in tokamaks journal, March 1981

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

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

The two-dimensional kinetic ballooning theory for ion temperature gradient mode in tokamak journal, October 2017

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

Isotope effects of trapped electron modes in the presence of impurities in tokamak plasmas journal, March 2016

Coupling of ion temperature gradient and trapped electron modes in the presence of impurities in tokamak plasmas journal, May 2014

On broken ballooning symmetry journal, July 1991

Linearized gyro-kinetics journal, July 1978

Short wavelength trapped electron modes in tokamak plasmas journal, April 2016

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

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

General theory of kinetic ballooning modes journal, January 1980

Kinetic-ballooning-mode theory in general geometry journal, November 1980

Electromagnetic kinetic toroidal eigenmodes for general magnetohydrodynamic equilibria journal, January 1982

A review of zonal flow experiments journal, December 2008

Introduction to Numerical Analysis journal, July 1970

Survey of theories of anomalous transport journal, May 1994

Toroidal microinstability studies of high‐temperature tokamaks journal, January 1990

Generalised ballooning theory of two-dimensional tokamak modes journal, December 2017

Zonal flows in plasma—a review journal, April 2005

Introduction to Numerical Analysis book, January 2002

Coupling of η i and trapped electron modes in plasmas with negative magnetic shear journal, March 1997

"Absolute Universal Instability" Is Not Universal journal, January 1978

Are Drift-Wave Eigenmodes Unstable? journal, January 1978

Universal Eigenmode in a Strongly Sheared Magnetic Field journal, August 1969

Collisional effects on kinetic electromagnetic modes and associated quasilinear transport journal, January 1987

Trapped electron stabilization of ballooning modes in low aspect ratio toroidal plasmas journal, October 2004

Structure of Micro-instabilities in Tokamak Plasmas: Stiff Transport or Plasma Eruptions? text, January 2014

Generalised ballooning theory of two dimensional tokamak modes text, January 2017

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

Microinstability theory in tokamaks
journal, August 1978

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

Ballooning-mode theory of trapped-electron instabilities in tokamaks
journal, March 1981

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

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

The two-dimensional kinetic ballooning theory for ion temperature gradient mode in tokamak
journal, October 2017

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

Isotope effects of trapped electron modes in the presence of impurities in tokamak plasmas
journal, March 2016

Coupling of ion temperature gradient and trapped electron modes in the presence of impurities in tokamak plasmas
journal, May 2014

On broken ballooning symmetry
journal, July 1991

Linearized gyro-kinetics
journal, July 1978

Short wavelength trapped electron modes in tokamak plasmas
journal, April 2016

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

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

General theory of kinetic ballooning modes
journal, January 1980

Kinetic-ballooning-mode theory in general geometry
journal, November 1980

Electromagnetic kinetic toroidal eigenmodes for general magnetohydrodynamic equilibria
journal, January 1982

A review of zonal flow experiments
journal, December 2008

Introduction to Numerical Analysis
journal, July 1970

Survey of theories of anomalous transport
journal, May 1994

Toroidal microinstability studies of high‐temperature tokamaks
journal, January 1990

Generalised ballooning theory of two-dimensional tokamak modes
journal, December 2017

Zonal flows in plasma—a review
journal, April 2005

Introduction to Numerical Analysis
book, January 2002

Coupling of η _i and trapped electron modes in plasmas with negative magnetic shear
journal, March 1997

"Absolute Universal Instability" Is Not Universal
journal, January 1978

Are Drift-Wave Eigenmodes Unstable?
journal, January 1978

Universal Eigenmode in a Strongly Sheared Magnetic Field
journal, August 1969

Collisional effects on kinetic electromagnetic modes and associated quasilinear transport
journal, January 1987

Trapped electron stabilization of ballooning modes in low aspect ratio toroidal plasmas
journal, October 2004

Structure of Micro-instabilities in Tokamak Plasmas: Stiff Transport or Plasma Eruptions?
text, January 2014

Generalised ballooning theory of two dimensional tokamak modes
text, January 2017