Energy spectrum of tearing mode turbulence in sheared background field
Abstract
The energy spectrum of tearing mode turbulence in a sheared background magnetic field is explored in this work. We observe the scenario where the nonlinear interaction of overlapping large-scale modes excites a broad spectrum of small-scale modes, generating tearing mode turbulence. The spectrum of such turbulence is of interest since it is relevant to the small-scale back-reaction on the large-scale field. The turbulence we report on here differs from traditional MHD turbulence mainly in two aspects. One is the existence of many linearly stable small-scale modes which cause an effective damping during the energy cascade. The other is the scale-independent anisotropy induced by the large-scale modes tilting the sheared background field, as opposed to the scale-dependent anisotropy frequently encountered in traditional critically balanced turbulence theories. Due to these two differences, the energy spectrum deviates from a simple power law and takes the form of a power law multiplied by an exponential falloff. Numerical simulations are carried out using visco-resistive MHD equations to verify our theoretical predictions, and a reasonable agreement is found between the numerical results and our model.
- Authors:
-
- Peking Univ., Beijing (China); ITER Organization, St. Paul Lez Durance (France); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Princeton Univ., NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Natural Science Foundation of China (NNSFC); China Scholarship Council
- OSTI Identifier:
- 1543854
- Grant/Contract Number:
- SC0016470
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 6; 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
Citation Formats
Hu, Di, Bhattacharjee, Amitava, and Huang, Yi-Min. Energy spectrum of tearing mode turbulence in sheared background field. United States: N. p., 2018.
Web. doi:10.1063/1.5022292.
Hu, Di, Bhattacharjee, Amitava, & Huang, Yi-Min. Energy spectrum of tearing mode turbulence in sheared background field. United States. doi:10.1063/1.5022292.
Hu, Di, Bhattacharjee, Amitava, and Huang, Yi-Min. Wed .
"Energy spectrum of tearing mode turbulence in sheared background field". United States. doi:10.1063/1.5022292. https://www.osti.gov/servlets/purl/1543854.
@article{osti_1543854,
title = {Energy spectrum of tearing mode turbulence in sheared background field},
author = {Hu, Di and Bhattacharjee, Amitava and Huang, Yi-Min},
abstractNote = {The energy spectrum of tearing mode turbulence in a sheared background magnetic field is explored in this work. We observe the scenario where the nonlinear interaction of overlapping large-scale modes excites a broad spectrum of small-scale modes, generating tearing mode turbulence. The spectrum of such turbulence is of interest since it is relevant to the small-scale back-reaction on the large-scale field. The turbulence we report on here differs from traditional MHD turbulence mainly in two aspects. One is the existence of many linearly stable small-scale modes which cause an effective damping during the energy cascade. The other is the scale-independent anisotropy induced by the large-scale modes tilting the sheared background field, as opposed to the scale-dependent anisotropy frequently encountered in traditional critically balanced turbulence theories. Due to these two differences, the energy spectrum deviates from a simple power law and takes the form of a power law multiplied by an exponential falloff. Numerical simulations are carried out using visco-resistive MHD equations to verify our theoretical predictions, and a reasonable agreement is found between the numerical results and our model.},
doi = {10.1063/1.5022292},
journal = {Physics of Plasmas},
number = 6,
volume = 25,
place = {United States},
year = {2018},
month = {6}
}
Figures / Tables:

Works referenced in this record:
Hyper-resistivity produced by tearing mode turbulence
journal, January 1986
- Strauss, H. R.
- Physics of Fluids, Vol. 29, Issue 11
Quasilinear perturbed equilibria of resistively unstable current carrying plasma
journal, November 2015
- Hu, Di; Zakharov, Leonid E.
- Journal of Plasma Physics, Vol. 81, Issue 6
Anisotropy in MHD turbulence due to a mean magnetic field
journal, June 1983
- Shebalin, John V.; Matthaeus, William H.; Montgomery, David
- Journal of Plasma Physics, Vol. 29, Issue 3
Reduced magnetohydrodynamic theory of oblique plasmoid instabilities
journal, February 2012
- Baalrud, S. D.; Bhattacharjee, A.; Huang, Y. -M.
- Physics of Plasmas, Vol. 19, Issue 2
Theory of anomalous tearing mode growth and the major tokamak disruption
journal, January 1984
- Diamond, P. H.; Hazeltine, R. D.; An, Z. G.
- Physics of Fluids, Vol. 27, Issue 6
Self-Consistent Dynamolike Activity in Turbulent Plasmas
journal, July 1986
- Bhattacharjee, A.; Hameiri, Eliezer
- Physical Review Letters, Vol. 57, Issue 2
Saturation of Gyrokinetic Turbulence through Damped Eigenmodes
journal, March 2011
- Hatch, D. R.; Terry, P. W.; Jenko, F.
- Physical Review Letters, Vol. 106, Issue 11
Three‐dimensional fluid simulations of the nonlinear drift‐resistive ballooning modes in tokamak edge plasmas
journal, October 1993
- Guzdar, P. N.; Drake, J. F.; McCarthy, D.
- Physics of Fluids B: Plasma Physics, Vol. 5, Issue 10
Magnetohydrodynamic Turbulence Revisited
journal, August 1997
- Goldreich, P.; Sridhar, S.
- The Astrophysical Journal, Vol. 485, Issue 2
Turbulent Magnetohydrodynamic Reconnection Mediated by the Plasmoid Instability
journal, February 2016
- Huang, Yi-Min; Bhattacharjee, A.
- The Astrophysical Journal, Vol. 818, Issue 1
Dissipation range turbulent cascades in plasmas
journal, May 2012
- Terry, P. W.; Almagri, A. F.; Fiksel, G.
- Physics of Plasmas, Vol. 19, Issue 5
Spectrum of Magnetohydrodynamic Turbulence
journal, March 2006
- Boldyrev, Stanislav
- Physical Review Letters, Vol. 96, Issue 11
Hyperresistivity due to viscous tearing mode turbulence
journal, September 2005
- Finn, John M.
- Physics of Plasmas, Vol. 12, Issue 9
Nonlinear growth of the tearing mode
journal, January 1973
- Rutherford, P. H.
- Physics of Fluids, Vol. 16, Issue 11
The Anisotropy of Magnetohydrodynamic Alfvenic Turbulence
journal, August 2000
- Cho, Jungyeon; Vishniac, Ethan T.
- The Astrophysical Journal, Vol. 539, Issue 1
Scaling of anisotropic spectra due to the weak interaction of shear-Alfvén wave packets
journal, March 1997
- Ng, C. S.; Bhattacharjee, A.
- Physics of Plasmas, Vol. 4, Issue 3
Resistive reconnection
journal, January 1986
- White, R. B.
- Reviews of Modern Physics, Vol. 58, Issue 1
Resistive instabilities in a diffuse linear pinch
journal, June 1966
- Coppi, Bruno; Greene, John M.; Johnson, John L.
- Nuclear Fusion, Vol. 6, Issue 2
Turbulent magnetic diffusion and magnetic field reversal
journal, January 1987
- Hameiri, Eliezer; Bhattacharjee, A.
- Physics of Fluids, Vol. 30, Issue 6
Ohm's law for mean magnetic fields
journal, February 1986
- Boozer, A. H.
- Journal of Plasma Physics, Vol. 35, Issue 1
Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence
journal, January 1995
- Goldreich, P.; Sridhar, S.
- The Astrophysical Journal, Vol. 438
Resistive instabilities in general toroidal plasma configurations
journal, January 1975
- Glasser, A. H.; Greene, J. M.; Johnson, J. L.
- Physics of Fluids, Vol. 18, Issue 7
Magnetohydrodynamic dissipation range spectra for isotropic viscosity and resistivity
journal, August 2009
- Terry, P. W.; Tangri, V.
- Physics of Plasmas, Vol. 16, Issue 8
A weak turbulence theory for incompressible magnetohydrodynamics
journal, June 2000
- Galtier, S.; Nazarenko, S. V.; Newell, A. C.
- Journal of Plasma Physics, Vol. 63, Issue 5
Magnetohydrodynamic turbulence in a strongly magnetised plasma
journal, January 2010
- Sridhar, S.
- Astronomische Nachrichten, Vol. 331, Issue 1
Imbalanced Weak Magnetohydrodynamic Turbulence
journal, January 2003
- Lithwick, Yoram; Goldreich, Peter
- The Astrophysical Journal, Vol. 582, Issue 2
Hyperresistivity due to densely packed tearing mode turbulence
journal, February 1991
- Craddock, G. G.
- Physics of Fluids B: Plasma Physics, Vol. 3, Issue 2
Interaction of Shear-Alfven Wave Packets: Implication for Weak Magnetohydrodynamic Turbulence in Astrophysical Plasmas
journal, July 1996
- Ng, C. S.; Bhattacharjee, A.
- The Astrophysical Journal, Vol. 465
Finite-Resistivity Instabilities of a Sheet Pinch
journal, January 1963
- Furth, Harold P.; Killeen, John; Rosenbluth, Marshall N.
- Physics of Fluids, Vol. 6, Issue 4
Role of electron physics in the development of turbulent magnetic reconnection in collisionless plasmas
journal, April 2011
- Daughton, W.; Roytershteyn, V.; Karimabadi, H.
- Nature Physics, Vol. 7, Issue 7
Role of subdominant stable modes in plasma microturbulence
journal, May 2011
- Hatch, D. R.; Terry, P. W.; Jenko, F.
- Physics of Plasmas, Vol. 18, Issue 5
Figures / Tables found in this record: