Algebraic motion of vertically displacing plasmas
Abstract
In this paper, the vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a non-linear “sinking” behaviour shown to be algebraic and decelerating. Finally, the acceleration of the plasma column often observed in experiments is thus concluded to originate from an early sharing of toroidal current between the core, the halo plasma, and the wall or from the thermal quenchmore »
- Authors:
-
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1429048
- Alternate Identifier(s):
- OSTI ID: 1422853
- Grant/Contract Number:
- AC02-09CH11466
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 2; 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; eddies; electronic circuits; condensed matter properties; electrical properties; plasma confinement; differential equations; classical electromagnetism
Citation Formats
Pfefferle, D., and Bhattacharjee, A. Algebraic motion of vertically displacing plasmas. United States: N. p., 2018.
Web. doi:10.1063/1.5011176.
Pfefferle, D., & Bhattacharjee, A. Algebraic motion of vertically displacing plasmas. United States. https://doi.org/10.1063/1.5011176
Pfefferle, D., and Bhattacharjee, A. Tue .
"Algebraic motion of vertically displacing plasmas". United States. https://doi.org/10.1063/1.5011176. https://www.osti.gov/servlets/purl/1429048.
@article{osti_1429048,
title = {Algebraic motion of vertically displacing plasmas},
author = {Pfefferle, D. and Bhattacharjee, A.},
abstractNote = {In this paper, the vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a non-linear “sinking” behaviour shown to be algebraic and decelerating. Finally, the acceleration of the plasma column often observed in experiments is thus concluded to originate from an early sharing of toroidal current between the core, the halo plasma, and the wall or from the thermal quench dynamics precipitating loss of plasma current.},
doi = {10.1063/1.5011176},
journal = {Physics of Plasmas},
number = 2,
volume = 25,
place = {United States},
year = {Tue Feb 27 00:00:00 EST 2018},
month = {Tue Feb 27 00:00:00 EST 2018}
}
Web of Science
Figures / Tables:
Works referenced in this record:
JET and COMPASS asymmetrical disruptions
journal, September 2015
- Gerasimov, S. N.; Abreu, P.; Baruzzo, M.
- Nuclear Fusion, Vol. 55, Issue 11
Equilibrium of a toroidal plasma in a magnetic field
journal, January 1963
- Shafranov, V. D.
- Journal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research, Vol. 5, Issue 4
Disruption Design Criteria for Joint European Torus In-Vessel Components
journal, June 2003
- Riccardo, Valeria T. G.; Andrew, Philip L.; Kaye, Alan Sandford
- Fusion Science and Technology, Vol. 43, Issue 4
Nonlinear magnetohydrodynamics simulation using high-order finite elements
journal, March 2004
- Sovinec, C. R.; Glasser, A. H.; Gianakon, T. A.
- Journal of Computational Physics, Vol. 195, Issue 1
MHD stability in X-point geometry: simulation of ELMs
journal, June 2007
- Huysmans, G. T. A.; Czarny, O.
- Nuclear Fusion, Vol. 47, Issue 7
Comparison of tokamak axisymmetric mode growth rates from linear MHD and equilibrium evolution approaches
journal, October 1997
- Galkin, S. A.; Ivanov, A. A.; Medvedev, S. Yu
- Nuclear Fusion, Vol. 37, Issue 10
Feedback stabilization of rigid axisymmetric modes in tokamaks
journal, August 1982
- Jardin, S. C.; Larrabee, D. A.
- Nuclear Fusion, Vol. 22, Issue 8
Studies of Plasma Equilibrium and Transport in a Tokamak Fusion Device with the Inverse-Variable Technique
journal, December 1993
- Khayrutdinov, R. R.; Lukash, V. E.
- Journal of Computational Physics, Vol. 109, Issue 2
Non-axisymmetric magnetic fields and toroidal plasma confinement
journal, January 2015
- Boozer, Allen H.
- Nuclear Fusion, Vol. 55, Issue 2
On fully three-dimensional resistive wall mode and feedback stabilization computations
journal, May 2008
- Strumberger, E.; Merkel, P.; Sempf, M.
- Physics of Plasmas, Vol. 15, Issue 5
TSC plasma halo simulation of a DIII-D vertical displacement episode
journal, July 1993
- Sayer, R. O.; Peng, Y. -K. M.; Jardin, S. C.
- Nuclear Fusion, Vol. 33, Issue 7
Control of the vertical instability in tokamaks
journal, January 1990
- Lazarus, E. A.; Lister, J. B.; Neilson, G. H.
- Nuclear Fusion, Vol. 30, Issue 1
Effect of Halo Current and Its Toroidal Asymmetry During Disruptions in JT-60U
journal, November 1995
- Neyatani, Y.; Yoshino, R.; Ando, T.
- Fusion Technology, Vol. 28, Issue 4
Model of vertical plasma motion during the current quench
journal, October 2017
- Kiramov, D. I.; Breizman, B. N.
- Physics of Plasmas, Vol. 24, Issue 10
Modeling of active control of external magnetohydrodynamic instabilities
journal, May 2001
- Bialek, James; Boozer, Allen H.; Mauel, M. E.
- Physics of Plasmas, Vol. 8, Issue 5
Magnetic Energy of Surface Currents on a Torus
journal, January 2013
- Essen, Hanno; Sten, Johan C. -E.; Nordmark, Arne B.
- Progress In Electromagnetics Research B, Vol. 46
Characterization of disruption halo currents in the National Spherical Torus Experiment
journal, April 2012
- Gerhardt, S. P.; Menard, J.; Sabbagh, S.
- Nuclear Fusion, Vol. 52, Issue 6
Dynamic modeling of transport and positional control of tokamaks
journal, October 1986
- Jardin, S. C.; Pomphrey, N.; Delucia, J.
- Journal of Computational Physics, Vol. 66, Issue 2
From least action in electrodynamics to magnetomechanical energy—a review
journal, March 2009
- Essén, Hanno
- European Journal of Physics, Vol. 30, Issue 3
General approach to the problem of disruption forces in tokamaks
journal, September 2015
- Pustovitov, V. D.
- Nuclear Fusion, Vol. 55, Issue 11
The theory of the kink mode during the vertical plasma disruption events in tokamaks
journal, June 2008
- Zakharov, Leonid E.
- Physics of Plasmas, Vol. 15, Issue 6
Plasma equilibrium in a Tokamak
journal, December 1971
- Mukhovatov, V. S.; Shafranov, V. D.
- Nuclear Fusion, Vol. 11, Issue 6
Disruptions in ITER and strategies for their control and mitigation
journal, August 2015
- Lehnen, M.; Aleynikova, K.; Aleynikov, P. B.
- Journal of Nuclear Materials, Vol. 463
Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states
journal, November 2009
- Ferraro, N. M.; Jardin, S. C.
- Journal of Computational Physics, Vol. 228, Issue 20
Feedback stabilization of nonaxisymmetric resistive wall modes in tokamaks. I. Electromagnetic model
journal, September 2000
- Liu, Y. Q.; Bondeson, A.; Fransson, C. M.
- Physics of Plasmas, Vol. 7, Issue 9
Electromagnetic disruption analysis in IGNITOR
journal, April 2015
- Villone, F.; Ramogida, G.; Rubinacci, G.
- Fusion Engineering and Design, Vol. 93
Chapter 3: MHD stability, operational limits and disruptions
journal, June 2007
- Hender, T. C.; Wesley, J. C.; Bialek, J.
- Nuclear Fusion, Vol. 47, Issue 6
The self and mutual-inductances of linear conductors
journal, January 1908
- Rosa, E. B.
- Bulletin of the Bureau of Standards, Vol. 4, Issue 2
Plasma Physics and Fusion Energy
journal, November 2008
- Dolan, Thomas J.
- Fusion Science and Technology, Vol. 54, Issue 4
Plasma Physics and Fusion Energy
journal, November 2008
- Dolan, Thomas J.
- Fusion Science and Technology, Vol. 54, Issue 4
Works referencing / citing this record:
Modelling of NSTX hot vertical displacement events using M3D-C1
journal, May 2018
- Pfefferlé, D.; Ferraro, N.; Jardin, S. C.
- Physics of Plasmas, Vol. 25, Issue 5
Physics of runaway electrons in tokamaks
journal, June 2019
- Breizman, Boris N.; Aleynikov, Pavel; Hollmann, Eric M.
- Nuclear Fusion, Vol. 59, Issue 8