On resistive magnetohydrodynamic studies of sawtooth oscillations in tokamaks
Abstract
A fundamental requirement for the validity and accuracy of any largescale computation is sufficiently wellresolved length and time scales relevant to the problem under study. Ironically, despite the enormous computational resources available today, poorly resolved length scales in sophisticated nonlinear calculations are not uncommon. Using the internal kink mode that is responsible for tokamak sawtooth oscillations as an example, consequences of not resolving in sufficient detail the linear and nonlinear layer widths of the resistive n = 1 mode and its nonlinear spectrum are examined. Poor radial and spectral resolution are shown to cause nonphysical, largescale stochasticity that can be erroneously associated with a fast temperature collapse and sawtooth crash. With the assistance of a nonlinear mode coupling model, a sufficiently wellresolved toroidal spectrum is shown to require at least an order of magnitude more toroidal modes than is commonly used at dissipation levels relevant to today's tokamaks. A subgridscale model is introduced that helps with the spectral resolution problem by reducing the required number of degrees of freedom from that of a wellresolved direct numerical simulation.
 Authors:
 National Fusion Research Institute, Daejeon 305806 (Korea, Republic of)
 Publication Date:
 OSTI Identifier:
 22408193
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ACCURACY; CALCULATION METHODS; COMPUTERIZED SIMULATION; DEGREES OF FREEDOM; MAGNETOHYDRODYNAMICS; NONLINEAR PROBLEMS; PLASMA INSTABILITY; SAWTOOTH OSCILLATIONS; SCALE MODELS; SPECTRA; TOKAMAK DEVICES
Citation Formats
Aydemir, A. Y., Email: aydemir@nfri.re.kr, Kim, J. Y., Park, B. H., and Seol, J. On resistive magnetohydrodynamic studies of sawtooth oscillations in tokamaks. United States: N. p., 2015.
Web. doi:10.1063/1.4914090.
Aydemir, A. Y., Email: aydemir@nfri.re.kr, Kim, J. Y., Park, B. H., & Seol, J. On resistive magnetohydrodynamic studies of sawtooth oscillations in tokamaks. United States. doi:10.1063/1.4914090.
Aydemir, A. Y., Email: aydemir@nfri.re.kr, Kim, J. Y., Park, B. H., and Seol, J. 2015.
"On resistive magnetohydrodynamic studies of sawtooth oscillations in tokamaks". United States.
doi:10.1063/1.4914090.
@article{osti_22408193,
title = {On resistive magnetohydrodynamic studies of sawtooth oscillations in tokamaks},
author = {Aydemir, A. Y., Email: aydemir@nfri.re.kr and Kim, J. Y. and Park, B. H. and Seol, J.},
abstractNote = {A fundamental requirement for the validity and accuracy of any largescale computation is sufficiently wellresolved length and time scales relevant to the problem under study. Ironically, despite the enormous computational resources available today, poorly resolved length scales in sophisticated nonlinear calculations are not uncommon. Using the internal kink mode that is responsible for tokamak sawtooth oscillations as an example, consequences of not resolving in sufficient detail the linear and nonlinear layer widths of the resistive n = 1 mode and its nonlinear spectrum are examined. Poor radial and spectral resolution are shown to cause nonphysical, largescale stochasticity that can be erroneously associated with a fast temperature collapse and sawtooth crash. With the assistance of a nonlinear mode coupling model, a sufficiently wellresolved toroidal spectrum is shown to require at least an order of magnitude more toroidal modes than is commonly used at dissipation levels relevant to today's tokamaks. A subgridscale model is introduced that helps with the spectral resolution problem by reducing the required number of degrees of freedom from that of a wellresolved direct numerical simulation.},
doi = {10.1063/1.4914090},
journal = {Physics of Plasmas},
number = 3,
volume = 22,
place = {United States},
year = 2015,
month = 3
}

Sawtooth oscillations in presentday tokamaks exhibit some features that can not be fully explained by the Kadomtsev model. In addition to double or compound sawteeth thought to be caused by multiple q=1 surfaces in the plasma, observed crash times are much faster than the predictions of the simple Kadomtsev reconnection process. Since the time scales involved appear to be too short for a resistive mode, Wesson has suggested that a pressuredriven ideal kink mode could be the responsible instability mechanism. This mode is always unstable in a cylinder for q{sub 0} < 1, and p' < 0, where q{sub 0}more »

Toroidal studies of sawtooth oscillations in tokamaks
Tokamak sawtooth oscillations are studied with a nonreduced, fully toroidal, resistive magnetohydrodynamic (MHD) model that includes Ohmic heating, and parallel and perpendicular thermal conductions. Effects of perpendicular transport in producing different types of sawteeth, varying from simple, periodic oscillations to giant sawteeth with temperature modulations of order unity, and compound sawteeth with multiple relaxations, are demonstrated. Some of the recent experimental observations from large tokamaks, such as the fast crash times and a presumed topological anomaly in the xray tomography pictures, thought to be inconsistent with the Kadomtsev reconnection model, are examined and possible explanations are offered. 
Local properties of magnetic reconnection in nonlinear resistive and extendedmagnetohydrodynamic toroidal simulations of the sawtooth crash
We diagnose local properties of magnetic reconnection during a sawtooth crash employing the threedimensional toroidal, extendedmagnetohydrodynamic (MHD) code M3DC ^{1}. To do so, we sample simulation data in the plane in which reconnection occurs, the plane perpendicular to the helical (m, n) = (1, 1) mode at the q = 1 surface, where m and n are the poloidal and toroidal mode numbers and q is the safety factor. We study the nonlinear evolution of a particular test equilibrium in a nonreduced field representation using both resistiveMHD and extendedMHD models. We find growth rates for the extendedMHD reconnection process exhibitmore » 
Ioncyclotronfrequency stabilization of internal kink mode and sawtooth oscillations in tokamaks
It is proposed that the ponderomotive force due to applied ioncyclotron resonancefrequency waves can stabilize the internal kink mode in tokamaks. The sufficient stability criterion is derived and the necessary power estimated. It is concluded that at the rf power level, present in the Joint European Torus experiment, the ponderomotive force effects are significant and may be responsible for the modification of the sawtooth activity observed in recent experiments.