A mechanism for tearing onset near ideal stability boundaries

Brennan, D. P.; Haye, R.J. La; Turnbull, A. D.; Chu, M. S.; Jensen, T. H.; Lao, L. L.; Luce, T. C.; Politzer, Peter; Strait, E. J.; Kruger, Scott; Schnack, D. D.

doi:10.1063/1.1555830

Cited by 68 publications

(79 citation statements)

References 19 publications

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“…It has to be integrated into the global MHD control approach to avoid the RWM triggering or suppress triggered mode by proper feedback action. It has to be mentioned that also resistive instabilities can be destabilized with increase of N β [72]. A possible solution is to avoid the most dangerous rational surfaces or stabilize the modes with external current drive.…”

Section: Triggering Of Rwm At Low Plasma Rotationmentioning

confidence: 99%

Physics of resistive wall modes

Igochine

2012

Nucl. Fusion

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The advanced tokamak regime is a promising candidate for steady state tokamak operation which is desirable for a fusion reactor. This regime is characterized by a high bootstrap current fraction and a flat or reversed safety factor profile, which leads to operation close to the pressure limit. At this limit, an external kink mode becomes unstable. This external kink is converted into the slowly growing Resistive Wall Mode (RWM) by the presence of a conducting wall. Reduction of the growth rate allows one to act on the mode and to stabilize it. There are two main factors which determine the stability of the RWM. The first factor comes from external magnetic perturbations (error fields, resistive wall, feedback coils, etc). This part of RWM physics is the same for tokamaks and reverse field pinch (RFP)configurations. The physics of this interaction is relatively well understood and based on classical electrodynamics. The second ingredient of RWM physics is the interaction of the mode with plasma flow and fast particles. These interactions are particularly important for tokamaks, which have higher plasma flow and stronger trapped particle effects. The influence of the fast particles will also be increasingly more important in ITER and DEMO which will have a large fraction of fusion born alpha particles. These interactions have kinetic origins which make the computations challenging since not only particles influence the mode, but also the mode acts on the particles. Correct prediction of the "plasma-RWM" interaction is an important ingredient which has to be combined with external fields influence (resistive wall, error fields and feedback) to make reliable predictions for RWM behavior in tokamaks. All these issues are reviewed in this paper.2

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Section: Triggering Of Rwm At Low Plasma Rotationmentioning

confidence: 99%

Physics of resistive wall modes

Igochine

2012

Nucl. Fusion

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“…The method has been applied to the Doublet III-D (DIII-D) tokamak and also to the Large Helical Device (LHD) stellarator in Japan. Comparison with observations is favorable in both cases (6,7). Sometimes the solution of the equations turns out not to be unique, and there may exist bifurcated equilibria that are nonlinearly stable when other theories predict linear instability.…”

Section: Formulation Of the Problemmentioning

confidence: 91%

Three-dimensional equilibria in axially symmetric tokamaks

Garabedian

2006

Proc. Natl. Acad. Sci. U.S.A.

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The NSTAB and TRAN computer codes have been developed to study equilibrium, stability, and transport in fusion plasmas with three-dimensional (3D) geometry. The numerical method that is applied calculates islands in tokamaks like the Doublet III-D at General Atomic and the International Thermonuclear Experimental Reactor. When bifurcated 3D solutions are used in Monte Carlo computations of the energy confinement time, a realistic simulation of transport is obtained. The significance of finding many 3D magnetohydrodynamic equilibria in axially symmetric tokamaks needs attention because their cumulative effect may contribute to the prompt loss of ␣ particles or to crashes and disruptions that are observed. The 3D theory predicts good performance for stellarators.magnetic fusion ͉ magnetohydrodynamics ͉ plasma physics ͉ stellarator ͉ weak solution Formulation of the Problem Computational science has led to significant progress in the theory of equilibrium, stability, and transport for fusion plasmas in three dimensions (1, 2). This has made it possible to design advanced tokamaks with net current producing a poloidal field, or stellarators with twisted coils generating rotational transform, as candidates for a fusion reactor. The research we describe is based on the NSTAB and TRAN computer codes (3-5). They enable us to calculate transport in tokamaks by using bifurcated equilibria that do not have two-dimensional (2D) symmetry. For both tokamaks and stellarators, correct solutions of the relevant differential equations have discontinuities associated with islands and current sheets.We apply the magnetohydrodynamic (MHD) variational principle to calculate equilibrium and stability of toroidal plasmas in three dimensions. Partial differential equations are solved in a conservation form that describes force balance correctly across islands that are treated as discontinuities. The method has been applied to the Doublet III-D (DIII-D) tokamak and also to the Large Helical Device (LHD) stellarator in Japan. Comparison with observations is favorable in both cases (6, 7). Sometimes the solution of the equations turns out not to be unique, and there may exist bifurcated equilibria that are nonlinearly stable when other theories predict linear instability. The calculations are consistent with high values of the plasma parameter ␤ ϭ 2p/B 2 observed in the LHD. The NSTAB code captures islands correctly despite a nested surface hypothesis made in the numerical algorithm that is used. The reliability of the code has been established by using it to study stellarators without pressure where islands are known to exist in equilibria found from potential theory (8). We have made convincing calculations of this phenomenon in which the rotational transform changes sign so that a sizeable island appears where it vanishes, but the computations are sensitive to details about the profile of . Computational Analysis3D computer codes are an accepted tool for the study of equilibrium and stability in plasma physics. Good resolution is achiev...

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“…In a similar way, a continuous spectrum occurs in linear stability analyses of axially symmetric configurations (7). Our computations overcome these difficulties by putting the MHD equations in conservation form and then looking for weak solutions that are allowed to have discontinuities but become well defined according to established rules from the theory of nonlinear partial differential equations (4,8). Finally, we note that in the NSTAB code, a desired change in a typical coefficient B mn of the spectrum can be accomplished by performing an appropriate alteration of the corresponding shape factor ⌬ mn defining the boundary of the plasma.…”

Section: Computational Science Of Magnetic Fusionmentioning

confidence: 99%

Three-dimensional analysis of tokamaks and stellarators

Garabedian

2008

Proc. Natl. Acad. Sci. U.S.A.

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The NSTAB equilibrium and stability code and the TRAN Monte Carlo transport code furnish a simple but effective numerical simulation of essential features of present tokamak and stellarator experiments. When the mesh size is comparable to the island width, an accurate radial difference scheme in conservation form captures magnetic islands successfully despite a nested surface hypothesis imposed by the mathematics. Three-dimensional asymmetries in bifurcated numerical solutions of the axially symmetric tokamak problem are relevant to the observation of unstable neoclassical tearing modes and edge localized modes in experiments. Islands in compact stellarators with quasiaxial symmetry are easier to control, so these configurations will become good candidates for magnetic fusion if difficulties with safety and stability are encountered in the International Thermonuclear Experimental Reactor (ITER) project. magnetic fusion ͉ numerical methods ͉ plasma physics M agnetic fusion reactors confine a plasma of electrons and of deuterium and tritium ions in a strong magnetic field so at high temperatures the ions can fuse to form helium and release neutrons as a practical source of energy. The geometry of such devices is usually toroidal to allow the hot particles to circulate with a mean free path exceeding by far the size of the reactor. The most thoroughly studied configurations are tokamaks, which are axially symmetric and require a destabilizing net current in the plasma to prevent charged particles from drifting out toroidally. There is an alternate concept called the stellarator, which uses fully three-dimensional (3D) coils to create a poloidal field eliminating the toroidal drift. Our interest lies in magnetohydrodynamic (MHD) partial differential equations governing equilibrium and stability of the plasma, and in guiding center orbits of the ions and the electrons that lead to numerical simulations of transport. The method we apply to this problem in computational science is to run the NSTAB equilibrium and stability code and the TRAN Monte Carlo code written by Octavio Betancourt and Mark Taylor (1-4). We calculate physically realistic predictions of limits on the average ratio ␤ ϭ 2p/B 2 of the fluid and magnetic pressures and reliable estimates of the energy confinement time, which is a measure of pressure times volume divided by power in magnetic fusion experiments. Computational Science of Magnetic FusionUsing the Maxwell stress tensor, we write the MHD equations for equilibrium and stability of a plasma in the conservation formwhere B is the magnetic field and p is the fluid pressure. To obtain an accurate numerical approximation of force balance across discontinuities like islands or current sheets, analogous difference equations are represented in the NSTAB code by a similar scheme that telescopes down through addition over grid points to an integral statement of equilibrium related to the divergence theorem. Elementary examples from shock capturing show that ignoring conservation form results in failure ...

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A mechanism for tearing onset near ideal stability boundaries

Cited by 68 publications

References 19 publications

Physics of resistive wall modes

Physics of resistive wall modes

Three-dimensional equilibria in axially symmetric tokamaks

Three-dimensional analysis of tokamaks and stellarators

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