The XTOR code for nonlinear 3D simulations of MHD instabilities in tokamak plasmas

Lütjens, H.; Luciani, J. F.

doi:10.1016/j.jcp.2008.04.003

Cited by 51 publications

(79 citation statements)

References 37 publications

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“…It is conceivable that an equilibrium state with a q = 1 island has a lower energy than the ideal configuration we calculate. For this purpose, more general equilibrium and stability codes, which are much more time consuming, would be required to assess whether equilibrium structures linked to saturated tearing modes are likely to be formed [14,15,[34][35][36][37].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Investigations of nonlinearly saturated m = 1, n = 1 ideal internal kinks have been pursued both analytically [10][11][12] and numerically with the application of large scale, computationally intensive codes [13][14][15]. Bifurcated equilibrium states in tokamaks were first obtained by adding a forcing term to the second variation of an energy principle, then removing it to get a static solution with perturbations around rational surfaces that were interpreted as indications of the formation of magnetic islands [16].…”

Section: Introductionmentioning

confidence: 99%

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Helical core tokamak MHD equilibrium states

Cooper

Graves²,

Sauter³

et al. 2011

Plasma Phys. Control. Fusion

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Bifurcated magnetohydrodynamic (MHD) tokamak equilibrium states with axisymmetric or helical core structure are computed. When a peaked pressure profile is chosen, the helical core structures appear like the snakes that are observed in the JET tokamak. They also have the allure of saturated ideal internal kinks. The existence of a magnetic island is not a requisite condition. Novel equilibrium states that can model the snake are obtained for a JET configuration when the q-profile has weak reversed magnetic shear with minimum q values in the range 0.94 to 1.03. At the lower end of this q min range, the equilibrium snake structure lies radially well inside the domain for which q min 1. Free boundary equilibria computed for the TCV tokamak develop helical cores when β N exceeds 0.3 and have a significant axis excursion for β N 0.4. At fixed β = 1.6%, the distortion of the magnetic axis is large in the range 0.95 q min 1.01. The plasma-vacuum interface is not significantly altered by the internal helical deformations.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Helical core tokamak MHD equilibrium states

Cooper

Graves²,

Sauter³

et al. 2011

Plasma Phys. Control. Fusion

View full text Add to dashboard Cite

show abstract

“…Typically until now, nonlinearly saturated mode structures have been calculated analytically [4] and with nonlinear magnetohydrodynamic (MHD) codes [5]. Alternatively, introducing a small forcing term in the second variation of the energy principle, then removing it after many iterations, can lead to bifurcated solutions with 3D characteristics [6].…”

Section: Introductionmentioning

confidence: 99%

Helical ITER hybrid scenario equilibria

Cooper

Graves

Sauter

2011

Plasma Phys. Control. Fusion

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Numerical computations of ITER equilibria in the hybrid scenario using a three-dimensional (3D) magnetohydrodynamic equilibrium code with nested magnetic flux surfaces demonstrate the formation of internal 3D helical cores similar to saturated ideal internal kink modes under reversed magnetic shear conditions when the minimum value of the inverse rotational transform is in the neighbourhood of unity.

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“…Nonlinear quasi-interchange [17] and internal kinkmodes, that are evolving slowly [18,19], have been calculated with hollow and flat q profiles with q ! 1 everywhere.…”

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confidence: 99%

Tokamak Magnetohydrodynamic Equilibrium States with Axisymmetric Boundary and a 3D Helical Core

et al. 2010

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Magnetohydrodynamic (MHD) equilibrium states with imposed axisymmetric boundary are computed in which a spontaneous bifurcation develops to produce an internal three-dimensional (3D) configuration with a helical structure in addition to the standard axisymmetric system. Equilibrium states with similar MHD energy levels are shown to develop very different geometric structures. The helical equilibrium states resemble saturated internal kink mode structures. The essential confinement of particles and energy in magnetically enclosed plasmas is described by magnetohydrodynamics (MHD). The tokamak is the leading fusion energy research concept in which the plasma is expected to be contained in an essentially axisymmetric configuration with relatively small ripple effects from the finite toroidal coils. Symmetry of the equilibrium state along the toroidal coordinate grants the tokamak many appealing properties such as toroidal mass flow, which is known to reduce MHD instability and reduce non-MHD transport of particles and energy, as well as important conservation properties of single particles, thus enhancing confinement on various scales.It is shown in this Letter that despite imposing axisymmetry (toroidal symmetry) at the edge of the plasma, enforced by the geometry of the coil system, the preferred lowest energy state of MHD equilibrium can be nonaxisymmetric in the plasma center. The computation of threedimensional (3D) helical cores constitutes a paradigm shift for the description of tokamak equilibria that opens the way for the application of theoretical and simulation tools developed for stellarator analysis of MHD stability, guiding center particle orbits, kinetic stability, wave propagation or heating, neoclassical transport, gyrokinetics, etc., to determine the impact of these novel 3D states on a large range of magnetic confinement physics phenomena.The ignorable toroidal angle coordinate in axisymmetric magnetic confinement systems allows a simplified description of the MHD equilibrium state through the GradShafranov equation [1,2]. A more sophisticated approach invokes the minimization of the MHD energy to achieve an equilibrium state which can be naturally extended to model 3D systems with the imposition of nested magnetic flux surfaces and a single magnetic axis [3][4][5][6][7][8][9]. Tokamak devices, though nominally axisymmetric, display internal plasma reorganization phenomena that can break the symmetry of the system. In the tokamak à configuration variable (TCV) [10], a transition is observed where core sawteeth relaxations are replaced by global oscillations with low poloidal and toroidal mode numbers [11,12]. In these discharges, the inverse rotational transform q profiles are nearly flat or slightly reversed. One possible explanation for this transition is that q min , the minimum value of safety factor q within the plasma, becomes greater than unity. Equilibria with q min near unity are of interest in the present contribution. Similarly saturated ideal modes in the MAST device have also been re...

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The XTOR code for nonlinear 3D simulations of MHD instabilities in tokamak plasmas

Cited by 51 publications

References 37 publications

Helical core tokamak MHD equilibrium states

Helical core tokamak MHD equilibrium states

Helical ITER hybrid scenario equilibria

Tokamak Magnetohydrodynamic Equilibrium States with Axisymmetric Boundary and a 3D Helical Core

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