Helical core tokamak MHD equilibrium states

Cooper, W. A.; Graves, J. P.; Sauter, O.; Rossel, J.; Albergante, M.; Coda, S.; Duval, B.P.; Labit, B.; Pochelon, A.; Reimerdes, H.

doi:10.1088/0741-3335/53/12/124005

Cited by 12 publications

(25 citation statements)

References 37 publications

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“…(1) derives from the calculation of the nonlinear m = n = 1 saturated kink mode for nonmonotonic q profiles with reversed shear having q min ≈ 1 at r = r 1 [11] while equation (2) is valid for the m = 1 mode for monotonic safety factor profiles with the q = 1 surface at r = r 1 [12]. However, when q min < 1 we found that the analytical predictions almost agree with the nonlinear results, but there is a significant deviation between the 3-D equilibrium calculations and the nonlinear simulations: while the helical distorsion predicted by ANIMEC decreases to 0 when q min ≈ 0.96, XTOR gives a residual distorsion in this region (as shown in figure 2) accordingly with the linear stability calculations performed with TERPSICHORE code [13]. Indeed this is to be expected because the analytic linear internal kink mode of Bussac [14] is unstable.…”

Section: Ideal Kink Instabilities In Iter-like Scenariossupporting

confidence: 65%

MHD properties in the core of ITER-like hybrid scenarios

Brunetti

Cooper

Graves

et al. 2012

J. Phys.: Conf. Ser.

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Abstract. MHD stability is studied in the frame of ITER like hybrid scenarios, characterized by weak reversed shear, with particular attention on ideal internal kink modes and infernal mode stability. Numerical simulations for ITER like equilibria, with hollow q profiles with an off axis minimum close to unity, were carried out using the 3-D equilibrium code ANIMEC, which showed the presence of a 3-D helical core [1] with the characteristics of a saturated internal kink mode. The internal kink perturbation has been investigated non-linearly using the XTOR code, in the ideal frame. A scan in the current was performed and it has been found that when the minimum of q is above the unity (low currents), the helical distorsion shows good agreement with the results provided by the 3-D ANIMEC simulations while for qmin below 1 (high currents), XTOR gives a residual distorsion in contrast with the ANIMEC results. Moreover infernal mode stability in hybrid scenarios has been studied analytically extending the quasi-interchange model with the inclusion of resistive and both electron and ion diamagnetic effects. This enables us to investigate kinetic effects on plasma scenarios susceptible to saturated kink structures exhibited into ANIMEC simulations. IntroductionStandard tokamak operation scenarios are characterized by monotonically increasing safety factors q , with usually q 0 < 1 (q 0 is the value of the safety factor on the magnetic axis), full inductive plasma current and the standard high-performance operation. Another mode of operation is the advanced scenario which has weak reversed shear, produced by bib-inductive current drive and bootstrap current. A mode of operation is the hybrid scenario, which is an intermediate step between the H-mode standard scenario and an advanced scenario characterized by an extended low shear region where the safety factor q ≈ 1. In recent hybrid experiments,

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Section: Ideal Kink Instabilities In Iter-like Scenariossupporting

confidence: 65%

MHD properties in the core of ITER-like hybrid scenarios

Brunetti

Cooper

Graves

et al. 2012

J. Phys.: Conf. Ser.

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“…3 The appearance of a helical core is understood as a bifurcation of a magnetohydrodynamic (MHD) equilibrium from an axisymmetric one to a non-axisymmetric one. [9][10][11][12][13] The bifurcated equilibrium is regarded as a non-axisymmetric solution to the MHD equilibrium equation, which has an ðm; nÞ ¼ ð1; 1Þ helical structure at the core, where m and n are the poloidal and toroidal mode numbers, respectively. It is remarked that this helical core structure appears, even when an axisymmetric boundary condition is imposed on the surface of the plasma.…”

Section: Introductionmentioning

confidence: 99%

“…These MHD instabilities can be an internal kink mode and a quasi-interchange mode for a flat q-profile in the core region, 14,15 and the correspondence between the helical core and the linear growth rate of ðm; nÞ ¼ ð1; 1Þ mode is presented in Ref. 13. In addition, nonlinear saturated ðm; nÞ ¼ ð1; 1Þ instabilities are compared to the helical core.…”

Section: Introductionmentioning

confidence: 99%

Influence of plasma boundary shape on helical core/long-lived mode in tokamak plasmas

2020

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Helical distortion of the core part of tokamak plasma, which is called a helical core or a long-lived mode, is investigated by means of three-dimensional magnetohydrodynamic equilibrium calculations. It is found that the magnitude of the helical distortion strongly depends on the shape of the plasma boundary for weakly reversed shear plasmas. The triangularity of the boundary enhances the amplitude of helical distortion. In addition, reversed D-shape plasmas also exhibit a helical core. It is also found that the triangularity lowers the critical b for the onset of a helical core; furthermore, the critical b vanishes when the triangularity exceeds a certain value. On the other hand, the influence of the ellipticity on the amplitude of helical distortion strongly depends on b. The ellipticity enhances the amplitude at high b, while it reduces the amplitude at low b.

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“…Numerical solutions and typical pictures of a tokamak ‘snake-like’ MHD equilibrium can be found in Cooper et al. (2011 a , b ), Sugiyama (2013). In the next section we report such ‘snake-like’ states in vacuum magnetic fields and show that the expansion can be carried out to all orders.…”

Section: Expansion In the Distance From A Flux Surface For Vacuum Magmentioning

confidence: 99%

Low-shear three-dimensional equilibria and vacuum magnetic fields with flux surfaces

Sengupta

Weitzner

2019

J. Plasma Phys.

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Stellarators are generically small current and low plasma beta (β = p/B 2 ≪ 1) devices. Often the construction of vacuum magnetic fields with good magnetic surfaces is the starting point for an equilibrium calculation. Although in cases with some continuous spatial symmetry flux functions can always be found for vacuum magnetic fields, an analogous function does not, in general, exist in three dimensions. This work examines several simple equilibria and vacuum magnetic field problems with the intent of demonstrating the possibilities and limitations in the construction of such states. Starting with a simple vacuum magnetic field with closed field lines in a topological torus (toroidal shell with a flat metric), we obtain a self-consistent formal perturbation series using the amplitude of the nonsymmetric vacuum fields as a small parameter. We show that systems possessing stellarator symmetry allow the construction order by order. We further indicate the significance of stellarator symmetry in the amplitude expansion of the full ideal magnetohydrodynamics (MHD) problem as well. We then investigate the conditions that guarantee neighboring flux surfaces given the data on one surface, by expanding in the distance from that surface. We show that it is much more difficult to find low shear vacuum fields with surfaces than force-free fields or ideal MHD equilibrium. Finally, we demonstrate the existence of a class of vacuum magnetic fields, analogous to "snakes" observed in tokamaks, which can be expanded to all orders.

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Helical core tokamak MHD equilibrium states

Cited by 12 publications

References 37 publications

MHD properties in the core of ITER-like hybrid scenarios

MHD properties in the core of ITER-like hybrid scenarios

Influence of plasma boundary shape on helical core/long-lived mode in tokamak plasmas

Low-shear three-dimensional equilibria and vacuum magnetic fields with flux surfaces

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