Magnetohydrodynamic equilibrium and the stability of tokamak and reversed-field pinch systems with 3D helical cores

Cooper, W. A.; Graves, J. P.; Sauter, O.; Terranova, D.; Gobbin, M.; Marrelli, L.; Martin, P.; Predebon, I.

doi:10.1088/0741-3335/53/8/084001

Cited by 3 publications

(4 citation statements)

References 36 publications

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“…Equilibrium solutions with helical cores were already found for several configurations, e.g. a m = 1, n = 1 helical core shape was found for TCV [2], MAST [5], and ITER-type equilibria [18], and a m = 1, n = 7 shape for RFX-mod equilibria [4,5,18].…”

Section: D Equilibrium Calculationsmentioning

confidence: 79%

MHD instabilities in 3D tokamaks

2014

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Three-dimensional, ideal MHD tokamak equilibria are computed with the free-boundary NEMEC code, and their stability properties are investigated with the CAS3DN code, which is an ideal, linear MHD code. Numerical problems are discussed in detail by means of a test equilibrium with a large helical core. Further computations are performed for AUG-type equilibria perturbed by resonant magnetic perturbation (RMP) fields, and an ITER scenario taking into account the toroidal field ripple and perturbation fields caused by test blanket modules (TBMs). Moreover, a quantitative measure of the corrugation of the flux surfaces is introduced. It is found that the contour of the corrugation on equilibrium flux surfaces reflect the ideal kink structures of rational-q surfaces, and the periodicity of the external perturbation fields. Both stabilizing and destabilizing effects of the RMP fields, and the influence of the TBMs on the stability properties are observed.

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Section: D Equilibrium Calculationsmentioning

confidence: 79%

MHD instabilities in 3D tokamaks

2014

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“…The ranges of Fourier modes for the global MHD stability analysis are m < 49 and n < 14 for the poloidal and toroidal modes, respectively. The typical marginal stability is represented by a threshold value of λ = −1 × 10 −4 and more negative eigenvalues than this crucial number are thought to be more unstable [38]. The simulation results reveal that a global MHD stability is obtained for β up to 1.35% (I bc = 38 kA).…”

Section: Effects Of Bootstrap Current On Mhd Stabilitymentioning

confidence: 87%

“…The unstable mode structure is dominated by the m/n = 2/1 term with the eigenvalue λ = −3.8724 × 10 −4 . In order to identify the category of these unstable modes, figure 5(b) shows radial profiles of surfaceaveraged plasma potential energy δW p which mainly includes two instability drive terms, δW p , κ s and δW j ∥ κ s [38,39]. The former drive term associates with ballooning modes in which the plasma pressure gradient interacts with the curvature of magnetic field lines.…”

Section: Effects Of Bootstrap Current On Mhd Stabilitymentioning

confidence: 99%

Effects of bootstrap current on magnetic configuration in Chinese first quasi-axisymmetric stellarator

Liu

zhang

et al. 2023

Nucl. Fusion

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Neoclassical properties in quasi-axisymmetric (QA) stellarators are analogous to these in tokamaks. Consequently, a substantial bootstrap current could significantly modify the MHD equilibrium properties of a QA stellarator, which is an important characteristic in this type of stellarator. This paper is dedicated to systemically investigate the effects of bootstrap current on the magnetic configuration in Chinese First Quasi-axisymmetric Stellarator (CFQS). For the first time, self-consistent bootstrap currents in free-boundary equilibria are calculated with an accurate Fokker–Planck neoclassical numerical mode in CFQS. Several important results are achieved: 1) As the bootstrap current grows with increasing volume-averaged normalized pressure β, the magnetic shear develops in the bulk plasma and meanwhile, a deep magnetic well is robustly sustained, which leads to improved stabilization of interchange modes up to β~2.0%. 2) In the analysis of global ideal MHD instability, as the bootstrap current rises to 39kA (β~1.3%), external kink modes become destabilized and the unstable mode with m/n= 2/1 is dominant. 3) From β=0 to 1.5%, the bootstrap current hardly changes the quasi-axisymmetric property and a low neoclassical transport is maintained. However, as β is enhanced beyond 2.0%, the substantial bootstrap current gives rise to an increase of non-quasi-axisymmetric magnetic field components, which weakens the neoclassical transport properties. 4) An increase of the negative magnetic shear at the core region by the bootstrap currents has a favorable effect on the properties of J (second adiabatic invariant). The maximum-J region can be extended by raising bootstrap currents.

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“…It has recently been discovered, on the basis of numerical simulations, that tokamaks can also evolve into 3D configurations. Persistent core-localized structures have been observed in tokamaks, which are the manifestations of a saturated ideal internal 3D mode 30,31 .…”

Section: Global Equilibrium and Stability Of 3d Configurationsmentioning

confidence: 99%

Computational challenges in magnetic-confinement fusion physics

et al. 2016

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Magnetic-fusion plasmas are complex self-organized systems with an extremely wide range of spatial and temporal scales, from the electron-orbit scales (⇠10 11 s, ⇠10 5 m) to the di usion time of electrical current through the plasma (⇠10 2 s) and the distance along the magnetic field between two solid surfaces in the region that determines the plasma-wall interactions (⇠100 m). The description of the individual phenomena and of the nonlinear coupling between them involves a hierarchy of models, which, when applied to realistic configurations, require the most advanced numerical techniques and algorithms and the use of state-of-the-art high-performance computers. The common thread of such models resides in the fact that the plasma components are at the same time sources of electromagnetic fields, via the charge and current densities that they generate, and subject to the action of electromagnetic fields. This leads to a wide variety of plasma modes of oscillations that resonate with the particle or fluid motion and makes the plasma dynamics much richer than that of conventional, neutral fluids.T he most straightforward way for describing plasmas would be the microscopic particle approach: solving the equations of motion for the many individual particles that form the plasma in externally imposed electromagnetic fields and in the fields that the particles themselves generate. However, this is computationally impossible to apply to realistic magnetic-fusion plasmas, which typically contain 10 22 -10 23 particles. (For a review of the basic concepts of magnetically confined fusion plasmas, see ref. 1.)A statistical treatment leads to the kinetic model, based on the Vlasov equation (equation (1)), essentially Liouville's theorem applied to the specific plasma environment, with interactions that are dominated by electromagnetic fields and a separation between particle collisions -that is, interactions at microscopic scales-and long-range fields. The Vlasov equation describes the evolution of f s (x,v,t), the single-particle phase-space distribution function of the species labelled 's' (electrons or ions), under the e ect of the longrange electric and magnetic fields E and B, which evolve according to Maxwell's equations with plasma charge and current densities as sources:Here, x, v, q s and m s stand for the position, velocity, charge and the mass of a particle of species 's' , respectively. In the Vlasov model, collisions are neglected, an approximation that is generally justified for fusion plasmas because small-scale e ects based on Coulomb interactions become very weak at high temperatures. In fact, Coulomb collisions' cross-sections for the exchange of momentum and energy, and related quantities such as the electrical resistivity ⌘, scale with T 3/2 . In ITER core plasmas (see ref. 1), for example, T ⇡ 10 keV (⇡10 8 K) and the electron-electron ('ee'), electron-ion ('ei') and ion-ion ('ii') collisional exchanges of momentum and energy ('E') occur over relatively long characteristic times:2)-justifying the collisi...

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Magnetohydrodynamic equilibrium and the stability of tokamak and reversed-field pinch systems with 3D helical cores

Cited by 3 publications

References 36 publications

MHD instabilities in 3D tokamaks

MHD instabilities in 3D tokamaks

Effects of bootstrap current on magnetic configuration in Chinese first quasi-axisymmetric stellarator

Computational challenges in magnetic-confinement fusion physics

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