Beta-limiting MHD phenomena in toroidal systems

Pustovitov, V. D.

doi:10.1134/1.1618887

Cited by 2 publications

(5 citation statements)

References 101 publications

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“…It is generally accepted that the NTM evolution must be described by the modified Rutherford equation (see [3, 4, 7-9, 11, 13, 16, 20, 34-36] and references therein). However, there are several competing theories that give different expressions for the terms in this equation, as discussed, for example, in the review paper [36]. Besides, some terms are often written in a singular form (with a 1/w or 1/w 3 dependence), which gives infinity when the island width, w, is zero.…”

Section: Rfa and Mode Rotationmentioning

confidence: 99%

Resonant field amplification as a mechanism for seed island formation

Pustovitov

2005

Nucl. Fusion

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The evolution of neoclassical tearing modes (NTMs) is usually described by the generalized Rutherford equation allowing the mode growth from a finite level, which is referred to as a seed island. It is generally accepted that the seed island is induced by some MHD event, but sometimes the NTMs start without visible triggers. Here we discuss a possible role of the error fields in producing the seeds. The analysis is based on the Maxwell equations and Ohm's law for magnetic perturbations outside the plasma, which are considered in a cylindrical approximation. The plasma enters the problem via boundary conditions. In the model, its contribution is described by the decay/growth rate and the toroidal rotation frequency of the perturbation. The model also assumes a resonant harmonic in the spectrum of the error field. It is shown that the resonant field amplification near the stability boundary of the mode may be a mechanism resulting in the ‘spontaneous’ formation of the seed island. This applies to modes non-rotating or slowly rotating at the onset. In contrast to NTM seeding due to sawteeth, fishbones or edge localized modes, the considered mechanism needs a longer time. However, all the estimates give realistic values consistent with typical experimental conditions.

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Section: Rfa and Mode Rotationmentioning

confidence: 99%

Resonant field amplification as a mechanism for seed island formation

Pustovitov

2005

Nucl. Fusion

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“…Therefore, a step to solve the intrinsic rotation mystery could be carried out by analysing the integral (global) torque balance (2), applying it, for example, to a steady state with ∂L/∂t = 0 without variations of plasma density and velocity. To move in this direction, we have to calculate both T in (5) and T f in (6). The latter, in a typical case, can be the known T NBI .…”

Section: Momentum Equationsmentioning

confidence: 99%

“…with dS pointed out (down in figure 1), and T f is the volume integral (6). The electromagnetic term can be calculated or measured using any convenient axisymmetric toroidal surface S ax enclosing the plasma.…”

Section: Geometry and Boundary Conditionsmentioning

confidence: 99%

“…It is known that plasma rotation plays an important role in tokamak physics [1][2][3]. It affects the triggering and/or sustaining of internal transport barrier (ITB) [1,4], stability of the resistive wall modes (RWMs) [2,5], tearing and neoclassical tearing modes (NTMs) [2,[6][7][8][9][10] and the plasma tolerance to magnetic perturbations (error fields) [2,11]. In all these cases the effect of rotation is substantial and beneficial (though, sometimes, when the rotation is properly directed [1,4,7]).…”

Section: Introductionmentioning

confidence: 99%

“…is the viscous torque. These general formulae, all expressed through the surface integrals, are a convenient basis for a discussion of the integral torque balance (2), also containing T f given by the volume integral (6). With definition (10), a part of T f (or T f itself) must be the torque T NBI due to the NBs, which must be known in experiments.…”

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Integral torque balance in tokamaks

Pustovitov

2011

Nucl. Fusion

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The study is aimed at clarifying the balance between the sinks and sources in the problem of intrinsic plasma rotation in tokamaks reviewed recently by deGrassie (2009 Plasma Phys. Control. Fusion 51 124047). The integral torque on the toroidal plasma is calculated analytically using the most general magnetohydrodynamic (MHD) plasma model taking account of plasma anisotropy and viscosity. The contributions due to several mechanisms are separated and compared. It is shown that some of them, though, possibly, important in establishing the rotation velocity profile in the plasma, may give small input into the integral torque, but an important contribution can come from the magnetic field breaking the axial symmetry of the configuration. In tokamaks, this can be the error field, the toroidal field ripple or the magnetic perturbation created by the correction coils in the dedicated experiments. The estimates for the error-field-induced electromagnetic torque show that the amplitude of this torque is comparable to the typical values of torques introduced into the plasma by neutral beam injection. The obtained relations allow us to quantify the effect that can be produced by the existing correction coils in tokamaks on the plasma rotation, which can be used in experiments to study the origin and physics of intrinsic rotation in tokamaks. Several problems are proposed for theoretical studies and experimental tests.

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Beta-limiting MHD phenomena in toroidal systems

Cited by 2 publications

References 101 publications

Resonant field amplification as a mechanism for seed island formation

Resonant field amplification as a mechanism for seed island formation

Integral torque balance in tokamaks

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