Equilibrium Plasma Rotation Research Articles

Frequency multiplication with toroidal mode number of kink/fishbone modes on a static HL-2A-like tokamak

In the presence of energetic particles (EPs), the long-lived mode (LLM) frequency multiplication with n = 1, 2, 3, or higher is often observed on HL-2A, where n is the toroidal mode number. Hybrid kinetic-MHD model simulations of the energetic particle (EP) driven kink/fishbone modes on a static HL-2A-like tokamak using NIMROD code find that when the background plasma pressure is relatively high, and the EP pressure and the beam energy are relatively low, the mode frequency increases almost linearly with EP pressure, and the frequency is proportional to n (‘frequency multiplication’), even in the absence of any equilibrium plasma rotation. In addition, the frequency multiplication persists as the safety factor at the magnetic axis q 0 varies. In the absence of EPs, the growth rate of the 1/1 mode is the largest; however, as the EP pressure increases, the growth rate of 2/2 modes or 3/3 modes becomes dominant, suggesting that higher-n modes are more vulnerable to EPs. These results may shed light on the understanding of the toroidal mode number dependence of kink/fishbone modes in the advanced scenarios of tokamaks with weak or reversed central magnetic shear.

Dependence of locked mode behavior on frequency and polarity of a rotating external magnetic perturbation

Active control and stabilization of locked modes (LM) via rotating external magnetic perturbations are numerically investigated under a realistic low resistivity condition. To explore plasma responses to rotating and/or static external magnetic perturbations, we have developed a resistive magnetohydrodynamic code ‘AEOLUS-IT’. By using AEOLUS-IT, dependencies of mode behavior on frequency and polarity of the rotating magnetic perturbation are successfully clarified. Here, the rotational direction of the rotating magnetic perturbation to the equilibrium plasma rotation in the laboratory frame is referred to as ‘polarity’. The rotating magnetic perturbation acts on the background rotating plasma in the presence of a static field. Under such circumstances, there exist bifurcated states of the background rotating plasma, which should be taken into account when studying the dependence of the mode behavior on the rotating magnetic perturbation. It is found that there exist an optimum frequency and polarity of the rotating magnetic perturbation to control the LM, and that the LM is effectively stabilized by a co-polarity magnetic perturbation in comparison with a counter-polarity one.

Influence of toroidal rotation on resistive tearing modes in tokamaks

Influence of toroidal equilibrium plasma rotation on m/n = 2/1 resistive tearing modes is studied numerically using a 3D toroidal MHD code (CLT). It is found that the toroidal rotation with or without shear can suppress the tearing instability and the Coriolis effect in the toroidal geometry plays a dominant role on the rotation induced stabilization. For a high viscosity plasma (τR/τV ≫ 1, where τR and τV represent resistive and viscous diffusion time, respectively), the effect of the rotation shear combined with the viscosity appears to be stabilizing. For a low viscosity plasmas (τR/τV ≪ 1), the rotation shear shows a destabilizing effect when the rotation is large.

Geodesic acoustic modes and zonal flows in rotating large-aspect-ratio tokamak plasmas

The effect of equilibrium plasma rotation (toroidal and poloidal) on low-frequency, electrostatic modes—the geodesic acoustic modes (GAMs) and the zonal flows (ZFs)—in large aspect ratio tokamaks is studied within the framework of ideal MHD. It is shown that the plasma rotation results in a frequency up-shift of the ordinary GAM. The new branch of continuum modes induced by the poloidal rotation is found. This mode originates from the opposite sign Doppler shift of frequency due to poloidal rotation for m = ±1 poloidal side-band harmonics of the perturbed mass density, pressure and parallel velocity. In the case of slow poloidal rotation (ΩP ≪ cs/qR0) its frequency is close to the sound frequency cs/qR0 (ΩP is the poloidal angular velocity, cs is the speed of sound, q is the safety factor and R0 is the major radius of tokamak). The mode can be called the rotation-induced acoustic mode. This mode disappears in the case of purely toroidal plasma rotation. The frequency of the new mode in the case of relatively slow poloidal rotation (ΩP ⩽ cs/qR0) is lower than the frequency of the ordinary GAM modified by plasma rotation. In the case of larger poloidal angular velocities ΩP (ΩP ⩾ 2cs/qR0) the mode becomes unstable and is identified as the unstable ZF. With a further increase in the poloidal angular velocity at constant toroidal angular velocity the instability is suppressed, and the mode turns again into a marginally stable, oscillating mode.

Plasma rotation in a quasi-symmetric stellarator

The equilibrium plasma rotation in a general toroidal magnetic field is nearly always subsonic and is determined by the requirement that the collisional particle transport should be ambipolar in lowest order in the small-ion-gyroradius expansion. Only in quasi-symmetric fields, where collisional particle transport is intrinsically ambipolar, can the plasma rotate freely and then only in the quasi-symmetry direction. Sonic rotation velocities are allowed in this case. In this paper the effect of rotation in a quasi-axisymmetric field is investigated, and it is found that the symmetry is broken when the rotation speed exceeds the diamagnetic speed appreciably, leading to reappearance of the non-intrinsically ambipolar 1/ν-transport regime. Fortunately, this transport scales with the fourth power of the rotation Mach number and is expected to be modest in most plasmas of interest.

Overview of Transport, Damping, and Wave Couplings from Separatrix Dissipation in an Axisymmetric Plasma

Axial variations in magnetic or electrostatic confinement fields create local trapping separatrices, and traditional neo-classical theory analyzes the effects from collision-induced separatrix crossings. Recent experiments and theory have characterized the distinctive neo-classical effects from chaotic separatrix crossings, induced by equilibrium plasma rotation across θ-ruffled separatrices, or by wave-induced separatrix fluctuations. Experiments on nominally-symmetric pure electron plasmas with controlled separatrices agree quantitatively with theory in 3 broad areas: 1) radial particle transport is driven by a static z- and θ-asymmetry; 2) both E × B drift waves and Langmuir waves are damped; and 3) novel dissipative wave-wave couplings are observed. The new chaotic neo-classical effects scale as ν0B-1, whereas traditional plateau-regime collisional effects scale as ν1/2B-1/2.

Chaotic Neoclassical Transport at Azimuthally Perturbed or Wave-Mingled Separatrix

Variations in magnetic or electrostatic confinement fields give rise to trapping separatrices, and standard neoclassical transport theory analyzes effects from collision-induced separatrix crossings. Experiments and theory have now characterized novel transport effects arising from “chaotic“ separatrix crossings, which occur due to equilibrium plasma rotation across θ-ruffled separatrices, and/or due to wave-induced separatrix fluctuations.

Chaotic Transport and Damping fromθ-Ruffled Separatrices

Variations in magnetic or electrostatic confinement fields give rise to trapping separatrices, and neoclassical transport theory analyzes effects from collision-induced separatrix crossings. Experiments on pure electron plasmas now quantitatively characterize a broad range of transport and wave damping effects due to "chaotic" separatrix crossings, which occur due to equilibrium plasma rotation across θ-ruffled separatrices, and due to wave-induced separatrix fluctuations.

The Velikhov and anti-Velikhov effects in the theory of magnetorotational instability

A theory of magnetorotational instability (MRI) allowing an equilibrium plasma pressure gradient and nonaxisymmetry of perturbations is developed. This approach reveals that in addition to the Velikhov effect driving the MRI due to negative rotation frequency profile, dΘ2/dr < 0, there is an opposite effect (the anti-Velikhov effect) weakening this driving (here, Θ is the rotation frequency and r is the radial coordinate). It is shown that in addition to the Velikhov mechanism, two new mechanisms of MRI driving are possible, one of which is due to the pressure gradient squared and the other is due to the product of the pressure and density gradients. The analysis includes both the one-fluid magnetohydrodynamic plasma model and the kinetics allowing collisionless effects. In addition to the pure plasma containing ions and electrons, the dusty plasma is considered. The charged dust effect on stability is analyzed using the approximation of immobile dust. In the presence of dust, a term with the electric field appears in the one-fluid equation of plasma motion. This electric field affects the equilibrium plasma rotation and also gives rise to a family of instabilities of the rotating plasma, called the dust-induced rotational instabilities.

Magnetorotational instabilities in a dusty plasma

The charged dust effect on stability of a magnetized rotating plasma is analysed using approximation of immobile dust. In the presence of the dust, a term with the electric field appears in the one-fluid equation of plasma motion. This electric field affects the equilibrium plasma rotation and also gives rise to a family of instabilities of the rotating plasma called dust-induced rotational instabilities (DRIs). The DRIs are related to the charge imbalance between the plasma ions and electrons because of the charged dust. In contrast to the well-known magnetorotational instability driven by the radially decreasing plasma rotation frequency, the DRI can appear for an arbitrary rotation frequency profile. A mathematical technique for the analysis of the magnetorotational phenomena is presented. It is based on the one-fluid magnetohydrodynamic approach developed for a pure plasma and generalized to include the immobile dust effects. The mode equation and local dispersion relation are derived in terms of the canonical parameters.

Numerical modelling of error field penetration

Error field (or externally applied helical field) penetration is studied numerically based on the two fluids equations. It is shown that there is a minimum in the required field amplitude when the applied helical field frequency is the same as the mode frequency being determined by both the background equilibrium plasma rotation and the diamagnetic drift. The mode penetration threshold significantly increases as the field frequency deviates from the mode frequency and can become asymmetric on the two sides of the minimum due to parallel heat transport. After mode penetration the nonlinear saturated island width is found to be smaller for a larger electron diamagnetic drift frequency.

Effect of sheared equilibrium plasma rotation on the classical tearing mode in a cylindrical geometry

The effect of sheared equilibrium plasma rotation on the stability of tearing modes in an Ohmic (low plasma β) regime is investigated. It is found, by means of numerical MHD simulations in a cylindrical geometry, that plasma rotation in the equivalent toroidal direction can result either in the increase or in the decrease of the instability growth rate. Perpendicular plasma viscosity and plasma rotation shear at the modes’ rational surface play a key role on assessing the effect of shear flow. While destabilizing for low viscosity plasmas (ratio of the resistive to viscous diffusion time scales τR∕τV≪1), for viscous plasmas (τR∕τV&amp;gt;1) shear flow reduces the growth rate. Above a given threshold in the rotation shear (that depends on the ratio τR∕τV) a tearing mode, unstable in the absence of rotation, can be stabilized. The effect of sheared toroidal flow on mode stability, in both viscosity regimes that are considered in the paper, is qualitatively independent of the aspect ratio.

Variational quadratic form for low-frequency electromagnetic perturbations. I. Formalism

A variational formalism is obtained in the limit of large perpendicular wavenumber which simultaneously includes electrostatic and electromagnetic perturbations, finite Larmor radius corrections, equilibrium plasma rotation, and arbitrary particle bounce effects. A tractable final expression is obtained and kinetic integrals are evaluated in special limits. The more accurate noneikonal expression is obtained from the asymptotic matching of the eikonal form to more restrictive noneikonal quadratic forms derived elsewhere.

Influence of equilibrium shear flow along the magnetic field on the resistive tearing instability

The influence of shear plasma flow along the magnetic field on the resistive tearing instability has been investigated in plane geometry. It is shown that such flows, even at significantly sub-Alfvénic speeds, have a destabilizing effect. Moreover, in nonsymmetric cases, the well-known threshold for tearing mode instability Δ′ext =0 is removed. Thus, in magnetic configurations which would otherwise be stable in the absence of flow, a shear plasma flow can induce instability. Approximate growth rates have been obtained for tokamaks with significant equilibrium plasma rotation and an application to the ISX-B experiments is briefly discussed.