Stability Of Magnetic Islands Research Articles

A semi-analytical model of RF condensation that can handle localized power depositions

A nonlinear effect, RF (radio frequency) condensation, can be used to facilitate RF stabilization of magnetic islands. Previously studied semi-analytical models for RF condensation are suited mainly for broad deposition profiles and are unable to handle power depositions that are localized in the interior of a magnetic island. The power deposition profile of electron cyclotron waves, in particular, can be highly localized near a cyclotron resonance. Here, a model is developed that can handle both localized profiles and broad profiles. This allows a comparison of RF condensation for narrow vs broad deposition profiles, and it allows a study of the dependence of RF condensation of localized deposition profiles on key parameters.

Calculating RF current condensation with consistent ray-tracing and island heating

By exploiting the nonlinear amplification of the power deposition of RF waves, current condensation promises new pathways to the stabilization of magnetic islands. We present a numerical analysis of current condensation, coupling a geometrical optics treatment of wave propagation and damping to a thermal diffusion equation solver in the island. Taking into account the island geometry and relativistic damping, previous analytical theory can be made more precise and specific scenarios can be realistically predicted. With this more precise description, bifurcations and associated hysteresis effects could be obtained in an ITER-like scenario at realistic parameter values. Moreover, it is shown that dynamically varying the RF wave launching angles can lead to hysteresis and help to avoid the nonlinear shadowing effect.

Numerical experiments of island stabilization by RF heating with stiff temperature profile

The nature of turbulent transport in tokamak plasmas results in temperature profiles that are called resilient or stiff, and the stabilization of magnetic islands by a localized heat source is expected to be extremely sensitive to the stiffness strength. Theoretical expectations are verified with nonlinear simulations, showing a good agreement and confirming the enhanced stabilization efficiency due to large profile stiffness, when the power used for the control is small compared with the heating power producing the equilibrium profiles. Heat sources, which are present in the island region before RF heating is applied, contribute to reducing the island size, but at the same time, severely dampen the control capability.

Influence of resonant magnetic perturbation on a rotating helical plasma

Nonlinear stability of magnetic islands in a helical plasma with resonant magnetic perturbation (RMP) is investigated using reduced magnetohydrodynamic equations including neoclassical viscosity. Coexistence of RMP-driven islands and the resistive interchange mode is numerically simulated. The self-healing of locked magnetic islands by neoclassical flows is observed. It is found that the curvature effect modifies the threshold of the self-healing, where the unfavorable curvature drives not only the interchange mode but also the curvature-driven tearing mode. An analytical model based on a Rutherford equation with a momentum equation is also introduced to understand the simulation results. Criterion of the self-healing considering the curvature effect is newly obtained.

Nonlinear stability of magnetic islands in a rotating helical plasma

Coexistence of the forced magnetic reconnection by a resonant magnetic perturbation (RMP) and the curvature-driven tearing mode is investigated in a helical (stellarator) plasma rotated by helical trapped particle-induced neoclassical flows. A set of Rutherford-type equations of rotating magnetic islands and a poloidal flow evolution equation is revisited. Using the model, analytical expressions of criteria of spontaneous shrinkage (self-healing) of magnetic islands and sudden growth of locked magnetic islands (penetration of RMP) are obtained, where nonlinear saturation states of islands show bifurcation structures and hysteresis characteristics. Considering radial profile of poloidal flows across magnetic islands, it is found that the self-healing is driven by neoclassical viscosity even in the absence of micro-turbulence-induced anomalous viscosity. Effects of unfavorable curvature in stellarators are found to modify the critical values. The scalings of criteria are consistent with low-β experiments in the large helical device.

Experimental Study of the Effect of Poloidal Flow on Stability of Magnetic Islands in LHD and TJ‐II

AbstractThe effect of the poloidal flow on the magnetic island is studied. The self‐healing of the magnetic island has been observed in the Large Helical Device (LHD) and TJ‐II. In TJ‐II plasmas, the magnetic island is healed in case the radial electric field is positive. In the LHD experiment, on the other hand, the radial electric field is negative when the magnetic island is healed. The relation between the magnitudes of the E×B flow and ion diamagnetic flow is important to consider the effect of the poloidal flow on magnetic island (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of local E×B flow shear on the stability of magnetic islands in tokamak plasmas

The influence of local E×B flow shear on a relatively wide, constant-ψ, magnetic island embedded in a large-aspect-ratio, low-β, circular cross-section tokamak plasma is examined, using a slab approximation to model the magnetic geometry. It is found that there are three separate solution branches characterized by low, intermediate, and high values of the shear. Flow shear is found to have a stabilizing effect on island solutions lying on the low and high shear branches, via a nonlinear modification of the ion polarization term in the Rutherford island width evolution equation, but to have a destabilizing effect on solutions lying on the intermediate shear branch. Moreover, the effect is independent of the sign of the shear. The modification of island stability by local E×B flow shear is found to peak when the magnitude of the shear is approximately vi/Ls, where vi is the ion thermal velocity, and Ls the magnetic shear length.

Automatic real-time tracking and stabilization of magnetic islands in a Tokamak using temperature fluctuations and ECW power

The control of rotating instabilities in a tokamak can be achieved by localized injection of radio-frequency (RF) driven current. Real-time detection of the radial location of the unstable magnetic islands and of the RF power deposition has been achieved in a device designed, built, and tested on the FTU tokamak.

On neoclassical effects in the theory of magnetic islands

Neoclassical viscosity affects the stability of magnetic islands by providing additional source of the transverve electric current contributing to the net longitudinal current in the magnetic island. One component of such neoclassical longitudinal current has a structure similar to the ion polarization current with enhanced plasma inertia and was investigated previosly. We show that in addition to the neoclassical inertia term, there is additional neoclassical current associated with variations of plasma pressure within the perturbed magnetic surfaces. Such variations can be caused by the ion polarization drift across the magnetic surface and finite heat conductivity in the parallel direction. A contribution of the neoclassical current due to plasma pressure variations is of the same order or larger than the standard ion polarization and bootstrap current terms. New terms will affect overall stability of magnetic islands and may provide a new threshold mechanism for the neoclassical tearing modes.

Role of the shear flow profile on the stability of magnetic islands

Plasma flow affects the stability of a magnetic island via modification of the ion inertial current. It is shown here that certain profiles of plasma velocity with shear may provide a stabilizing influence on the magnetic island. Such profiles of the plasma flow are characterized by inite plasma circulation inside a magnetic island.

Stabilization of magnetic islands due to the sheared plasma flow and viscosity

It is shown that the asymmetric deformation of the magnetic island caused bythe finite plasma viscosity gives a stabilizing effect on the magneticislands in the Rutherford regime. Such stabilization typically overcomes thedestabilizing effect of the ion polarization current.

Rotating nonlinear magnetic islands in a tokamak plasma

The nonlinear dynamics of rotating low m (poloidal mode number) tearing modes in a tokamak with external resonant magnetic perturbations is examined. Nonlinear evolution equations for the island width and the toroidal rotation frequency are derived within the two-fluid magnetohydrodynamic model, taking into account the plasma rotation and neoclassical parallel viscosity. The nonlinear stability of magnetic islands interacting with a static external magnetic perturbation is considered, and the critical magnetic field for the appearance of a locked mode is determined. It is shown that the coupling of the perpendicular and longitudinal plasma flow due to the neoclassical plasma viscosity enhances the amplitude of the critical magnetic field compared to the value obtained in a slab approximation. The perpendicular plasma viscosity causes a finite phase shift between the applied external field and the magnetic island, and further increases the value of the critical magnetic field required to induce a magnetic island.

Stability of bootstrap current-driven magnetic islands in stellarators

The stability of magnetic island producing perturbations due to fluctuations in the bootstrap current in stellarator configuration is examined. The stability criterion depends on the sign of the derivative of the rotational transform, the pressure gradient, and the direction of the equilibrium bootstrap current, which is determined by the structure of ‖B‖. It is found that quasihelically symmetric stellarator configurations with p′/ι′<0 are unstable to the formation of bootstrap current-driven magnetic islands. The stability of conventional stellarator configurations depends upon the field structure.

Suppression of magnetic islands by energetic ions in toroidal plasmas

This is a study of the effect of an energetic ion population injected from a neutral beam source on the nonlinear stability of magnetic islands. A kinetic theory is used to obtain the island current, which includes previously known modifications resulting from bootstrap currents and resistive interchanges. The island current thus obtained is used in an asymptotic treatment of the perturbed Ampère’s law, which yields an evolution equation for the island width. It is shown that the island width saturates at a very small amplitude in tokamaks (with Δ′>0) when the energetic ion density profile peaks just outside the rational surface. Energetic ions can also be used to modify the island width in three-dimensional equilibria. It is found that in stellarator equilibria with large vacuum islands, energetic ions can be injected to reduce the widths of equilibrium islands.