Island Rotation Research Articles

Collisionality dependence of the polarization current caused by a rotating magnetic island

The effect of collisions on the polarization current caused by a rotating island in a Tokamak plasma is studied with guiding center particle simulations. The simulations are performed with a δf code which includes a Monte Carlo model for Coulomb collisions. The transition between the two limiting cases of low and high collision frequency ν (compared to the island rotation frequency ω) is found to occur at ν≈ω in agreement with a recent analytic theory.

Role of Kinetic Effects on the Polarization Current around a Magnetic Island

The polarization current due to a magnetic island rotating in a tokamak plasma is believed to play a central role in the initial evolution of the neoclassical tearing mode. Monte Carlo delta f simulations are performed which also cover a parameter range that is not amenable to analytic treatment but is relevant to experiments. It is shown that the polarization current can change sign when the island rotation frequency is of the order of the ion parallel streaming around the island. Moreover, the current is reduced when the island width is of the order of the ion banana width. Finally, the transition to the enhanced high-collisionality regime is shown to occur for collision frequencies higher than those typical of today's experiments.

Kinetic calculation of the polarization current in the presence of a neoclassical tearing mode

The polarization current associated with a neoclassical tearing mode (NTM) is studied by means of drift kinetic δf simulations. This current has been invoked as a possible explanation for both the observed threshold for the minimum island size that can grow unstable and the scaling of the plasma pressure at the mode onset with the normalized gyroradius, even though the theory is not able to predict the island rotation direction and hence the role (whether stabilizing or destabilizing) of the polarization current for the island evolution. In the numerical approach presented in this paper, the island rotation frequency can be assigned as an input parameter and the corresponding behaviour of the current can be studied. The calculations are performed in toroidal geometry in the presence of a helical perturbation. It is found that kinetic effects lead to a sign reversal of the polarization current for rotation frequencies close to the diamagnetic frequency even for flat pressure profiles, thus influencing both the sign and size of the polarization-current contribution to the NTM evolution.

Evolution of the Current Density Profile Associated with Magnetic Island Formation in JT-60U

Evolution of the current density profile associated with magnetic island formation of an m/n=2/1 tearing mode was measured using a motional Stark effect (MSE) diagnostic for the first time in the JT-60U tokamak. With the island growth, the current density profile turned flat at the radial region of the island, followed by an appearance of a hollow structure. As the island shrank, the flat region became narrower, and it finally diminished after the disappearance of the island. The fluctuation of the local poloidal magnetic field from MSE showed a strong correlation with a slow island rotation. This indicates that the observed deformation in the current density profile is localized at the island O point.

Plasma flow and confinement in the vicinity of a rotating island in collisional tokamak plasmas

The theory for the electric field, plasma flows, and plasma confinement in the vicinity of a rotating magnetic island in tokamaks [Phys. Plasmas 9, 3470 (2002)] is extended to the collisional plasmas, i.e., the plateau-Pfirsch–Schluter regime. The electric field that is parallel to the magnetic field B, E∥, is assumed to vanish. It is found that plasmas flow in the toroidal direction at the same rate as the island rotation frequency. Island rotation frequency is calculated using an island-induced symmetry-breaking viscosity. The radial electric field in the vicinity of the island is also determined from the toroidal momentum balance equation that includes island-induced toroidal viscosity.

Plasma flow and confinement in the vicinity of a rotating island in tokamaks

The theory for the electric field and the plasma confinement in the vicinity of a magnetic island in tokamaks [Phys. Plasmas 9, 3470 (2002)] is extended to the situation where the magnetic island is rotating. The electric field that is parallel to the magnetic field, E∥, is assumed to vanish. With this assumption, the theory for a nonrotating island is applicable to a rotating island if the radial electric field in the nonrotating theory is replaced by the radial gradient of ℱ. Here, ℱ is the part of the electrostatic potential that is constant on the rotating island magnetic surface. As an application of the theory, the radial electric field, toroidal flow speed, ambipolar particle flux, heat flux, and island rotation frequency in the collisionless regime are also presented.

Effects of parallel viscosity on rotation of magnetic islands in tokamaks

Effects of parallel viscosity on rotation of magnetic islands in tokamaks are studied. The Pfirsch–Schlüter regime is considered with following generalization of the results to the plateau and banana regimes. Assuming the parallel viscosity to be prevailing over the perpendicular viscosity, the superdrift magnetic islands are studied. It is found that in this case, first, the electrostatic potential profile function is of the Rutherford-type and, second, in contrast to the cylindrical geometry, the island rotation frequency does not depend on the nonstationarity of the profile function but is determined by a volume integral from the parallel viscosity.

Transport threshold model of neoclassical tearing modes in the presence of anomalous perpendicular viscosity

Bootstrap drive of neoclassical tearing modes (NTMs) in the presence of anomalous perpendicular viscosity is calculated. Viscosity is shown to lead to dependence of the perturbed bootstrap current on the perturbed electric field. As a result, the bootstrap drive is qualitatively modified by the island rotation frequency and direction of the island rotation. The modified bootstrap drive is incorporated into the transport threshold model of NTMs.

Multilayer growth of Ag [formula omitted]: a simulation study

The multilayer growth of Ag/Ag(1 1 0) is studied by kinetic Monte Carlo simulations based on model in the full fcc geometry with realistic activation barriers. The model is able to describe both the island rotation in the submonolayer regime and the ripple rotation in multilayer growth, in very good quantitative agreement with the experiments. The ripple wavelength and slope are calculated, and the results are compared also to simple analytical estimates, finding a good agreement in the case of the low-temperature cross-channel ripples. The role of the different elementary microscopic mechanisms is studied by varying one by one the values of the activation barriers; this has allowed to set limits on the values of the barrier themselves.

Effect of Microscopic Turbulence on Magnetic Island

The dynamics of the magnetic island affected by the microscopic turbulence is analyzed using the renormalized reduced MHD equations. The evolution equations of the island width w ( t ) and rotation frequency ω( t ) are derived in the cold ion approximation. It is found that the effects of the current flowing in a layer close to the separatrix are important to evaluate the effects of turbulent diffusions on the island rotation. As the result, the rotation of the magnetic island is driven by anomalous resistivity, and suppressed by anomalous ion viscosity and thermal conductivity.

Rotation-transport threshold model of neoclassical tearing modes

A rotation-transport threshold model of neoclassical tearing modes (NTMs) issuggested. It is assumed that weakening of the bootstrap currenteffect is determined by competition of perpendicular transportand island rotation, which is in contrast to the known transportthreshold models dealing with the parallel transport or parallelconvection instead of island rotation. It is shown that forsufficiently strong island rotation the perpendicular transportdoes not lead to decreasing the bootstrap current contributioninto the island width evolution equation. It is explained that theisland rotation can prevail over the parallel transport/convectionmainly for the case of ion contribution into the bootstrapcurrent effect. Interrelation between the rotation-transportthreshold model and the known ones is discussed. A generalizedtransport threshold model of NTMs describing the competition ofthe perpendicular transport with the island rotation, paralleltransport and parallel convection is formulated. It is shown thatthe perpendicular transport can lead to weakening the bootstrapdrive contribution only if it overpowers all the competitive effects.

The role of polarization current in magnetic island evolution

The polarization current plays an important role in the evolution of magnetic islands with a width comparable to the characteristic ion orbit width. Understanding the evolution of such small magnetic islands is important for two reasons: (1) to investigate the threshold mechanisms for growth of large-scale islands (e.g., neoclassical tearing modes), and (2) to describe the drive mechanisms for small-scale magnetic turbulence and consequent transport. This article presents a two-fluid, cold ion, collisional analysis of the role of the polarization current in magnetic island evolution in slab geometry. It focuses on the role played by the conjunction of parallel electron dynamics and perpendicular transport (particle diffusion and viscosity) in determining the island rotation frequency and the distribution of the polarization current within the island.

A nonlinear two-fluid model for toroidal plasmas

A nonlinear numerical model for the two-fluid (electron and ion fluid) description of the evolution of a plasma in toroidal geometry, MH3D-T, is described. The model extends the “drift” ordering for small perturbations to arbitrary perturbation size. It is similar, but not identical, to the collisional Braginskii equations. The ion gyroviscous stress tensor, Hall terms, temperature diamagnetic drifts, and a separate electron pressure evolution are included. The model stresses the (fluid) parallel dynamics by solving the density evolution together with the temperature equations, including the thermal equilibration along the magnetic field. It includes the neoclassical, collisional parallel viscous forces for electrons and ions. The model has been benchmarked against the stabilizing effects of the ion diamagnetic drift ω*i on the m=1, n=1 reconnecting mode in a cylinder. The stabilization mechanism is shown to be poloidal rotation of the global kink flow of the plasma mass vi within q<1, relative to the location of the magnetic field X-point within the reconnection layer. The ion ω*i-drift is also shown to cause frequency-splitting for the toroidal Alfvén eigenmode (TAE). Basic diamagnetic and neoclassical magnetohydrodynamic (MHD) effects on magnetic island evolution and rotation are discussed. The dynamics of the plasma along the magnetic field, when compressibility, parallel thermal conductivity, plasma density evolution, and full toroidal geometry are kept, are found to have strong effects on both linear growth rates and nonlinear evolution. The nonlinear coupling of magnetic islands, driven by perturbations of different toroidal mode number, is enhanced by the density evolution in both MHD and two-fluids.

Possible resolution of the “main intrigue” of the neoclassical tearing mode theory

The dilemma is discussed whether the polarization current effect on the neoclassical tearing modes is stabilizing or destabilizing. It is suggested that, if the island rotation frequency is formed due to the perpendicular viscosity and if one uses the correct expression for the viscosity allowing for the heat flux derivatives and takes into account the perpendicular heat flux in the ion heat balance equation, this effect should be stabilizing.

An approach to calculation of magnetic island rotation frequency

The problem of magnetic island rotation is analyzed. It is noted that for the correct solution of this problem the nonstationarity of profile functions should be taken into account. An approach to solving equations for nonstationary profile functions is developed for cases when drift and neoclassical effects can be neglected. The principal role of perpendicular viscosity in determining island rotation frequency is emphasized. The possibility of the existence of stationary magnetic islands in tokamaks with a rotating plasma and a resistive wall is shown.

Control of neoclassical tearing modes in large tokamaks

Some self-consistent effects pertaining to feedback control of neoclassical tearing modes in high temperature large tokamaks are investigated. For the ECRH scheme of local electron heating, it is shown that the self-consistent bootstrap currents created by the driven pressure gradients within the island are comparable to those due to the usually considered resistivity change mechanism. Similar self-consistent currents can also arise from pressure gradients created by density and energy deposition from neutral beams, thereby offering a new possibility for neoclassical mode control. The stabilizing current in such an application of neutral beams is estimated. It is further shown that such a feedback scheme can be made even more effective through appropriate modulation of the beam source to match the phase variation arising from the island rotation.

Resonant interaction of energetic ions with magnetic islands

A resonance ω = k||v|| between energetic ions and a magnetic island with a half-width greater than the bulk ion Larmor radius is considered. As a result of such a resonant interaction, energetic ions with a relative density of a few per cent contribute significantly to the toroidal torque balance, leading to considerable modification of the equilibrium island rotation frequency ω. The possibility of a frequency pulsation scenario, instead of a stationary toroidal torque balance, is indicated.

On the stabilization of neoclassical tearing modes by electron cyclotron waves

The control of neoclassical tearing modes in tokamaks by means of electron cyclotron current drive and heating is investigated. The nonlinear evolution of the amplitude in absence and in presence of the stabilizing terms of an auxiliary current inside the island and of the associate heating is solved self-consistently with the evolution of the rotation frequency for International Thermonuclear Experimental Reactor (ITER) reference magnetic equilibrium [ITER-JCT and Home Teams, Plasma Phys. Controlled Fusion 37, A19 (1995)]. It is shown that, unless the wall braking torque is neutralized by external means, neoclassical tearing modes in ITER will be locked in a very short time. On the other hand, for rotating islands, the beneficial effect of modulating the current source in phase with the island rotation is pointed out, after an analysis of the time scales of the relevant phenomena (time response of the driven current, island rotation frequency, power pulse duration, and inductive response of the plasma). Consideration is given to different effects that may reduce the efficiency of the control of the flux reconnection rate and to the benefits of wall stabilization associated to the island rotation frequency. A quantitative assessment of the EC (electron cyclotron) power required to keep the island width at a reasonable level is given, both in absence and in presence of wall stabilization.

Dynamical modelling of tearing mode stabilization by RF current drive

The theory of tearing mode stabilization in toroidal plasmas by RF driven currents that are modulated in phase with the island rotation is investigated. A time-scale analysis of the phenomena involved indicates that transient effects, such as finite time response of the driven currents, island rotation during the power pulses and the inductive response of the plasma, are intrinsically important. A dynamical model of such effects is developed, based on a 3-D Fokker-Planck code coupled to both the electric field diffusion equation and the island evolution equation. Extensive applications to both ECCD and LHCD in ITER are presented.

Active control of 2/1 magnetic islands in a tokamak

Closed and open loop control techniques were applied to growing m/n=2/1 rotating islands in wall-stabilized plasmas in the High Beta Tokamak-Extended Pulse (HBT-EP) [J. Fusion Energy 12, 303 (1993)]. HBT-EP combines an adjustable, segmented conducting wall (which slows the growth or stabilizes ideal external kinks) with a number of small (6° wide toroidally) driven saddle coils located between the gaps of the conducting wall. Two-phase driven magnetic island rotation control from 5 to 15 kHz has been demonstrated powered by two 10 MW linear amplifiers. The phase instability has been observed and is well modeled by the single-helicity predictions of nonlinear Rutherford island dynamics for 2/1 tearing modes including important effects of ion inertia and finite Larmor radius, which appear as a damping term in the model equations. The closed loop response of active feedback control of the 2/1 mode at moderate gain was observed to be in good agreement with the theory. Suppression of the 2/1 island growth has been demonstrated using an asynchronous frequency modulation drive which maintains the inertial flow damping of the island by application of rotating control fields with frequencies alternating above and below the natural mode frequency. This frequency modulation control technique was also able to prevent disruptions normally observed to follow giant sawtooth crashes in the plasma core.