Islands In Tokamaks Research Articles

Isochronous bifurcations of magnetic islands in tokamaks

On a rational magnetic surface, an isochronous bifurcation transforms one island chain into another chain with the same winding number. This transformation has been the subject of recent studies in tokamak plasmas. Namely, visco-resistive magnetohydrodynamic simulations of NSTX-U and DIII-D plasmas showed the onset of bifurcations with new magnetic isochronous islands for two competing helical perturbations on the same rational magnetic surface. To investigate these bifurcations, we use a cylindrical plasma model, with first-order correction for toroidicity, subject to externally applied magnetic perturbations, generated by a pair of resonant helical windings (RHWs) on the external wall and superposed to a helical current sheet (HCS) located on a rational plasma surface. We numerically integrate the magnetic field line equation and show that isochronous islands emerge when the perturbation created by the HCS increases. We present examples of such bifurcations on primary and secondary magnetic surfaces for different RHW configurations.

Unveiling non-flat profiles within magnetic islands in tokamaks

The presence of non-flat profiles on magnetic island is studied for the first time through gyrokinetic simulations alongside a simplified Lagrangian model. We have identified that inside a magnetic island, the non-flatness of density and temperature profiles is controlled by a dimensionless parameter α≡w*ŝϵ/qρ*, which is a function of normalized island width w*=w/a0, magnetic shear ŝ, inverse aspect ratio ϵ=a0/R, safety factor q, and normalized gyroradius ρ*=ρ/a0. The gyroradius ρ* dependence of the control parameter α leads to a species-selective transition of profiles from flat to concave only for electrons having high α∼O(1). The finding elucidates that electron profiles tend to increasingly deviate from the flat state for a larger magnetic island, in contrast to the conventional wisdom.

Long Term Vortex Flow Evolution around a Magnetic Island in Tokamaks.

We present a gyrokinetic analysis of the vortex flow evolution in a magnetic island in collisionless tokamak plasmas. In a short term ω[over ¯]_{D}t<1, where ω[over ¯]_{D} is the secular magnetic drift of the orbit center, initial monopolar vortex flow approaches to its residual level determined by the neoclassical enhancement of polarization shielding after collisionless relaxation. The residual level depends on the location inside an island and is higher than the Rosenbluth-Hinton level [M.N. Rosenbluth and F.L. Hinton, Phys. Rev. Lett. 80, 724 (1998)PRLTAO0031-900710.1103/PhysRevLett.80.724] due to finite island width. In a long term ω[over ¯]_{D}t>1, the residual vortex flow evolves to a dipolar zonal-vortex flow mixture due to toroidicity-induced breaking of a helical symmetry. The mixture forms localized flow shear layers near the island separatrix away from X points. The deviation of the streamlines of the mixture flows from magnetic surfaces allows turbulence advection across the island. We expect a small island w≲qρ_{Ti}/s[over ^] provides a favorable condition for this mixture flow formation, while the monopolar vortex flow persists for a larger island.

Study of stability and rotation of a chain of saturated, freely-rotating magnetic islands in tokamaks

The non-linear dynamics of a chain of stationary, saturated magnetic islands is studied by solving a four-field system of equations that include non-ideal effects, lowest order finite Larmor radius corrections and neoclassical terms. The magnetic island rotation velocity is calculated self-consistently with the fields profiles. The solutions for the island rotation velocity and for the ion polarization current are determined as a function of the characteristic parameters of the system and the results are discussed. The results of the calculations show that island rotation velocity and the ion polarization current depend in a non-trivial way on the parameters characterizing the system, and some clear patterns emerge only in particular cases. An analysis of magnetic island rotation velocity is performed on experiments in COMPASS tokamak. Measured island rotation velocity is compared with the calculated ion and electron flow velocities, for different hypotheses on the toroidal rotation of the plasma. The comparison shows that the island rotation velocity is consistent with the ion flow velocity, under the hypothesis of slow toroidal rotation and low collisionality. Theoretical calculation of the island rotation velocity according to the model here developed suggests that the islands rotate weakly in the ion direction, in the hypothesis of slow toroidal rotation and high collisionality. The impossibility of directly measuring the plasma rotation velocity makes it difficult to distinguish between these different regimes.

Experimental Observation of Magnetic Island Heteroclinic Bifurcation in Tokamaks.

We report empirical observations of magnetic island heteroclinic bifurcation for the first time. This behavior is observed in interacting coupled 2/1 tearing modes in the core of a DIII-D tokamak plasma. Poincaré maps constrained by measured magnetic amplitudes and phasing show bifurcation from heteroclinic to homoclinic topology in the 2/1 island as the 4/2 relative amplitude (R_{4/2}) decreases. Initially, the local electron temperature peak in the 2/1 island splits, consistent with two O points. As R_{4/2} decreases a single peak forms, consistent with one O point. These call for developing tearing stability theory and control solutions for heteroclinic islands in tokamaks.

Effects of plasma turbulence on the nonlinear evolution of magnetic island in tokamak

Magnetic islands (MIs), resulting from a magnetic field reconnection, are ubiquitous structures in magnetized plasmas. In tokamak plasmas, recent researches suggested that the interaction between an MI and ambient turbulence can be important for the nonlinear MI evolution, but a lack of detailed experimental observations and analyses has prevented further understanding. Here, we provide comprehensive observations such as turbulence spreading into an MI and turbulence enhancement at the reconnection site, elucidating intricate effects of plasma turbulence on the nonlinear MI evolution.

GTC simulation of linear stability of tearing mode and a model magnetic island stabilization by ECCD in toroidal plasma

Stabilization of a model magnetic island in tokamaks by localized electron cyclotron current drive (ECCD) has been studied using a fluid-kinetic hybrid model coupled with ray tracing and Fokker−Planck equations. Even though a gyrokinetic toroidal code at present is not able to simulate the long-time evolution of tearing modes, which starts from small perturbation and evolves to the Rutherford regime, we can still calculate a model magnetic island and its stabilization by ECCD. Gyrokinetic simulations find that the model magnetic island can be fully stabilized by the ECCD with the 1 MW 68 GHz X2-mode in HL-2A-like equilibrium, while the model magnetic island in the DIII-D tokamak is only partially stabilized with the same ECCD power. A helicoidal current drive is more efficient than a continuous ECCD to stabilize the model magnetic island. Simulation results further indicate that, without external current drive, thermal ion kinetic effects could also reduce the magnetic island width and the linear growth rate of tearing modes.

A reduced MHD model for ITG-NTM interplay

A six-field reduced-MHD model is derived for plasma dynamics. The new model describes coherently both ion temperature gradient (ITG) mode and tearing mode and includes neoclassical effects. The model allows the construction of an energylike quantity with a linear pressure contribution that is conserved except for dissipative, finite Larmor radius, and neoclassical terms. This model may be used to study the nonlinear interaction between ITG microturbulence and neoclassical tearing mode, which is responsible for large-scale magnetic islands in tokamaks, and opens the way to a coherent description of turbulent impurity transport in magnetic islands.

Global gyrokinetic simulation of microturbulence with kinetic electrons in the presence of magnetic island in tokamak

An electrostatic model has been formulated and implemented in the gyrokinetic toroidal code to study the nonlinear ion temperature gradient (ITG) turbulence in the presence of an n = 1, m = 2 magnetic island. The ions are described by the gyrokinetic equation while the electrons are treated with the drift-kinetic equation. In our simulation, an n = 1, m = 2 electrostatic mode is formed with the same vortex structure of the magnetic island. When the magnetic island flattening effect is turned on, the island vortex mode is well preserved and couples to the n = 0, m = 0 geodesic acoustic mode. Simulation shows that the magnetic island can suppress the ITG turbulence at the island O-point and strengthen it near the X-point. We show that the vortex mode can generate a substantial helical shear flow around the island. We also find that the turbulence and transport are suppressed inside the island and enhanced at the island X-point.

Near-singular equilibrium currents near magnetic islands with broken symmetry

The conventional cylindrical analytical model of a magnetic island is symmetric with respect to combined reflection in the poloidal and toroidal angles, a symmetry property sometimes called ‘stellarator symmetry’. There are cancellations in the pressure driven currents when an island is stellarator symmetric that are not there when the symmetry is broken. When the symmetry is broken, new aspects of the island physics emerge. The diamagnetic current driven by the scalar pressure is no longer ambipolar. The pressure-driven current generally has a logarithmic (integrable) singularity at the island separatrix. These effects manifest themselves when taking into account incomplete flattening of the pressure along magnetic field lines. A small magnetic island has only a small effect on the ambient pressure gradient, so that the pressure is not constant on the flux surfaces near the island. For larger islands, this behavior persists near the X-lines. The equilibrium solutions with a small island are to be compared with three-dimensional magnetohydrodynamic equilibrium solutions that are constrained to have simply nested flux surfaces, where the pressure-driven current goes like 1/x near rational surfaces, where x is the distance from the rational surface. This paper presents an investigation of the pressure driven current near a small magnetic island in a cylindrical magnetic field with perturbed circular flux surfaces. The conventional analytical cylindrical model of a field with a magnetic island is augmented with a resonant component that breaks the stellarator symmetry without breaking the flux surfaces. The effects of stellarator symmetry on magnetic islands in tokamaks are of particular interest in the context of the stabilization of edge localized modes by resonant magnetic perturbations. In stellarators, the design studies for the major contemporary devices have discarded half the design parameters available for optimization at the outset by assuming stellarator symmetry.

A four-field gyrofluid model with neoclassical effects for the study of the rotation velocity of magnetic islands in tokamaks

A four-field system of equations which includes the neoclassical flow damping effects and the lowest-order finite-Larmor-radius (FLR) corrections is deduced from a system of gyrofluid equations. The FLR corrections to the poloidal flow damping are calculated by solving a simplified version of the gyrokinetic equation. This system of equations is applied to the study of a chain of freely rotating magnetic islands in a tokamak, resulting from the nonlinear evolution of a resistive tearing mode, to determine the island rotation velocity consistently with the fields' radial profiles close to the resonant surface. The island rotation velocity is determined by imposing the torque balance condition. The equations thus deduced are applied to the study of two different collisionality regimes, namely the weak-damping regime and the intermediate-damping regime. The equations reduce, in the weak-damping regime, to a form already obtained in previous works, while an additional term, containing the lowest order FLR corrections to the poloidal flow damping, appears in the intermediate-damping regime. The numerical integration of the final system of equations allows the determination of the dependence of the island rotation velocity on the plasma collisionality and the island width compared to the ion Larmor radius. The results show that, in the intermediate-damping regime, the island rotation velocity is almost completely determined by the neoclassical effects, with the island width playing a minor role. The parameter ηi=Ln/LT, where Ln and LT are the density and temperature gradient length scales, plays an important role in determining the island rotation velocity.

Kinetic effects on the currents determining the stability of a magnetic island in tokamaks

The role of the bootstrap and polarization currents for the stability of ă neoclassical tearing modes is investigated employing both a drift ă kinetic and a gyrokinetic approach. The adiabatic response of the ions ă around the island separatrix implies, for island widths below or around ă the ion thermal banana width, density flattening for islands rotating at ă the ion diamagnetic frequency, while for islands rotating at the ă electron diamagnetic frequency the density is unperturbed and the only ă contribution to the neoclassical drive arises from electron temperature ă flattening. As for the polarization current, the full inclusion of ă finite orbit width effects in the calculation of the potential ă developing in a rotating island leads to a smoothing of the ă discontinuous derivatives exhibited by the analytic potential on which ă the polarization term used in the modeling is based. This leads to a ă reduction of the polarization-current contribution with respect to the ă analytic estimate, in line with other studies. Other contributions to ă the perpendicular ion current, related to the response of the particles ă around the island separatrix, are found to compete or even dominate the ă polarization-current term for realistic island rotation frequencies.

Rotation profile flattening and toroidal flow shear reversal due to the coupling of magnetic islands in tokamaks

The electromagnetic coupling of helical modes, even those having different toroidal mode numbers, modifies the distribution of toroidal angular momentum in tokamak discharges. This can have deleterious effects on other transport channels as well as on magnetohydrodynamic (MHD) stability and disruptivity. At low levels of externally injected momentum, the coupling of core-localized modes initiates a chain of events, whereby flattening of the core rotation profile inside successive rational surfaces leads to the onset of a large m/n = 2/1 tearing mode and locked-mode disruption. With increased torque from neutral beam injection, neoclassical tearing modes in the core may phase-lock to each other without locking to external fields or structures that are stationary in the laboratory frame. The dynamic processes observed in these cases are in general agreement with theory, and detailed diagnosis allows for momentum transport analysis to be performed, revealing a significant torque density that peaks near the 2/1 rational surface. However, as the coupled rational surfaces are brought closer together by reducing q95, additional momentum transport in excess of that required to attain a phase-locked state is sometimes observed. Rather than maintaining zero differential rotation (as is predicted to be dynamically stable by single-fluid, resistive MHD theory), these discharges develop hollow toroidal plasma fluid rotation profiles with reversed plasma flow shear in the region between the m/n = 3/2 and 2/1 islands. The additional forces expressed in this state are not readily accounted for, and therefore, analysis of these data highlights the impact of mode coupling on torque balance and the challenges associated with predicting the rotation dynamics of a fusion reactor—a key issue for ITER.

Kinetic Effects on the Currents Determining The Stability of a Magnetic Island in Tokamaks

Kinetic Effects on the Currents Determining The Stability of a Magnetic Island in Tokamaks

Gyrokinetic determination of the electrostatic potential of rotating magnetic islands in tokamaks

The electrostatic potential related to a magnetic island structure with imposed width and rotation frequency is studied by means of gyrokinetic simulations, which allow its self-consistent determination via the Poisson equation. An adiabatic response of the trapped ions at the island separatrix leads to a significant smoothing of the potential with respect to analytic calculations based on a complete flattening of the pressure profile inside the island. As a consequence, the magnitude of the polarization current is drastically reduced. When the island size is comparable to the ion banana width, the adiabatic response covers the whole island region, leading to a reduced density flattening for islands rotating in the electron diamagnetic direction. This confirms previous results based on drift-kinetic simulations.

Gyrokinetic and gyrofluid investigation of magnetic islands in tokamaks

The evolution of a tearing mode is a multi-scale problem, involving lengths from below the ion gyroradius up to the dimensions of the system. The effects due to finite ion Larmor radius on the island dynamics are investigated by means of numerical gyrokinetic and gyrofluid simulations in tokamak geometry. In gyrokinetic runs, the magnetic island is prescribed. The coupling induced by a static island between small and large scale fluctuations in the case of electrostatic turbulence is discussed and the role of the perturbed magnetic geometry on the electron response is highlighted. Simulations in the presence of a rotating island, excluding background turbulence, allow a clear, self-consistent determination of the electrostatic potential associated with the island rotation and of the relevant plasma profiles for arbitrary island widths. Finally, the first gyrofluid simulations showing the growth of an island in the presence of electromagnetic turbulence for parameters typical of a mid-size tokamak are presented.

Gyrokinetic investigation of magnetic islands in tokamaks

A powerful new numerical tool to carry out investigations into magnetic islands by means of the gyrokinetic equations is described in the present paper. An island structure, with imposed width and rotation, has been implemented in the flux-tube code GKW. Numerical simulations retaining finite Larmor radius effects (FLRs), toroidicity, kinetic electrons and self-consistent electrostatic potential are presented, concerning, among others, the incomplete density profile flattening for small magnetic islands, the dependency of the island potential on the island rotation frequency and the emission of drift waves connected to the island rotation. Turbulent fluctuations are not fully resolved by filtering out short wavelengths.

Kinetic effects on slowly rotating magnetic islands in tokamaks

The current flowing around a magnetic island and connected to its rotation with respect to the plasma is studied by means of a drift-kinetic approach. It is shown that the current due to a change in the precession frequency of the trapped particles in the island potential can compete with the standard polarization current for island rotation frequencies close to or below the diamagnetic frequency. The passing particles are found, on the contrary, to have little impact on the standard picture. The analytical results are shown to explain the features of the island current seen in numerical simulations.

Control of magnetic islands by pellet injection in tokamaks

The appearance of magnetic islands in tokamaks degrades plasma confinement. It is therefore important to control or eliminate the growth of the islands to improve the performance of a tokamak. A theory is developed to control magnetic islands using the localized pressure gradient driven bootstrap current by injecting pellets at the O-point of the island to create a peaked plasma pressure profile inside the island. This localized bootstrap current replenishes the missing equilibrium bootstrap current density that causes the island to grow in the first place. It is shown that the effect of the localized bootstrap current tends to reduce or eliminate the original drive for the growth of the island in the island evolution equation. The theory is also valid for the localized bootstrap current created by localized heating, but with much less effectiveness. A possibility of eliminating the island by controlling the equilibrium profiles is also discussed.

Island-induced bootstrap current on the saturation of a thin magnetic island in tokamaks

It is shown that island-induced bootstrap current density, which results from the symmetry breaking of the ∣B∣ when an island is embedded in the equilibrium magnetic field B, modifies the evolution equation and the saturation level for a thin magnetic island in tokamaks. This modification is independent of the fraction of the equilibrium bootstrap current density. It is found that island-induced bootstrap current density increases the saturation level for modes with positive values of Δ′. Here, Δ′ is the stability parameter for the linear tearing modes.