Chain Of Magnetic Islands Research Articles

Experimental study of the tearing mode instability during the current ramp up stage in Sino-United Spherical Tokamak

The fierce magnetohydrodynamic (MHD) activity observed during the current ramp up stage of a tokamak discharge, which significantly limits the performance of the plasma, has been experimentally studied in Sino-United Spherical Tokamak (SUNIST). The mode structure extracted by magnetic measurements appears to be typically decreasing from to , where m and n are the poloidal and toroidal mode numbers. A phase reversal layer in the spatial distribution of the magnetic perturbation extracts the approximate position of the magnetic island chain, which gives insight on the evolution of the internal structure of the MHD activity. A matrix equation method that includes corrections for the shadowing effect of the probe array has been developed so as to derive a more accurate estimation of the current density profile. The resulting current profile evolution qualitatively explains the decrease in poloidal mode number and the spontaneous suppression of the MHD activity. Statistical results of the MHD response suggest that the deterioration of the plasma confinement is closely related to the phase inversion position of the poloidal magnetic perturbation.

Nonlinear neoclassical two-fluid theory of response of tokamak plasma to resonant error-field

A nonlinear, neoclassical, two-fluid theory of the interaction of a single-helicity magnetic island chain with a resonant error-field in a quasi-cylindrical, low-β, tokamak plasma is presented. In particular, the analysis of Fitzpatrick [Phys. Plasmas 25, 042503 (2018)] is generalized to take explicit time dependence into account. Aside from the ability to more accurately treat time-varying problems, the main physical effect that is introduced into the theory by the incorporation of explicit time dependence is ion inertia. The formalism developed in the paper is used to analyze two time-varying problems. First, the interaction of a pre-existing magnetic island chain with a resonant error-field. Second, an error-field-maintained magnetic island chain. The latter problem is of direct relevance to experiments in which deliberately applied, multi-harmonic, resonant magnetic perturbations are used to suppress edge localized modes (ELMs) in tokamak plasmas. Indeed, the predictions of the theory are strikingly similar to data recently obtained from ELM suppression experiments in the DIII-D tokamak [R. Nazikian et al., Nucl. Fusion 58, 106010 (2018)].

Reduced magneto-hydrodynamic theory of coherent magnetic chains in the solar wind

An analytic theory is presented of magnetic structures in collisionless, high-$\unicode[STIX]{x1D6FD}$plasmas. Using a reduced magnetohydrodynamic model, a stationary nonlinear solution is constructed in the form of a Kelvin–Stuart cat’s eyes chain of magnetic islands, on the spatial scale that exceeds the characteristic ion lengths. The solution is imbedded in a background current sheet and possesses both a significant plasma density perturbation trapped inside the magnetic islands and a compressional magnetic field component that is driven mostly by a current loop located at the separatrix of the islands. This theory may provide an explanation for the magnetic structures observed in the solar wind close to the Earth by the Cluster spacecraft.

Impact of magnetic islands in the plasma edge on particle fueling and exhaust in the HSX and W7-X stellarators

The edge magnetic structure in the Helically Symmetric eXperiment (HSX) and Wendelstein 7X (W7-X) stellarators has been shown to have a significant impact on the particle fueling and exhaust of the plasma main species (hydrogen) as well as impurity helium. For HSX, the plasma sourcing to exhaust ratio, quantified by the effective and global particle confinement times τp* and τp,H, respectively, increases when a magnetic island chain is located in the plasma edge. The fueling efficiency is reduced by 25% when the plasma boundary is deformed by the magnetic islands. The X-point geometry also yields higher plasma temperatures in front of the main recycling region. When the island is moved radially inward, both τp* and τp decrease by 10%–25% depending on plasma density. The τp,H results rely heavily on EMC3-EIRENE modeling which confirms reduced fueling efficiency due to more rapid ionization in the outward shifted island position. These findings suggest that for a helically optimized system like HSX, the plasma fueling from the recycling source, as well as from active gas injection, can be controlled by the magnetic island chain in the plasma edge—which is a basic requirement for a divertor system. This process is also effective for the control of effective helium exhaust times, as τp,He* measured by perturbative gas puff experiments is reduced by up to 40% when the islands are shifted inwards. For Wendelstein 7-X, a similar reduction of τp,He* was inferred when magnetic islands were moved from the far plasma edge into the confined plasma region. However, the effective confinement features of H as the main plasma species were not affected due to the non-optimal position of the magnetic islands with respect to the highly localized ionization domain during the limiter startup campaign.

The Role of Magnetic Islands in Collisionless Driven Reconnection: A Kinetic Approach to Multi-Scale Phenomena

The role of magnetic islands in collisionless driven reconnection has been investigated from the standpoint of a kinetic approach to multi-scale phenomena by means of two-dimensional particle-in-cell (PIC) simulation. There are two different types of the solutions in the evolution of the reconnection system. One is a steady solution in which the system relaxes into a steady state, and no island is generated (the no-island case). The other is an intermittent solution in which the system does not reach a steady state, and magnetic islands are frequently generated in the current sheet (the multi-island case). It is found that the electromagnetic energy is more effectively transferred to the particle energy in the multi-island case compared with the no-island case. The transferred energy is stored inside the magnetic island in the form of the thermal energy through compressional heating, and is carried away together with the magnetic island from the reconnection region. These results suggest that the formation of a magnetic island chain may have a potential to bridge the energy gap between macroscopic and microscopic physics by widening the dissipation region and strengthening the energy dissipation rate.

A neoclassical drift-magnetohydrodynamical fluid model of the interaction of a magnetic island chain with a resonant error-field in a high temperature tokamak plasma

A two-fluid, neoclassical theory of the interaction of a single magnetic island chain with a resonant error-field in a quasi-cylindrical, low-β, tokamak plasma is presented. The plasmas typically found in large hot tokamaks lie in the so-called weak neoclassical flow-damping regime in which the neoclassical ion stress tensor is not the dominant term in the ion parallel equation of motion. Nevertheless, flow-damping in such plasmas dominates ion perpendicular viscosity, and is largely responsible for determining the phase velocity of a freely rotating island chain (which is in the ion diamagnetic direction relative to the local E × B frame at the rational surface). The critical vacuum island width required to lock the island chain is mostly determined by the ion neoclassical poloidal flow damping rate at the rational surface. The stabilizing effect of the average field-line curvature, as well as the destabilizing effect of the perturbed bootstrap current, is the same for a freely rotating, a non-uniformly rotating, and a locked island chain. The destabilizing effect of the error-field averages to zero when the chain is rotating and only manifests itself when the chain locks. The perturbed ion polarization current has a small destabilizing effect on a freely rotating island chain, but a large destabilizing effect on both a non-uniformly rotating and a locked island chain. This behavior may account for the experimentally observed fact that locked island chains are much more unstable than corresponding freely rotating chains.

Note: Development of a multichannel magnetic probe array for magnetohydrodynamic activity studies in Sino-United Spherical Tokamak.

A 30-channel movable magnetic probe radial array measuring the poloidal magnetic field's time derivative Ḃθ has been developed and installed on the Sino-United Spherical Tokamak to investigate the magnetohydrodynamic (MHD) activities in ohmic discharges. The probe array consists of thirty identical commercial chip inductors mounted on a slim printed circuit board and shielded by a customized quartz tube of 14 mm in outer diameter. With the application of instrumentation amplifiers, the system exhibits a good signal to noise ratio and the measured vertical field spatial distribution agrees well with the simulation result. The measured spatial and temporal distribution of Ḃθ during the MHD activities exhibits a clear phase reversal layer, which is a direct proof of tearing mode and provides a reliable indication of the magnetic island chain position.

Bootstrap current control studies in the Wendelstein 7-X stellarator using the free-plasma-boundary version of the SIESTA MHD equilibrium code

The recently developed free-plasma-boundary version of the SIESTA MHD equilibrium code (Hirshman et al 2011 Phys. Plasmas 18 062504; Peraza-Rodriguez et al 2017 Phys. Plasmas 24 082516) is used for the first time to study scenarios with considerable bootstrap currents for the Wendelstein 7-X (W7-X) stellarator. Bootstrap currents in the range of tens of kAs can lead to the formation of unwanted magnetic island chains or stochastic regions within the plasma and alter the boundary rotational transform due to the small shear in W7-X. The latter issue is of relevance since the island divertor operation of W7-X relies on a proper positioning of magnetic island chains at the plasma edge to control the particle and energy exhaust towards the divertor plates. Two scenarios are examined with the new free-plasma-boundary capabilities of SIESTA: a freely evolving bootstrap current one that illustrates the difficulties arising from the dislocation of the boundary islands, and a second one in which off-axis electron cyclotron current drive (ECCD) is applied to compensate the effects of the bootstrap current and keep the island divertor configuration intact. SIESTA finds that off-axis ECCD is indeed able to keep the location and phase of the edge magnetic island chain unchanged, but it may also lead to an undesired stochastization of parts of the confined plasma if the EC deposition radial profile becomes too narrow.

Interaction of a magnetic island chain in a tokamak plasma with a resonant magnetic perturbation of rapidly oscillating phase

An investigation is made into the interaction of a magnetic island chain, embedded in a tokamak plasma, with an externally generated magnetic perturbation of the same helicity whose helical phase is rapidly oscillating. The analysis is similar in form to the classic analysis used by Kapitza [Sov. Phys. JETP 21, 588 (1951)] to examine the angular motion of a rigid pendulum whose pivot point undergoes rapid vertical oscillations. The phase oscillations are found to modify the existing terms, and also to give rise to new terms, in the equations governing the secular evolution of the island chain's radial width and helical phase. An examination of the properties of the new secular evolution equation reveals that it is possible to phase-lock an island chain to an external magnetic perturbation with an oscillating helical phase in a stabilizing phase relation provided that the amplitude, ϵ, of the phase oscillations (in radians) is such that |J0(ϵ)|≪1, and the mean angular frequency of the perturbation closely matches the natural angular frequency of the island chain.

Dissipation of the striped pulsar wind

Rapidly rotating neutron stars blow a relativistic, magnetized wind mainly composed of electron-positron pairs. The free expansion of the wind terminates far from the neutron star where a weakly magnetized pulsar wind nebula forms, implying efficient magnetic dissipation somewhere upstream. The wind current sheet that separates the two magnetic polarities is usually considered as the most natural place for magnetic dissipation via relativistic reconnection, but its efficiency remains an open question. Here, the goal of this work is to revisit this issue in light of the most recent progress in the understanding of reconnection and pulsar electrodynamics. We perform large two-dimensional particle-in-cell simulations of the oblique rotator to capture the multi-scale evolution of the wind. We find that the current sheet breaks up into a dynamical chain of magnetic islands separated by secondary thin current sheets. The sheet thickness increases linearly with radius while the Poynting flux decreases monotonically as reconnection proceeds. The radius of complete annihilation of the stripes is given by the plasma multiplicity parameter at the light cylinder. Current starvation within the sheets does not occur before complete dissipation as long as there is enough charges where the sheets form. Particles are efficiently heated up to a characteristic energy set by the magnetization parameter at the light cylinder. Energetic pulsed synchrotron emission peaks close to the light cylinder, and presents sub-pulse variability associated with the formation of plasmoids in the sheet. This study suggests that the striped component of the wind dissipates far before reaching the termination shock in isolated pulsars, even in very-high-multiplicity systems such as the Crab pulsar. Pulsars in binary systems may provide the best environments to study magnetic dissipation in the wind.

Effects of magnetic islands on resonant field penetration and toroidal torques at slow plasma flow

The presence of a chain of magnetic islands, produced by externally applied tri-dimensional fields at a rational surface, is numerically found to have significant effects on the resonant response, as well as on the associated toroidal torques, in a toroidal tokamak plasma with conventional aspect ratio, strong shaping, and in the regime of slow toroidal flow. With an ad hoc assumption of the local flattening of the equilibrium pressure profile by the islands, it is found that the primary effect is the increasing of the resonant response by islands, at slow flow, due to the reduction of the favourable average curvature effect. This also leads to the reduction of the toroidal torques, in particular that associated with the neoclassical toroidal viscosity. Partial or complete flattening of the local pressure profile, depending on the island size, results in partial or full recovering of the so called constant-ψ plasma response regime. Computational results are well fitted by analytic models for the two extreme cases: the case of complete flattening and the case of no flattening of the local pressure.

Effect of nonlinear energy transport on neoclassical tearing mode stability in tokamak plasmas

An investigation is made into the effect of the reduction in anomalous perpendicular electron heat transport inside the separatrix of a magnetic island chain associated with a neoclassical tearing mode in a tokamak plasma, due to the flattening of the electron temperature profile in this region, on the overall stability of the mode. The onset of the neoclassical tearing mode is governed by the ratio of the divergences of the parallel and perpendicular electron heat fluxes in the vicinity of the island chain. By increasing the degree of transport reduction, the onset of the mode, as the divergence ratio is gradually increased, can be made more and more abrupt. Eventually, when the degree of transport reduction passes a certain critical value, the onset of the neoclassical tearing mode becomes discontinuous. In other words, when some critical value of the divergence ratio is reached, there is a sudden bifurcation to a branch of neoclassical tearing mode solutions. Moreover, once this bifurcation has been triggered, the divergence ratio must be reduced by a substantial factor to trigger the inverse bifurcation.

Nonlinear effects associated with kinetic Alfvén wave in magnetic islands

Observations show that kinetic Alfvén waves (KAWs) play a very important role in turbulence as well as in magnetic reconnection and have also been a topic of debate in the context of particle heating. In this paper, we aim to investigate the effect of magnetic islands on the dynamics of the nonlinear KAW. The formation of current sheet/coherent structures has been explored due to the propagation of the nonlinear KAW through the chain of pre-existing fully developed chain of magnetic islands. It is found that the field localization is more intense when the density perturbation due to nonlinearity and the field perturbation due to background islands are taken into account in comparison to the perturbation created by both the sources separately. Thus, it is expected that both nonlinearity and islands (reconnection generated) will aid the field localization and hence turbulence. Based on these coherent structures, we have evaluated the power spectrum and found the scaling after first breakpoint to be consistent with the observation by Chaston et al. [Phys. Rev. Lett. 102, 015001 (2009)] in the ion diffusion region of the magnetotail.

Helical temperature perturbations associated with radially asymmetric magnetic island chains in tokamak plasmas

The simple analysis of Rutherford [Phys. Fluids 16, 1903 (1973)] is generalized in order to incorporate radial magnetic island asymmetry into the nonlinear theory of tearing mode stability in a low-β, large aspect-ratio, quasi-cylindrical, tokamak plasma. The calculation is restricted to cases in which the radial shifts of the island X- and O-points are (almost) equal and opposite. For the sake of simplicity, the calculation concentrates on a particular (but fairly general) class of radially asymmetric island magnetic flux-surfaces that can all be mapped to the same symmetric flux-surfaces by means of a suitable coordinate transform. The combination of island asymmetry (in which the radial shifts of the X- and O-points are almost equal and opposite) and temperature-induced changes in the inductive current profile in the immediate vicinity of the island is found to have no effect on tearing mode stability.

An improved neoclassical drift-magnetohydrodynamical fluid model of helical magnetic island equilibria in tokamak plasmas

The effect of the perturbed ion polarization current on the stability of neoclassical tearing modes in tokamak plasmas is calculated using an improved, neoclassical, four-field, drift-magnetohydrodynamical model. The calculation involves the self-consistent determination of the pressure and scalar electric potential profiles in the vicinity of the associated magnetic island chain, which allows the chain's propagation velocity to be fixed. Two regimes are considered. First, a regime in which neoclassical ion poloidal flow damping is not strong enough to enhance the magnitude of the polarization current (relative to that found in slab geometry). Second, a regime in which neoclassical ion poloidal flow damping is strong enough to significantly enhance the magnitude of the polarization current. In both regimes, two types of solution are considered. First, a freely rotating solution (i.e., an island chain that is not interacting with a static, resonant, magnetic perturbation). Second, a locked solution (i.e., an island chain that has been brought to rest in the laboratory frame via interaction with a static, resonant, magnetic perturbation). In all cases, the polarization current is found to be either always stabilizing or stabilizing provided that ηi≡dlnTi/dlnne does not exceed some threshold value. In certain ranges of ηi, the polarization current is found to have a stabilizing effect on a freely rotating island, but a destabilizing effect on a corresponding locked island.

Effect of magnetic islands on the localization of kinetic Alfvén wave

Recent studies have revealed an intimate link between magnetic reconnection and turbulence. Observations show that kinetic Alfvén waves (KAWs) play a very crucial role in magnetic reconnection and have been a topic of interest from decades in the context of turbulence and particle heating. In the present paper, we study the role that KAW plays in the formation of coherent structures/current sheets when KAW is propagating in the pre-existing fully developed chain of magnetic islands. We derived the dynamical equation of KAW in the presence of chain of magnetic islands and solved it using numerical simulations well as analytic tools. Due to pre-existing chain of magnetic islands, KAW splits into coherent structures and the scale size of these structures along transverse directions (with respect to background magnetic field) comes out to be either less than or greater than ion gyro radius. Therefore, the present work may be the first step towards understanding how magnetic reconnection generated islands may affect the KAW localization and eventually contribute to magnetic turbulence. In this way the present approach may be helpful to understand the interplay between magnetic reconnection and turbulence in ion diffusion region.

Three-dimensional equilibria and island energy transport due to resonant magnetic perturbation edge localized mode suppression on DIII-D

Experiments in the DIII-D tokamak show that the plasma responds to resonant magnetic perturbations (RMPs) with toroidal mode numbers of n = 2 and n = 3 without field line reconnection, consistent with resistive magnetohydrodynamic predictions, while a strong nonlinear bifurcation is apparent when edge localized modes (ELMs) are suppressed. The magnetic response associated with this bifurcation is localized to the high field side of the machine and exhibits a dominant n = 1 component despite the application of a constant amplitude, slowly toroidally rotating, n = 2 applied field. The n = 1 mode is born locked to the vacuum vessel wall, while the n = 2 mode is entrained to the rotating field. Based on these magnetic response measurements and Thomson scattering measurements of flattening of the electron temperature profile, it is likely that these modes are magnetic island chains near the H-mode pedestal. The reduction in ∇Te occurs near the q = 4 and 5 rational surfaces, suggesting five unique islands are possible (m = 8, 9, or 10 for n = 2) and (m = 4 or 5 for n = 1). In all cases, the island width is estimated to be 2–3 cm. The Chang-Callen calculated confinement degradation due to the presence of an individual island of this size is 8%–12%, which is close to the 13%–14% measured between the ELMs and suppressed states. This suggests that edge tearing modes may alter the pedestal causing peeling-ballooning stability during RMP induced ELM suppression.

Analytical theory of the shear Alfvén continuum in the presence of a magnetic island

The effect of a magnetic island chain on the shear Alfvén continuum is calculated analytically. Using a WKB approximation of the linearized ideal MHD equations, the island is shown to cause an upshift in the continuum accumulation point frequency. This minimum of the frequency spectrum is shifted from the rational surface to the island separatrix. The structure of the eigenmodes is also presented.

Linear and nonlinear response of a rotating tokamak plasma to a resonant error-field

An in-depth investigation of the effect of a resonant error-field on a rotating, quasi-cylindrical, tokamak plasma is preformed within the context of constant-ψ, resistive-magnetohydrodynamical theory. General expressions for the response of the plasma at the rational surface to the error-field are derived in both the linear and nonlinear regimes, and the extents of these regimes mapped out in parameter space. Torque-balance equations are also obtained in both regimes. These equations are used to determine the steady-state plasma rotation at the rational surface in the presence of the error-field. It is found that, provided the intrinsic plasma rotation is sufficiently large, the torque-balance equations possess dynamically stable low-rotation and high-rotation solution branches, separated by a forbidden band of dynamically unstable solutions. Moreover, bifurcations between the two stable solution branches are triggered as the amplitude of the error-field is varied. A low- to high-rotation bifurcation is invariably associated with a significant reduction in the width of the magnetic island chain driven at the rational surface, and vice versa. General expressions for the bifurcation thresholds are derived and their domains of validity mapped out in parameter space.

Phase-locking of magnetic islands diagnosed by ECE-imaging.

Millimeter-wave imaging diagnostics identify phase-locking and the satisfaction of 3-wave coupling selection criteria among multiple magnetic island chains by providing a localized, internal measurement of the 2D power spectral density, S(ω, kpol). In high-confinement tokamak discharges, these interactions impact both plasma rotation and tearing stability. Nonlinear coupling among neoclassical tearing modes of different n-number, with islands not satisfying the poloidal mode number selection criterion ⟨m, m('), m - m(')⟩, contributes to a reduction in core rotation and flow shear in the vicinity of the modes.