Chain Of Magnetic Islands Research Articles

Characteristics of divertor heat flux distribution with an island divertor configuration on the J-TEXT tokamak

On J-TEXT, the temporal evolution of heat flux distribution on the high-field side (HFS) divertor plate has been measured by an infrared (IR) camera during the plasma operation with an island divertor configuration. In experiments, the island divertor configuration is an edge magnetic island chain structure surrounded by stochastic layers, which can be induced by resonant magnetic perturbations (RMPs). The experimental results show that the heat flux distribution on the HFS target plate depends significantly on the edge magnetic topology. Furthermore, the impact of hydrogen fueling using supersonic molecular beam injection (SMBI) on the divertor heat flux distributions is studied on J-TEXT with an island divertor configuration. It has been observed that power detachment can be achieved when the radiation front approaches the last closed flux surface (LCFS) after each SMBI pulse. This result may provide a method of access for divertor detachment on a fusion device with a three-dimensional (3D) boundary magnetic structure.

Roles of non-axisymmetric perturbations in free drift vertical displacement events on EAST

The safe operation of most tokamaks, especially the large ones, relies on the feedback control of vertical displacement events (VDEs). However, most of these feedback control systems are based on axisymmetric VDE models. In this study, we use NIMROD simulations to study the role of non-axisymmetric perturbations in free drift vertical displacement events on EAST. The high-n modes in the non-axisymmetric VDE grow first, which drives the formation of high-n magnetic island chains. Subsequently, the magnetic island chains grow and overlap with each other, leading to the destruction of the magnetic flux surface, which induces a minor disruption and accelerates the start of the following major disruption. The magnetic island and the stochastic magnetic field allow the toroidally non-axisymmetric poloidal plasma current to jet towards the hoop force direction, forming finger-like and filamentary structures. Such a plasma current non-axisymmetry strongly depends on the anisotropy in the thermal transport coefficients.

Conditions and benefits of X-point radiation for the island divertor

We present a method to geometrically quantify the three magnetic island chains with the poloidal mode numbers m = 4, 5, and 6 (referred to in this paper as high-iota, standard, and low-iota islands, respectively), on which the W7-X divertor relies. The focus is on a comparative study of their detachment performance using a series of models of different physical and geometrical complexity, ranging from one- to three-dimensional (1D to 3D). In particular, it aims to identify the key physical elements behind the correlation between impurity radiation and island geometry and the associated detachment stability. Assuming intrinsic carbon as a radiator, we scan the three island chains with the EMC3-Eirene code based on otherwise identical code inputs. We find that the three islands behave differently in the radiation distribution, in the development of the radiation zones during detachment, and in the ‘radiation costs’, defined as the product of impurity and electron density near the last closed flux surface. While the radiation costs for the iota = 5/4 and 5/5 island chains linearly increase with the total radiation, the low-iota island with iota = 5/6 shows a bifurcation behavior in the sense that the radiation costs initially increase and then decrease when the total radiation exceeds a critical level. Consistent with the numerical trends, stable detachment, which is experimentally easy and robust to achieve with the standard iota = 5/5 island chain, remains an experimental challenge with the low-iota configuration. Dedicated numerical experiments show that the recycling neutrals and the ratio of parallel to perpendicular heat transport, which depends closely on the field line pitch, play a significant role in the formation and evolution of the radiation layer. A deeper understanding of the underlying physics relies on simpler models that explain why and how flux expansion can reduce the radiation costs. From these insights, we derive the conditions in which detached plasmas can benefit from the expansion of flux surfaces around the X-point. We show and explain why the current divertor design limits the actual capability of the high-iota configuration and propose solutions. The work is presented within a theoretical/numerical framework but cites relevant experimental evidence to emphasize its practical significance.

Effects of edge-localized electron cyclotron current drive on edge-localized mode suppression by resonant magnetic perturbations in DIII-D

According to recent DIII-D experiments (Logan et al 2024 Nucl. Fusion 64 014003), injecting edge localized electron cyclotron current drive (ECCD) in the counter-plasma-current (counter-I p) direction reduces the n = 3 resonant magnetic perturbation (RMP) current threshold for edge-localized mode (ELM) suppression, while co-I p ECCD during the suppressed ELM phase causes a back transition to ELMing. This paper presents nonlinear two-fluid simulations on the ECCD manipulation of edge magnetic islands induced by RMP using the TM1 code. In the presence of a magnetic island chain at the pedestal-top, co-I p ECCD is found to decrease the island width and restore the initially degraded pedestal pressure when its radial deposition location is close to the rational surface of the island. With a sufficiently strong co-I p ECCD current, the RMP-driven magnetic island can be healed, and the pedestal pressure fully recovers to its initial ELMing state. On the contrary, counter-I p ECCD is found to increase the island width and further reduce the pedestal pressure to levels significantly below the peeling-ballooning-mode limited height, leading to even stationary ELM suppression. These simulations align with the results from DIII-D experiments. However, when multiple magnetic island chains are present at the pedestal-top, the ECCD current experiences substantial broadening, and its effects on the island width and pedestal pressure become negligible. Further simulations reveal that counter-I p ECCD enhances RMP penetration by lowering the penetration threshold, with the degree of reduction proportional to the amplitude of ECCD current. For the ∼1 MW ECCD in DIII-D, the predicted decrease in the RMP penetration threshold for ELM suppression is approximately 20%, consistent with experimental observations. These simulations indicate that edge-localized ECCD can be used to either facilitate RMP-driven ELM suppression or optimize the confinement degradation.

Localization of beam generated whistler wave and turbulence generation in reconnection region of magnetopause

Whistler waves have been studied for many years in relation to turbulence and particle heating, and observations show that they are crucial to magnetic reconnection. Recent research has revealed a close relationship between magnetic reconnection and turbulence. The current work investigates the whistler turbulence caused by the energetic electron beam in the magnetic reconnection sites of magnetopause and also due to dynamic evolution of magnetic islands. For this, we develop a model based upon the two-fluid approximation to study whistler dynamics, propagating in the medium with the pre-existing chain of magnetic islands and under the influence of background density perturbation originating from ponderomotive nonlinearity of wave. Dynamics of nonlinear whistler have been solved with pseudo-spectral approach and a finite difference method with a modified predictor–corrector method and a Runge Kutta method for the semianalytical model. In the current research, we study how the nonlinear whistler wave contributes to the significant space phenomenon, i.e., turbulence, localization, and magnetic reconnection. We have also investigated the formation of a current sheet in a magnetopause region of the order of few-electron inertial length. We analyzed the power spectrum at the magnetopause when the system reached a quasi-steady condition. Our new approach to study whistler turbulence by an energetic electron beam at the magnetic reconnection sites has extensive applications to space plasmas, shedding a new light on the study of magnetic reconnection in nature.

Theoretical investigation of the triggering of neoclassical tearing modes by transient resonant magnetic perturbations in NSTX

The extended perturbed equilibrium code asymptotic matching code is used to simulate the triggering of n = 1 neoclassical tearing modes (NTMs) by a pulsed, rotating, n = 1, resonant magnetic perturbation (RMP) in two example NSTX discharges. Although the two discharges are significantly different from one another, the results of the two sets of simulations are quite similar. The critical n = 1 RMP pulse amplitude required to trigger an n = 1 NTM is minimized when the RMP pulse rotation frequency matches the linear natural frequency of an n = 1 tearing mode, resonant within the plasma, that is metastable to an NTM. However, if there is a frequency mismatch, then the seed magnetic island chain driven at the relevant resonant surface is forced to rotate with respect to the RMP, because the RMP pulse amplitude is nowhere near sufficient to lock the island chain to the RMP. This rotation causes the critical RMP pulse amplitude required to trigger an NTM to oscillate as the RMP pulse duration is varied. The critical amplitude is minimized when the RMP pulse duration is such that seed island chain executes a half-integer number of rotations with respect to the pulse. All of the minima have the same value.

The shear Alfvén continuum with a magnetic island chain in tokamak plasmas

The shear Alfvén continuum spectrum is studied for a tokamak with a single island chain using the ideal magnetohydrodynamics theory. We have taken into account the toroidal geometry and toroidal mode coupling with the island considered as a highly-shaped stellarator. Various new frequency gaps open up inside the island due to its asymmetry both poloidally and toroidally, such as the mirror-induced Alfvén eigenmode (MAE) gap and the helicity-induced Alfvén eigenmode (HAE) gap. We have shown that the MAE gap acts as the continuation of the outside toroidal Alfvén eigenmode (TAE) gap into the island. However, the combined TAE/MAE gap is getting narrower as the island grows, leaving only half of its original width with a moderate island size as much as 3.2% of the minor radius. In addition, the two-dimensional eigenfunction of the continuum mode on the lower tip of the MAE gap now has highly localised structures around the island’s long axis, contrary to the usual oscillatory global solutions found with no or a low level of toroidal asymmetry—an indication of the continuous spectrum becoming discrete and dense. These results have implications for the frequency, mode structure and continuum damping of global TAEs residing in the gap.

Multi-harmonic Rutherford island theory

Rutherford island theory, which governs the nonlinear evolution of tearing modes in tokamak plasmas, is generalized to take into account situations in which the conventional one-harmonic approximation is not valid. The analysis incorporates non-inductive currents driven by radio frequency (RF) electromagnetic waves injected into the plasma. A multi-harmonic tearing mode dispersion relation is derived that takes the form of a nonlinear inhomogeneous matrix eigenvalue problem. The dispersion relation is solved in the so-called two-harmonic approximation, in which only the principal Fourier harmonic of the perturbed magnetic flux and its first overtone are included in the calculation. In the absence of RF current drive, the nonlinear behavior of a tearing mode predicted in the two-harmonic approximation does not differ substantially from that predicted in the one-harmonic approximation. On the other hand, RF current drive that is sufficiently localized in the vicinity of the O-points of the mode's magnetic island chain is capable of triggering bifurcations of the O-points (which is impossible in the one-harmonic approximation). However, the current drive is incapable of triggering bifurcations of the island X-points. This finding is significant because Bardóczi and Evans [Phys. Rev. Lett. 126, 085003 (2021)] recently observed bifurcations of magnetic island chain O-points in the presence of RF current drive in the DIII-D tokamak but did not observe bifurcations of the X-points. Finally, the changes in the topology of the magnetic island flux-surfaces induced by RF current drive are found to facilitate the stabilization of the tearing mode.

Electromagnetic Fireworks: Fast Radio Bursts from Rapid Reconnection in the Compressed Magnetar Wind

One scenario for the generation of fast radio bursts (FRBs) is magnetic reconnection in a current sheet of the magnetar wind. Compressed by a strong magnetic pulse induced by a magnetar flare, the current sheet fragments into a self-similar chain of magnetic islands. Time-dependent plasma currents at their interfaces produce coherent radiation during their hierarchical coalescence. We investigate this scenario using 2D radiative relativistic particle-in-cell simulations to compute the efficiency of the coherent emission and to obtain frequency scalings. Consistent with expectations, a fraction of the reconnected magnetic field energy, f ∼ 0.002, is converted to packets of high-frequency fast magnetosonic waves, which can escape from the magnetar wind as radio emission. In agreement with analytical estimates, we find that magnetic pulses of 1047 erg s−1 can trigger relatively narrowband GHz emission with luminosities of approximately 1042 erg s−1, sufficient to explain bright extragalactic FRBs. The mechanism provides a natural explanation for a downward frequency drift of burst signals, as well as the ∼100 ns substructure recently detected in FRB 20200120E .

Global fluid simulation of plasma turbulence in a stellarator with an island divertor

Results of a three-dimensional, flux-driven, electrostatic, global, two-fluid turbulence simulation for a five-field period stellarator with an island divertor are presented. The numerical simulation is carried out with the GBS code, recently extended to simulate plasma turbulence in non-axisymmetric magnetic equilibria. The vacuum magnetic field used in the simulation is generated with the theory of Dommaschk potentials, and describes a configuration with a central region of nested flux surfaces, surrounded by a chain of magnetic islands, similar to the diverted configurations of W7-X. The heat outflowing from the core reaches the island region and is transported along the magnetic islands, striking the vessel walls, which correspond to the boundary of the simulation domain. The radial transport of particles and heat is found to be mainly driven by a field-aligned coherent mode with poloidal number m = 4. The analysis of this mode, based on non-local linear theory considerations, shows its ballooning nature. In contrast to tokamak simulations and experiments, where blobs often contribute to transport, we do not observe the presence of intermittent transport events.

Metastability and dynamic modes in magnetic island chains

The uniform states of a model for one-dimensional chains of thin magnetic islands on a nonmagnetic substrate coupled via dipolar interactions are described here. Magnetic islands oriented with their long axes perpendicular to the chain direction are assumed, whose shape anisotropy imposes a preference for the dipoles to point perpendicular to the chain. The competition between anisotropy and dipolar interactions leads to three types of uniform states of distinctly different symmetries, including metastable transverse or remanent states, transverse antiferromagnetic states, and longitudinal states where all dipoles align with the chain direction. The stability limits and normal modes of oscillation are found for all three types of states, even including infinite range dipole interactions. The normal mode frequencies are shown to be determined from the eigenvalues of the stability problem.

Passive deconfinement of runaway electrons using an in-vessel helical coil

A helical coil designed to passively generate non-axisymmetric fields during a plasma disruption is shown (via electromagnetic analysis, linear MHD modeling, and relativistic drift orbit tracing) to be effective at deconfining runaway electrons (REs) on a time scale significantly faster than the plasma current quench. Magnetic equilibria from DIII-D RE-producing scenarios are used to calculate the toroidal electric field generated during the current quench phase of a disruption, which in turn drives current in the proposed n = 1 in-vessel helical coil, without the need for any external power supplies or disruption detection or prediction techniques. Simulations of the plasma evolution using the TokSys GS Evolve code predict the inductive coupling of coil currents up to 12% of the pre-disruption plasma current into the helical coil. The coil geometry is parametrically varied to maximize both the non-resonant and resonant components of the 3D magnetic perturbation, resulting in δB/B ≈ 10−2 and a vacuum island overlap width of up to 0.7ψ N . The REORBIT module of the MARS-F code is used to model the full non-axisymmetric magnetic field and trace RE drift orbits to determine the effect on RE deconfinement, with up to 70% of the RE orbits lost after 0.2 ms. A two-stage evolution of the RE orbit loss fraction is observed to be caused by resonant trapping between multiple magnetic island chains. Finally, electromagnetic and thermal stresses on the coil are calculated to be within operational limits for installation in DIII-D, and scale favorably to a reactor-size device. These findings motivate future experimental study of the helical coil concept in DIII-D or other tokamaks.

Investigation of annular/central collapse events triggered by the double tearing modes in EAST

Annular/central collapses of electron temperature have been investigated in the EAST tokamak. The precursor modes are excited before the annular/central collapse events, and the coexistence of multi magnetic island chains can be observed synchronously for the core concentration of high-Z impurities. The primary magnetic islands for the two cases are located in the same region of 0.25 ⩽ ρ(r/a) ⩽ 0.35, while the secondary magnetic islands for central and annular cases are located inside (ρ ≈ 0.1) and outside (ρ ≈ 0.4) respectively. The similar simulation has been performed by the toroidal resistive MHD code CLT (Zhang et al 2020 Phys. Plasmas 27 122509), and the annular/central collapse events can be reproduced by the magnetic reconnection of m/n = 2/1 double tearing modes, m and n are the poloidal and toroidal mode numbers respectively. The combination of lower hybrid current driven and off-axis electron cyclotron resonance heating is an essential condition for the establishment of reversed magnetic shear. The different penetration depth of high-Z impurity density plays an important role for excitation of the annular/central collapse events, e.g. the steeper gradient of T e-profile can be formed accordingly in the annular region of 0.1 ⩽ ρ ⩽ 0.4, together with excitation of the precursor modes.

Experimental inference of flux tunneling between magnetic island chains in tokamaks

We report confinement bifurcations due to flux tunneling in magnetic islands in toroidal plasmas. This occurs in 2/1 islands, triggered by decoupling of non-overlapping adjacent 5/2 islands. While subject to electron cyclotron current drive (ECCD), the temperature at the 2/1 O-point is flat before but peaks after decoupling. This is shown to be due to a bifurcation from stochastic to nested magnetic structure, caused by the removal of flux tunneling through intersecting manifolds of overlapping heteroclinic tangles. 2/1 island stability correlates with coupling events in an ITER baseline scenario plasma where ECCD can not stabilize the coupled islands, showing the critical impact of flux tunneling on disruption avoidance in tokamaks.

Further modeling of q95 windows for the suppression of edge localized modes by resonant magnetic perturbations in the DIII-D tokamak

An improved resonant plasma response model that more accurately captures the physics of the interaction between a tokamak plasma and a resonant magnetic perturbation (RMP) is developed. The model interpolates between the linear and the nonlinear response regimes and takes into account the fact that the slip-frequency is non-zero in the nonlinear regime. The improved model is incorporated into the extended perturbed equilibrium code (EPEC) toroidal asymptotic matching code. The modified EPEC code is used to investigate RMP-induced edge-localized-mode (ELM) suppression in DIII-D H-mode discharge #145380. Somewhat surprisingly, allowing for a finite slip-frequency (i.e., relaxing the so-called no-slip constraint) is found to only slightly facilitate the locking of driven magnetic island chains to the RMP, and, hence, to only slightly facilitate RMP-induced ELM suppression. This is true despite the fact that the nature of non-locked island solutions is radically different when the no-slip constraint is imposed compared to when it is relaxed (in the first case, the widths of the island chains driven at the rational surfaces pulsate, and in the second case, they remain steady). The previously obtained conclusion that the response of a typical H-mode tokamak plasma to an RMP cannot be accurately modeled by linear theory is confirmed. The previously obtained conclusion that the best agreement between theory and observations is achieved by assuming that the natural frequencies of tearing modes, in the absence of the RMP, are determined by the local equilibrium E×B velocity is also confirmed.

Nonlinear evolution of dispersive Alfvén waves and the effect of magnetic islands in the solar wind plasmas

Solar wind is often known as a source of energizing Earth's magnetosphere and it is a highly complex system displaying various phenomena. Alfvén waves are believed to play a crucial role in its dynamics. The dispersive Alfvén waves (DAWs) may explain various plasma processes, for example, the transfer of energy over different length scales, particle energization, etc., and it is one of the promising sources in the context of magnetic reconnection. We develop a model based upon the two-fluid approximation to study the Alfvén waves, which becomes dispersive on account of the finite frequency correction of the wave, propagating in the medium with a pre-existing chain of magnetic islands and under the impact of the background density fluctuations arising from the ponderomotive nonlinearity of the wave. In the present paper, we study how the dispersive Alfvén waves (DAWs) contribute in the two significant space phenomena, i.e., turbulence and magnetic reconnection. We show that DAWs are important in the generation of localized (coherent) structures and the formation of current sheets. A strong and weak DAW is studied using numerical simulation and semi-analytical approaches in the vicinity of magnetic reconnection sites, i.e., reconnection induced magnetic islands. For the case of strong DAWs, the power spectral density of the fluctuations has been obtained for studying the behavior of the generated turbulence in the solar wind plasmas at 1 AU. The consistency of these results with the observational findings is also reported.

An improved theory of the response of DIII-D H-mode discharges to static resonant magnetic perturbations and its implications for the suppression of edge localized modes

The plasma response to an externally generated, static, n = 2, resonant magnetic perturbation (RMP) in the pedestal region of DIII-D H-mode discharge #158115 is investigated using a toroidal generalization of the asymptotic matching model presented by Fitzpatrick [Phys. Plasmas 27, 042506 (2020)]. Just as in a recent paper [Q. M. Hu et al., Phys. Plasmas 26, 120702 (2019)], it is hypothesized that the density pump-out phenomenon is due to locked magnetic island chains induced at the bottom of the pedestal, whereas the suppression of edge localized modes is associated with a locked magnetic island chain induced at the top of the pedestal. Neutral penetration inside the last closed magnetic flux-surface is found to have a significant influence on locked magnetic island chain formation at the bottom of the pedestal. It is found that locked island formation at the top of the pedestal is only possible when q95 lies in certain narrow windows. Finally, it is inferred that, in order to successfully induce a locked island chain at the top of the pedestal, an external RMP field-coil system must generate a magnetic field that is simultaneously strongly amplified by the plasma (via the ideal kink response) and has a large resonant component at a rational surface that lies close to the top of the pedestal.

Multi-diagnostic analysis of plasma filaments in the island divertor

Filaments or blobs are well known structures in turbulence in magnetic fusion devices, they are considered to be the major cross-transport channel in the scrape off layer. They originate at the last closed magnetic flux surface and propagate out on the low field side of toroidal devices due to polarization in the curved magnetic field. The Wendelstein 7-X stellarator has a complex three-dimensional magnetic field structure and additionally the plasma is bounded by a chain of magnetic islands, forming an island divertor. After the first observation of filaments in Wendelstein 7-X with video cameras a multi-diagnostic study is presented in this paper to reveal their 3D structure and dynamics. Filaments are seen to be born at the edge and, at least in some cases, seen to extend to up to 4 toroidal turns. After moving radially out a few cm they enter the edge island. Here they disappear from the equatorial plane and about 200 microseconds later reappear on the outboard side of the island. A long-wavelength (∼20–30 cm) quasi coherent mode is observed in both regions where filaments appear. The similarities and differences between the filaments seen in W7-X and other devices are discussed. Possible explanations for this strange radial propagation are considered, together with the likely role of filaments in the edge and island density profile.

Characterization of the W7-X scrape-off layer using reciprocating probes

The W7-X scrape-off layer (SOL) with its characteristic magnetic island chain has been investigated using electric probes mounted on a reciprocating manipulator close to the outboard mid-plane. A survey of the W7-X configuration space shows that the presence and particular topology of magnetic islands significantly affects the SOL profiles of electron temperature, density, electric field and plasma flows. Particularly relevant for divertor operation, very wide SOL heat flux profiles have been observed in some magnetic configurations, which we link to the presence of magnetic islands. In these situations, the islands can feature a local minimum of the plasma potential accompanied by a direction reversal of driven dynamics measured by probe arrays.

Effects of plasmoid formation on sawtooth process in a tokamak

For realistic values of the Lundquist number in tokamak plasmas, 1/1 magnetic islands lead to the formation of a secondary thin current sheet, which breaks up into a chain of small magnetic islands, called plasmoids. The role of plasmoid dynamics during the sawtooth reconnection process in fusion plasmas remains an unresolved issue. In this study, systematic simulations are performed to investigate the resistive internal kink mode using the full resistive magnetohydrodynamics equations implemented in the NIMROD code in a simplified tokamak geometry. For Lundquist number S≥1.6×107, the secondary current sheet is found to be unstable to plasmoids during the nonlinear resistive kink mode evolution with a critical aspect ratio of the current sheet of ∼70. The merging of small plasmoids leads to the formation of a monster plasmoid that can significantly affect the primary island evolution. This may provide an explanation for the partial reconnection observed in sawtooth experiments.