Magnetic Perturbations Research Articles

On how finite β and three-dimensional magnetic perturbations affect the instability of toroidal ion temperature gradient mode

Abstract The effects of finite β (the ratio of plasma kinetic pressure to magnetic pressure) and three-dimensional (3D) magnetic perturbations (MPs) on the instability of toroidal ion temperature gradient (ITG) mode are studied in this work. The expression of ion magnetic drift frequency ω_di modified by the effects from both finite β and 3D MPs is firstly derived based on the local 3D equilibrium model. Then, under the assumptions of adiabatic electrons and localized mode structure around the outboard mid-plane (ϑ_p=0), the dispersion equation of the long wavelength toroidal ITG mode with considering the parallel ion dynamics is derived and solved. The results show that the distribution of ω_di around the outboard mid-plane, including both ω_(di,0)=├ ω_di ┤|_(ϑ_p=0) and ω_(di,0)^''≡├ (d^2 ω_di \/dϑ_p^2 )┤|_(ϑ_p=0) (twist parameter quantifying the degree of concave or convex of ω_di), is the key for affecting the toroidal ITG mode instability. The diamagnetic effects from finite β and the effects from 3D MPs can suppress the instability by reducing |ω_(di,0) |. Via reducing |ω_(di,0)^'' | under the prerequisite of unchanged sign of ω_(di,0)^'', there also exist stabilization effects on the instability from 3D MPs and the modification of local magnetic shear by finite β effects. In addition, the stabilization effects induced by reducing |ω_(di,0)^'' | are closely associated with the global magnetic shear. The mechanisms for the effects of finite β and 3D MPs on the instability of toroidal ITG mode revealed in this work are helpful to the comprehensive understanding of the relationship between internal kink mode induced non-axisymmetric flux surface distortion and internal transport barrier physics in tokamak plasmas.

Kinetic Alfvén wave cascade in sub-ion range plasma turbulence

Kinetic Alfvén waves (KAWs) are simulated with a 3D particle-in-cell (PIC) code by using the eigenvector relations of density, velocity, electric, and magnetic field fluctuations derived from a two-fluid KAW model. Similar simulations are also performed with a whistler waves setup. The 2D two-fluid eigenvector relations are converted into 3D by using rotation of the reference frame. The initial condition for the simulations is a superposition of several waves at scales slightly larger than the ion skin depth. The nonlinear interactions produce a transfer of energy to smaller scales. The magnetic field perturbation ratios, velocity perturbation, and density perturbation ratios are calculated from the simulation at higher wavenumbers and compared with the analytically expected ratios for KAWs and whistler waves. We find that in both types of simulations, initialized either with an ensemble of KAWs or with whistlers, the observed polarization relations at later times match better with the KAW relations compared to whistlers. This indicates a preference for excitation of KAW fluctuations at smaller scales. The power spectrum in the perpendicular direction is calculated, and it shows similar indices as measured in the solar wind power spectrum in the transition (sub-ion) region. The power law extends to smaller scales when a higher ion-to-electron mass ratio is taken. The 2D magnetic power spectrum in magnetic field parallel and perpendicular directions shows typical anisotropy where the power spreads more in the perpendicular direction than in the parallel direction. This study shows that KAWs can explain features of the sub-ion range plasma turbulence in the solar wind.

Observation of magnetic islands in tokamak plasmas during the suppression of edge-localized modes

AbstractIn tokamaks, a leading platform for fusion energy, periodic filamentary plasma eruptions known as edge-localized modes occur in plasmas with high-energy confinement and steep pressure profiles at the plasma edge. These edge-localized modes could damage the tokamak wall but can be suppressed using small three-dimensional magnetic perturbations. Here we demonstrate that these magnetic perturbations can change the magnetic topology just inside the steep gradient region of the plasma edge. We identify signatures of a magnetic island, and their observation is linked to the suppression of edge-localized modes. We compare high-resolution measurements of perturbed magnetic surfaces with predictions from ideal magnetohydrodynamic theory where the magnetic topology is preserved. Although ideal magnetohydrodynamics adequately describes the measurements in plasmas exhibiting edge-localized modes, it proves insufficient for plasmas where these modes are suppressed. Nonlinear resistive magnetohydrodynamic modelling supports this observation. Our study experimentally confirms the predicted role of magnetic islands in inhibiting the occurrence of edge-localized modes. This will be beneficial for physics-based predictions in future fusion devices to control these modes.

Application of three-dimensional MHD equilibrium calculation coupled with plasma response to island divertor experiments on J-TEXT

Three-dimensional (3D) equilibrium calculations, including the plasma rotation shielding effect to resonant magnetic perturbations (RMPs) produced by the island divertor (ID) coils, were carried out using the HINT and MARS-F codes on J-TEXT. Validation of 3D equilibrium calculations with experimental observations demonstrates that the shielding effect will prevent the penetration of the edge m/n = 3/1 mode component when the ID coil current is 4 kA, while change the size of magnetic islands once the current exceeds the penetration threshold. This indicates that equilibrium calculations including the plasma rotation shielding effect to RMPs can lead to better agreements with experimental observations compared to the vacuum approximation method. Additionally, the magnetic topology at the boundary undergoes changes, impacting the interaction between the plasma and the target plate. These results may be important in understanding RMP effects on edge transport and magnetohydrodynamic (MHD) instability control, as well as divertor heat and particle flux distribution control.

2D PIC modeling of the helical scrape-off layer current driven by hybrid divertor biased targets in tokamak plasmas

Abstract The heat flux control of the divertor plate via strike-point splitting generated by biased targets was proposed in the HL-2A tokamak (Cui et al 2021 Fusion Eng. Des. 173 112963). To understand the helical scrape-off layer (SOL) currents driven by hybrid biasing, two SOL current models (model A and B) are employed. Model A is a simplified 2D model that focuses on investigating the effect of biasing on the sheath and elucidating the fundamental physical mechanism of bias-driven SOL current paths. The potential, charge density, electric field and current densities are calculated. Model B takes into account the actual tokamak geometry and computes the resonant magnetic perturbations (RMPs) generated by bias-driven linear decay currents. Additionally, strike-point splitting is observed in the HL-2A tokamak, indicating that the SOL currents generated by hybrid biasing are capable of generating strong RMPs and consequently influence the magnetic topology. These results confirm the potential of heat/particle flux control by hybrid divertor biased targets.

Anomalous transient conductivity of magnetic elastomer under the action of strain and magnetic field

Abstract Magnetoactive (aka magnetorheological) elastomer composites, which are elastic polymer matrices filled with micron-sized particles of a ferromagnet, are a novel type of magnetically controllable material. In addition to their complex magnetomechanical behavior, magnetoactive elastomers, as conducting substances, possess electrical resistivity that is highly sensitive to both mechanical stress and the applied magnetic field. Here, we present a study on the response of such composites to pulse mechanical or magnetic perturbations. Remarkably, a transient electric process induced by any of those stimuli is always non-monotonic. The electric current measurements reveal that before settling at the new equilibrium level, the resistivity always undergoes a substantial jump-up independently on the sign of the perturbation: a pressure on/off or the field on/off. The main goal of the work is to register the encountered effect in detail.

Neuronal current imaging of epileptic activity: An MRI study in patients with a first unprovoked epileptic seizure.

This study evaluates the performance of the novel MRI sequence stimulus-induced rotary saturation (SIRS) to map responses to interictal epileptic activity in the human cortex. Spin-lock pulses have been applied to indirectly detect neuronal activity through magnetic field perturbations. Following initial reports about the feasibility of the method in humans and animals with epilepsy, we aimed to investigate the diagnostic yield of spin-lock MR pulses in comparison with scalp-EEG in first seizure patients. We employed a novel method for measurements of neuronal activity through the detection of a resonant oscillating field, stimulus-induced rotary saturation contrast (SIRS) at spin-lock frequencies of 120 and 240 Hz acquired at a single 3T MRI system. Within a prospective observational study, we conducted SIRS experiments in 55 patients within 7 days after a suspected first unprovoked epileptic seizure and 61 healthy control subjects. In this study, we report on the analysis of data from a single 3T MRI system, encompassing 35 first seizure patients and 31 controls. The SIRS method was applicable in all patients and healthy controls at frequencies of 120 and 240 Hz. We did not observe any significant age- or sex-related differences. Specificity of SIRS at 120 Hz was 90.3% and 93.5% at 240 Hz. Sensitivity was 17.1% at 120 Hz and 40.0% at 240 Hz. SIRS targets neuronal oscillating magnetic fields in patients with epilepsy. The coupling of presaturated spins to epilepsy-related magnetic field perturbations may serve as a-at this stage experimental-diagnostic test in first seizure patients to complement EEG findings as a standard screening test. Routine diagnostic tests carry several limitations when applied after a suspected first seizure. SIRS is a noninvasive MRI method to enable time-sensitive diagnosis of image correlates of epileptic activity with increased sensitivity compared to routine EEG.

Gyrokinetic simulation of the toroidal rotation driven by the ambipolar radial electric field induced by stochastic magnetic perturbations in a tokamak plasma

Gyrokinetic simulation of the toroidal rotation driven by the ambipolar radial electric field induced by stochastic magnetic perturbations in a tokamak plasma

Finite Time Path Field Theory Perturbative Methods for Local Quantum Spin Chain Quenches

We discuss local magnetic field quenches using perturbative methods of finite time path field theory (FTPFT) in the following spin chains: Ising and XY in a transverse magnetic field. Their common characteristics are: (i) they are integrable via mapping to a second quantized noninteracting fermion problem; and (ii) when the ground state is nondegenerate (true for finite chains except in special cases), it can be represented as a vacuum of Bogoliubov fermions. By switching on a local magnetic field perturbation at finite time, the problem becomes nonintegrable and must be approached via numeric or perturbative methods. Using the formalism of FTPFT based on Wigner transforms (WTs) of projected functions, we show how to: (i) calculate the basic “bubble” diagram in the Loschmidt echo (LE) of a quenched chain to any order in the perturbation; and (ii) resum the generalized Schwinger–Dyson equation for the fermion two-point retarded functions in the “bubble” diagram, hence achieving the resummation of perturbative expansion of LE for a wide range of perturbation strengths under certain analyticity assumptions. Limitations of the assumptions and possible generalizations beyond it and also for other spin chains are further discussed.

Helical resonant magnetic perturbation coils for controlling edge localized modes: a robustness study

Abstract Plasma response to helical resonant magnetic perturbation coil current is numerically computed for tokamak plasmas, with optimization results compared with that for conventional window-frame coils. The key aspect of study is the robustness of the proposed new concept against variation of plasma equilibrium parameters including (i) the plasma resistivity, (ii) the toroidal rotation and (iii) the plasma shaping (both elongation and triangularity). Toroidal modeling results yield several important conclusions. First, assuming the same coil current, the optimal helical coils robustly outperform the optimal window-frame coils against variation of the aforementioned plasma equilibrium parameters. Secondly, for a chosen toroidal spectrum, the optimal helical coil geometry including the poloidal location, poloidal coverage and the overall shape, is robust against variation of plasma parameters except the safety factor. Finally, in all cases, optimization based on the plasma response naturally yields a single row of helical coils located near the outboard mid-plane of the torus, ensuring a relatively simple design of the coil geometry.

Occurrence and Causes of Large dB/dt Events and AL Bays in the Pre‐Midnight and Dawn Sectors

AbstractA necessary condition for the generation of Geomagnetically Induced Currents (GICs) that can pose hazards for technological infrastructure is the occurrence of large, rapid changes in the magnetic field at the surface of the Earth. We investigate the causes of such events or “spikes” observed by SuperMAG at auroral latitudes, by comparing with the time‐series of different types of geomagnetic activity for the duration of 2010. Spikes are found to occur predominantly in the pre‐midnight and dawn sectors. We find that pre‐midnight spikes are associated with substorm onsets. Dawn sector spikes are not directly associated with substorms, but with auroral activity occurring within the westward electrojet region. Azimuthally‐spaced auroral features drift sunwards, producing Ps6 (10–20 min period) magnetic perturbations on the ground. The magnitude of is determined by the flow speed in the convection return flow region, which in turn is related to the strength of solar wind‐magnetospheric coupling. Pre‐midnight and dawn sector spikes can occur at the same time, as strong coupling favors both substorms and westward electrojet activity; however, the mechanisms that create them seem somewhat independent. The dawn auroral features share some characteristics with omega bands, but can also appear as north‐south aligned auroral streamers. We suggest that these two phenomena share a single underlying cause. The associated fluctuations in the westward electrojet produce quasi‐periodic negative excursions in the AL index, which can be mis‐identified as recurrent substorm intensifications.

VUV imaging of type-I ELM filamentary structures and their temporal characteristics on EAST

In the H-mode experiments conducted on the Experimental Advanced Superconducting Tokamak (EAST), fluctuations induced by the so-called edge localized modes (ELMs) are captured by a high-speed vacuum ultraviolet (VUV) imaging system. Clear field line-aligned filamentary structures are analyzed in this work. Ion transport induced by ELM filaments in the scrape-off layer (SOL) under different discharge conditions is analyzed by comparing the VUV signals with the divertor probe signals. It is found that convective transport along open field lines towards the divertor target dominates the parallel ion particle transport mechanism during ELMs. The toroidal mode number of the filamentary structure derived from the VUV images increases with the electron density pedestal height. The analysis of the toroidal distribution characteristics during ELM bursts reveals toroidal asymmetry. The influence of resonance magnetic perturbation (RMP) on the ELM size is also analyzed using VUV imaging data. When the phase difference of the coil changes periodically, the widths of the filaments change as well. Additionally, the temporal evolution of the ELMs on the VUV signals provides rise time and decay time for each single ELM event, and the results indicate a negative correlation trend between these two times.

The root cause of disruptive NTMs and paths to stable operation in DIII-D ITER baseline scenario plasmas

Abstract Analyses of the DIII-D ITER Baseline Scenario database support that the disruptive m,n=2,1 magnetic islands are pressure gradient driven, non-linear instabilities seeded in a sequence of stochastic transient magnetic perturbations, and that the current profile relaxation does not affect the m,n=2,1 island onset rate. At low torque, these Neoclassical Tearing Modes are most commonly seeded by non-linear 3-wave coupling when the differential rotation between the q=1 & q=2 rational surfaces approaches zero. Lack of statistically significant difference between the current profiles of stable and unstable states, as well as lack of correlation between the tearing mode onset rate and the current profile relaxation both reject causality between the current profile evolution and the 2,1 magnetic island onsets in these plasmas. These support that preserving the differential rotation between the q=1 and q=2 rational surfaces is key to long pulse stable operation in the plasma scenario planned for ITER, while optimization of the current profile within the explored parameter space may lead to much weaker improvements than sustaining the differential rotation.

Nonlinear Alfvén-wave Dynamics and Premerger Emission from Crustal Oscillations in Neutron Star Mergers

Neutron stars have solid crusts threaded by strong magnetic fields. Perturbations in the crust can excite nonradial oscillations, which can in turn launch Alfvén waves into the magnetosphere. In the case of a compact binary close to merger involving at least one neutron star, this can happen through tidal interactions causing resonant excitations that shatter the neutron star crust. We present the first numerical study that elucidates the dynamics of Alfvén waves launched in a compact binary magnetosphere. We seed a magnetic field perturbation on the neutron star crust, which we then evolve in fully general-relativistic force-free electrodynamics using a GPU-based implementation. We show that Alfvén waves steepen nonlinearly before reaching the orbital light cylinder, form flares, and dissipate energy in a transient current sheet. Our results predict radio and X-ray precursor emission from this process.

Effect of Shear Flow on the Double Tearing Mode Induced by Resonant Magnetic Perturbation

Effect of Shear Flow on the Double Tearing Mode Induced by Resonant Magnetic Perturbation

Non-linear MHD modelling of transients in tokamaks: a review of recent advances with the JOREK code

Abstract Transient MHD events like edge localized modes (ELMs) or disruptions are a concern for magnetic confinement fusion power plants. Research with the MHD code JOREK towards understanding control of such instabilities is reviewed here. Experimental validation for unmitigated vertical displacement events (VDEs) progressed. The mechanism of vertical force mitigation by impurity injection was identified. Two-way eddy current coupling to CARIDDI was completed. Shattered pellet injection (SPI) was simulated in JET, KSTAR and ASDEX Upgrade (AUG) and ITER. Benign runaway electron (RE) beam termination in JET and ITER was studied. Coupling of kinetic REs to the MHD is ongoing and a virtual RE synchrotron radiation diagnostic was developed. Regarding pedestal physics, regimes devoid of large ELMs in AUG were simulated and predictive JT60-SA simulations are ongoing. For ELM suppression by resonant magnetic perturbations (RMPs), AUG, ITER and EAST simulations were performed. A free boundary RMP model was validated against experiments. Evidence for penetrated magnetic islands at the pedestal top based on AUG experiments and simulations was found. Simulations of the naturally ELM-free quiescent H-mode (QH) in AUG and HL-3 show external kink mode formation prevents pedestal build-up towards an ELM within windows of the edge safety factor. With kinetic neutral particles, high field side high density (HFSHD) formation in ITER was simulated and with kinetic impurities, tungsten transport in AUG RMP plasmas was studied. To capture turbulent transport, electro-static full-f PiC models for ion temperature gradient (ITG) and trapped electron modes (TEM) were established and benchmarked. Application to RMP plasmas shows enhanced turbulence in comparison to unperturbed states. Energetic particle (EP) interactions with MHD were studied. Flux-pumping that prevents the safety factor on axis from dropping below unity was simulated. First non-linear stellarator applications include current relaxation in l=2 stellarators, while verification for advanced stellarators progresses.

Loss of energetic particles due to feedback control of resistive wall mode in HL-3

Effects of three-dimensional (3D) magnetic field perturbations due to feedback control of an unstable ( is toroidal mode number) resistive wall mode (RWM) on the energetic particle (EP) losses are systematically investigated for the HL-3 tokamak. The MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) code, facilitated by the test particle guiding center tracing module REORBIT, is utilized for the study. The RWM is found to generally produce no EP loss for co-current particles in HL-3. Assuming the same perturbation level at the sensor location for the close-loop system, feedback produces nearly the same loss of counter-current EPs compared to the open-loop case. Assuming however that the sensor signal is ten times smaller in the close-loop system than the open-loop counter part (reflecting the fact that the RWM is more stable with feedback), the counter-current EP loss is found significantly reduced in the former. Most of EP losses occur only for particles launched close to the plasma edge, while particles launched further away from the plasma boundary experience much less loss. The strike points of lost EPs on the HL-3 limiting surface become more scattered for particles launched closer to the plasma boundary. Taking into account the full gyro-orbit of particles while approaching the limiting surface, REORBIT finds slightly enhanced loss fraction.

Total Magnetic Field Perturbations at Martian Low Altitudes (≤500 km): MAVEN Observations in 2014–2023

AbstractMagnetic perturbations in the Martian ionosphere are often considered as representing plasma irregularities, but thorough statistical comparisons between the two independent phenomena have been rarely conducted. In this study, we investigate the statistical relationship between total magnetic field perturbations and those of O2+ density as observed by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft at altitudes below 500 km in 2014–2023. From the 1 Hz time series of magnetic field strength, perturbation intensity is estimated by subtracting a signal smoothed with a Savitzky‐Golay filter (window size ∼36 km). Statistically, the magnetic perturbations are stronger on the dayside than at night, in the local summer hemisphere than in winter, and away from crustal magnetic anomalies than nearby. Also, day‐to‐day variability of the magnetic perturbations exhibits a weak but significant correlation with that of solar wind electron density. The statistical behavior of total magnetic field perturbations is not the same as that of O2+ density perturbations: that is, the former is not a perfect proxy for the latter. The seemingly counter‐intuitive discrepancy can be explained by effects of inhomogeneous background magnetic field strength (participating in total pressure balance across plasma perturbations) and localized ionospheric currents at altitudes unreachable by MAVEN.

Merging Mesoscale Magnetotail Features and Ground B‐Field Perturbation Network Connectivity During Substorm Activity

AbstractThe connection between the magnetosphere and ionosphere is particularly dynamic during substorms. Mesoscale features in the magnetotail are consistent with substorm activity, including magnetic reconnection in the tail, flow channels, and particle injections. Observations of substorm related phenomena can be made using energetic neutral atom (ENA) imagers, in situ satellite measurements, and ground based magnetic field perturbation measurements. Analysis of the 10 October 2014 isolated substorm event is presented. Comparison of the spatial and temporal dynamics of the features seen in equatorial maps generated from ENA data are made with inner magnetosphere in situ measurements and ionospheric features with network analysis of the SuperMAG data. An MHD simulation of the event using OpenGGCM is also compared with the data.

On the Association of Substorm Identification Methods

AbstractSubstorms are a rapid release of energy that is redistributed throughout the magnetosphere‐ionosphere system, resulting in many observable signals, such as enhancements in the aurora, energetic particle injections, and ground magnetic field perturbations. Numerous substorm identification techniques and onset lists based on each of these signals have been provided in the literature, but often with no cross‐calibration. Since the signals produced are not necessarily unique to substorms and may not be sufficiently similar to be identified for each and every substorm, individual event lists may miss or misidentify substorms, hindering our understanding and the development and validation of substorm models. To gauge the scale of this problem, we use metrics derived from contingency tables to quantify the association between lists of substorms derived from SuperMAG SML/SMU indices, midlatitude magnetometer data, particle injections, and auroral enhancements. Overall, although some degree of pairwise association is found between the lists, even lists generated by applying conceptually similar gradient‐based identification to ground magnetometer data achieve an association with less than 50% event coincidence. We discuss possible explanations of the levels of association seen from our results, as well as their implications for substorm analyses.