Magnetohydrodynamic Instabilities Research Articles

Magnetohydrodynamic instability of fluid flow in a bidisperse porous medium

Magnetohydrodynamic instability of fluid flow in a bidisperse porous medium

Resistive wall mode and fishbone mode in ITER steady state scenario: roles of fusion-born alphas and plasma flow

Abstract Drift-kinetic effects of fusion-born alpha particles on the n=1 (n is the toroidal mode number) resistive wall mode (RWM) is numerically investigated for a recent design of the ITER 10 MA steady state plasma scenario, utilizing a magneto-hydrodynamic (MHD)-kinetic hybrid toroidal model. While the fluid theory predicts unstable RWM as the normalized plasma pressure βN exceeds the no-wall Troyon limit and with the mode growth rate monotonically increasing with βN, inclusion of the drift-kinetic contribution of trapped alphas qualitatively modifies the behavior by stabilizing the mode at high βN. In fact, a complete stabilization of the n=1 RWM up to the ideal-wall Troyon limit is found. On the other hand, another unstable branch - the alpha-driven n=1 fishbone mode (FB) – is identified in the high-βN regime, with the mode frequency matching that of the toroidal precession frequency of trapped alphas. Fast plasma toroidal flow however helps mitigate the FB instability. Kinetic stabilization of the RWM and flow stabilization of the (alpha-triggered) FB result in an enhancement of βN from the design value of 3.22 to 3.52 for the ITER scenario considered, while still maintaining stable plasma operation against the aforementioned MHD instabilities.

Hybrid model predictive control techniques for safety factor profile and stored energy regulation while incorporating NBI constraints

A novel hybrid Model Predictive Control (MPC) algorithm has been designed for simultaneous safety factor (q) profile and stored energy (w) control while incorporating the pulse-width-modulation constraints associated with the neutral beam injection (NBI) system. Regulation of the q-profile has been extensively shown to be a key factor for improved confinement as well as non-inductive sustainment of the plasma current. Simultaneous control of w is necessary to prevent the triggering of pressure-driven magnetohydrodynamic instabilities as the controller shapes the q profile. Conventional MPC schemes proposed for q-profile control have considered the NBI powers as continuous-time signals, ignoring the discrete-time nature of these actuators and leading in some cases to performance loss. The hybrid MPC scheme in this work has the capability of incorporating the discrete-time actuator dynamics as additional constraints. In nonlinear simulations, the proposed hybrid MPC scheme demonstrates improved q-profile+w control performance for NSTX-U operating scenarios.

Development of a neural network model for peeling–ballooning stability analysis in the KSTAR tokamak pedestals

The neural network model, MISHKA-NN is developed to mitigate the computational burden associated with the linear ideal magnetohydrodynamic (MHD) stability analysis of the pedestal based on the peeling–ballooning (P–B) model. By utilizing both 1D plasma profiles (current density, pressure gradient, and safety factor) and 0D parameters (plasma geometry, total current, and toroidal mode number), the model predicts linear growth rate of edge-localized ideal MHD instability in a given equilibrium state. By enabling the prediction of each instability within a second, the model reduces the time required for plotting a pedestal P–B stability diagram ( j−α diagram) from approximately 100 CPU hours to a few CPU minutes. Notably, even with the utilization of parametric pressure and current profiles and plasma boundary shapes for the training dataset, the model shows a satisfactory level of performance in benchmarking the j−α diagram for the reconstructed equilibrium from a KSTAR tokamak experiment. We anticipate the model to serve as a versatile alternative to 2D linear MHD stability codes, alleviating numerical costs.

Kinetic-magnetohydrodynamic hybrid simulation of infernal modes in circular tokamak plasmas with effects of kinetic thermal ions

Effects of the kinetic thermal ions (KTIs) on ideal infernal modes and resistive infernal modes have been investigated by using magnetohydrodynamic (MHD) simulation without KTIs and kinetic-MHD hybrid simulation with KTIs. For the ideal infernal modes, the pressure profile is significantly flattened at the saturated state for both the models with and without the KTIs. As the beta value decreases, the ideal infernal modes are stabilized while the resistive infernal modes are still unstable. For the resistive infernal modes, while the saturated pressure profile is significantly flattened in the MHD simulation without KTIs, the pressure profile is not flattened at the saturated state in the kinetic-MHD hybrid simulation with KTIs. The suppression of the saturation level by the effects of the KTIs results from the phase mismatch between the radial velocity and perturbed pressure mode structures. This indicates that KTIs play an essential role for the suppression of pressure profile flattening due to slowly growing resistive MHD instabilities.

Discovery of a Shock-compressed Magnetic Field in the Northwestern Rim of the Young Supernova Remnant RX J1713.7–3946 with X-Ray Polarimetry

Supernova remnants (SNRs) provide insights into cosmic-ray acceleration and magnetic field dynamics at shock fronts. Recent X-ray polarimetric measurements by the Imaging X-ray Polarimetry Explorer (IXPE) have revealed radial magnetic fields near particle acceleration sites in young SNRs, including Cassiopeia A, Tycho, and SN 1006. We present here the spatially resolved IXPE X-ray polarimetric observation of the northwestern rim of SNR RX J1713.7–3946. For the first time, our analysis shows that the magnetic field in the particle acceleration sites of this SNR is oriented tangentially with respect to the shock front. Because of the lack of precise Faraday rotation measurements in the radio band, this was not possible before. The average measured polarization degree (PD) of the synchrotron emission is 12.5% ± 3.3%, lower than the one measured by IXPE in SN 1006, comparable to the Tycho one, but notably higher than the one in Cassiopeia A. On subparsec scales, localized patches within RX J1713.7–3946 display a PD of up to 41.5% ± 9.5%. These results are compatible with a shock-compressed magnetic field. However, in order to explain the observed PD, either the presence of a radial net magnetic field upstream of the shock or partial reisotropization of the turbulence downstream by radial magnetohydrodynamical instabilities can be invoked. From comparison of PD and magnetic field distribution with γ-rays and 12CO data, our results provide new inputs in favor of a leptonic origin of the γ-ray emission.

Study of the influence of magnetic shear on the linear MHD instabilities in the pedestal of elongated divertor configurations using CLT code

AbstractEdge localized modes resulted from magnetohydrodynamic (MHD) instabilities in the pedestal region are a significant concern for future tokamaks. In this work, Ci‐Liu‐Ti (CLT), an MHD code in the three‐dimensional toroidal geometry, is applied for the linear simulation of the ideal pedestal MHD instabilities. The simulations are performed for the experimental advanced superconducting tokamak‐like elongated divertor configuration with large triangularity, which is generated by the high‐accuracy free‐boundary equilibrium solver (CLT‐EQuilibrium, i.e., CLT‐EQ) developed recently. The present work focuses on the influence of the magnetic shear, which is scanned by adjusting the pedestal current with a fixed pedestal pressure profile. As the pedestal current increases, both the local (Slocal) and global (Sglobal) magnetic shear decrease. The ballooning mode is destabilized along with the decrease of Slocal, and stabilized when Slocal is negative for the whole region of bad curvature, which implies the access of the second stable region. Further increase of the pedestal current leads to the destabilization of the kink mode, which is stabilized again until Sglobal is negative at the location of significant gradient of current density. The simulated results are consistent with the findings in Radovanovic et al. Nucl. Fusion 62 (2022) 086004 and C. K. Sun et al. Phys. Plasmas 25 (2018) 082106, which indicates the availability of CLT in the linear simulation of the ideal pedestal instabilities.

Role of electrostatic perturbation on kinetic resistive wall mode with application to spherical tokamak

Role of electrostatic perturbation on kinetic resistive wall mode with application to spherical tokamak

Degradation of fast-ion confinement depending on the neutral beam power in MHD quiescent LHD plasmas

We investigated the degradation of neutral beam (NB) fast-ion confinement depending on the NB power without magnetohydrodynamics instabilities in the Large Helical Device (LHD). In the LHD deuterium experiment, the neutron emission rate per NB power decreased by up to 20% with increasing injected NBs during a single discharge. Because there were no significant variations in the electron temperature and density, the NB shine-through rate, or the magnetic fluctuation due to the change in NB power, the reduction in the neutron emission rate indicates the degradation of the fast-ion confinement. In this paper, we formulated this degradation depending on the NB power and quantitatively estimated the degraded effective confinement time. In addition, we performed neutron emission rate simulations using the obtained effective confinement time. The simulation and experimental results were in good agreement, suggesting that the degraded effective confinement time is valid.

Imaging and spectroscopic observations of a confined solar filament eruption with two-stage evolution

Abstract Solar filament eruptions are often characterized by stepwise evolution due to the involvement of multiple mechanisms, such as magnetohydrodynamic instabilities and magnetic reconnection. In this article, we investigated a confined filament eruption with a distinct two-stage evolution by using the imaging and spectroscopic observations from the Interface Region Imaging Spectrograph (IRIS) and the Solar Dynamics Observatory (SDO). The eruption originated from a kinked filament thread that separated from an active region filament. In the first stage, the filament thread rose slowly and was obstructed due to flux pile-up in its front. This obstruction brought the filament thread into reconnection with a nearby loop-like structure, which enlarged the flux rope and changed its connectivity through the foot-point migration. The newly formed flux rope became more kink unstable and drove the rapid eruption in the second stage. It ascended into the upper atmosphere and initiated the reconnection with the overlying field. Finally, the flux rope was totally disintegrated, producing several solar jets along the overlying field. These observations demonstrate that the external reconnection between the flux rope and overlying field can destroy the flux rope, thus playing a crucial role in confining the solar eruptions.

A model of solar magnetic flux rope eruption initiated primarily by magnetic reconnection

ABSTRACT There is a heated debate regarding the specific roles played by ideal magnetohydrodynamic (MHD) instability and magnetic reconnection in triggering solar eruptions. In the context of a pre-existing magnetic flux rope (MFR) before an eruption, it is widely believed that an ideal MHD instability, in particular, the torus instability, is responsible for triggering and driving the eruption, while reconnection, as invoked in the wake of the erupting MFR, plays a secondary role. Here, we present a new numerical MHD model in which the eruption of a pre-existing MFR is primarily triggered and driven by reconnection. In this model, a stable MFR embedded in a strapping field is set as the initial condition. A surface converging flow is then applied at the lower boundary, pushing magnetic flux towards the main polarity inversion line. It drives a quasi-static evolution of the system, during which a current layer is built up below the MFR with decreasing thickness. Once reconnection starts in the current sheet, the eruption commences, which indicates that the reconnection plays a determining role in triggering the eruption. By further analysing the works done by the magnetic flux of the pre-existing MFR and the newly reconnected flux during the acceleration stage of the eruption, we find that the latter plays a major role in driving the eruption. Such a model may explain observed eruptions in which the pre-eruption MFR has not reached the conditions for ideal instability.

Response of Energetic-Particle-Driven Magnetohydrodynamics (MHD) Instability to Modulated ECH in Heliotron J

Response of Energetic-Particle-Driven Magnetohydrodynamics (MHD) Instability to Modulated ECH in Heliotron J

Dust Dynamics in Hall-effected Protoplanetary Disks. I. Background Drift Hall Instability

Recent studies have shown that the large-scale gas dynamics of protoplanetary disks (PPDs) are controlled by nonideal magnetohydrodynamics (MHD), but how this influences dust dynamics is not fully understood. To this end, we investigate the stability of dusty, magnetized disks subject to the Hall effect, which applies to planet-forming regions of PPDs. We find a novel background drift Hall instability (BDHI) that may facilitate planetesimal formation in Hall-effected disk regions. Through a combination of linear analysis and nonlinear simulations, we demonstrate the viability and characteristics of BDHI. We find it can potentially dominate over the classical streaming instability (SI) and standard MHD instabilities at low dust-to-gas ratios and weak magnetic fields. We also identify magnetized versions of the classic SI, but these are usually subdominant. We highlight the complex interplay between magnetic fields and dust-gas dynamics in PPDs, underscoring the need to consider nonideal MHD like the Hall effect in the broader narrative of planet formation.

Identification of MHD modes on EAST using a deep learning framework

The improvement of plasma parameters is severely limited by magnetohydrodynamic (MHD) instabilities. The identification of MHD modes is crucial for the study and control of MHD instabilities. In this study, an MHD mode identifier is developed based on a temporal convolutional network and long short-term memory (LSTM) network. The identifier is trained and tested on a small dataset containing 33 shots. Firstly, the temporal convolutional network encodes 27 diagnostic signals and then decodes them using LSTM network with different parameters to obtain the MHD modes and their frequency and intensity. The identifier exhibits an accuracy of approximately 98.38% on the test set and can accurately calculate the frequency and intensity of the MHD modes. To further examine the performance of the identifier, seven shots outside the dataset are used for shot-by-shot testing. The identifier can accurately identify the time period of tearing modes, and the identification accuracies of 2/1 and 3/2 tearing modes are 92.7% and 100%, respectively. The identification accuracy of the fishbone mode is slightly worse, only 82.1%. This is because the fishbone mode occurs intermittently. The frequent switching between the fishbone mode and no MHD behavior affects the identification of the fishbone mode. Overall, through the training of the small datasets, the identifier exhibits a good identification performance for the MHD modes. The proposed data-driven identifier can serve as a reference for establishing a large MHD mode database of EAST as well as a real-time MHD identification and control algorithm.

Rayleigh-Taylor instability in magnetohydrodynamics with finite resistivity in a horizontalmagnetic field.

Recent studies have revealed the significant influence of finite resistivity on high-energy-density plasmas, contrary to the previous findings of Jukes [J. Fluid Mech. 16, 177 (1963)0022-112010.1017/S0022112063000677]. This paper reexamines Jukes' theory in the context of magneto-Rayleigh-Taylor instability in magnetohydrodynamics with finite resistivity represented by η. The inadequacy of Jukes' approach due to an erroneous boundary condition is demonstrated, and it is shown that although the theory provides some physical insights, it fails to capture crucial features. The dispersion relation proposed in this study highlights that larger growth rates tend to diffuse the magnetic field rapidly, negating its suppressive effect. Moreover, the Atwood number has a significant influence on the growth-rate curves' shape, which differs from those of viscous or elastic flows and ideal magnetohydrodynamics. Additionally, long wavelengths grow proportionally to η^{1/3}, while α indicating growth rates behaves classically when the magnetic field is entirely diffused.

Effects of the resonance modification by electron cyclotron current drive on the linear and nonlinear dynamics of energetic particle driven magnetohydrodynamics modes in Heliotron J

This study investigates the effects of electron cyclotron current drive (ECCD) on the linear and nonlinear dynamics of energetic-particle (EP)-driven magnetohydrodynamics (MHD) instability (mode) in Heliotron J (HJ), using MEGA, a nonlinear hybrid EP-MHD simulation code. The effects of ECCD are included through the modification of the equilibrium magnetic field. Five MHD equilibria with plasma currents () of −2.00, −1.00, 0.00, 0.50, and 1.00 kA are considered, where negative and positive represent counter and co-ECCD, respectively. To account for the EP finite charge-exchange loss observed in HJ, a bump-on-tail velocity distribution is assumed for EP. The study finds that the stabilization trends in terms of the linear growth rate () are qualitatively similar to the FAR3D linear simulation and experimental results. In addition to the enhancements of the local magnetic shear and continuum damping by ECCD as proposed in previous studies, the study suggests that changes in the linear EP and shear Alfvén wave resonance are another important factor, especially for the mode. The study shows that in the currentless equilibrium, the high-velocity toroidicity-induced resonance between the mode and the co-passing EP () has the highest EP energy transfer rate, but is located slightly below the NBI injection velocity. The co-ECCD and cntr-ECCD can shift this resonance into higher and lower velocity regions, respectively. This can lead to resonance removal for co-ECCD, while cntr-ECCD can initially increase the number of resonant EPs for a small value of shift. If the shift of the resonance by cntr-ECCD is sufficiently large, the study observes stabilization due to the reduction in the EP population in the low-velocity region. The study also finds that changes in resonance affect nonlinear dynamics such as EP transport and frequency chirping. The convective transport of the co- and counter-passing EPs can be controlled, which can only be achieved for energetic-particle-mode due to the asymmetry in the resonance velocity between co- and cntr-passing EPs. The changes in the frequency chirping from the downward chirping branch to the upward chirping branch can also be explained by the changes in the resonance velocity caused by ECCD.

Weibel-like instability in magnetohydrodynamics

In magnetohydrodynamics (MHD), a density perturbation perpendicular to an electron temperature gradient generates a magnetic field around itself that acts to increase the perturbation, which can lead to instability. An MHD dispersion relation is obtained for perturbations perpendicular to a fixed electron temperature gradient with an initial in-plane magnetic field, including resistivity, viscosity, and the electrothermal coefficient. Instability occurs for sufficiently small electron temperature-gradient scale lengths determined by the ion collisionless skin depth. Both viscosity and resistivity are required to prevent growth at arbitrarily small spatial scales and to give a physical result for the fastest growing mode. The perpendicular electrothermal coefficient is only significant for a narrow range of low electron Hall parameters, causing a modest reduction in magnetic field growth and modifying the criteria for instability in the presence of viscosity. If the definition of the Weibel instability [E. S. Weibel, Phys. Rev. Lett. 2, 83 (1959)] is extended to include all instabilities due to anisotropy in the electron velocity distribution, then this is a Weibel-like instability because an electron temperature gradient implies an anisotropic electron velocity distribution. The implications for the formation of filaments in laser-produced plasmas and for the verification of MHD codes are considered.

Subdiffusive transport of runaway electrons in presence of small amplitude MHD perturbations in COMPASS

Radial transport of runaway electrons (REs) in tokamaks is affected by the presence of magnetic perturbations, either caused by internal magnetohydrodynamic instabilities or induced by external coils. The magnetic field configuration inside the plasma volume consists in general of intact magnetic surfaces alternated with magnetic islands and stochastic layers, which make the usual diffusive approach, based on the Rechester–Rosenbluth formula, inadequate to the study of transport. Here the fractional diffusion approach is employed to model RE transport in presence of intrinsic magnetic perturbations (magnetic islands) in the flat-top phase of RE-dedicated discharges on COMPASS tokamak. The character of RE transport is found to be subdiffusive. The degree of subdiffusion is evaluated by running simulations with the ORBIT code and a time-fractional diffusion equation is applied to calculate the time evolution of RE particle number. The results are compared with the observed RE losses, estimated from the time integrated neutron signal.

Anisotropic evolutions of the magnetohydrodynamic Richtmyer-Meshkov instability induced by a converging shock.

The investigation of the converging shock-induced Richtmyer-Meshkov instability, which arises from the interaction of converging shocks with the interface between materials of differing densities in cylindrical capsules, is of significant importance in the field of inertial confinement fusion (ICF). The use of converging shocks, which exhibit higher efficiency than planar shocks in the development of the RMI due to the Bell-Plesset effects, is particularly relevant to energy production in the ICF. Moreover, external magnetic fields are often utilized to mitigate the development of the RMI. This paper presents a systematic investigation of the anisotropic nature of the Richtmyer-Meshkov instability in magnetohydrodynamic induced by the interaction between converging shocks and perturbed semicylindrical density interfaces (DI) based on numerical simulations using Athena++. The results reveal that magnetic fields with β=1000, 100, and 10 (β is defined as the ratio of the plasma pressure to the magnetic pressure) lead to an anisotropic intensification of magnetic fields, anisotropic accelerations of various shock waves [including the converging incident shock (CIS), transmitted shock (TS), and reflected shock (RS)], and anisotropic growth of the DI with subsequent anisotropic vorticity distribution. Upon closer inspection, it becomes evident that these phenomena are strongly interconnected. In particular, the region where the wave front of the CIS impacts the middle point of semicylindrical DI, where the magnetic field is more perpendicular to the fluid motion, experiences a more significant amplification of the magnetic fields. This generates higher-pressure jumps, which in turn accelerates the shock wave near this region. Furthermore, the anisotropic amplification of the magnetic fields reduces the movement of the RMI near the middle point of semicylindrical DI and leads to the anisotropic formation of RMI-induced bubbles and spikes, as well as vortices. By examining vorticity distributions, the results underscore the crucial role of magnetic tension forces in inhibiting fluid rotation.

Resistive instabilities in toroidal anisotropic plasmas

Resistive singular layer equations are developed by applying the magnetohydrodynamic (MHD) model to toroidal anisotropic plasmas. This work extends the previous ideal MHD theory [Shi et al. Phys. Plasmas 23, 082121 (2016)] to the resistive case. These layer equations can be used to investigate resistive localized MHD instabilities, such as tearing instability and resistive interchange instability. Compared to existing resistive theory [Johnson and Hastie, Phys. Fluids 31, 1609 (1988)], our model includes plasma compressibility, allowing for a study of the coupling between parallel motion to perpendicular one, which is known as the apparent mass effect. In addition, these obtained equations are valid for low n modes, where n is the toroidal mode number. The dispersion relation is derived in a reduced model. We find that the anisotropic pressure effect (when p⊥ > p‖) not only increases the stable threshold of the resistive interchange mode but also raises the critical value Δc of the tearing mode stability index Δ′, which represents the logarithmic jump of the radial magnetic field perturbation across the rational surface. This discovery holds significant practical implications for mitigating neoclassical tearing modes in high confinement plasmas, particularly those characterized by a low aspect ratio (such as spherical tokamaks) or low magnetic shear (as designed in ITER hybrid scenarios). However, it enhances the growth rate of the tearing mode in a low growth rate region, where p‖ and p⊥ denote the pressure components parallel and perpendicular to the magnetic fields, respectively.