Magnetohydrodynamic Instabilities Research Articles

Magnetic pickup coil systems on the HL-3 tokamak

HL-3 is a new medium-sized copper conducting tokamak, which is dedicated to the plasma shaping control for plasma high performance and flexible operation, especially the advanced divertor configurations. According to the physics needs of the project, three types of magnetic pickup coils are designed and developed on HL-3 for magnetic field measurements. The coils emphasize different geometry sizes and array layouts. The coils are installed carefully by using high-precision positioning equipment to ensure the measurement accuracy of the system. After calibration, the magnetic field measurements are supplied for real-time equilibrium reconstruction and plasma control, e.g., with snowflake-shaped divertor configuration reconstruction. Mirnov coils satisfy the requirements for physical analysis, including determining the mode number from raw signals and detecting the magnetohydrodynamic instabilities.

Radiative Magnetohydrodynamic Simulation of the Confined Eruption of a Magnetic Flux Rope: Unveiling the Driving and Constraining Forces

We analyze the forces that control the dynamic evolution of a flux rope eruption in a three-dimensional radiative magnetohydrodynamic simulation. The confined eruption of the flux rope gives rise to a C8.5 flare. The flux rope rises slowly with an almost constant velocity of a few kilometers per second in the early stage when the gravity and Lorentz force are nearly counterbalanced. After the flux rope rises to the height at which the decay index of the external poloidal field satisfies the torus instability criterion, the significantly enhanced Lorentz force breaks the force balance and drives the rapid acceleration of the flux rope. Fast magnetic reconnection is immediately induced within the current sheet under the erupting flux rope, which provides strong positive feedback to the eruption. The eruption is eventually confined due to the tension force from the strong external toroidal field. Our results suggest that the gravity of plasma plays an important role in sustaining the quasi-static evolution of the preeruptive flux rope. The Lorentz force, which is contributed from both the ideal magnetohydrodynamic instability and magnetic reconnection, dominates the dynamic evolution during the eruption process.

Coronal energy release by MHD avalanches

Context. A possible key element for large-scale energy release in the solar corona is a magnetohydrodynamic (MHD) kink instability in a single twisted magnetic flux tube. An initial helical current sheet progressively fragments in a turbulent way into smaller-scale sheets. Dissipation of these sheets is similar to a nanoflare storm. Since the loop expands in the radial direction during the relaxation process, an unstable loop can disrupt nearby stable loops and trigger an MHD avalanche. Aims. Exploratory investigations have been conducted in previous works with relatively simplified loop configurations. In this work, we address a more realistic environment that comprehensively accounts for most of the physical effects involved in a stratified atmosphere typical of an active region. The questions we investigate are whether the avalanche process will be triggered, with what timescales, and how will it develop as compared with the original, simpler approach. Methods. We used three-dimensional MHD simulations to describe the interaction of magnetic flux tubes, which have a stratified atmosphere with chromospheric layers, a thin transition region to the corona, and a related transition from high-β to dlow-β regions. The model also includes the effects of thermal conduction and of optically thin radiation. Results. Our simulations address the case where one flux tube amongst a few is twisted at the footpoints faster than its neighbours. We show that this flux tube becomes kink unstable first in conditions in agreement with those predicted by analytical models. It then rapidly affects nearby stable tubes, instigating significant magnetic reconnection and dissipation of energy as heat. In turn, the heating brings about chromospheric evaporation as the temperature rises up to about 107 K, close to microflare observations. Conclusions. This work confirms, in more realistic conditions, that avalanches are a viable mechanism for the storing and release of magnetic energy in plasma confined in closed coronal loops as a result of photospheric motions.

Computational and experimental case study on the instability of water with gold, silver and platinum nanoparticles

Research in the field of thermal enhancement is going to increase due to their diverse applications in the field of chemical industries and engineering domains. Nanofluids deal with the concentration of nano-sized particles that act as base fluids, such as vegetable oil, vinegar, ethylene glycol, water, etc. In the current study, the hydro-dynamic or MHD (Magneto-hydrodynamic) instability of nanofluid in which nanoparticles (gold, silver and bentonite) are considered to encounter wastewater treatment. Here, the special nature of the magnetic field known as the transverse magnetic field is used in the current analysis. Reynold’s number with various parameters is analyzed for the stability of wastewater. Nanoparticles dispersed due to the effect of magnetic effect in a base fluid (water) are employed. This experiment is done by using Reynold operations, it is observed that first, the fluid flow is not stable and adding a nanoparticle flow to be more stable. The critical Reynolds number, temperature, time, pressure, and volume fraction of nanoparticles are estimated and given numerically in tables and graphs. The instabilities of nanofluids that contain nanoparticles with water as the based fluid for different embedded physical parameters are compared and discussed using growth rate and neutral graphs.

Positivity-preserving entropy filtering for the ideal magnetohydrodynamics equations

In this work, we present a positivity-preserving adaptive filtering approach for discontinuous spectral element approximations of the ideal magnetohydrodynamics equations. This approach combines the entropy filtering method (Dzanic and Witherden, 2022) for shock capturing in gas dynamics along with the eight-wave method for enforcing a divergence-free magnetic field. Due to the inclusion of non-conservative source terms, an operator-splitting approach is introduced to ensure that the positivity and entropy constraints remain satisfied by the discrete solution. Furthermore, a computationally efficient algorithm for solving the optimization process for this nonlinear filtering approach is presented. The resulting scheme can robustly resolve strong discontinuities on general unstructured grids without tunable parameters while recovering high-order accuracy for smooth solutions. The efficacy of the scheme is shown in numerical experiments on various problems including extremely magnetized blast waves and three-dimensional magnetohydrodynamic instabilities.

An Approach for Suppressing Fluid Instabilities in Liquid Metal Battery with an Internal Structure

The instabilities of fluid in the liquid metal battery (LMB) can easily cause a short circuit and lead to safety accidents, which have become a bottleneck in LMB industrial applications. In this case, a structure named grid-structure (GS) based on the inner cavity of the LMB has been used to suppress the fluid instabilities. Based on OpenFOAM-4 x numerical simulation, we analyzed the critical electric potential in basic structures, which is introduced as the threshold of magnetohydrodynamic (MHD) instabilities. We constructed the GS with a different number of baffles. The simulation results show that the GS can effectively change the spatial distribution of the magnetic field and the flow field. And it can improve the charging/discharging efficiency and enhance the stability of LMB. Simulation results also show that the number of baffles has a positive relationship with the effect of suppressing the instabilities of MHD. This study helps determine the influencing factors of MHD instabilities and proves the universality of the GS.

Diffusion–convection model of runaway electrons due to large magnetohydrodynamic perturbations in post-thermal quench plasmas

Systematic test particle tracing simulations for runaway electrons (REs) are performed for six post-thermal quench equilibria from DIII-D and ITER, where large scale, kink-like n = 1 (n is the toroidal mode number) magnetohydrodynamic (MHD) instabilities are found. The modeled particle guiding center orbits allow extraction of the effective diffusion–convection coefficients of REs in the presence of large three-dimensional (3D) perturbations up to 10% of the equilibrium toroidal field. With a fixed spatial distribution of the field perturbation, the RE transport coefficients along the plasma radial coordinate track reasonably well with the surface-averaged perturbation level. A substantial variation in the value of the transport coefficients—by three orders of magnitude in most cases, however, occurs with varying launching location of REs along the plasma radius. Large 3D perturbations almost always lead to comparable diffusion and convection processes, meaning that diffusion alone is insufficient to describe the particle motion. At lower (but still high) level of perturbation, the RE convection is found to be dominant over diffusion. A similar observation is made when the perturbation is too strong. In the presence of large perturbation, the dependence of the RE transport on the particle energy is sensitive to the spatial distribution of the perturbation. Based on numerically obtained RE transport coefficients, an analytic fitting model is proposed to quantify the particle diffusion and convection processes due to large MHD events in post-thermal quench plasmas. The model is shown to reasonably well reproduce the direct test particle tracing results for the RE loss fraction and can, thus, be useful for incorporating into other kinetic RE codes in order to simulate the RE beam evolution in the presence of large 3D perturbations.

A physics-informed deep learning model of the hot tail runaway electron seed

A challenging aspect of the description of a tokamak disruption is evaluating the hot tail runaway electron seed that emerges during the thermal quench. This problem is made challenging due to the requirement of describing a strongly non-thermal electron distribution, together with the need to incorporate a diverse range of multiphysics processes, including magnetohydrodynamic instabilities, impurity transport, and radiative losses. This work develops a physics-informed neural network (PINN) tailored to the solution of the hot tail seed during an axisymmetric thermal quench. Here, a PINN is developed to identify solutions to the adjoint relativistic Fokker–Planck equation in the presence of a rapid quench of the plasma's thermal energy. It is shown that the PINN is able to accurately predict the hot tail seed across a range of parameters, including the thermal quench timescale, initial plasma temperature, and local current density, in the absence of experimental or simulation data. The hot tail PINN is verified by comparison with direct Monte Carlo simulations, with excellent agreement found across a broad range of thermal quench conditions.

Real-time MHD feedback control system in Keda Torus eXperiment

This article describes the feedback control system in magnetic confinement devices, aiming to mitigate magnetohydrodynamic (MHD) instabilities and optimize plasma confinement within the Keda Torus eXperiment (KTX). The system includes saddle sensors as the input signal, a real-time control system as the core controller, a digital power amplifier (DPA) array as the actuator, and saddle coils as the brake to restrain the MHD instabilities. A flexible, distributed real-time control system based on field-programmable gate array (FPGA) has been developed and implemented for MHD control in KTX. This is the first time FPGA has been used to verify presupposed magnetic field mode, perform data acquisition, real-time calculation, and real-time feedback in KTX. It fulfills the real-time requirements of the experiment completely. The system is presently utilized in MHD control experiments, successfully achieving experiments at the current stage that reach the limit of Ohmic discharge, with good reproducibility.

Structure of Fluctuations in the Edge Plasma of a Stellarator in Modes with Transport Transitions

The evolution of fluctuating signals from electrostatic and magnetic probes and reflectometry on the L-2M stellarator is presented. The L-2M facility is a quasi-stationary toroidal magnetic trap in which plasma is generated and heated by high-power pulsed microwave radiation. Pulses with transitions to improved confinement modes accompanied by an increase in energy, increase in plasma density, and restructuring of the peripheral electric field, were analyzed. Spectral analysis of signals is carried out using Fourier analysis and various wavelets. The possible influence of magnetohydrodynamic and kinetic instabilities on the development of transient processes is considered.

Structure of Fluctuations in the Edge Plasma of a Stellarator in Modes with Transport Transitions

The evolution of fluctuating signals from electrostatic and magnetic probes and reflectometry on the L-2M stellarator is presented. The L-2M facility is a quasi-stationary toroidal magnetic trap in which plasma is generated and heated by high-power pulsed microwave radiation. Pulses with transitions to improved confinement modes accompanied by an increase in energy, increase in plasma density, and restructuring of the peripheral electric field, were analyzed. Spectral analysis of signals is carried out using Fourier analysis and various wavelets. The possible influence of magnetohydrodynamic and kinetic instabilities on the development of transient processes is considered.

Nonlinear control of safety factor gradient in tokamaks using spatially variable electron cyclotron current drives

Active control of plasma properties may be necessary to achieve stable operation of next-generation tokamaks over large time scales. Such control algorithms can regulate the plasma properties to avoid the onset of magnetohydrodynamic (MHD) instabilities. For instance, the global and local properties of the safety factor profile are linked to the onset of neoclassical tearing modes (NTMs). This work proposes a model-based control approach for deterring/delaying NTMs through active modulation of one of the safety factor properties - the gradient of the safety factor profile at a particular rational safety factor surface. In particular, a novel control-oriented model for the local safety factor gradient is developed. The nonlinear control model is governed by a nonautonomous ordinary differential equation that accounts for a given rational safety factor surface’s spatial variation over time. To improve the controllability of the spatially evolving parameter, the control model treats ECH&CD positions, along with noninductive powers, as controllable variables. A nonlinear control algorithm based on feedback linearization with optimization is synthesized to achieve the objective of regulating the safety factor gradient around a given target. The proposed algorithm allocates optimal ECH&CD positions, in addition to auxiliary powers, at each time instant as the rational safety factor surface drifts to locations with a low control authority. Stability guarantees of the proposed control law are also discussed in this work. The proposed algorithm is tested for a DIII-D tokamak scenario in nonlinear simulations carried out using the Control Oriented Transport SIMulator (COTSIM). Both fixed and moving ECH&CD cases are studied, and their outcomes are compared. Simulation results demonstrate that enthusiastic regulation of the safety factor gradient can be achieved during the ramp-up and flat-top phases of tokamak operation in both fixed and moving ECH&CD cases. However, real-time updates of ECH&CD positions can prevent the saturation of auxiliary powers.

Magnetohydrodynamic instability with bichromatic perturbations in aluminum reduction cells

Magnetohydrodynamic instability with bichromatic perturbations in aluminum reduction cells

Effects of NBI-induced energetic ions on internal kink stability in HL-2M

A systematic investigation is carried out, studying the effect of the neutral beam injection induced energetic particles (EPs) on the n = 1 (n is the toroidal mode number) internal kink (IK) instability in the HL-2M tokamak, utilizing the MARS-F/K code [Liu et al., Phys. Plasmas 7, 3681 (2000) and 15, 112503 (2008)]. A high-beta sawteething HL-2M scenario, simulated by the TRANSP code [Breslau et al. Computer Software (2018)], is chosen for this study. Compared to the fluid model, non-perturbative magnetohydrodynamic (MHD)-kinetic hybrid computations with MARS-K show a generally stabilization effect on the IK, due to drift kinetic resonances associated with EPs. The bounce resonance of trapped EPs has minor influence on the mode stability. In the absence of the plasma equilibrium flow and with the assumed particle pitch distribution, the transit resonance of co-current (countercurrent) passing EPs destabilizes (stabilizes) the IK. With plasma flow, both co- and countercurrent passing EPs tend to stabilize the mode, but the effect is stronger with the countercurrent particles. These modeling results provide useful guidance for interpreting MHD instabilities in the future high-performance experiments in HL-2M.

Simultaneous control of safety factor profile and normalized beta for JT-60SA using reinforcement learning

Plasma with an internal transport barrier (ITB) will be developed in JT-60SA as an attractive operation appropriate for a steady-state fusion reactor. To achieve the ITB plasma while avoiding magnetohydrodynamic instabilities, it is advantageous to simultaneously control the safety factor (q) profile and the normalized beta (). In this study, a control system for simultaneous control of the q profile and is studied in simulations prior to the real experiment in JT-60SA. The bootstrap current dominates the total current in the ITB region, which results in a coupling between the pressure profile and the q profile. Thus, it is crucial to control the q profile and according to the strength of the ITB. A two-stage neural network (NN)-based control system was developed to address this problem. The first stage estimates the transport properties (i.e. ITB strength) of the plasma from measurements. The second stage consists of several NNs for control of the q profile and . According to the ITB strength estimated by the NN in the first stage, the appropriate NN for control is selected from those in the second stage. Each NN in the second stage is trained to control plasmas with different ITB strengths through reinforcement learning employing RAPTOR, an integrated transport code. To validate this system, it is tested in a simulation employing another integrated transport code, TOPICS, to mimic the plasma control in JT-60SA plasmas with various ITB strengths. Stable control of the q profile and is achieved in ITB plasmas simulated by both the RAPTOR and TOPICS codes.

Model predictive current profile control in tokamaks by exploiting spatially moving electron cyclotron current drives

The plasma control systems in next-generation tokamaks like ITER will balance competing control objectives to achieve the desired level of performance in advanced scenarios while preventing magnetohydrodynamic instabilities and disruptions. During normal tokamak operation, the points of incidence of the electromagnetic waves generated by the electron cyclotron heating and current drives (EC H&CDs) are usually fixed in space. However, the points of incidence can be modified in real-time by changing the angles of the mirrors that reflect the EC H&CD waves. Altering the points of incidence, in turn, varies the ability of the plasma control system to regulate a plasma property. For instance, changing the EC H&CD wave incidence location may place the power demands necessary to achieve a particular plasma target within saturation limits. Therefore, using the EC H&CD deposition location, which is related to the EC H&CD mirror angle, as a supplementary controllable variable may facilitate access to a given target scenario. However, active scenario-control algorithms have not been designed so far to fully exploit this capability in real time. In this work, a model predictive controller that can handle actuation locations as control inputs is developed. In particular, the controller is designed to regulate both the auxiliary powers and the EC H&CD deposition locations in a pre-defined optimal sense to achieve the control objective of attaining and sustaining a target current profile. The proposed controller is tested for a DIII-D tokamak scenario in nonlinear simulations using the Control Oriented Transport SIMulator (COTSIM).

Observation of plasma dynamics in a theta pinch by a novel method

A novel experimental method is proposed for observing plasma dynamics subjected to magnetic fields based on a newly developed cylindrical theta-pinch device. By measuring simultaneously the temporal profiles of multiple parameters including the drive current, luminosity, plasma density, and plasma temperature, it provides a basis for observing the plasma dynamics of the theta pinch, such as shock transport and magnetohydrodynamic instability. We show that the plasma evolution can be distinguished as three phases. First, in the radial implosion phase, the trajectories of the current sheath and shock wave are ascertained by combining experimental data with a snowplow model (Lee model) in a self-consistent way. Second, in the axial flow phase, we demonstrate that m = 0 (sausage) instability associated with the plasma axial flow suppresses the plasma end-loss. Third, in the newly observed anomalous heating phase, the lower-hybrid-drift instability may develop near the current sheath, which induces anomalous resistivity and enhanced plasma heating. The present experimental data and novel method offer better understanding of plasma dynamics in the presence of magnetic fields, thereby providing important support for relevant research in magneto-inertial fusion.

Hydrodynamics and Nucleosynthesis of Jet-driven Supernovae. I. Parameter Study of the Dependence on Jet Energetics

Rotating massive stars with initial progenitor masses M prog ∼ 25–140 M ⊙ can leave rapidly rotating black holes to become collapsars. The black holes and the surrounding accretion disks may develop powerful jets by magnetohydrodynamics instabilities. The propagation of the jet in the stellar envelope provides the necessary shock heating for triggering nucleosynthesis unseen in canonical core-collapse supernovae. However, the energy budget of the jet and its effects on the final chemical abundance pattern are unclear. In this exploratory work, we present a survey on the parameter dependence of collapsar nucleosynthesis on jet energetics. We use the zero-metallicity star with M prog ∼ 40 M ⊙ as the progenitor. The parameters include the jet duration, its energy deposition rate, deposited energy, and the opening angle. We examine the correlations of the following observables: (1) the ejecta and remnant masses; (2) the energy deposition efficiency; (3) the 56Ni production and its correlation with the ejecta velocity, deposited energy, and the ejected mass; (4) the Sc–Ti–V correlation as observed in metal-poor stars; and (5) the [Zn/Fe] ratio as observed in some metal-poor stars. We also provide the chemical abundance table of these explosion models for the use of the galactic chemical evolution and stellar archeology.

Use of intrinsic hysteresis for the active control of internal transport barriers in magnetically confined fusion plasmas

In magnetically confined fusion devices, control of internal transport barriers (ITBs) is important both to enhance and suppress the turbulent transport to improve confinement control. Barrier control should allow for the improvement of confinement to aid in achieving the needed fusion criteria while also permitting the degradation of confinement to control profiles and clean the device by moving out the impurities accumulated near the core. In this work, we present a novel control scenario that takes advantage of the hysteresis intrinsic to transport barriers to easily cycle through enhanced and degraded confinement regimes. The control scenario is illustrated using a five-field simplified transport model for an ITB using typical parameters of a neutral beam injection-heated DIII-D tokamak discharge. Pellets and ion cyclotron resonance frequency power are used as control knobs for this active control scenario. These knobs adequately modify at will the local gradients and, therefore, the growth rates and shearing rates, allowing for easy and efficient control of the barrier by taking advantage of the barrier hysteresis. The result is a control cycle that could be operated with a relatively small amount of power in high performance regimes which, nowadays, typically require large power to control. It may also have advantages to avoid, or at least ameliorate, the appearance of magnetohydrodynamic instabilities in the barrier region.

Cosmic ray-driven magnetohydrodynamic waves in magnetized self-gravitating dusty molecular clouds

ABSTRACT The impact of galactic cosmic rays (CRs) in terms of CR pressure and parallel CR diffusion has been investigated on the low-frequency magnetohydrodynamic (MHD) waves and linear gravitational instability in the typical dusty plasma environment of molecular clouds (MCs). The dusty fluid model is formulated by combining the equations of the magnetized electrons/ions and dust particles, including the CR effects. The interactions between CR fluid and gravitating magnetized dusty plasma have been studied with the help of modified dispersion properties of the MHD waves and instabilities using the hydrodynamic fluid–fluid (CR–plasma) approach. CR diffusion affects the coupling of CR pressure-driven mode with dust-Alfvén MHD mode and causes damping in the MHD waves. It persists in its effect along the direction of the magnetic field and is diminished across the magnetic field. The phase-speed diagram shows that for super-Alfvénic wave, the slow mode becomes the intermediate Alfvén mode. The fundamental Jeans instability criterion remains unaffected due to CR effects, but in the absence of CR diffusion, the effects of dust-acoustic speed and CR pressure-driven wave speed are observed in the instability criterion. It is found that CR pressure stabilizes while CR diffusion destabilizes the growth rates of Jeans instability and significantly affects the gravitational collapse of dusty MCs. The charged dust grains play a dominant role in the sub-Alfvénic and super-Alfvénic MHD waves and the collapse of MCs, triggering gravitational instability. The consequences have been discussed to understand the gravitational instability in the dense photodissociation regions of dusty MCs.