Plasma Current Density Research Articles

Numerical study of runaway current impact on sawtooth oscillations in tokamaks

Abstract This study investigates the influence of runaway current in runaway plasmas on the dynamics of sawtooth oscillations and resultant loss of runaway electrons (RE) using the 3D magnetohydrodynamic (MHD) code M3D-C$^{1}$ (Jardin {\it et al} 2012 {\it J. Comput. Sci. Discovery} {\bf 6} 014002). Using an HL-2A-like equilibrium, we confirm that in the linear phase, the impact of REs on resistive internal kink instabilities is consistent with previous research.
In the nonlinear phase, as the runaway current fully replaces the plasmas current, we observe a significant suppression of sawtooth oscillations, with the first sawtooth cycle occurring earlier compared to the case without runaway current. Following the first sawtooth collapse, plasma current density, runaway current density, and safety factor ($q$) flatten within the $q=1$ surface, albeit displaying fine structures. Subsequently, the growing high torodial ($n$) and poloidal ($m$) mode number modes disrupt the magnetic surfaces, leading to the loss of REs outside the $q=1$ surface, while minimally affecting the majority of REs well-confined within it. Thus, in the current model, the physical processes associated with the presence of sawtooth oscillations do not effectively dissipate runaway current, as REs are assumed to be collisionless. In addition, the final profile of runaway current density exhibits increased steepening near the $q=1$ surface in contrast to the initial profile, displaying a distinctive corrugated inhomogeneity influenced by the growing fluctuation of the $n=0$ component. Finally, detailed convergence tests are conducted to validate the numerical simulations.

Tokamak plasma equilibria with n=1 toroidal asymmetry

A general approach of how to construct plasma equilibrium in a tokamak with n=1 violation of toroidal symmetry is proposed. For an arbitrary axisymmetric tokamak plasma equilibrium, there exists the small n=1 deformation of the initial magnetic configuration that keeps the nesting of the magnetic surfaces (as in the initial configuration) and provides plasma equilibrium; such deformation and final equilibrium configuration are calculated analytically. The asymmetric analogue of the Solov'ev's equilibrium with non-degenerated plasma pressure and current density profiles is presented as an example of the application of the developed algorithm.

Optimisation of the poloidal field system for advanced divertor configurations in STEP

The power exhaust proves to be one of the most challenging and concept–defining aspects in the design of a commercial fusion power plant, while the magnetic coil system, capable of supporting advanced exhaust solutions, emerges as one of the main design and cost drivers. Consequently, much effort should be dedicated to the optimisation of a robust global magnetic configuration, which integrates both the plasma and edge scenarios, while ensuring engineering feasibility and compatibility with the available technology. Here we present a multidisciplinary framework employed to analyse, evaluate, and optimise the Spherical Tokamak for Energy Production (STEP) equilibrium configuration, coupled with a viable divertor solution, and a compatible poloidal field coil system. The complexity of this task leads to a multitude of potentially conflicting requirements and competing constraints. We identify interfaces and conflicts between the aspects of the design that were previously considered independently, and highlight the key benefits, trends, and trade–offs between alternative configurations. We demonstrate that advanced exhaust solutions, simultaneously applied to both inboard and outboard divertors, are accessible with feasible coil sets under conditions relevant for STEP. We show that the most promising inner–X geometry, paired with the outer super–X configuration, can significantly enhance divertor’s power handling capability, allowing access to stable detached regimes. The coil set feasibility is further assessed considering its compatibility with the assumed plasma initiation scenario, and with the most demanding plasma current density profiles utilising alternative heating and current drive schemes.

Accelerating particle-in-cell kinetic plasma simulations via reduced-order modeling of space-charge dynamics using dynamic mode decomposition.

We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD-based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. We demonstrate the proposed DMD-EMPIC scheme for reduced-order modeling of current density and speedup in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.

Deep learning approaches to recover the plasma current density profile from the safety factor based on Grad–Shafranov solutions across multiple tokamaks

Many magnetohydrodynamic stability analyses require generation of a set of equilibria with a fixed safety factor q-profile while varying other plasma parameters. A neural network (NN)-based approach is investigated that facilitates such a process. Both multilayer perceptron (MLP)-based NN and convolutional neural network (CNN) models are trained to map the q-profile to the plasma current density J-profile, and vice versa, while satisfying the Grad–Shafranov radial force balance constraint. When the initial target models are trained, using a database of semi-analytically constructed numerical equilibria, an initial CNN with one convolutional layer is found to perform better than an initial MLP model. In particular, a trained initial CNN model can also predict the q- or J-profile for experimental tokamak equilibria. The performance of both initial target models is further improved by fine-tuning the training database, i.e. by adding realistic experimental equilibria with Gaussian noise. The fine-tuned target models, referred to as fine-tuned MLP and fine-tuned CNN, well reproduce the target q- or J-profile across multiple tokamak devices. As an important application, these NN-based equilibrium profile convertors can be utilized to provide a good initial guess for iterative equilibrium solvers, where the desired input quantity is the safety factor instead of the plasma current density.

A global model for evaluating discharge characteristics and performance of hollow cathodes

Hollow cathode, with the highest plasma density, current density, and temperature, becomes one of the most important components in the electro-thruster system. As the electric-propulsion thruster performance is directly related to the ionization rate, reliability, and lifetime of the hollow cathode, this paper develops a global model to study the effects of discharge current, gas flow rate, and gas species on the discharge characteristics in the insert and orifice regions of the hollow cathode. The emitter wall temperatures of hollow cathodes predicted by the global model are compared with experimental results from NSTAR thruster neutralization cathodes, confirming the model's validity. The influence of hollow cathode emitter material and structure sizes on the plasma parameters in the internal regions was also evaluated. The simulation results show that there is an optimal matching relationship between the discharge current and gas flow rate to guarantee the maximum ionization rate. The optimal working region for the hollow cathode has been determined under different energetic, regime and structural parameters. The global model established in this paper can quickly determine the key structure and operating parameters of hollow cathode at the design stage, and provide the theoretical basis for hollow cathode design and development.

Influence of temperature and pressure gradient on power deposition and field pattern in High Magnetic field Helicon eXperiment

AbstractBased on High Magnetic field Helicon eXperiment, considering the parabolic distribution and Gaussian distribution of radial plasma density, HELIC code was used to study the influence of temperature and pressure gradient on power deposition, electric field, and current density of Helicon Wave Plasma. Three different gradients (positive, negative, and zero gradient) were selected. The results show that positive temperature gradient is beneficial to increase the relative absorption power at the center of plasma. Compared with negative and zero pressure gradients, positive pressure gradient increases the relative absorption power and weakens the current density at the center of plasma, and increases the electric field intensity at the edge of plasma. Larger edge heating will cause the relative absorption power at edge to rise rapidly, which is not conducive to the coupling at the center of plasma. In practical experiments, it is particularly important to reduce the heating effect at edge by cooling the antenna itself. Three different gradients of temperature and pressure have little effect on electric field intensity and current density in plasma, and the variation trend is basically similar, which proves the stability of the antenna mode: m = 1.

Numerical analysis of arc physics and energy transfer under circumferential gas constraint effect

Energy dispersion and easy instability associated with arcs, the traditional metal processing heat source, restrict its development and application in the modern high-precision welding and additive manufacturing. This work aims to study the characteristics of a novel arc under circumferential gas constraint effect which can improve the arc stability and processing accuracy. A magnetohydrodynamics model was established to calculate the arc physics and heat transfer, considering the electron emission characteristics of tungsten and the effect of metal vapor. It indicates that the annular flexible constrained gas flow can significantly increase the physical characteristics such as arc temperature, plasma flow velocity and current density compared with traditional free arc which is named GTA. The arc heat generation increasement of the novel arc makes the heat transfer from arc to base metal higher than that of GTA. The additional annular gas flow inhibits the diffusion of metal vapor, stabilizing the arc and protecting the tungsten electrode from contamination. However, as the arc length decreases, eddy of arc plasma flow appears inside the arc, which can cause metal vapor to contaminate the tungsten. It's found that this novel gas flow constrained arc needs to be applied with a small current when welding with small arc length to avoid the eddy. Finally, the accuracy of the calculation model is verified by experimental detection of arc temperature.

Characterization of early current quench time during massive impurity injection in JT-60SA

Characteristics of the early current quench (CQ) time in mitigated disruptions are studied for a full-current (5.5 MA) scenario in the JT-60SA superconducting tokamak. Self-consistent evolution of the plasma temperature and current density profiles during the early CQ phase before the plasma moves vertically is simulated using the axisymmetric disruption code INDEX for given impurity source profiles. It is shown that the hollow (flat) impurity density profiles peaks (flattens) the current density, and it causes a temporal change in the internal inductance in this phase. However the resultant CQ time is found to be insensitive to the impurity source profile for the same assimilated quantity. The simulation results are interpreted by the L/R model including the temporal change in the internal inductance as well as the effect of a gap between the plasma and the conducting vessel structures and stabilizing plates. This results will improve the accuracy to estimate the amount of impurity assimilated into plasma from the observed CQ rate in the massive gas injection (MGI) experiment planned in JT-60SA. The accessible range in which the CQ time can be scanned as well as the electron densities to suppress runaway electrons is also shown for different injected amounts of neon, argon, and their deuterium mixture under the limitation of the MGI gas amount. Mitigated disruptions in JT-60SA typically lead to the CQ time shorter than the vessel wall time, which is expected to produce relevant contributions to disruption mitigation in ITER and future reactors.

Simulation of neutral beam current drive on EAST tokamak

A neutral beam current drive on the EAST tokamak is studied by using Monte Carlo test particle code TGCO. The phase-space structure of the steady-state fast ion distribution is examined and visualized. We find that trapped ions carry co-current current near the edge and countercurrent current near the core. However, the magnitude of the trapped ion current is one order smaller than that of the passing ions. Therefore, their contribution to the fast ion current is negligible (1% of the fast ion current). We examine the dependence of the fast ion current on two basic plasma parameters: the plasma current Ip and plasma density ne. The results indicate that the dependence of fast ion current on Ip is not monotonic: with Ip increasing, the fast ion current first increases and then decreases. This dependence can be explained by the change of trapped fraction and drift-orbit width with Ip. The fast ion current decreases with the increase in plasma density ne. This dependence is related to the variation of the slowing-down time with ne, which is already well known and is confirmed in our specific situation. The electron shielding effect to the fast ion current is taken into account by using a fitting formula applicable to general tokamak equilibria and arbitrary collisionality regime. The dependence of the net current on the plasma current and density follows the same trend as that of the fast ion current.

Microplasma Illumination Enhancement in N+P‐Co‐Ion‐Implanted Nanocrystalline Diamond Films

N‐ and P‐co‐ion implantation enhances the electrical conductivity of nanocrystalline diamond films to 6.9 s cm−1 and improves the microplasma illumination (MI) characteristics of the films to a low breakdown voltage of 340 V, large plasma current density of 6.3 mA cm−2 (@510 V) with plasma life‐time stability of 10 h. N ions induce nanographitic phases in the films and P ions lower the resistance at the diamond‐to‐Si interface together promoting the conducting channels for effective electron transport, consequently attaining the improved MI properties of the films.

Improved mechanical and wear properties of H13 tool steel by nitrogen-expanded martensite using current-controlled plasma nitriding

Nitrogen-expanded martensite is a crystalline structure formed by incorporating nitrogen atoms into the interstitial sites of martensitic steels. It has recently gained significant industrial attention due to its excellent mechanical and wear-resistance properties. However, the major challenge in synthesizing nitrogen-expanded martensite is obtaining a phase free of iron or chromium nitrides precipitates. In this study, the effects of varying temperature (460, 480, and 500 °C) and plasma current density (0.5, 1.0, and 1.5 mA/cm2) during plasma nitriding of H13 tool steel were investigated to evaluate their influence on crystalline phases. The results of X-ray diffraction analysis indicate that expanded martensite free of nitride precipitates can be obtained at a temperature of 480 °C and low current density. Moreover, wear analysis using a ball-on-disk wear tester showed that the lowest wear rates were achieved under similar conditions. Grazing incidence X-ray diffraction analysis revealed that the outer region of the nitrided zone had a disordered structure, which could be attributed to a nano crystallization process. The nanoindentation analysis demonstrated that the expanded martensite phase has rigid-elastic properties characterized by high elastic energy (144.5 nJ) and high resistance to plastic deformation.

White noise characterization and thermo-mechanical analysis of DTT pick-up coils

The Divertor Tokamak Test (DTT) [1] is presently in the start-up phase of construction. Among diagnostics, the magnetic ones are the first components that will have to be ready for installation and commissioning when DTT vacuum vessel and magnets will be assembled. In this paper, the white noise characterization of DTT in-vessel pick up coil measurements and the thermo-mechanical analysis of ex-vessel pick up coils will be presented referring to the 2021 probe configuration. In particular, the systematic error due to white noise affecting the 80 internal pick-up coil measurements on plasma position reconstruction has been assessed. Such plasma reconstruction has been done by assuming a filamentary representation of the plasma current density. The effect of noise on the measurements is characterized evaluating the mean error, the mean square error and the standard deviation, on the difference between the noisy inverse reconstruction and the ideal inverse reconstruction evaluated on suitable plasma-wall gaps.Moreover, a feasibility study of mounting a torlon pick-up coil between the vacuum vessel and the thermal shield, in terms of bulk has been developed. In addition, the probe thermomechanical stresses are preliminarily investigated for backing and operative conditions, assuming a welding as mounting solution. The study shows that no bulk criticality is present for mounting the external pick-up coil. The operative temperature results to be far from thermomechanical critical condition. On the contrary, the baking temperature T = 220 °C presents some critical issues. The achieved results are propaedeutic to make more detailed choice in the following design steps, such as the probe fixing solution, the bolt dimension and the materials. When detailed pick-up coils mounting solution will be defined, the stresses on the contact region between the pick-up coils and the vacuum vessel accurately evaluate.

Substorm Influences on Plasma Pressure and Current Densities Inside the Geosynchronous Orbit

AbstractPlasma in the inner magnetosphere is affected by various processes, such as substorms. In this study, we have statistically investigated the ring current properties based on the observations of Van Allen Probes from 2012 to 2019 to examine the substorm effects on the plasma pressure and current system in the inner magnetosphere. The results show that the plasma pressure increases significantly, leading to a ∼3 nT/hr geomagnetic depression during intense substorms. The contribution of <100 keV H+ ions to the plasma pressure increases during substorms, which is more significant at lower L‐shells. Opposite to the H+ ions, the proportion of >10 keV O+ ions contributing to the plasma pressure increases as substorm intensity increases. In addition, the rise of plasma pressure is mainly distributed from dusk to midnight, resulting in the enhancement of asymmetric ring current and the region II field‐aligned currents connecting to the ionosphere. Our results provide a comprehensive view of the variation of plasma pressure and current system in the inner magnetosphere during quiet periods and intense substorms.

Kv1.3-dependent immune system activation is regulated by KCNE4.

Kv1.3 is a voltage-gated potassium channel that regulates leukocyte physiology. The association of Kv1.3 with the regulatory subunit KCNE4 fine-tunes the channel's activity. KCNE4 is a transmembrane protein that interacts with Kv1.3 through both of their cytoplasmic C-terminal ends. The protein regulates the membrane trafficking of the channel, affecting the magnitude of the currents and the C-type inactivation. Anomalies in Kv1.3 activity cause several autoimmune diseases, such as systemic lupus erythematosus, rheumatoid arthritis, or multiple sclerosis. Therefore, the therapeutic relevance of Kv1.3 postulates KCNE4 as a potential modulator of the immune system physiology. In this study, we investigated the effect of KCNE4 on the activity of Kv1.3 in different leukocyte cell lines. We analyzed the expression of KCNE4 in a model of Jurkat T-lymphocytes and in CY15 dendritic antigen-presenting cells. Dendritic cells exhibit a high expression of the ancillary peptide. Manipulation of KCNE4 abundance affected the Kv1.3-dependent T cell physiology, having an impact on the channel's translocation to the immunological synapse (IS) and IL-2 production. In CY15 cells, activation with LPS increased the Kv1.3/KCNE4 ratio and the current density of the cells. The oligomeric Kv1.3-KCNE4 channel has a variable stoichiometry as demonstrated by single fluorescence bleaching steps. Each tetramer can bind up to four molecules of KCNE4, affecting plasma membrane trafficking and current density of Kv1.3 in a progressive manner. Contrarily, a single KCNE4 subunit was able to enhance the C-type inactivation of the channel. Our results prove that KCNE4 acts as a regulatory element in Kv1.3-dependent immune system physiology. Kv1.3 is differentially modulated by the KCNE4 availability influencing the Kv1.3/KCNE4 architecture of the oligomeric channel and its physiological function. Supported by the Ministerio de Ciencia e Innovación (MICINN/AEI), Spain (PID2020-112647RB-I00 and 10.13039/501100011033) and European Regional Development Fund (FEDER).

The scalings of the thermal energy confinement time in EAST H-mode plasmas

This paper describes scalings of the H-mode confinement database of neutral beam injection (NBI)-lower hybrid wave (LHW) and electron cyclotron resonant heating-LHW plasmas in the EAST tokamak. Fundamental information of the EAST H-mode database and the details of calculation of the thermal energy confinement time in EAST are presented. The result of the scaling model of the thermal energy confinement time in NBI-LHW plasmas with root-mean-square-error , compared with the multi-machine scaling model derived from the multi-machine database (mainly NBI heating) with , is obtained. The scaling presents a similar dependency on plasma current and power loss and a lower dependency on plasma density and elongation, but stronger dependency on toroidal field than in . The scaling demonstrates a similar dependency on plasma current and power loss and lower dependency on plasma density, but a negative dependency with large error bars on elongation compared with in NBI-LHW plasmas. The comparison of EAST models with the more recent multi-tokamak scaling ITPA20-IL shows a similar engineering dependency on plasma current, power loss and plasma density, but opposite dependency on toroidal field.

Effect of deposition location of electron cyclotron resonance heating on active control of fishbone modes in the HL-2A tokamak

Experiment on suppressing fishbone activities is carried out in HL-2A tokamak by electron cyclotron resonance heating (ECRH). To achieve multiple deposition locations of ECRH, the magnetic field is in a range of 1.22–1.4 T from shot to shot. It is found that the fishbone modes exhibit different characteristics at different radial deposition locations. With the same injected power, the effect of off-axis ECRH is much better than that of on-axis heating. The fishbone modes can be completely suppressed when ECRH is deposited nearby the <i>q</i> = 1 rational surface, but would only mitigate in other cases. Further analysis indicate that injection of high power ECRH leads the electron temperature to increase, then the pressure gradient and plasma current density to change, finally safety factor to change and the minimum safety factor to reach a value larger than 1. Meanwhile, M3D-K simulation results show that the growth rate of fishbone mode declines with the increase of <i>q</i><sub>min</sub>. In other words, the growth of safety factor and disappearance of <i>q</i> = 1 rational surface induced by ECRH contribute to the suppression of fishbone activities. The experimental results reported here may not only help to better understand complex effects of ECRH on magnetohydrodynamic instability, but also provide a physics basis for actively controlling the energetic particle driven modes in the future magnetic confined fusion devices.

Non-linear free boundary simulations of the plasma response to resonant magnetic perturbations in ASDEX Upgrade plasmas

A promising method for the control of Edge Localized Modes (ELMs) in H-Mode tokamak plasmas is the application of Resonant Magnetic Perturbations (RMPs), where small helical field perturbations are introduced into the plasma via a set of external coils. While RMPs are used for suppression of ELMs in many present-day tokamaks, the mechanisms that lead to RMP-ELM control are still subject of debate.Here, we use the non-linear MHD code JOREK to investigate the penetration of the magnetic perturbation fields into ASDEX Upgrade (AUG) plasmas. We present an extension of the coupled JOREK-STARWALL code, that replaces the commonly used fixed boundary treatment with a free boundary treatment. Instead of prescribing the magnetic field at the boundary according to the vacuum field using Dirichlet boundary conditions, natural boundary conditions are applied, so that the magnetic field and plasma current density are evolving freely at the boundary. This allows a fully self-consistent development of the plasma response and the magnetic perturbation in the whole computational domain. The direct comparison of both approaches demonstrates that the artificial suppression of the plasma response with the fixed boundary treatment reduces the excitation of marginally stable modes. An overall larger perturbation is observed using the free boundary approach.The presented simulations are performed in realistic geometry with fully realistic plasma parameters and plasma flows based on reconstructions of experimental AUG equilibria. While the use of realistic plasma parameters makes the simulations particularly challenging, it also allows for quantitative comparisons to the experiment. When the RMP induced corrugation of the boundary is compared to electron density measurements from the lithium beam emission spectroscopy, only the free boundary approach shows excellent agreement with the experiment.

Surrogate models for plasma displacement and current in 3D perturbed magnetohydrodynamic equilibria in tokamaks

A numerical database of over one thousand perturbed three-dimensional (3D) equilibria has been generated, constructed based on the MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) computed plasma response to the externally applied 3D field sources in multiple tokamak devices. Perturbed 3D equilibria with the n = 1–4 (n is the toroidal mode number) toroidal periodicity are computed. Surrogate models are created for the computed perturbed 3D equilibrium utilizing model order reduction (MOR) techniques. In particular, retaining the first few eigenstates from the singular value decomposition (SVD) of the data is found to produce reasonably accurate MOR-representations for the key perturbed quantities, such as the perturbed parallel plasma current density and the plasma radial displacement. SVD also helps to reveal the core versus edge plasma response to the applied 3D field. For the database covering the conventional aspect ratio devices, about 95% of data can be represented by the truncated SVD-series with inclusion of only the first five eigenstates, achieving a relative error (RE) below 20%. The MOR-data is further utilized to train neural networks (NNs) to enable fast reconstruction of perturbed 3D equilibria, based on the two-dimensional equilibrium input and the 3D source field. The best NN-training is achieved for the MOR-data obtained with a global SVD approach, where the full set of samples used for NN training and testing are stretched and form a large matrix which is then subject to SVD. The fully connected multi-layer perceptron, with one or two hidden layers, can be trained to predict the MOR-data with less than 10% RE. As a key insight, a better strategy is to train separate NNs for the plasma response fields with different toroidal mode numbers. It is also better to apply MOR and to subsequently train NNs separately for conventional and low aspect ratio devices, due to enhanced toroidal coupling of Fourier spectra in the plasma response in the latter case.

Stabilization of double tearing mode growth by resonant magnetic perturbations

It is well known that for non-monotonic profiles of the safety factor q with two q = m/n resonant surfaces inside the plasma (m/n being the poloidal/toroidal mode numbers), the low-m double tearing modes (DTMs) are usually unstable, especially for plasmas with a high bootstrap current fraction as required for the steady operation of advanced scenarios. The effect of applied resonant magnetic perturbations (RMPs) on the m/n = 2/1 DTM growth is investigated numerically in this paper using two-fluid equations. The DTM growth is found to be stabilized by moderate static m/n = 2/1, 4/2 or 6/3 RMPs below their penetration threshold if the distance between the two resonant surfaces and the local plasma rotation velocity at the outer resonant surface are sufficiently large. The outer magnetic island is stabilized due to the change of the local plasma current density gradient around the outer resonant surface caused by RMPs, while the inner island growth is stabilized by the bootstrap current perturbation in the negative magnetic shear region. The mode stabilization is more effective for a higher electron temperature, indicating a possible method to improve the DTM stability in a fusion reactor.