Plasma Boundary Research Articles

KSTAR plasma commissioning to support the tokamak physics experiments

At the beginning of every KSTAR campaign, during the plasma commissioning period, a stable tokamak plasma operation condition is aimed to be established to support various physics experiments throughout the rest of the KSTAR campaign. To achieve this, considering the KSTAR's superconducting operation, the plasma startup recipe is confirmed, and every component of auxiliary devices for fuel, heating, and diagnostics must be checked. A robust plasma startup scenario has been secured at the beginning of every plasma commissioning period for all plasma experiments. Then, the commissioning work deals with the plasma shaping and the auxiliary devices for fueling and heating. As the last stage, the radial profile diagnostics are tested by moving the plasma boundary and varying the operating toroidal magnetic field for cross-validation in a dedicated session. This paper explains in detail the established routine process for plasma commissioning in the KSTAR campaign.

Experimental study of the mechanism of prepulse current on Z-pinch plasma using Faraday rotation diagnosis.

The prepulse current is an effective way to optimize the load structure and improve the implosion quality of the Z-pinch plasma. Investigating the strong coupling between the preconditioned plasma and pulsed magnetic field is essential for the design and improvement of prepulse current. In this study, the mechanism of the prepulse current on the Z-pinch plasma was revealed by determining the two-dimensional magnetic field distribution of preconditioned and nonpreconditioned single-wire Z-pinch plasma with a high-sensitivity Faraday rotation diagnosis. When the wire was nonpreconditioned, the current path was consistent with the plasma boundary. When the wire was preconditioned, the distributions of current and mass density presented good imploding axial uniformity, and the imploding speed of the current shell was higher than that of the mass shell. In addition, the mechanism of the prepulse current suppressing the magneto-Rayleigh-Taylor instability was revealed, which formed a sharp density profile of the imploding plasma and slowed the shock wave driven by the magnetic pressure. This discovery is essential and instructive for the design of preconditioned wire-array Z-pinch experiments.

Effects of the Parker spiral angle of the interplanetary magnetic field on the dawn-dusk asymmetry of the Martian magnetotail

Context. The draping of the interplanetary magnetic field (IMF) around unmagnetized planets induces a magnetotail with a two-lobe plasma structure. On Mars, due to the impact of the IMF Parker spiral angle, the structure of its induced magnetotail is dawn-dusk asymmetric. Observational and numerical studies have shown the dawn-dusk asymmetric size of magnetic lobes and the shift of the polarity reversal layer and the inverse polarity reversal layer under different Parker spiral angles. Variation in the tail-region induced magnetic field with the Parker spiral angle is important in the evolution of the magnetotail. Further studies should investigate the influence of the magnetic pressure and field direction on the magnetic lobe structure and plasma boundary locations, as well as the relationship between the polarity reverse of the IMF and the Parker spiral angle. Aims. This study aims to investigate the dawn-dusk asymmetric structure of the Martian magnetotail under different Parker-spiral IMF orientations. In this study, we used a multispecies magnetohydro-dynamic (MHD) model, which has been shown to self-consistently calculate the Mars-solar wind interaction, to investigate the effects of the Parker spiral angle on the structure of the Martian magnetotail. By comparing the magnetic field, large-scale configurations, and plasma boundary locations across various cases, we aim to clarify how variations in the IMF Parker spiral angle affect the magnetic pressure and field direction in the magnetotail and the locations and shapes of the magnetic lobes, polarity reversal layer, and inverse polarity reversal layer. Methods. A three-dimensional and parallelized multispecies MHD model was constructed to simulate the global solar wind interaction with Mars. Four ion species, H+, O2+, O+, and CO2+, as well as the chemical reactions between them, such as photoionization, charge exchange, and recombination, were considered in the model to accurately calculate the ion distributions in the magnetosphere and ionosphere of Mars. Three cases with Parker spiral angles of 90, 56, and 30 degrees were examined, representing the perpendicular, standard, and quasi-parallel IMF relative to the solar wind flow, respectively. Results. A symmetric magnetotail was reproduced in the case with a Parker spiral angle of 90° degrees. When the Parker spiral angle decreases, the magnetic pressure in the magnetic lobes reduces, and the flaring angle of the magnetic field becomes larger on the dawn side than on the dusk side. These two factors result in the shrinkage and extension of the magnetic lobes. Furthermore, the variation in magnetic pressure results in a polarity reversal layer bent toward the dawn side. Finally, we found that the inverse polarity reversal layer shrinks toward Mars with a decrease in the Parker spiral angle.

Forces, electric fields and currents at the subsolar martian MPB: MAVEN observations and multifluid MHD simulation

The Martian MPB (Magnetic Pileup Boundary) is a key boundary in the Mars/Solar Wind interaction as it is here that part of the momentum and energy from the solar wind plasma are transferred to the planetary plasma. Since this interaction is for the most part collisionless, the transfer is mediated by electric and magnetic fields. The acceleration processes and the interaction of particles with electromagnetic fields operate at spatial scales determined by the ambient particle populations. In particular, in regions with sizes of the order of the ion inertial length (ion scales), the Hall electric field is expected to be dominant.In the present work we combine data from the MAVEN spacecraft along one orbit around Mars and multifluid MHD simulation results to study the role of electric fields, currents and forces at the MPB at ion scales. In particular, we find that the current densities deduced from MAVEN data (J ∼ 238 nA/m2) of the same order as the values obtained in the simulation (J ∼ 56-156 nA/m2) and that the Hall electric force points sunward in both cases. In addition, we find that in the subsolar MPB current layer the Hall electric field (∼3.2 mV/m) dominates over the solar wind convective electric field (∼0.4 mV/m) and electron pressure gradient (∼0.8 mV/m). These values are consistent with previous results suggesting that the MPB thickness is of the order of the solar wind proton inertial length and support the idea that non ideal terms in Ohm’s law must be considered when analysing the dynamics of particles around plasma boundaries with ion scale thicknesses.

General Approach to the Evolving Plasma Equilibria with a Resistive Wall in Tokamaks

The dynamic problem of plasma equilibrium in a tokamak is considered taking into account the electromagnetic reaction of the vacuum vessel resistive wall. The currents induced in the wall during transient events contribute to the external magnetic field that determines the plasma shape and position. Accordingly, the plasma geometry must evolve so that the inductive excitation of the wall current would properly compensate for the resistive losses. Simultaneous consideration of these factors presents the main difficulty of the description. It is performed in a general form using the Green’s function method that guarantees the mathematical accuracy of expressions for the magnetic fields from each source. At the same time, it is desirable to minimize the related complications, which is one of the goals here. The starting point is the standard solution of the external equilibrium problem given by integral relating the poloidal magnetic flux to the magnetic field at the plasma boundary. In the evolutionary problem, the additional equations for the plasma-wall electromagnetic coupling are transformed to an equation with a similar integral over the wall, but with either the time derivative of the poloidal magnetic flux or the wall current density in the integrand. The mentioned similarity allows to use the already developed techniques, which makes this formulation compact and convenient. It provides the basis for extension of the existing analytical theory of equilibrium to the case with non-circular plasma and wall.

Parametric excitation of plane waves and traveling nonlinear surface charge structures by an oscillating electric field at the plasma boundary

With the help of a single equation, to which it was possible to reduce the original system of equations, it turned out to be possible to describe the excitation of parametric instability on plane surface waves in an alternating electric field, its saturation due to the nonlinearity of the surface charge and the generation of nonlinear structures of this charge propagating along the boundary and depending on the parameters of external influence. The amplitude of saturation of the increasing plane waves was found as a result of stabilization of parametric instability by the nonlinear effect of the surface charge. An example of a nonlinear wave structure propagating along the surface of the boundary as a result of the interaction of an external electric field with a nonlinear surface charge is presented.

Shafranov shift correction to the Furth–Yoshikawa scaling of tokamak adiabatic compression

In 1970, Furth and Yoshikawa (1970 Phys. Fluids 13 2593–6) introduced the scalings of adiabatic plasma compression. Basically, if the shape of the external plasma boundary and the aspect ratio are preserved during the compression, then the density, kinetic pressure, beta and current scale respectively as , , , , , where C is the linear compression ratio, that is, the ratio between initial and final major radii. In this work, we show analytically, by expanding the Grad–Shafranov equation in terms of C, that the deviation to the Furth–Yoshikawa scaling is related to the Shafranov shift that arises when beta increases at large compression ratios. There is an obvious effect of the Shafranov shift because the axis is moved to a region with larger volume element, and an indirect effect, associated to the relation between flux and radius. The latter effect adds to the first, and is of the same order of magnitude. The result is that the pressure increases less than the C 5 scaling, which can have a significant impact on the fusion power achieved at maximum compression. The analytical results are backed up by equilibrium simulations carried out with the CHEASE code. Equilibria are obtained for different values of C, with conservation of the total fluxes, q profile, and entropy of the plasma. The agreement of the theory and simulations is very good when the boundary of the plasma is circular and the aspect ratio small. When the aspect ratio is close to 1, and/or the boundary not circular, the analytical result gives the gist of the reduction of compression. Finally, a pressure anisotropy approximately equal to the increase in normalized Shafranov shift is predicted.

A fast, accurate and easy to implement Kapur–Rokhlin quadrature scheme for singular integrals in axisymmetric geometries

Many applications in magnetic confinement fusion require the efficient calculation of surface integrals with singular integrands. The singularity subtraction approaches typically used to handle such singularities are complicated to implement and low-order accurate. In contrast, we demonstrate that the Kapur–Rokhlin quadrature scheme is well-suited for the logarithmically singular integrals encountered for a toroidally axisymmetric confinement system, is easy to implement and is high-order accurate. As an illustration, we show how to apply this quadrature scheme for the efficient and accurate calculation of the normal component of the magnetic field due to the plasma current on the plasma boundary, via the virtual-casing principle.

Toroidal vs cylindrical analytical description of the magnetic field outside the elongated evolving plasma in tokamaks

In the plasma equilibrium theory, Gajewski's analytical expression [Gajewski, Phys. Fluids 15, 70 (1972)] for the poloidal magnetic flux ψ outside the plasma is known. It was obtained as a solution of the two-dimensional Laplace equation outside an infinite straight cylinder with an elliptical cross section and a uniform current density j ζ. An example of its use for analysis of static configurations is given in the study by Porcelli and Yolbarsop [Phys. Plasmas 26, 054501 (2019)]. Here, we consider the question of its applicability in dynamic problems including, for example, the current quench (CQ) or vertical displacement event (VDE), when the electromagnetic response of the vacuum vessel to the plasma magnetic field evolution has to be accounted for. It is shown that the mentioned cylindrical model does not provide enough information for calculation of the current induced in the wall. Mathematically, this manifests itself in the fact that Gajewski's expression contains an indefinite constant of integration ψ b (hereinafter it is ψ at the plasma boundary), which, in analytical applications, is replaced either by zero or by a value that makes ψ = 0 on the magnetic axis. This does not affect the magnitude of the magnetic field B, but it would incorrectly give the electric field at ∂ B / ∂ t ≠ 0. To eliminate this shortcoming, an additional block of calculations in the toroidal geometry is needed. Here, the problem is solved analytically. The resulting final expression with ψ b well-defined in the toroidal configuration also includes the effects of the Shafranov's shift and inhomogeneity of j ζ. The proposed extensions allow generalization of the earlier results to a wider area and cover such events as CQ or VDE.

Effects of trapped electrons on the sheath at the boundary of a dusty plasma

In the present paper, the characteristic behaviors of the sheath in an unmagnetized dusty plasma that contained trapped electrons, cold ions, and variable-charged dusts are investigated, based on the Sagdeev potential approach. The result shows that both the formation and structure of the sheath are modified by the trapped electrons. At the sheath edge, the critical ion Mach number decreases as the trapping parameter β increases. It is noted that the effect of electron trapping on the ion-entering-sheath-velocity is indirect, and closely related to the dust charge variation. In the sheath, the increased β leads to the enlargement of the sheath thickness and the absolute value of electrostatic potential, which results in the redistribution of particle densities. Moreover, the results of the Maxwellian case are essentially recovered when β = 1. As expected, the present results can give more insight into the interaction processes that happened on the plasma-wall interface.

Collisionless dissipation at the boundary sheath of magnetized low temperature plasmas

In partially magnetized technological plasmas like magnetron discharges or Hall-effect thrusters, the interaction of gyrating electrons with the plasma boundary sheath plays an important role. This study shows that the interaction can be described as a dissipative process. It is assumed that the Debye length is much smaller than the electron gyroradius , and in turn much smaller than the mean free path λ and the field gradient length l. Focusing on the scale of the gyroradius, the sheath is assumed as thin (), collisions are neglected (), the magnetic field is taken as homogeneous, and electric fields (= potential gradients) in the bulk are neglected (). The interaction of an electron with the electric field of the plasma boundary sheath is represented by specular reflection, , where v is the electron velocity and n is the sheath normal. A previous study showed that this set-up leads to a scattering process where gyrophase invariant incoming velocity distributions are scattered into outgoing distributions with fractal dependence on the gyrophase (Krüger and Brinkmann 2017 Plasma Sources Sci. Technol. 26 115009). The present research focuses on the subsequent evolution. It is shown that the gyromotion results in fast phase mixing with respect to the gyrophase which quickly restores the gyrophase invariance. In combination, the two phases of the sheath interaction constitute a mapping within the space of gyrophase invariant distributions. This combined process is dissipative and leads to isotropization. As an explicit comparison shows, it acts similarly to elastic electron-neutral collisions and can even dominate the latter in low pressure plasmas. A simplified version of the operator that applies for weakly anisotropic distributions is suited for practical simulation work.

Development of the neutral model in the nonlinear MHD code JOREK: Application to E × B drifts in ITER PFPO-1 plasmas

The prediction of power fluxes and plasma-wall interactions impacted by MHD processes during ITER operation [disruption, Edge Localized Modes (ELMs), 3D magnetic fields applied for ELM control, etc.] requires models that include an accurate description of the MHD processes themselves, as well as of the edge plasma and plasma-wall interaction processes. In this paper, we report progress on improving the edge plasma physics models in the nonlinear extended MHD code JOREK, which has capabilities to simulate the MHD response of the plasma to the applied external 3D fields, disruptions and ELMs. The extended MHD model includes E × B drifts, diamagnetic drifts, and neoclassical flows. These drifts can have large influences, on e.g., divertor asymmetries. Realistic divertor conditions are important for impurity sputtering, transport, and their effect on the plasma. In this work, we implemented kinetic and fluid neutral physics modules, investigated the influence of poloidal flows under divertor conditions in the ITER PFPO-1 (1.8T/5MA) H-mode plasma scenario, and compared the divertor plasma conditions and heat flux to the wall for both the fluid and kinetic neutral model (in JOREK) to the well-established 2D boundary plasma simulation code suite SOLPS-ITER. As an application of the newly developed model, we investigated time-dependent divertor solutions and the transition from attached to partially detached plasmas. We present the formation of a high-field-side high-density-region and how it is driven by poloidal E × B drifts.

Optical plasma boundary detection and its reconstruction on EAST tokamak

Plasma boundary detection and reconstruction are important not only for plasma operation but also for plasma facing materials. Traditional methods, for example, EFIT code, which is constrained by electromagnetic measurement, and is very challenging for detecting the plasma boundary in long-pulse burning plasma devices such as ITER. A novel algorithm for the reconstruction of the plasma boundary using one visible camera has been developed on experimental advanced superconducting tokamak (EAST) for fusion reactors. A U-Net convolutional neural network was used to identify the plasma boundary and the pixel coordinates of the boundary points were fitted with EFIT via the XGBoost model. This algorithm can transform the boundary from the image plane to the poloidal plane of the Tokamak based on machine learning without traditional spatial calibration, and then the reconstruction of the plasma configuration shall be realized based on a monocular visible light camera. The reconstruction accuracy of this algorithm is relatively high. The average error on the test set was only 7.36 mm (<1 cm) and satisfied the accuracy requirements of control for EAST tokamak. This result can contribute to the development of the plasma boundary reconstruction and operation based on one visible camera.

Classification and Distribution of the Dayside Ion Upflows Associated with Auroral Particle Precipitation

Two important phenomena of the solar wind–magnetosphere–ionosphere coupling are auroral particle precipitation and the formation of ions flowing upward from the ionosphere. They have opposite transport directions of energy and substance. Based on the observations of particle precipitation and ion drift from the DMSP F13 satellite in January and July 2005, the ionospheric ion upflows in dayside auroral oval (0600–1800 MLT) can be divided into five types according to the velocity of ion upflows and the spectrum characteristics of auroral particle precipitation, and the distribution for different types of ion upflows is studied. The results show that the ion upflows mainly occur in the geomagnetic latitude (MLAT) range of 70–80°.The main magnetospheric source region of ion upflows (type A and D) caused by the accelerated electron (mainly the soft electron) corresponds to Low Latitude Boundary Layer (LLBL) and Cusp, and ion upflows of type B and C (related to the process of ambipolar diffusion caused by electron acceleration) mainly occur in LLBL and Boundary Plasma Sheet (BPS), while ion upflows of type E without electron acceleration mainly occur in the central plasma sheet (CPS).The dawn–dusk asymmetry is obvious in the winter season, with the ion upflows mainly occurring on the dawn/dusk side ionosphere. However, the ion upflows in summer mainly occur at the magnetic noon, with a symmetric distribution centered at the magnetic noon. The occurrence of ion upflow in winter is significantly higher than that in summer, and it is significantly enhanced during the period of moderate geomagnetic activity. The upward region expands to the lower latitude when the geomagnetic activity is enhanced. The effect of interplanetary magnetic field (IMF) components has also been studied in this paper. When IMF Bx is negative, the upflow occurrence increases in the region of 1500–1800 MLT and 0600–0900 MLT, with the MLAT range below 70°. The direction of IMF By may lead to the high-incidence area reverse at the prenoon or postnoon region. The occurrence of ion upflows with the MLAT range below 75° increases significantly when IMF is southward. Type A ion upflow has the highest velocity of ion upflows, followed by type E, and type D has the lowest. The average velocity of ion upflows in winter is significantly higher than that in summer.

Time-dependent SOLPS-ITER simulations of the tokamak plasma boundary for model predictive control using SINDy *

Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the sparse identification of nonlinear dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane and the electron temperature at the outer divertor . Note that is not necessarily the peak value of T e along the divertor. The identified reduced models are interpretable by construction (i.e. not black box), and have the form of coupled ordinary differential equations. Despite significant noise in , the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5% in and 5%–10% in for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A model predictive control strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in using the integrated plasma simulator framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.

Interferometric measurements of laser-induced shockwaves in air: Variable laser energy

When focused to a small spot size in air, a sufficiently energetic laser pulse initiates a rapidly expanding plasma. After a delay, a shockwave detaches from the plasma boundary and propagates. General features of the shockwaves can be deduced from condenser microphone measurements. However, the minimum range is limited by damage thresholds, and the presence of the microphone introduces a number of measurement artifacts. Distortion of the signal is caused by diffraction around the sensor, and the limited bandwidth does not allow rise times to be correctly quantified. In contrast, optical interferometry is a nonintrusive diagnostic for quantifying shockwave characteristics. In this study, a Nd:YAG laser is focused through a converging lens in order to generate laser-induced shockwaves. By using a variable attenuator, four laser energy outputs are examined: 25, 50, 75, and 100% of the maximum energy transmission. Heterodyne Mach–Zehnder interferometer measurements are made from 10 mm to 200 mm from the focal point of the lens. Virtual velocity signals, proportional to the time derivative of optical phase differences, are used to estimate density and pressure time histories, along with peak pressure as a function of distance.

Effects of Force in the Martian Plasma Environment With Solar Wind Dynamic Pressure Enhancement

AbstractDisturbed solar wind dynamic pressure is one of the important external drivers which could cause significant impacts on Martian plasma environment. In this study, a 3D multifluid multispecies numerical model is established to simulate the interaction between solar wind and Mars. Functions of electromagnetic forces applied on different ion species were analyzed. We found that the total electromagnetic force peaks near bow shock (BS) and magnetic pileup boundary (MPB) with clear asymmetry features, acting to decelerate solar wind plasma across boundary layers, and compresses heavy ions toward the planet inside the MPB. For solar wind protons, electron pressure gradient force dominates near BS and Hall electric field force dominates near MPB, controlling the location of plasma boundary. Furthermore, the morphology of motional electric field force shows clear north‐south asymmetry, leading to the formation of asymmetric structures and plasma flow in Martian space environment. The response of BS, MPB to a solar wind dynamic pressure enhancement event, as well as the effects of electromagnetic forces in this process are also investigated. After the arrival of solar wind pulse, the magnitudes of electromagnetic forces increased simultaneously to balance the enhanced solar wind dynamic pressure, while the peaks of forces moved inward with BS and MPB. The magnitudes and peaks of ion velocity in subsolar region show similar variations as well, with the greater enhancement of forces leading to the greater increase of ion velocities, indicating that the changes of forces influence boundary layers through the variation of plasma speed.

First 3D modelling of tungsten erosion and migration in WEST discharges adopting a toroidally non-symmetric wall geometry

Numerical analysis is a useful tool to investigate tungsten (W) sources and transport across plasma in W Environment Steady state Tokamak (WEST) plasma discharges, as it highlights physical mechanisms not always directly observable in experiments. Modelling activities were performed to study W erosion from WEST plasma-facing components (PFCs), as well as W migration through the plasma. For the first time, it was adopted a toroidally asymmetric wall geometry consisting of toroidally localized objects representing WEST antennas. To simulate WEST boundary plasma, 3D non-axisymmetric SOLEDGE transport simulations were performed with simplifying assumptions (pure deuterium plasma, a fluid model for neutrals). Results were then used as background for ERO2.0 runs to model W migration. On the sides of the toroidally localized objects, two thin stripes modelled WEST W antenna protections. Simulations suggest that particles eroded from the antennas protections may dominate the core W contamination in the analysed wall configuration. The findings suggest that these 3D non-axisymmetric models may be needed on a broader range of plasma conditions and wall configurations to accurately model the W migration in WEST.

Development of multi-band and high-speed visible endoscope diagnostic on EAST with catadioptric optics

A new multi-band and high-speed endoscope diagnostic for the observation of visible light has been successfully developed on the Experimental Advanced Superconducting Tokamak. The mirror with an aperture is designed at the head of the optical system. Based on two dichroic mirrors, the system is divided into three imaging mirror groups with different bands, i.e. B (380–500 nm), G (500–580 nm) and R (580–750 nm) bands, and its focal length is 16 mm with a relatively large aperture of D/f = 1:4. The spatial resolution is less than 5 mm near the object distance of with the camera NAC ACS-1 M60. This optical system will be used to contrastively study both the spatial distribution and time evolution of different impurities in the same field of view. The experimental results confirm that it can be applied to the recognition of plasma boundary and related physical research.

Terahertz radiation in the interaction of a focused laser pulse with plasma

The theory of terahertz (THz) wave emission at the oblique incidence of a focused s-polarized laser pulse on the boundary of a rarefied plasma is developed. The angular, spectral and energy characteristics of the THz signal as a function of the focal spot size and the incidence angle of laser radiation, as well as the plasma density, are investigated. It is shown that the THz radiation energy increases with a decrease in the laser pulse focal spot and has the maximum value when the tightly focused laser pulse is incident at the angle of total reflection on the plasma boundary.