High-beta Plasma Research Articles

Initial results from neoclassical tearing mode stabilization experiment in KSTAR high normalized beta plasmas

Abstract Active stabilization of neoclassical tearing modes (NTMs) is critical for high beta plasma operation in the KSTAR tokamak. In recent device operation, an experiment was conducted to develop a m/n = 2/1 NTM stabilization in high normalized beta (βN) plasmas having βN > 3 by using electron cyclotron current drive (ECCD). The experiment is designed to first demonstrate the direct mode stabilization effect of the device EC system by varying the ECCD deposition location around the mode rational surface to prepare for future NTM stabilization in KSTAR using feedback schemes. In the experiment, the toroidal magnetic field strength, BT, is reduced to 1.5–1.6 T to create a highly localized ECCD profile on a large island width expected to produce a high stabilization effect. To align the ECCD with the mode, BT is varied between discharges by keeping the EC wave injection angles fixed to move the current deposition location across the q = 2 mode rational surface in ~1 cm steps along the plasma midplane. The result shows a prompt reduction of the mode amplitude by ~60% with a partial recovery of the loss of stored energy when the ECCD with 0.7 MW power is applied promptly after the mode onset at BT = 1.54 T. This abrupt reduction of the mode amplitude is significantly weaker or disappears in other discharges having slightly different BT in which the ECCD is deposited a few centimeters away. This result indicates a direct interaction between the driven EC current and the radially localized island structure first observed in the device. The EC ray-tracing analysis using the TORAY code shows that the applied EC-driven current aligns with the mode rational surface when the mode amplitude is observed to decrease. The stability of the observed 2/1 NTM is examined by constructing the modified Rutherford equation (MRE). The calculated EC power requirement for complete mode stabilization by assuming perfect alignment of ECCD on the mode is 0.8-1.7 MW by considering the uncertainties in the equation. This MRE-computed mode stability agrees with the experiment. The result projects that the present KSTAR EC system can stabilize the 2/1 NTM disrupting high βN plasmas, and provides the requirement of the mode-ECCD alignment for complete mode stabilization in future experiments in which an accurate alignment is planned to be made by feedback schemes being developed.

Poloidal magnetic field reconstruction by laser-driven ion-beam trace probe in spherical tokamak

The poloidal magnetic field ( plays a critical role in plasma equilibrium, confinement and transport of magnetic confinement devices. Multiple diagnostic methods are needed to complement each other to obtain a more accurate profile. Recently, the laser-driven ion-beam trace probe (LITP) has been proposed as a promising tool for diagnosing and radial electric field ( ) profiles in tokamaks [Yang X Y et al 2014 Rev. Sci. Instrum. 85 11E429]. The spherical tokamak (ST) is a promising compact device with high plasma beta and naturally large elongation. However, when applying LITP to diagnosing in STs, the larger invalidates the linear reconstruction relationship for conventional tokamaks, necessitating the development of a nonlinear reconstruction principle tailored to STs. This novel approach employs an iterative reconstruction method based on Newton’s method to solve the nonlinear equation. Subsequently, a simulation model to reconstruct the profile of STs is developed and the experimental setup of LITP is designed for EXL-50, a middle-sized ST. Simulation results of the reconstruction show that the relative errors of reconstruction are mostly below 5%. Moreover, even with 5 mm measurement error on beam traces or 1 cm flux surface shape error, the average relative error of reconstruction remains below 15%, initially demonstrating the robustness of LITP in diagnosing profiles in STs.

Effect of parallel flow on resonant layer responses in high beta plasmas

Effect of parallel flow on resonant layer responses in high beta plasmas

NSTX-U research advancing the physics of spherical tokamaks

The objectives of NSTX-U research are to reinforce the advantages of STs while addressing the challenges. To extend confinement physics of low-A, high beta plasmas to lower collisionality levels, understanding of the transport mechanisms that set confinement performance and pedestal profiles is being advanced through gyrokinetic simulations, reduced model development, and comparison to NSTX experiment, as well as improved simulation of RF heating. To develop stable non-inductive scenarios needed for steady-state operation, various performance-limiting modes of instability were studied, including MHD, tearing modes, and energetic particle instabilities. Predictive tools were developed, covering disruptions, runaway electrons, equilibrium reconstruction, and control tools. To develop power and particle handling techniques to optimize plasma exhaust in high performance scenarios, innovative lithium-based solutions are being developed to handle the very high heat flux levels that the increased heating power and compact geometry of NSTX-U will produce, and will be seen in future STs. Predictive capabilities accounting for plasma phenomena, like edge harmonic oscillations, ELMs, and blobs, are being tested and improved. In these ways, NSTX-U researchers are advancing the physics understanding of ST plasmas to maximize the benefit that will be gained from further NSTX-U experiments and to increase confidence in projections to future devices.

Investigation of electromagnetic fluctuations in a magnetically screened high beta plasma

We report low-frequency electromagnetic turbulence in large-volume plasma devices in a region that receives magnetically screened plasma. The magnetic screen is produced by the activation of a large solenoid that generates a strong magnetic field ( BEEF ) transverse to the background axial magnetic field ( Bz ). The magnetic field strength variation in BEEF controls the plasma diffusion and is responsible for parametric profile modifications in large volume plasma devices. The turbulence is characterized by the observed features of an electromagnetic mode having frequency ordering in the lower hybrid range (f ci < f < f LH). The free energy source for the excited turbulence is believed to be the prevalent finite radial pressure gradient in the system. The excited electromagnetic mode shows typical scales for the wave number, k⊥ ∼ 0.13 cm−1 and frequency f ∼ 6 kHz and propagates with phase velocity comparable to ion acoustic velocity, C s in electron diamagnetic drift direction. It is believed that the low-frequency pressure gradient-driven electromagnetic mode exhibits coupling with the lower hybrid or whistler wave.

Ion heating characteristics of merging spherical tokamak plasmas for burning high-beta plasma formation

High-power ion heating of merging spherical tokamak (ST) plasma has been investigated using TS-3U, TS-4, and UTST at the University of Tokyo for future direct access to burning high-beta ST plasma without using any additional heating. We developed a two-fluid/kinetic interpretation of the promising scaling of ion heating energy that increases with the square of reconnecting magnetic field B rec ∼ poloidal magnetic field B p. We find that reconnection heating creates interesting high-beta ST plasmas with hollow currents and broad/hollow T i profiles. These high-beta ST plasmas often have reversed-shear or absolute minimum-B profiles, depending on their reconnection heating power and q-values.

Quasi-perpendicular shocks of galaxy clusters in hybrid kinetic simulations

Context. Cosmic ray acceleration in galaxy clusters is still an ongoing puzzle, with relativistic electrons forming radio relics at merger shocks and emitting synchrotron radiation. These shocks are also potential sources of ultra-high-energy cosmic rays, gamma rays, and neutrinos. Our recent work focuses on electron acceleration at low Mach number merger shocks in the hot intracluster medium which is characterized by high plasma beta. Using particle-in-cell (PIC) simulations, we previously showed that electrons are energized through the stochastic shock-drift acceleration process, which is facilitated by multi-scale turbulence, including ion-scale shock surface rippling. For the present work, we performed hybrid-kinetic simulations in a range of various quasi-perpendicular foreshock conditions, including plasma beta, magnetic obliquity, and the shock Mach number. Aims. We study the ion kinetic physics, which is responsible for the shock structure and wave turbulence, that in turn affects the particle acceleration processes. We cover the spatial and temporal scales, which allow the development of large-scale ion turbulence modes in the system. Methods. We applied a recently developed generalized fluid-particle hybrid numerical code that can combine fluid modeling for both electrons and ions with an arbitrary number of kinetic species. We limited this model to a standard hybrid simulation configuration with kinetic ions and fluid electrons. The model utilizes the exact form of the generalized Ohm’s law, allowing for an arbitrary choice of mass and energy densities, as well as the charge-to-mass ratio of the kinetic species. Results. We show that the properties of ion-driven multi-scale magnetic turbulence in merger shocks are in agreement with the ion structures observed in PIC simulations. In typical shocks with the sonic Mach number Ms = 3, the magnetic structures and shock front density ripples grow and saturate at wavelengths reaching approximately four ion Larmor radii. Only shocks with Ms ≳ 2.3 develop ripples. At very weak shocks with Ms ≲ 2.3, weak turbulence is formed downstream of the shock. We observed a moderate dependence of the strength of magnetic field fluctuations on the quasi-perpendicular magnetic field obliquity. However, as the field obliquity decreases, the shock front ripples exhibit longer wavelengths. Finally, we note that the steady-state structure of Ms = 3 shocks in high-beta plasmas shows evidence that there is little difference between 2D and 3D simulations. The turbulence near the shock front seems to be a 2D-like structure in 3D simulations.

Effects observed in numerical simulation of high-beta plasma with hot ions in an axisymmetric mirror machine

We present the results of numerical simulation by two-dimensional hybrid particle-in-cell code of high-beta plasma with hot ions in an axisymmetric mirror machine. Two particular effects are discussed: the self-rotating of plasma with Maxwellian ions in regime of diamagnetic confinement and the excitation of axisymmetric magnetosonic waves in a high-beta plasma with sloshing ions.

Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry

Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations.

Kinetic numerical analysis of electromagnetic ion cyclotron instability in non-thermal Vasyliunas-Cairns distributed plasmas

Enhanced fluctuations driven by non-thermal features of particle-distributions are reported frequently in the variety of space plasma observations. In the rare-collisional plasmas, these amplified fluctuations scatter the particles in various direction and governs the dynamics of space plasma environments effectively. Electromagnetic ion cyclotron (EMIC) waves usually responsible for low frequency interplanetary magnetic field fluctuations. These are natural emissions in numerous natural environments of plasmas which usually operates underneath the ion/proton cyclotron frequencies. These are identified as left hand circular polarization (L-mode) with a propagation directed towards the ambient magnetic field. Various space missions and in situ measurements unveil the perpendicular temperature anisotropies of non-thermal populations of ions/protons i.e. in heliospheric regions and solar wind. These proton temperature anisotropies excite EMIC instability which in turn the pitch angle scatters the ions and restrained the anisotropy in certain ranges. In Vasyliunas-Cairns distributed hybrid non-thermal electromagnetic proton plasma, the transverse dielectric response function (TDERF) is calculated for L-mode. It is then numerically solved in order to show the impact of non-thermal populations due to non-thermal parameters α and κ on the dispersion and growth rates of EMIC instability in low and high plasma beta β regimes. Possible variation in the real oscillatory and imaginary frequencies spectrum is also analyzed with the variation in the values of other pertinent parameters i.e. temperature anisotropy τ and β. The parametric numerical analysis of the present work has relevance about that plasma phenomena of space regions where non-thermal distributed populations are prevalent.

Solar Wind Parameters Influencing Magnetosheath Jet Formation: Low and High IMF Cone Angle Regimes

AbstractMagnetosheath jets are localized flows of enhanced dynamic pressure that are frequently observed downstream of the Earth's bow shock. They are significantly more likely to occur downstream of the quasi‐parallel shock than the quasi‐perpendicular shock. However, as the quasi‐perpendicular geometry is a more common configuration at the Earth's subsolar bow shock, quasi‐perpendicular jets comprise a significant fraction of the observed jets. We study the influence of solar wind conditions on jet formation by looking separately at jets during low and high interplanetary magnetic field (IMF) cone angles. According to our results, jet formation commences when Alfvén Mach number MA ≳ 5. We find that during low IMF cone angles (downstream of the quasi‐parallel shock) other solar wind parameters do not influence jet occurrence. However, during high IMF cone angles (downstream of the quasi‐perpendicular shock) jet occurrence is higher during low IMF magnitude, low density, high plasma beta (β), and high MA conditions. The distribution of quasi‐parallel (quasi‐perpendicular) jet sizes parallel to flow peaks at ∼0.3 RE (∼0.1 RE). Some quasi‐perpendicular jets formed during high β and MA are particularly small. We show two examples of high β and MA quasi‐perpendicular shock crossings. Jets were observed in the transition region, but not deeper in the magnetosheath. A more detailed look into one jet revealed signatures of gyrating ions, indicating that gyrobunched ions near the shock may produce jet‐like enhancements. Our results suggest that jets form as part of the quasi‐perpendicular shock dynamics amplified by high solar wind MA and β.

Gyro orbit simulations of neutral beam injection in Wendelstein 7-X

Simulations exploring neutral beam operation in Wendelstein 7-X (W7-X) at reduced magnetic field are performed using a newly implemented gyro orbit model in the BEAMS3D code. Operation at field strengths below the nominal 2.5 T are seen as a path to explore both high beta plasmas and as a means to access magnetic configurations not possible at 2.5 T. As the field strength becomes smaller, the gyro radius for 55 keV fast protons grows from at 2.5 T to at 0.75 T in a device with minor radius bringing into question the applicability of the gyro center approximation. To address this a gyro orbit model was implemented in the BEAMS3D code. Agreement is found between the gyro center and gyro orbit models in a circular cross section tokamak equilibrium at high field. A set of W7-X equilibria are assessed with fixed density and temperature profiles but decreasing magnetic field strength (increasing plasma beta). Neutral beam deposition is found to be mostly unaffected with changes in the core of the plasma associated with the Shafranov-shift. In general good agreement is found between gyro orbit and gyro center simulations at 2.5 T. Both models indicate increasing losses with decreasing magnetic field strength with the gyro orbit losses being higher at all field strengths. Gyro orbit simulations to the first wall of W7-X show a change in loss pattern with decreasing magnetic field strength. A preliminary assessment of losses to fast ion loss detectors are made.

Pressure anisotropy and viscous heating in weakly collisional plasma turbulence

Pressure anisotropy can strongly influence the dynamics of weakly collisional, high-beta plasmas, but its effects are missed by standard magnetohydrodynamics (MHD). Small changes to the magnetic-field strength generate large pressure-anisotropy forces, heating the plasma, driving instabilities and rearranging flows, even on scales far above the particles’ gyroscales where kinetic effects are traditionally considered most important. Here, we study the influence of pressure anisotropy on turbulent plasmas threaded by a mean magnetic field (Alfvénic turbulence). Extending previous results that were concerned with Braginskii MHD, we consider a wide range of regimes and parameters using a simplified fluid model based on drift kinetics with heat fluxes calculated using a Landau-fluid closure. We show that viscous (pressure-anisotropy) heating dissipates between a quarter (in collisionless regimes) and half (in collisional regimes) of the turbulent-cascade power injected at large scales; this does not depend strongly on either plasma beta or the ion-to-electron temperature ratio. This will in turn influence the plasma's thermodynamics by regulating energy partition between different dissipation channels (e.g. electron and ion heat). Due to the pressure anisotropy's rapid dynamic feedback onto the flows that create it – an effect we term ‘magneto-immutability’ – the viscous heating is confined to a narrow range of scales near the forcing scale, supporting a nearly conservative, MHD-like inertial-range cascade, via which the rest of the energy is transferred to small scales. Despite the simplified model, our results – including the viscous heating rate, distributions and turbulent spectra – compare favourably with recent hybrid-kinetic simulations. This is promising for the more general use of extended-fluid (or even MHD) approaches to model weakly collisional plasmas such as the intracluster medium, hot accretion flows and the solar wind.

Theory and Transport of Nearly Incompressible Magnetohydrodynamic Turbulence: High Plasma Beta Regime

Nearly incompressible magnetohydrodynamic (NI MHD) theory for β ∼ 1 (or β ≪ 1) plasma has been developed and applied to the study of solar wind turbulence. The leading-order term in β ∼ 1 or β ≪ 1 plasma describes the majority of 2D turbulence, while the higher-order term describes the minority of slab turbulence. Here, we develop new NI MHD turbulence transport model equations in the high plasma beta regime. The leading-order term in a β ≫ 1 plasma is fully incompressible and admits both structures (flux ropes or magnetic islands) and slab (Alfvén waves) fluctuations. This paper couples the NI MHD turbulence transport equations with three fluid (proton, electron, and pickup ion) equations, and solves the 1D steady-state equations from 1–75 au. The model is tested against 27 yr of Voyager 2 data, and Ulysses and NH SWAP data. The results agree remarkably well, with some scatter, about the theoretical predictions.

Fundamental Scaling of Adiabatic Compression of Field Reversed Configuration Thermonuclear Fusion Plasmas

Field Reversed Configuration (FRC) plasmas are plasma devices that have demonstrated that through magnetic compression they can be heated to thermonuclear fusion conditions in the parameter space of an energy-producing generator Kirtley et al. (IEEE Symposium on Fusion Engineering, 2021). Of particular interest, FRCs are high-beta, in that the plasma particle kinetic energy is in balance with an externally applied magnetic field at all stages of operation. The following work will show that a cylindrical approximation for the energy and particle distribution within an FRC can, within 11%, match the fusion performance results of both full Magnetohydrodynamic (MHD) simulations as well as all robust, modern theoretical spatial and energy distribution models. Further, by using the simplified cylindrical model, detailed fusion reaction, radiation, and energy transport equations are now numerically-tractable and can be modelled over a wide parameter space. In the second section of this work, a detailed numerical model will be presented with the key theoretical performance of the compression of high-beta fusion plasmas in both deuterium–tritium (D–T) and deuterium–helium-3 (D–He-3) fuels. As will be shown, a high-beta D–He-3 plasma outperforms a low-beta D–T fuel and can theoretically yield a net-positive fusion generator.

RF conditioning to suppress multipactor discharge for helicon wave current drive in KSTAR

The efficient off-axis non-inductive current drive using auxiliary power is essential for the steady state operation of tokamaks. In previous studies, a helicon wave current drive has been proposed for high beta plasma in several fusion devices, and the 476-MHz radio-frequency (RF) system for the proposed helicon wave has been installed in KSTAR. However, multipactor discharge occurred inside the waveguide system, including the vacuum feedthrough (VFT), and it interrupted the normal RF propagation to plasma. Thus, for successful helicon wave current drive, suppressing the multipactor discharge in the waveguide system, including the 6–1/8″ coaxial type VFT and the newly manufactured helical type traveling wave antenna (TWA) is essential before installation in KSTAR. RF conditioning utilizing a short pulse modulation during a long period helps suppress the multipactor discharge, enabling the 1-MW 476-MHz RF to pass through the entire waveguide system despite the existence of multipactor discharge. Following RF conditioning in VFT with a short pulse modulation, the newly manufactured helical type TWA and VFT for helicon wave current drive have been successfully installed in KSTAR.

Wall stabilization of high-beta anisotropic plasmas in an axisymmetric mirror trap

The stabilization of the ‘rigid’ flute and ballooning modes both with and without the effect of additional MHD anchors in an axisymmetric mirror trap, with the help of a perfectly conducting lateral wall, is studied using a model pressure distribution of a plasma with a steep-angle neutral beam injection at the magnetic field minimum. The calculations were performed for an anisotropic plasma in a model that simulates the pressure distribution during the injection of beams of fast neutral atoms into the magnetic field minimum. It is assumed that the lateral wall is an axisymmetric shell surrounding the plasma that follows the shape of the magnetic field line and is placed at a certain distance to the plasma border. It has been found that for the effective stabilization of the modes by the lateral wall only the parameter beta (β, ratio of plasma pressure to the magnetic field pressure) must exceed some critical value β crit. When combined with the conducting end plates imitating the MHD end stabilizers, there are two critical beta values and two stability zones and that can merge, making the entire range of allowable beta values stable. The dependence of the critical betas on the degree of plasma anisotropy, the mirror ratio, and the width of the vacuum gap between the plasma and the lateral wall is studied. In contrast to the previous studies focusing on a plasma model with a sharp boundary, we calculated the stability zones for a number of diffuse radial pressure profiles and several axial magnetic field profiles.

Integration of high confinement, high poloidal beta plasma with dual radiated power and detachment controls for divertor protection and ELM suppression

Integration of high confinement, high poloidal beta plasma with dual radiated power and detachment controls for divertor protection and ELM suppression

The ECRH-Power Upgrade at the Wendelstein 7-X Stellarator

The existing ECRH system at W7-X consists of 10 gyrotrons, with output power levels ranging from 0.6 MW up to 1.0 MW each at a frequency of 140 GHz, quasi-optical transmission lines and microwave launchers at the plasma vessel. Compared to other large fusion experiments, W7-X has a relatively low power-to-volume ratio. However high heating power is particularly necessary for achieving high plasma beta values, where the improved confinement of fast ions, one of the optimization criteria of W7-X, can be examined. It is therefore necessary to expand the ECRH systems in several consecutive steps. It is planned to increase the number of gyrotron positions from 10 to 12 and at the same time to evolve the gyrotron output power in several development steps from 1 MW to nominal 1.5 MW and, finally, up to 2 MW. At the same time, the transmission lines will also be upgraded for 2 MW operation. A special effort is also made to improve the reliability of the system by the fast control system.

As a Matter of Dynamical Range – Scale Dependent Energy Dynamics in MHD Turbulence

Magnetized turbulence is ubiquitous in many astrophysical and terrestrial plasmas but no universal theory exists. Even the detailed energy dynamics in magnetohydrodynamic (MHD) turbulence are still not well understood. We present a suite of subsonic, super-Alfvénic, high plasma beta MHD turbulence simulations that only vary in their dynamical range, i.e., in their separation between the large-scale forcing and dissipation scales, and their dissipation mechanism (implicit large eddy simulation, ILES, and direct numerical simulation (DNS)). Using an energy transfer analysis framework we calculate the effective numerical viscosities and resistivities, and demonstrate that all ILES calculations of MHD turbulence are resolved and correspond to an equivalent visco-resistive MHD turbulence calculation. Increasing the number of grid points used in an ILES corresponds to lowering the dissipation coefficients, i.e., larger (kinetic and magnetic) Reynolds numbers for a constant forcing scale. Independently, we use this same framework to demonstrate that—contrary to hydrodynamic turbulence—the cross-scale energy fluxes are not constant in MHD turbulence. This applies both to different mediators (such as cascade processes or magnetic tension) for a given dynamical range as well as to a dependence on the dynamical range itself, which determines the physical properties of the flow. We do not observe any indication of convergence even at the highest resolution (largest Reynolds numbers) simulation at 20483 cells, calling into question whether an asymptotic regime in MHD turbulence exists, and, if so, what it looks like.