High-beta Plasma Research Articles

Alfvén acoustic channel for ion energy in high-beta tokamak plasmas.

When the plasma beta (ratio of thermal to magnetic pressure) in the core of a tokamak is raised to values of several percent, as required for a thermonuclear fusion reactor, continuous spectra of long-wavelength slow magnetosonic waves enter the frequency band occupied by continuous spectra of shear Alfvén waves. It is found that these two branches can couple strongly, so that Alfvén modes that are resonantly driven by suprathermal ions transfer some of their energy to sound waves. Since sound waves are heavily damped by thermal ion Landau resonances, these results reveal a new energy channel that contributes to the damping of Alfvénic instabilities and the noncollisional heating of bulk ions, with potentially important consequences for confinement and fusion performance.

Simulation and quasilinear theory of proton firehose instability

The electromagnetic proton firehose instability is driven by excessive parallel temperature anisotropy, T∥ > T⊥ (or more precisely, parallel pressure anisotropy, P∥ > P⊥) in high-beta plasmas. Together with kinetic instabilities driven by excessive perpendicular temperature anisotropy, namely, electromagnetic proton cyclotron and mirror instabilities, its role in providing the upper limit for the temperature anisotropy in the solar wind is well-known. A recent Letter [Seough et al., Phys. Rev. Lett. 110, 071103 (2013)] employed quasilinear kinetic theory for these instabilities to explain the observed temperature anisotropy upper bound in the solar wind. However, the validity of quasilinear approach has not been rigorously tested until recently. In a recent paper [Seough et al., Phys. Plasmas 21, 062118 (2014)], a comparative study is carried out for the first time in which quasilinear theory of proton cyclotron instability is tested against results obtained from the particle-in-cell simulation method, and it was demonstrated that the agreement was rather excellent. The present paper addresses the same issue involving the proton firehose instability. Unlike the proton cyclotron instability, however, it is found that the quasilinear approximation enjoys only a limited range of validity, especially for the wave dynamics and for the relatively high-beta regime. Possible causes and mechanisms responsible for the discrepancies are speculated and discussed.

NON-THERMAL ELECTRON ACCELERATION IN LOW MACH NUMBER COLLISIONLESS SHOCKS. II. FIREHOSE-MEDIATED FERMI ACCELERATION AND ITS DEPENDENCE ON PRE-SHOCK CONDITIONS

Electron acceleration to non-thermal energies is known to occur in low Mach number (M<5) shocks in galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Using two-dimensional (2D) particle-in-cell (PIC) plasma simulations, we showed in Paper I that electrons are efficiently accelerated in low Mach number (M=3) quasi-perpendicular shocks via a Fermi-like process. The electrons bounce between the upstream region and the shock front, with each reflection at the shock resulting in energy gain via shock drift acceleration. The upstream scattering is provided by oblique magnetic waves, that are self-generated by the electrons escaping ahead of the shock. In the present work, we employ additional 2D PIC simulations to address the nature of the upstream oblique waves. We find that the waves are generated by the shock-reflected electrons via the firehose instability, which is driven by an anisotropy in the electron velocity distribution. We systematically explore how the efficiency of wave generation and of electron acceleration depend on the magnetic field obliquity, the flow magnetization (or equivalently, the plasma beta), and the upstream electron temperature. We find that the mechanism works for shocks with high plasma beta (>20) at nearly all magnetic field obliquities, and for electron temperatures in the range relevant for galaxy clusters. Our findings offer a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.

Magnetic control of magnetohydrodynamic instabilities in tokamaks

Externally applied, non-axisymmetric magnetic fields form the basis of several relatively simple and direct methods to control magnetohydrodynamic (MHD) instabilities in a tokamak, and most present and planned tokamaks now include a set of non-axisymmetric control coils for application of fields with low toroidal mode numbers. Non-axisymmetric applied fields are routinely used to compensate small asymmetries (δB/B∼10−3 to 10−4) of the nominally axisymmetric field, which otherwise can lead to instabilities through braking of plasma rotation and through direct stimulus of tearing modes or kink modes. This compensation may be feedback-controlled, based on the magnetic response of the plasma to the external fields. Non-axisymmetric fields are used for direct magnetic stabilization of the resistive wall mode—a kink instability with a growth rate slow enough that feedback control is practical. Saturated magnetic islands are also manipulated directly with non-axisymmetric fields, in order to unlock them from the wall and spin them to aid stabilization, or position them for suppression by localized current drive. Several recent scientific advances form the foundation of these developments in the control of instabilities. Most fundamental is the understanding that stable kink modes play a crucial role in the coupling of non-axisymmetric fields to the plasma, determining which field configurations couple most strongly, how the coupling depends on plasma conditions, and whether external asymmetries are amplified by the plasma. A major advance for the physics of high-beta plasmas (β = plasma pressure/magnetic field pressure) has been the understanding that drift-kinetic resonances can stabilize the resistive wall mode at pressures well above the ideal-MHD stability limit, but also that such discharges can be very sensitive to external asymmetries. The common physics of stable kink modes has brought significant unification to the topics of static error fields at low beta and resistive wall modes at high beta. These and other scientific advances, and their application to control of MHD instabilities, will be reviewed with emphasis on the most recent results and their applicability to ITER.

Electromagnetic effects on plasma blob-filament transport

Both microscopic and macroscopic impacts of the electromagnetic effects on blob dynamics are considered. Linear stability analysis and nonlinear BOUT++ simulations demonstrate that electromagnetic effects in high temperature or high beta plasmas suppress the resistive drift wave turbulence in the blob when resistivity drops below a certain value. In the course of blob’s motion in the SOL its temperature is reduced, which leads to enhancement of resistive effects, so the blob can switch from electromagnetic to electrostatic regime, where resistive drift wave turbulence become important. It is found that inhomogeneity of magnetic curvature or plasma pressure along the filament length leads to bending of the high-beta blob filaments. This is caused by the increase of the propagation time of plasma current (Alfvén time) in higher-density plasma. The effects of sheath boundary conditions on the part of the blob away from the boundary are also diminished by the increased Alfvén time.

COLLISIONLESS DAMPING OF CIRCULARLY POLARIZED NONLINEAR ALFVÉN WAVES IN SOLAR WIND PLASMAS WITH AND WITHOUT BEAM PROTONS

The damping process of field-aligned, low-frequency right-handed polarized nonlinear Alfven waves (NAWs) in solar wind plasmas with and without proton beams is studied by using a two-dimensional ion hybrid code. The numerical results show that the obliquely propagating kinetic Alfven waves (KAWs) excited by beam protons affect the damping of the low-frequency NAW in low beta plasmas, while the nonlinear wave-wave interaction between parallel propagating waves and nonlinear Landau damping due to the envelope modulation are the dominant damping process in high beta plasmas. The nonlinear interaction between the NAWs and KAWs does not cause effective energy transfer to the perpendicular direction. Numerical results suggest that while the collisionless damping due to the compressibility of the envelope-modulated NAW plays an important role in the damping of the field-aligned NAW, the effect of the beam instabilities may not be negligible in low beta solar wind plasmas.

Proton temperature-anisotropy-driven instabilities in weakly collisional plasmas: Hybrid simulations

Kinetic instabilities in weakly collisional, high beta plasmas are investigated using two-dimensional hybrid expanding box simulations with Coulomb collisions modeled through the Langevin equation (corresponding to the Fokker-Planck one). The expansion drives a parallel or perpendicular temperature anisotropy (depending on the orientation of the ambient magnetic field). For the chosen parameters the Coulomb collisions are important with respect to the driver but are not strong enough to keep the system stable with respect to instabilities driven by the proton temperature anisotropy. In the case of the parallel temperature anisotropy the dominant oblique fire hose instability efficiently reduces the anisotropy in a quasilinear manner. In the case of the perpendicular temperature anisotropy the dominant mirror instability generates coherent compressive structures which scatter protons and reduce the temperature anisotropy. For both the cases the instabilities generate temporarily enough wave energy so that the corresponding (anomalous) transport coefficients dominate over the collisional ones and their properties are similar to those in collisionless plasmas.

ARTEMIS observations of extreme diamagnetic fields in the lunar wake

We present two Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) observations of diamagnetic fields in the lunar wake at strengths exceeding twice the ambient magnetic field during high plasma beta conditions. The first observation was 350 km from the lunar surface while the Moon was located in the terrestrial magnetosheath with elevated particle temperatures. The second observation was in the solar wind ranging from 500 to 2000 km downstream, with a relatively low magnetic field strength of approximately 1.6 nT. In both cases, the plasma beta exceeded 10. We discuss the observations and compare the data to hybrid plasma simulations in order to validate the model under such extreme conditions and to elucidate the global structure of the lunar wake during these observations. The extreme nature of the diamagnetic field in the lunar wake provides an important end-member test case for theoretical and modeling studies of the various plasma processes operating in the lunar wake.

Role of energetic electrons during current ramp-up and production of high poloidal beta plasma in non-inductive current drive on QUEST

A scenario for non-inductive current ramp-up has been demonstrated using electron cyclotron waves in the spherical tokamak QUEST. The configuration was characterized by a high toroidal magnetic mirror ratio of 2 and a steady vertical magnetic field of more than 10% of the toroidal magnetic field. The generation and confinement of energetic electrons having energy greater than 10 keV were studied using hard x-rays. Because of the energetic electron pressure, a natural divertor formed with an inboard poloidal field null at the high poloidal beta (approximately 3–4).

MAGNETIC FIELD AMPLIFICATION AND EVOLUTION IN TURBULENT COLLISIONLESS MAGNETOHYDRODYNAMICS: AN APPLICATION TO THE INTRACLUSTER MEDIUM

The amplification and maintenance of the observed magnetic fields in the ICM are usually attributed to the turbulent dynamo action. This is generally derived employing a collisional MHD model. However, in the ICM the ion mean free path between collisions is of the order of the dynamical scales, thus requiring a collisionless MHD description. Unlike collisional MHD simulations, our study uses an anisotropic plasma pressure with respect to the direction of the local magnetic field, which brings the plasma within a parameter space where collisionless instabilities should take place. Within the adopted model these instabilities are contained at bay through the relaxation term of the pressure anisotropy which simulates the feedback of the mirror and firehose instabilities. This relaxation acts to get the plasma distribution function consistent with the empirical studies of collisionless plasmas. Our 3D numerical simulations of forced transonic turbulence motivated by modeling of the turbulent ICM are performed for different initial values of the magnetic field intensity, and different relaxation rates of the pressure anisotropy. We found that in the high beta plasma regime corresponding to the ICM conditions, a fast anisotropy relaxation rate gives results which are similar to the collisional-MHD model as far as the statistical properties of the turbulence are concerned. Also, the amplification of seed magnetic fields due to the turbulent dynamo action is similar to the collisional-MHD model. Our simulations that do not employ the anisotropy relaxation deviate significantly from the collisional-MHD results, and show more power at the small-scale fluctuations of both density and velocity representing the results of the instabilities. For these simulations the large scale fluctuations in the magnetic field are mostly suppressed and the turbulent dynamo fails in amplifying seed magnetic fields.

Resistive wall mode active control physics design for KSTAR

As KSTAR H-mode operation approaches the region where the resistive wall mode (RWM) can be unstable, an important issue for future long pulse, high beta plasma operation is to evaluate RWM active feedback control performance using a planned active/passive RWM stabilization system on the device. In particular, an optimal design of feedback sensors allows mode stabilization up to the highest achievable βN close to the ideal with-wall limit, βNwall, with reduced control power requirements. The computed ideal n = 1 mode structure from the DCON code has been input to the VALEN-3D code to calculate the projected performance of an active RWM control system in the KSTAR three-dimensional conducting structure device geometry. Control performance with the midplane locked mode detection sensors, off-midplane saddle loops, and magnetic pickup coils is examined. The midplane sensors measuring the radial component of the mode perturbation is found to be strongly affected by the wall eddy current. The off-axis saddle loops with proper compensation of the prompt applied field are computed to provide stabilization at βN up to 86% of βNwall but the low RWM amplitude computed in the off-axis regions near the sensors can produce a low signal-to-noise ratio. The required control power and bandwidth are also estimated with varied noise levels in the feedback sensors. Further improvements have been explored by examining a new RWM sensor design motivated by the off-midplane poloidal magnetic field sensors in NSTX. The new sensors mounted off of the copper passive stabilizer plates near the device midplane show a clear advantage in control performance corresponding to achieving 99% of βNwall without the need of compensation of the prompt field. The result shows a significant improvement of RWM feedback stabilization using the new sensor set which motivates a future feedback sensor upgrade.

Plasma pressure distribution in the surrounding the Earth plasma ring and its role in the magnetospheric dynamics

We analyzed the characteristics of the plasma region surrounding the Earth at the geocentric distances between 6 and 15RE using the data of THEMIS mission from April 2007 to September 2012. The obtained averaged distributions of plasma pressure, of pressure anisotropy, and of magnetic field near the equatorial plane showed the presence of a ring-shaped structure surrounding the Earth. It was found that for quiet geomagnetic conditions the plasma pressure is nearly isotropic for all magnetic local times at geocentric distances >6RE. Taking into consideration that the minimal values of the magnetic field at the field lines near noon are shifted from the equatorial plane, we estimate the value of plasma beta parameter in the region of minimal values of the magnetic field using the Tsyganenko-2001 magnetic field model. It was found that the values of plasma beta parameter are of the order of unity for the nightside part of the ring-shaped structure in the equatorial plane and for the region of minimal values of the magnetic field in the dayside, indicating that the ring-shaped structure should play an active role in the magnetic field distortion. Comparison of obtained distribution of plasma pressure at the equatorial plane with the values of plasma pressure at low altitudes, showed that the considerable part of the auroral oval can be mapped into the analyzed plasma ring. The role of the high-beta plasma ring surrounding the Earth for Earth–Sun System disturbances is discussed.

The turbulence evolution in the high β region of the Earth's foreshock

In this paper, we study the foreshock turbulence evolution in high β region via both Cluster observation on 29 March 2002 and 1‐D hybrid simulation. The quasi‐sinusoidal and the irregular wave trains are both detected in this event. The former one is believed to be generated by ion‐ion right‐hand nonresonant instability due to the right‐hand polarization and antisunward propagation in the plasma frame. Since the ion distribution associated with the wave train is more “intermediate” rather than “diffused”, we suggest that the wave train reported in this paper can be viewed as a “midstep” of “isolated” and “irregular”. From the quasi‐sinusoidal to the irregular waveform, the corresponding polarizations appear to transit: right‐hand wave of higher frequency (wave number) is substituted by a left‐hand wave with lower frequency (wave number) in spacecraft frame. Then the 1‐D hybrid simulation is applied for two cases with various velocities to study such polarization transition. By comparing observation results with the simulation, such polarization transition and “inversed cascade” (wave energy transferring from large wave number to small wave number) can be understood as the consequence of decay instability. Although decay instability cannot be initiated in high beta (β &gt; 1) plasma in magnetohydrodynamic theory, such β dependence can be modified by ion kinetic effect. Moreover, it is found that in simulation no matter which right‐hand instability is dominant in early stage, left‐hand wave will be the prime component of magnetic field disturbance in the final stage.

Three-dimensional numerical simulation of magnetohydrodynamic-gravity waves and vortices in the solar atmosphere

With the adaptation of the FLASH code we simulate magnetohydrodynamic-gravity waves and vortices as well as their response in the magnetized three-dimensional (3D) solar atmosphere at different heights to understand the localized energy transport processes. In the solar atmosphere strongly structured by gravitational and magnetic forces, we launch a localized velocity pulse (in horizontal and vertical components) within a bottom layer of 3D solar atmosphere modelled by initial VAL-IIIC conditions, which triggers waves and vortices. The rotation direction of vortices depends on the orientation of an initial perturbation. The vertical driver generates magnetoacoustic-gravity waves which result in oscillations of the transition region, and it leads to the eddies with their symmetry axis oriented vertically. The horizontal pulse excites all magnetohydrodynamic-gravity waves and horizontally oriented eddies. These waves propagate upwards, penetrate the transition region, and enter the solar corona. In the high-beta plasma regions the magnetic field lines move with the plasma and the temporal evolution show that they swirl with eddies. We estimate the energy fluxes carried out by the waves in the magnetized solar atmosphere and conclude that such wave dynamics and vortices may be significant in transporting the energy to sufficiently balance the energy losses in the localized corona. Moreover, the structure of the transition region highly affects such energy transports, and causes the channelling of the propagating waves into the inner corona.

Dispersion relation of electromagnetic ion cyclotron waves using Cluster observations

Abstract. Multi-point wave observations on Cluster spacecraft are used to infer the dispersion relation of electromagnetic ion cyclotron (EMIC) waves. In this study we use a phase differencing method and observations from STAFF and WHISPER during a well-studied event of 30 March 2002. The phase differencing method requires the knowledge of the direction of the wave vector, which was obtained using minimum variance analysis. Wave vector amplitudes were calculated for a number of frequencies to infer the dispersion relation experimentally. The obtained dispersion relation is largely consistent with the cold plasma dispersion relation. The presented method allows inferring the dispersion relation experimentally. It can be also used in the future to analyse the hot plasma dispersion relation of waves near the local gyrofrequency that can occur under high plasma beta conditions.

Low frequency Whistler waves excited in fast magnetic reconnection processes

Whistler waves generated in fast magnetic reconnection processes of collisionless high beta plasmas are reviewed in experiments and satellite observations, as well as in theory and simulation, and further studied in the two-fluid theory. It is found that low frequency whistler waves can be excited in the ion inertial range of the reconnection region. The wave is found right-handed polarized with a quadrupolar out-of-plane magnetic perturbation, in accord with satellite observations in the geomagnetosphere.

Progress in simulating turbulent electron thermal transport in NSTX

Nonlinear simulations based on multiple NSTX discharge scenarios have progressed to help differentiate unique instability mechanisms and to validate with experimental turbulence and transport data. First nonlinear gyrokinetic simulations of microtearing turbulence in a high-beta NSTX H-mode discharge predict experimental levels of electron thermal transport that are dominated by magnetic flutter and increase with collisionality, roughly consistent with energy confinement times in dimensionless collisionality scaling experiments. Electron temperature gradient (ETG) simulations predict significant electron thermal transport in some low- and high-beta discharges when ion scales are suppressed by E × B shear. Although the predicted transport in H-modes is insensitive to variation in collisionality (inconsistent with confinement scaling), it is sensitive to variations in other parameters, particularly density gradient stabilization. In reversed shear L-mode discharges that exhibit electron internal transport barriers, ETG transport has also been shown to be suppressed nonlinearly by strong negative magnetic shear, s ≪ 0. In many high-beta plasmas, instabilities which exhibit a stiff beta dependence characteristic of kinetic ballooning modes (KBMs) are sometimes found in the core region. However, they do not have a distinct finite beta threshold, instead transitioning gradually to a trapped electron mode (TEM) as beta is reduced to zero. Nonlinear simulations of this ‘hybrid’ TEM/KBM predict significant transport in all channels, with substantial contributions from compressional magnetic perturbations. As multiple instabilities are often unstable simultaneously in the same plasma discharge, even on the same flux surface, unique parametric dependencies are discussed which may be useful for distinguishing the different mechanisms experimentally.

Fusion alpha-particle losses in a high-beta rippled tokamak

In tokamak plasmas, the confinement of energetic ions depends on the magnetic field structure. If the plasma pressure is finite, the equilibrium current (i.e., the Pfirsch-Schlüter current and diamagnetic current) flows in the plasma to maintain the magnetohydrodynamic (MHD) equilibrium. These plasma currents generate poloidal and toroidal magnetic field and alter the field structure. Moreover, if we consider the non-axisymmetry of magnetic field structures such as toroidal field (TF) ripples, the non-axisymmetric component of the equilibrium current can alter TF ripples themselves. When the plasma beta becomes high, the changes in the field structure due to the equilibrium current might affect the confinement of energetic ions significantly. We intend to clarify how these currents alter the field structure and affect the confinement of alpha particles in high-beta plasma. The MHD equilibrium is calculated using VMEC and the orbits of fusion alpha particles are followed by using the fully three-dimensional magnetic field orbit-following Monte Carlo code. In relatively low-beta plasma (e.g., the volume-averaged beta value ⟨β⟩≤2%), the changes in the magnetic field component due to the plasma current negligibly affect the confinement of alpha particles except for the Shafranov shift effect. However, for ⟨β⟩≥3%, the diamagnetic effect reduces the magnetic field strength and significantly increases alpha-particle losses. In these high-beta cases, the non-axisymmetric field component generated by the equilibrium current also increases these losses, but not as effectively as compared to the diamagnetic effect.

A primitive kinetic-fluid model for quasi-parallel propagating magnetohydrodynamic waves

The extension and limitation of the existing one-dimensional kinetic-fluid model (Vlasov-MHD (magnetohydrodynamic) model), which has been used to analyze parametric instabilities of parallel propagating Alfvén waves, are discussed. The inconsistency among the given velocity distribution functions in the past studies is resolved through the systematic derivation of the multi-dimensional Vlasov-MHD model. The linear dispersion analysis of the present model indicates that the collisionless damping of the slow modes is adequately evaluated in low beta plasmas, although the deviation between the present model and the full-Vlasov theory increases with increasing plasma beta and increasing propagation angle. This is because the transit-time damping is not correctly evaluated in the present model. It is also shown that the ponderomotive density fluctuations associated with the envelope-modulated quasi-parallel propagating Alfvén waves derived from the present model is not consistent with those derived from the other models such as the Landau-fluid model, except for low beta plasmas. The result indicates the present model would be useful to understand the linear and nonlinear development of the Alfvénic turbulence in the inner heliosphere, whose condition is relatively low beta, while the existing model and the present model are insufficient to discuss the parametric instabilities of Alfvén waves in high beta plasmas and the obliquely propagating waves.

Effect of re-entering fast ions on NBI heating power in high-beta plasmas of the Large Helical Device

We calculate the heating power of the neutral beam injection (NBI) in a 〈β〉 = 4.8% high-beta discharge achieved in the Large Helical Device (LHD). We investigate the difference of the heating efficiency and the heating power profile with and without the re-entering fast ion effects. When the re-entering fast ion effects are taken into account, the heating efficiency of the co-injection of the NBI (co-NBI case) is improved and it is about 1.8 times larger than that without the re-entering effects. In contrast, the heating efficiency with the re-entering effects in the counter-injection of the NBI (ctr-NBI case) scarcely differs from that without the re-entering ones. We also study the re-entering fast ion effects on the transport properties in the LHD high-beta discharges. It is found that the tendency of the thermal conductivities on the beta value is not so much sensitive with and without the re-entering effects. In addition, we investigate the difference in the re-entering fast ion effects caused by the field strength and the magnetic configuration. In the co-NBI case, the heating efficiency with the re-entering effect was improved with a decrease in the field strength. In contrast, in the ctr-NBI case, it barely differs by changing the field strength.