Cross-field Flow Research Articles

Electric field effects during disruptions

Tokamak disruptions are associated with breaking magnetic surfaces, which makes magnetic field lines chaotic in large regions of the plasma. The enforcement of quasi-neutrality in a region of chaotic field lines requires an electric potential that has both short and long correlation distances across the magnetic field lines. The short correlation distances produce a Bohm-like diffusion coefficient ∼Te/eB and the long correlation distances aT produce a large scale flow ∼Te/eBaT. This cross-field diffusion and flow are important for sweeping impurities into the core of a disrupting tokamak. The analysis separates the electric field in a plasma into the sum of a divergence-free, E→B, and a curl-free, E→q, part, a Helmholtz decomposition. The divergence-free part of E→ determines the evolution of the magnetic field. The curl-free part enforces quasi-neutrality, E→q=−∇→Φq. Magnetic helicity evolution gives the required boundary condition for a unique Helmholtz decomposition and an unfortunate constraint on steady-state tokamak maintenance.

Conceptual design of a Doppler spectrometer for 102m/s cross-field flows in tokamak divertors.

The cross-field transport in the scrape-off-layers (SOLs) and divertors in tokamaks is of a similar size to the poloidal component of the parallel flow, thereby significantly impacting the plasma transport there. However, its direct observation has been challenging because the drift velocity (102-103 m/s) is significantly below the detection limit of conventional diagnostics. To realize cross-field ion flow measurement, a variety of systematic uncertainties in the system must be narrowed down. Here, we develop a conceptual design of the Doppler spectrometry that enables us to measure the impurity flows with 102-m/s accuracy based on an in situ wavelength-calibration technique developed in the astrophysics field, the iodine-cell method. We discuss its properties and applicability. In particular, the scaling relation between wavelength accuracy and various spectroscopic parameters is newly presented, which suggests the high importance of the wavelength resolution of the system. Based on transport simulations for the JT-60SA divertor, the feasibility of the system is assessed.

Filamentary transport in global edge-SOL simulations of ASDEX Upgrade

The understanding and the predictive capability for turbulence in the plasma edge and scrape-off layer (SOL) are crucial for the development of magnetic confinement fusion reactors. To this end, we characterise turbulent transport across the edge and SOL of the diverted ASDEX Upgrade tokamak in attached L-mode conditions by means of validated, global simulations. The collisionality is controlled by the divertor neutrals density, as their ionization increases the plasma density and decreases the temperature. The radial E×B particle and heat transport, quantified by effective diffusivities, rises strongly with collisionality. The modest increase in fluctuation amplitudes is not a sufficient explanation. The reason is shown to be the destabilisation of resistive drift-ballooning modes, resulting in larger phase shifts between the pressure and electrostatic potential. The transport varies both radially and poloidally. Due to its ballooning nature, radial transport is close to zero on the inboard mid-plane. On the outboard mid-plane, significant transport is driven in the SOL by large filaments (blobs) with amplitudes of up to 250% of the mean, propagating ballistically from the separatrix to the wall. This non-local transport leads to large radial variations of diffusivities, as they do not necessarily correlate with the local gradient. Ion temperature fluctuations in the plasma edge are shown to be involved in blob seeding at the separatrix, and are the largest in the SOL. Radial diffusivities peak at the top and bottom of the device, since gradients are flatter there due to the flux expansion while the cross-field flow is sustained by streamers—a feature which should be considered in mean-field transport modeling. The increase of SOL E×B transport with collisionality is likely fostered by the simultaneously decreasing radial electric field, resulting from a flattened electron temperature profile. Large amplitude blobs are a hazard for plasma facing components of fusion reactors, but they could be restrained by control of SOL collisionality.

Electron cyclotron drift instability and anomalous transport: two-fluid moment theory and modeling

In the presence of a strong electric field perpendicular to the magnetic field, the electron cross-field (E × B) flow relative to the unmagnetized ions can cause the so-called electron cyclotron drift instability (ECDI) due to resonances of the ion acoustic mode and the electron cyclotron harmonics. This occurs in, for example, collisionless shock ramps in space, and in E × B discharge devices such as Hall thrusters. A prominent feature of ECDI is its capability to induce an electron flow parallel to the background E field at a speed greatly exceeding predictions by classical collision theory. Such anomalous transport is important due to its role in particle thermalization at space shocks, and in causing plasma flows towards the walls of E × B devices, leading to unfavorable erosion and performance degradation, etc. The development of ECDI and anomalous transport is often considered requiring a fully kinetic treatment. In this work, however, we demonstrate that a reduced variant of this instability, and more importantly, the associated anomalous transport, can be treated self-consistently in a collisionless two-fluid framework without any adjustable collision parameter. By treating both electron and ion species on an equal footing, the free energy due to the inter-species velocity shear allows the growth of an anomalous electron flow parallel to the background E field. We will first present linear analyses of the instability in the two-fluid five- and ten-moment models, and compare them against the fully-kinetic theory. At low temperatures, the two-fluid models predict the fastest-growing mode in good agreement with the kinetic result. Also, by including more moments, secondary (and possibly higher) unstable branches can be recovered. The dependence of the instability on ion-to-electron mass ratio, plasma temperature, and background B field strength is also thoroughly explored. We then carry out direct numerical simulations of the cross-field setup using the five-moment model. The development of the instability, as well as the anomalous transport, is confirmed and in excellent agreement with theoretical predictions. The force balance properties are also studied using the five-moment simulation data. This work casts new insights into the nature of ECDI and the associated anomalous transport and demonstrates the potential of the two-fluid moment model in efficient modeling of E × B plasmas.

Three-dimensional cross-field flows at the plasma-material interface in an oblique magnetic field

This article describes experimental evidence that the magnetic presheath is a fully three-dimensional structure modified by ion–neutral collisions. Velocity distributions of both ions and neutrals, obtained via laser-induced fluorescence, show that cross field ion drifts do not result from entrainment of ions in a flowing neutral background. Ion flows parallel to E×B arise and accelerate to as much as 0.2cs within several ion gyroradii of the boundary surface, where cs is the sound speed. Within measurement resolution, the onset of the E×B aligned flow occurs at the same distance to the surface that ions begin to deflect from travel along magnetic field lines. Collisional fluid and particle-in-cell simulations of the boundary region are compared to the experimental measurements. We find that, in contrast to the classical collisionless Chodura model, collisional effects between the ions and the non-flowing neutral population are essential to quantitatively predict the observed ion drift velocities. No momentum coupling between ions and neutrals, separable from noise and other effects, is observed in either signal. We discuss several explanations and implications of this observation.

Direct measurements of classical and enhanced gradient-aligned cross-field ion flows in a helicon plasma source using laser-induced fluorescence

Direct laser induced fluorescence measurements are shown of cross-field ion flows normal to an absorbing boundary that is aligned parallel to the axial magnetic field in a helicon plasma. We show Langmuir and emissive probe measurements of local density and plasma potential in the same region, as well as floating probe spectra near the boundary. With these measurements, we investigate the influence of ion-neutral collisionality on radial ion transport by varying the ratio of the ion gyro-radius, ρi, to the ion-neutral collision length, λ, over the range 0.34 ≤ ρiλ−1 ≤ 1.60. Classical drift-diffusion transport along density and potential gradients is sufficient to describe flow profiles for most cases. For two parameter regimes (ρiλ−1 = 0.65 and 0.44), low-frequency electrostatic fluctuations (f < 10 kHz) and enhanced cross-field bulk ion flow to the boundary are observed.

Cross-field flow and electric potential in a plasma slab

Abstract. We consider cross-field plasma flow inside a field-aligned plasma slab embedded in a uniform background in a 1-dimensional geometry. This situation may arise, for instance, when long-lasting reconnection pulses inject plasma into the inner magnetosphere. The present paper presents a detailed analysis of the structure of the interfaces that separate the slab from the background plasma on either side; a fully kinetic model is used to do so. Since the velocity shear across both interfaces has opposite signs, and given the typical gyroradius differences between injected and background ions and electrons, the structure of both interfaces can be very different. The behaviour of the slab and its interfaces depends critically on the flow of the plasma transverse to the magnetic field; in particular, it is shown that there are bounds to the flow speed that can be supported by the magnetised plasma. Further complicating the picture is the effect of the potential difference between the slab and its environment.

Magnetohydrodynamic turbulent cascade of coronal loop magnetic fields

The Parker model for coronal heating is investigated through a high resolution simulation. An inertial range is resolved where fluctuating magnetic energy EMk[Please see symbol]) [Please see symbol] k[Please see symbol](-2.7) exceeds kinetic energy EK(k[Please see symbol])[Please see symbol]k[Please see symbol](-0.6). Increments scale as δbℓ ~/= ℓ(-0.85) and δuℓ ~/= ℓ(+0.2) with velocity increasing at small scales, indicating that magnetic reconnection plays a prime role in this turbulent system. We show that spectral energy transport is akin to standard magnetohydrodynamic (MHD) turbulence even for a system of reconnecting current sheets sustained by the boundary. In this new MHD turbulent cascade, kinetic energy flows are negligible while cross-field flows are enhanced, and through a series of "reflections" between the two fields, cascade more than half of the total spectral energy flow.

“Multi-layer” one-dimensional model for stability analysis on partially detached divertor plasmas

We propose a “multi-layer (ML)” 1D model for understanding behaviors of partially detached divertor plasmas. The basic idea is to analyze interaction among the adjacent flux tubes for the attached and detached states in the divertor region. Cross-field transport terms in both SOL and divertor regions are considered in this model. We show some preliminary simulations which indicate necessity of the ML 1D model. According to the simulations, cross-field energy flow in the divertor region can affect stability of a detachment front of partially detached plasmas, i.e. such flow can decrease the front speed towards the X point.

Vector and Scalar Tomography of Compact Toroid Plasmas

Multichannel spectroscopic diagnostics have been installed on the TS-4 compact toroid experiment at the University of Tokyo with view chords designed for measuring 2D ion bulk flow velocities and temperatures. Computerized vector tomography reconstructs velocities from the Doppler-shifted line shapes and scalar emissivity from the scalar tomography of the zeroth moment measurements. The first results show bulk ion flow field in a 2D plane with significant cross-field flow possibly due to the slingshot effect during reconnection merging of two counter-helicity spheromaks. The results are limited by a center column and available viewports in the vacuum chamber. This proof-of-principle experiment shows that, with increased access, 3D velocity flow fields can be completely reconstructed in compact toroid plasma experiments.

Development of fully 3-D numerical model for cross-field swirling flow simulation

Swirling flow plays an important role in many engineering applications. Its function not only can increase the fuel/air mixing effect, but also can create a recirculation region in the downstream to stabilize the flame. Since the geometry of the boiler is irregular and with several wall-burners, a fully 3-D numerical modelfor flow field simulation is required. For validation, the axi-symmetric swirling flow field is first calculated and used to compare with Lilley's measured date. Next, the confinement geometry is changed from round to rectangle and the injection area ratio is varied to study the recirculation flow behavior. In the following,the effect of four swirling flow injection interactions on the whole flow field structure will be discussed. The results show that the case with single entry the rectangular boundary creates a secondary flow and squeezing the recirculation zone to force it stretches. The degree of squeezing depends upon the expansion area ratio. However, the results with four entries show that the shape of recirculation zone of each burner is strongly dependent on the whole cross-field structure. In addition, the interactions of four swirl jets result in the formation of a central recirculation zone. The degree of the effect is strongly related to the inlet swirl strength.

Growth of resistive instabilities in E×B plasma discharge simulations

Two-dimensional hybrid numerical simulations of E×B discharges used in Hall thruster propulsion point to the presence of strong fluctuations attributable to resistive instabilities in the frequency range of f≈0.1–10MHz and the wavenumber range of λ−1≈10–500m−1. Analytical analyses confirm that these resistive modes are of the convective type, become increasingly unstable at low electron mobility, and are particularly intense at high voltage. The simulations, which model cross-field electron flow via an experimentally measured mobility, exhibit large fluctuation power in a region corresponding to a strong electron transport barrier. The analysis gives an electron mobility (μe) -dependent growth rate (γ) scaling as γ∼μe−1∕2. The predicted phase velocity of these waves is close to the ion velocity, somewhat lower than that seen in the simulations. Including the electron pressure contribution lowers the growth rate at high frequencies, and introduces a phase velocity that is shifted by ± the ion acoustic speed for the stable and unstable branch, respectively. Surprisingly, the phase velocity of the strong disturbances at high frequency seen in the simulations is found to be in agreement with that of the initially stable branch. Finite ionization/particle wall recombination does not change the overall conclusions at high frequencies. However, at lower f or larger λ, the growth rate of the instability is dominated by the ionization rate, and the disturbances are better described as “ionization” instabilities. The transition/competition between ionization, electron pressure, and resistive behavior gives rise to a “quiescent frequency band” where the growth rate is found to be small, consistent with what is seen in the numerical experiments. While simple linear analysis captures much of the observed simulation behavior, comparison with limited experimental data at low frequency suggests that other effects, in particular azimuthal dynamics, are very important, and further motivate extending the hybrid simulation models to three dimensions.

Spinning of a charged dust particle in a magnetized plasma

Abstract We present a novel mechanism for spinning of a charged dust particle in a magnetized plasma. Specifically, we show that the dust particle spinning is caused by a torque that is produced due to interactions between the electric field E and an asymmetric dust particle electric dipole that is induced by the cross-field (viz. the E × B , where B is the external magnetic field) plasma flow. The torque acting on the dust particle is proportional to | E | 2 , so that both laminar and turbulent electric fields can cause dust particle spinning. For plasma parameters typical of tokamak edges, the characteristic dust spinning frequency is of the order of several hundred kHz.

Study of strong cross-field sheared flow with the vorticity probe in the Large Plasma Device

This work reports evidence for the existence of coherent structures in steady-state shear-flow driven plasmas in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] facility at UCLA. The measurements are performed with the vorticity probe (VP), a probe that directly measures the plasma vorticity associated with the E×B shear flow by means of a method that is both simpler and more accurate than the methods used in neutral fluids. Because the rate of change of vorticity is a key quantity in nonlinear models, as in the Hasegawa-Mima equation, its direct measurement is critical for verification purposes. The physical origin of the rate of change of plasma vorticity from E×B flow is the divergence of the ion polarization current. Vortex coherent structures occur when the vorticity is a nonlinear function of the stream function. Statistical properties of vorticity are reported and shown to be consistent with the types of coherent structures created by the Kelvin-Helmholtz instability. Comparisons of the measured vortex characteristics with the results from nonlinear simulations of the systems is described.

Electron surfing acceleration in oblique magnetic fields

Initially, inhomogeneous plasma jets, ejected by active galactic nuclei and associated with gamma-ray bursts, are thermalized by the formation of internal shocks. Jet subpopulations can hereby collide at Lorentz factors of a few. As the resulting relativistic shock expands into the upstream plasma, a significant fraction of the upstream ions is reflected. These ions, together with downstream ions that leak through the shock, form relativistic beams of ions that outrun the shock. The thermalization of these beams via the two-stream instability is thought to contribute significantly to plasma heating and particle acceleration by the shock. Here, the capability of a two-stream instability to generate relativistic field-aligned and cross-field electron flow, is examined for a magnetized plasma by means of a particle-in-cell (PIC) simulation. The electrons interact with the developing quasi-electrostatic waves and oblique magnetic fields. The simulation results bring forward evidence that such waves, by their non-linear interactions with the plasma, produce a highly relativistic field-aligned electron flow and electron energies, which could contribute to the radio synchrotron emissions from astrophysical jets, to ultrarelativistic leptonic subpopulations propagating with the jet and to the halo particles surrounding the accretion disc of the black hole.

Resonant-to-nonresonant transition in electrostatic ion-cyclotron wave phase velocity

Abstract. Because of the implications for plasmas in the laboratory and in space, attention has been drawn to inhomogeneous energy-density driven (IEDD) waves that are sustained by velocity-shear-induced inhomogeneity in cross-field plasma flow. These waves have a frequency vr in the lab frame within an order of magnitude of the ion gyrofrequency vci, propagate nearly perpendicular to the magnetic field (kz /k^ << 1), and can be Landau resonant (0 < v1/kz < nd) with a parallel drifting electron population (drift speed nd), where subscripts 1 and r indicate frequency in the frame of flowing ions and in the lab frame, respectively, and kz is the parallel component of the wavevector. A transition in phase velocity from 0 < v1/kz < nd to 0 > v1/kz > nd for a pair of IEDD eigenmodes is observed as the degree of in-homogeneity in the transverse E × B flow is increased in a magnetized plasma column. For weaker velocity shear, both eigenmodes are dissipative, i.e. in Landau resonance, with kz nd > 0. For stronger shear, both eigenmodes become reactive, with one's wavevector component kz remaining parallel, but with v1/kz > nd , and the other's wavevector component kz becoming anti-parallel, so that 0 > v1/kz . For both eigenmodes, the transition (1) involves a small frequency shift and (2) does not involve a sign change in the wave energy density, which is proportional to vr v1, both of which are previously unrecognized aspects of inhomogeneous energy-density driven waves.

Origin of some anisotropic tailward flows in the plasma sheet

Abstract. We use a test particle model to explore anisotropy and fast flows in the central plasma sheet (CPS) that are a consequence of plasma sheet boundary layer (PSBL) ion beam dynamics. Ion distributions and flows (velocity moments) in the CPS and equatorial current sheet (CS) are compared and we find that mirroring of initially earthward beams from the PSBL, and their subsequent convection to the CS region, results in strong anisotropy throughout the CPS. At higher latitudes, velocity moments are field-aligned and feature earthward flow. Deeper in the CPS, velocity moments yield flows in the anti-earthward direction. There is no clear distinction between the PSBL and CPS, since velocity distributions with large streaming components occur throughout the model CPS, but in the CS region they are anisotropic and nongyrotropic. In the CS region velocity moments can feature anti-earthward cross field flows. These tailward flows (> 400 km/s) are observed in the CS region between X = - 20 to - 30 RE due to nonadiabatic effects. Model results suggest that fast tailward plasma flows can be obtained without necessarily appealing to magnetotail processes associated with dynamic geomagnetic activity.Key words. Magnetospheric physics (magnetospheric con-figuration and dynamics) – Space plasma physics (charge particle motion and acceleration; numerical simulation studies)

Generalized lower-hybrid drift instabilities in current-sheet equilibrium

A class of drift instabilities in one-dimensional current-sheet configuration, i.e., classical Harris equilibrium, with frequency ranging from low ion–cyclotron to intermediate lower-hybrid frequencies, are investigated with an emphasis placed on perturbations propagating along the direction of cross-field current flow. Nonlocal two-fluid stability analysis is carried out, and a class of unstable modes with multiple eigenstates, similar to that of the familiar quantum mechanical potential-well problem, are found by numerical means. It is found that the most unstable modes correspond to quasi-electrostatic, short-wavelength perturbations in the lower-hybrid frequency range, with wave functions localized at the edge of the current sheet where the density gradient is maximum. It is also found that there exist quasi-electromagnetic modes located near the center of the current sheet where the current density is maximum, with both kink- and sausage-type polarizations. These modes are low-frequency, long-wavelength perturbations. It turns out that the current-driven modes are low-order eigensolutions while the lower-hybrid-type modes are higher-order states, and there are intermediate solutions between the two extreme cases. Attempts are made to interpret the available simulation results in light of the present eigenmode analysis.

Effect of cross-field flow on inertial Alfvén waves of small transverse scale

This analytic study examines the effect of cross-field flow on a microscopic current channel. To illustrate the subtle interplay between finite electron inertia and flows, a simple model of excitation of a microscopic current channel is considered. The model consists of a slab antenna exciter with a transverse width on the order of the electron skin-depth driven at a single frequency. The antenna is fixed in the laboratory frame and embedded within a plasma that has a uniform drift across the confining magnetic field. The combined effects of the plasma flow and the intrinsic, collisionless, cross-field expansion of the current channel lead to standing wave structures across the confining magnetic field. The resulting parallel electric fields generate an array of current filaments of alternating polarity which individually have transverse width smaller than the original channel. These results may help interpret laboratory and spacecraft measurements of Alfvénic turbulence and could lead to the development of a diagnostic tool to map plasma flows.

Quasi-neutral particle simulation of magnetized plasma discharges: general formalism and application to ECR discharges

We have developed an electrostatic particle-in-cell/Monte Carlo (PIC/MC) simulation method for magnetized discharges, in which both internal electric fields and sheath potentials are determined from the requirement of quasineutrality within the bulk plasma, rather than by solving Poisson's equation. Thus the electric field is not sensitive to statistical noise which may occur in the small quantity n/sub e/-n/sub i/. Sheaths are treated self consistently as thin potential barriers, and the Bohm criterion for ion flux into the sheath is imposed as a boundary condition. Electron plasma oscillations do not appear in the model, and the debye length is essentially set to zero. Thus time steps and spatial gridding can be chosen to represent the characteristic macroscopic time and space scales of interest, which may be orders of magnitude larger than the plasma frequency/debye length scales. The simulation technique correctly represents kinetic features such as non-Maxwellian distributions and Landau damping and can be used for either collisional or collisionless plasmas. We present results from an axisymmetric simulation of an electron cyclotron resonance (ECR) discharge in low-pressure argon, which show that the discharge is strongly affected by cross-field ion flows, even when the vessel walls are insulators. We also present analytic calculations based on the model, which afford new insights into cross-field transport in a metallic vessel and show that the classic Simon diffusion can be strongly inhibited by the effect of sheath potentials.