ExB Drift Research Articles

Cover Picture: Contrib. Plasma Phys. 07/2024

Snapshots of poloidal planes with established electromagnetic turbulent profiles on a toroidal geometry with an outer limiter. Results are shown after 0.8 ms simulated time: (a) electron density, (b) electron temperature, (c) radial ExB drift, (d) electric potential, (e) parallel current density, and (f) parallel electromagnetic potential. Fig. 4 of the paper by R. Düll et al. https://onlinelibrary.wiley.com/doi/10.1002/ctpp.202300147image

3D simulations of positive streamers in air in a strong external magnetic field

We study how external magnetic fields from 0 to 40 T influence positive streamers in atmospheric pressure air, using 3D PIC-MCC (particle-in-cell, Monte Carlo collision) simulations. When a magnetic field B is applied perpendicular to the background electric field E , the streamers deflect towards the +B and −B directions which results in a branching into two main channels. With a stronger magnetic field the angle between the branches increases, and for the 40 T case the branches grow almost parallel to the magnetic field. Due to the E×B drift of electrons we also observe a streamer deviation in the opposite −E×B direction, where the minus sign appears because positive streamers propagate opposite to the electron drift velocity. The deviation due to this E×B effect is smaller than the deviation parallel to B . In both cases of B perpendicular and parallel to E , the streamer radius decreases with the magnetic field strength. We relate our observations to the effects of electric and magnetic fields on electron transport and reaction coefficients.

Ion temperature dynamics for the edge and scrape-off layer plasma turbulence: role of gyro-viscosity and vorticity

In the presence of magnetic curvature and density/pressure inhomogeneity, the edge and scrape-off layer (SOL) regions of a tokamak plasma are highly turbulent mainly because of the drift/interchange instability mechanisms. The divergence of ion polarization drift contains the ion diamagnetic drift and E⃗×B⃗ drift velocity to define the plasma vorticity and convection of fluid, which can be approximated in several ways using various combinations of these two drifts. Here, in this work, three different approximations are used to represent three different models and are solved numerically. The numerical results indicate that the basic results of turbulence like radial profiles, radial electric field gradients, fluctuation labels, and Reynolds stress are widely different from the three different models. As these models provide different results, therefore, one must be careful to use these approximations for the description of turbulence. This work may be useful in choosing appropriate approximations to include ion temperature gradients for the turbulence studies on tokamaks/stellarators. The role of gyro-viscosity for plasma turbulence has been identified in this work.

Responses of Total Electron Content to Solar Flares over Low and Mid-Latitude Regions during Sun Halo Day

The responses of total electron content (TEC) to solar flares over low- and mid-latitude regions during the sun halo days were investigated. The research is based on GPS data obtained from Bangalore (13.02117°N, 77.57038°E) on May 24, 2021; Cape Town (-33.918861°N, 18.423300°E) on October 26, 2020; and North Dakota (46.55756°N, -96.472300°E) on December 27, 2021, during the solar halo days. The results of this study demonstrate that the values of TEC increased at Bangalore and Cape Town stations during solar halo days as compared to other days. However, over the North Dakota station, TEC during the sun halo day was greater than that on the days before and after the halo day from around 19:00 UT to 23:59 UT hours. During the sun halo over Bangalore and Cape Town stations, positive relative changes in TEC prevail, suggesting that the action of the interplanetary electric field, the prompt penetration electric field, and the disturbance dynamo electric field lead to higher TEC values. However, during the sun halo over North Dakota station, negative relative changes in TEC prevail, which might be related to the consequence that low solar activity with no earth’s field disturbances (a positive Dst) leads to lower ionospheric TEC values. Stations that have greater relative changes in TEC have shown greater power spectrum and global wave spectrum energy. Cape Town has a greater relative change in TEC, a greater power spectrum, and a larger global wave spectrum than Bangalore and North Dakota stations. The values of TEC over three stations are different due to the latitudinal and longitudinal differences in addition to the universal time effects. Finally, solar flares have a major influence on ionosphere electrodynamics, and the upward drift velocity of ionospheres at the low latitude station is more strongly influenced by solar flares due to the effects of the ExB drifts, which induce TEC disturbances during the halo days over the suggested stations.

$$\textbf{E}\times \textbf{B}$$ Drift Particle Transport in Tokamaks

In tokamaks, modification of the plasma profiles can reduce plasma transport, improving particle confinement. However, this improvement is still not completely understood. In this work, we consider a drift wave test particle model to investigate the influence of the electric and magnetic field profiles on plasma transport. Test particle orbits subjected to ExB drift are numerically integrated and their transport coefficient is obtained. We conclude that sheared profiles reduce particle transport, even for high amplitude perturbations. In particular, nonmonotonic electric and magnetic fields produce shearless transport barriers, which are particularly resistant to perturbations and reduce even more the transport coefficient.

The Direct Cylindrical Boris Algorithm

A modification of Boris Algorithm in cylindrical coordinate used to solve Lorentz equation for axisymmetrical plasma simulation is proposed. The velocity updates are calculated directly using matrix operation. The inertial forces are evaluated at n-0.5 time steps. The algorithm is tested for several scenarios: electric field only, electric field dominated, |E| = |B|, ExB drift, gyration test, and a test devised by Delzanno. The result is compared to the standard Boris solver in cylindrical coordinate. The results show that even though generally the solver is not that accurate compared to the standard Boris solver, especially for a larger time step width, it is comparatively faster. Thus, the solver might be useful for plasma simulations that do not require detailed trajectory for each simulated particle.

INVESTIGATION OF THE PROPERTIES OF MICROPARTICLES IN THE GLOW DISCHARGE STRATUM IN A CROSSED ELECTRIC AND MAGNETIC FIELD

In this work, the behavior of charged micron-sized particles in the DC glow discharge stratum at low pressure in a crossed magnetic and electric field was experimentally studied. The experiment was conducted in a vertically oriented gas-discharge glass tube. A homogeneous magnetic field was created using a two-section Helmholtz coil. The results showed that the micron-sized dust particles move in the opposite direction to the ExB drift as the magnetic field induction increases. Once the induction reaches a specific threshold (B>10 mT), the dust particles start rotating and forming counter-rotating vortex pairs on the horizontal plane. Moreover, it was observed that the shape of the dust structures changes from a disk to an ellipsoid. The PIV (particle image velocimetry) method was employed to analyze the dust vortices' dynamic behavior, and the generation of the co-vortex rotation was explained through the dust particles' charge gradient, which was orthogonal to the ion drag force.

Global gyrokinetic simulation of edge coherent mode in EAST

Linear and nonlinear simulations are carried out for the edge coherent mode (ECM) using the global gyrokinetic code GEM based on the EAST experimental parameters. The linear simulation results show that ECM is an electrostatic mode with dominant toroidal mode number n = 18 and frequency about 48 kHz, and propagates along the direction of electron diamagnetic drift, which are consistent with the experimental results. In addition, the density and electron temperature gradients destabilize the mode, while the collision stabilizes the mode. The nonlinear simulation results show that the saturated particle and heat fluxes induced by ECM are mainly due to the perturbed electrostatic ExB drift, and the fluxes of electrons and ions are almost equal. The ECM drives significant outward particle and heat fluxes, thus greatly promoting the maintenance of the long pulse H-mode. The Fourier decomposition of fluxes and potentials demonstrate that the intermediate-n modes of n = 14, 18 grow fastest in the linear phase, while in the nonlinear saturation phase, the low-n modes such as n = 4, 6 dominate and the fluxes are mainly contributed by the mode of n = 10. It is found that zonal flow is not the dominant saturation mechanism of the turbulence. The inverse spectral cascade of turbulence is inevitably observed in the nonlinear saturation process, indicating that it is a more universal turbulence saturation mechanism. It is also found that radial electric field can greatly reduce the turbulence intensity and transport level. From the analyses of frequency and transport channels, it can be concluded that ECM appears to be the collisionless trapped electron mode.

Dynamics of dust particles in the glow discharge stratum in crossed E × B field

AbstractIn this work, the dynamic behaviour of micron‐sized dust particles suspended in the glow discharge stratum at low pressure in the crossed magnetic and electric fields was experimentally studied. The observations showed that the dust particles move in the direction opposite to the ExB drift with increasing magnetic field induction. When the magnetic field induction reaches a threshold point (B > 10 mT), the dust particles begin to rotate, forming pair of counter‐rotating vortex in the horizontal plane. It was also found that the shape of the dust structures changes from a disk shape to an ellipsoid shape. The dynamic behaviour of the dust vortices was analysed using the PIV (particle image velocimetry) method. The quantitative explanation of the generation of the co‐vortex rotation observed in the experiment was explained on the basis of the charge gradient of the dust particles, which was orthogonal to the ion drag force.

ICON Observations of Equatorial Ionospheric Vertical ExB and Field‐Aligned Plasma Drifts During the 2020–2021 SSW

AbstractPrevious studies have revealed large anomalies in vertical ExB drift during the sudden stratospheric warming (SSW), and little attention focused on the behaviors of field‐aligned plasma drift. We report the first simultaneous observations of the equatorial ionospheric vertical ExB and field‐aligned plasma drifts and neutral winds during the 2020–2021 SSW, using the Ionospheric Connections Explorer (ICON) satellite measurements. The downward ExB drift is observed in the afternoon equatorial topside ionosphere in longitudes of ∼180°–270°E, in good agreement with the Jicamarca incoherent scatter radar measurements. What is more, the ICON records the afternoon northward disturbance in field‐aligned plasma drift, which is mainly due to the disturbance meridional wind. The enhanced semidiurnal tides maybe contribute to the disturbances in equatorial topside plasma drifts and neutral winds. This study indicates that the field‐aligned motion is an important factor in the ionosphere‐thermosphere responses to SSW.

Signatures of Auroral Potential Structure Extending Through the Near‐Equatorial Inner Magnetosphere

AbstractThe auroral acceleration region plays an important role in the magnetosphere‐ionosphere coupling system. In this study, signatures of an auroral U‐shaped potential structure were found for the first time in the near‐equatorial inner magnetosphere by the Arase satellite at ∼6.0 RE geocentric distance and 11° magnetic latitude. The observed magnetic and electric field variations corresponded to the equatorward motion of the upward field‐aligned current and converging perpendicular electric field. Examining the three‐dimensional velocity distribution function of H+ and O+ ions, we demonstrate that upflowing ion beams were significantly deflected in an east‐west direction with a perpendicular velocity up to ∼80 km/s, which is consistent with the ExB drift velocity. A simple particle drift model with the inferred auroral perpendicular potential presents a new kink‐like drift path of ions from the magnetotail, implying that the auroral potential structure has a great impact on particle dynamics in the near‐earth plasma sheet.

Effect of the Electrode/Wall Area Ratio on the Plasma Potential in Discharge and Tokamak Plasmas

Plasma potential is a key parameter in plasma discharge or fusion plasma to control plasma–wall interaction or ExB drift. The magnitude of plasma potential depends on the overall energy transmitted to the plasma via direct current (dc) or radio frequency (RF) devices such as electrodes or antennas. Knowing the plasma potential from the exciting source is useful to prevent high energetic fluxes to the wall or to improve the plasma confinement or explaining shear velocity. The aim of the present model is to calculate this plasma potential with respect to a dc or RF source in a magnetized or unmagnetized plasma. This double saturated probe (DSP) model takes into account the electron saturation current and is able to derive the plasma potential as a function of the electrode/wall area ratio for a dc or RF discharge in a helium/argon plasma with or without a magnetic field. The results of the model are compared with Aanesland’s model in the case of unmagnetized capacitive sheath and particle-in-cell (PIC) simulations. The magnetized model is applied to a plasma column with a perpendicular capacitive current in an RF discharge. It appears that the plasma potential can increase to almost the RF potential value at a low wall/electrode area ratio ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A_{\text {wall}}/A_{\text {el}}$ </tex-math></inline-formula> lower than 5), while the same potential collapses as soon as the area ratio (perpendicular over the parallel current area) is higher than the electron/ion saturation current ratio. This is directly due to the saturation of electron current, preventing the plasma potential from following the imposed RF potential by the electrode, so that the maximum value can be as lower as the floating potential. The perpendicular current involved is mainly a conduction current modeled as a resistive collisional current. In fusion plasma, the maximum plasma potential can rise to higher values than in plasma discharges, but the collapse of the potential still occurs for long collisional biased flux tubes.

Trapping secondary electrons in ExB drift for an alpha generating penning ion source

A Penning ion source test stand has been developed by D-Pace to characterize alpha ion extraction from a helium discharge with variations in: extraction potential up to 15 kV, gas flow rate up to 30 sccm, and magnetic field confinement up to 1.1 Tesla. A brief summary of the Penning ion source design is described. Attempts at extraction of ions leads to severe sparking events on the high voltage insulator due to ExB drifts of secondary electrons. This paper shows the design of two sets of electrodes which together trap most electrons moving towards this insulator due to ExB drifts. This eliminates the severe high voltage breakdown on the insulator and allows for a more robust operation of the ion source.

A self‐consistent mean‐field model for turbulent particle and heat transport in 2D interchange‐dominated electrostatic ExB turbulence in a sheath‐limited scrape‐off layer

AbstractIn this paper, a self‐consistent model for the average radial turbulent transport of heat and particles in 2D anisothermal interchange‐dominated electrostatic ExB drift turbulence in sheath‐limited scrape‐off layers is presented. Diffusion models are used for the turbulent particle and heat fluxes, in which the transport coefficients scale with the square root of the turbulent kinetic energy (). The interchange drive proves to be the main source of turbulent kinetic energy, while the sheath term provides the main sink. These observations are qualitatively the same as for the isothermal case studied earlier. An analytical relation for the interchange term is derived, showing that the turbulent ExB thermal energy flux is the direct driver for through the interchange source. A series decomposition of the sheath term in the equation shows it includes a sink contribution that was also present in the isothermal case, but also a new source due to the sheath‐driven conducting‐wall (SCW) instability caused by electron temperature fluctuations. Using a simple regression model to close the total sheath term, a closed model for the turbulent transport is obtained. The interchange drive due to the ExB energy flux leads to a self‐saturation mechanism in the model, where the gradients and turbulence intensity increase until a sufficient transport level is reached to carry the power and particles across the field lines to find a balance with the sheath sink. An implementation of this model in a 1D mean‐field code approximates the profiles of the turbulence simulations with remarkable accuracy in part of the parameter space, while the error increases in parameter regimes where the relative importance of the SCW term is varied.

English

The present paper reviews CODG TEC response to the moderate storm of July 26, 2003 and that of July 29 at Niamey station in West African equatorial station (Geo Lat 13&deg; 28&#39;45.3 &quot;N; Geo long: 02&deg; 10&#39;59.5&quot; E) in Niger. These two moderate geomagnetic storms are of solar wind origin. The study showed an increase in CODG TEC values during the initial phase of the storm and a decrease in CODG TEC values during the main and recovery phases of the storm. In general, in the equatorial region, positive and negative storms occurred (increase and decrease in TEC values). Here we highlight the prereversal enhancement (PRE), a particularity of the equatorial ionosphere. Our investigations show M, B and R profiles in addition to the well-known dome profile in the variation of the CODG TEC in Niamey. This work suggests a variation of the equatorial electrojet intensity during the storm recovery phase, the appearance of the counter-electrojet as well as a disturbance of the ExB drift. This study is local, in the equatorial region in the West African sector. Data are needed to corroborate some hypotheses such as changes in profiles associated with the presence or absence of electrojet and counter-electrojet currents. We advocate for a new IHY for Africa and for data exchange between researchers. Key words: Ionosphere, solar wind, disturbance, total electron content (TEC).

Ion acceleration to 100 keV by the ExB wave mechanism in collision-less shocks

ABSTRACTIt is shown that ions can be accelerated to about 100 keV in the direction perpendicular to the magnetic field by the ExB mechanism of electrostatic waves. The acceleration occurs in discrete steps of duration being a small fraction of the gyroperiod and can explain observations of ion energization to 10 keV at quasi-perpendicular shocks and to hundreds keV at quasi-parallel shocks. A general expression is provided for the maximum energy of ions accelerated in shocks of arbitrary configuration. The waves involved in the acceleration are related to three cross-field current-driven instabilities: the lower hybrid drift (LHD) instability induced by the density gradients in shocks and shocklets, followed by the modified two-stream (MTS) and electron cyclotron drift (ECD) instabilities, induced by the ExB drift of electrons in the strong LHD wave electric field. The ExB wave mechanism accelerates heavy ions to energies proportional to the atomic mass number, which is consistent with satellite observations upstream of the bow shock and also with observations of post-shocks in supernovae remnants. The results are compared with other acceleration mechanisms traditionally discussed in the literature.

Modeling of ExB effects on tungsten re-deposition and transport in the DIII-D divertor

Mixed-material DIVIMP–WallDYN modeling, now incorporating ExB drifts, is presented that simultaneously reproduces tungsten (W) erosion and deposition patterns observed during the DIII-D metal rings campaign, in which a toroidally symmetric set of W-coated tiles were installed in the carbon (C) DIII-D divertor. Since most reactor plasma facing component (PFC) designs call for mixed-material environments, including ITER’s W/Be environment, the divertor targets will quickly evolve into reconstituted surfaces of multiple elements. This work identifies controlling physics that affects material migration patterns in the divertor, which impact PFC lifetimes and impurity leakage from the divertor to the core. These simulations indicate that radial and poloidal ExB transport dominates over parallel force balance for high-Z impurities such as W in the divertor region of DIII-D. It is demonstrated that ExB drifts are required to reproduce the experimental observation of non-local W and C co-accumulation in a band ∼7–9 cm outboard of the outer-strike-point (OSP) W source, for attached L-mode conditions in the unfavorable ion grad-B drift direction. In addition, W gross erosion is localized to the region outboard of the OSP, as the formation of C co-deposits suppresses W erosion at the strike point. Time-dependent simulations with scaled ExB impurity drifts (60% of the OEDGE-calculated drift velocity) and W re-erosion quantitatively reproduce these features, including depth-resolved W/C ratios, within a factor of 2 over ∼115 s of accumulated plasma exposure. The location of co-deposition regions is shown to be well-represented by an analytic leakage model, driven largely by poloidal ExB drifts. Qualitative agreement is also found between campaign-integrated W deposition measurements and simulations for the favorable ion grad-B drift direction, the standard mode of operation for most tokamaks. These results imply that a long-term inward radial migration of material from the outer divertor through the private flux region may occur in future devices.

Generalized non-linear Compton-Getting transformation for energetic particles: Applications throughout the heliosphere

We develop the theoretical basis for a non-linear frame transformation of energetic ion intensity anisotropies (i.e., a generalized Compton-Getting transformation). Within the basic physics-motivated assumption that the anisotropies are gyrotropic in the transform frame, the rather general formulation allows us to examine a wide range of ion intensity distributions throughout the heliosphere. In addition to generalizing more familiar applications of the Compton-Getting transformation (that utilizes the bulk plasma velocity V for the transformation), we also apply the component (V^) transverse to the magnetic field (B). The physical justification is that (V^) is the ExB drift velocity with which the magnetic field lines “move”. In this paper, we have focused on two quite different areas: the elucidation of the strong field-aligned anisotropies and steep energy spectra being observed near the Sun from Parker Solar Probe (and Solar Orbiter), and the extraction of the bulk plasma velocity in the heliosheath at ∼100 AU using the anisotropies in energetic ion intensities observed on Voyager 1&2.

Stochastic ion and electron heating on drift instabilities at the bow shock

Abstract The analysis of the wave content inside a perpendicular bow shock indicates that heating of ions is related to the lower hybrid drift (LHD) instability, and heating of electrons is related to the electron cyclotron drift (ECD) instability. Both processes represent stochastic acceleration caused by the electric field gradients on the electron gyroradius scales, produced by the two instabilities. Stochastic heating is a single-particle mechanism where large gradients break adiabatic invariants and expose particles to direct acceleration by the direct current and wave fields. The acceleration is controlled by function $\chi = m_iq_i^{-1} B^{-2}$div(E), which represents a general diagnostic tool for processes of energy transfer between electromagnetic fields and particles, and the measure of the local charge non-neutrality. The identification was made with multipoint measurements obtained from the Magnetospheric Multiscale spacecraft. The source for the LHD instability is the diamagnetic drift of ions, and for the ECD instability the source is ExB drift of electrons. The conclusions are supported by laboratory diagnostics of the ECD instability in Hall ion thrusters.

Modeling ExB drift transport in conceptual slot divertor configurations

AbstractAt DIII‐D, a slot divertor concept, called small‐angle‐slot (SAS), is under development, aiming to enable detachment at relatively low plasma edge density. We report on simulations using the SOLPS‐ITER two‐dimensional edge code to examine the performance of conceptual “SAS 2” slot configurations. The focus of the analysis is on E × B drift effects on upstream density at detachment (UDD), with detachment marked by electron temperature Te ≤ 3 eV at the outer strike point (OSP). With toroidal field such that radial E × B drift carries particles from the OSP towards the private flux region (PFR), placing the OSP near the inner slot wall gives ≈20% lower UDD than having the OSP near the outer wall. The inner wall effectively traps the radial E × B drift flux, resulting in low Te and associated radial electric field in the PFR, and thus small losses from the slot to the inner target via poloidal E × B drift flux. With toroidal field reversed such that radial E × B drift is reversed, OSP placement near the inner wall gives ≈10% lower UDD than OSP placement near the outer wall. Although radial E × B flux is from the OSP towards the outer wall, this flux largely escapes the slot, raising the UDD. A change in the slot shaping is suggested with the goal of eliminating such E × B‐driven particle losses from the slot.