Cross-field Diffusion Coefficient Research Articles

Dynamic measurement of impurity ion transport in runaway electron plateaus in DIII-D

The first dynamic (time-dependent) measurements of impurity ion radial (cross field) and parallel (along-field) diffusion coefficients for post-disruption runaway electron plateaus are presented. Small (∼1 mm diameter) carbon or silicon pellets are fired into the edge of steady-state runaway electron (RE) plateaus, and the resulting radial and toroidal transport of singly charged impurity ions (C+ or Si+) is monitored with spatially distributed visible spectrometers. Consistent with previous steady-state particle balance estimates of Ar+ radial transport, radial (cross field) diffusion coefficients D⊥≈2–5 m2/s are obtained, about 10× larger than expected from neo-classical theory. Parallel diffusion coefficients D∥≈30–80 m2/s are estimated, also much (≈50×) larger than classical. It is speculated at present that these large diffusion coefficients may be due to turbulent transport. Indications of fairly significant (almost 2×) toroidal variation in electron density are seen in the RE plateaus, and this appears to cause some toroidal variation in impurity radial diffusion rates. Indications of slow (≈1 Hz) toroidal rotation in the impurity ions are observed, although the uncertainty in this measurement is large.

Magnetized wake driven anomalous diffusion in complex plasma

Diffusion of a three-dimensional dust ensemble embedded in a flowing plasma in the presence of a moderate magnetic field is investigated using Langevin dynamics simulation. It is found that the asymmetric wake potential created due to streaming ions drive the dusty plasma from the subdiffusive to the superdiffusive regime. A novel wake dominant regime is identified that shows superdiffusive behavior for suitable adjustment of the magnetic field. The dependence of the cross field diffusion coefficient on the magnetic field exhibits three distinct behaviors characterized by (a) B2−3 for an ultra-low magnetic field and strongly correlated state, (b) B≃0.1 for a moderate magnetic field, and (c) classical B−2 for a relatively large magnetic field. Our analysis shows that the magnetic field is mediated via the streaming ions in regimes (a) and (b) of relatively low magnetic field where the dependence of the diffusion coefficient on the magnetic field is faster than the usual classical regime.

The effect of turbulence strength on meandering field lines and Solar Energetic Particle event extents

Insights into the processes of Solar Energetic Particle (SEP) propagation are essential for understanding how solar eruptions affect the radiation environment of near-Earth space. SEP propagation is influenced by turbulent magnetic fields in the solar wind, resulting in stochastic transport of the particles from their acceleration site to Earth. While the conventional approach for SEP modelling focuses mainly on the transport of particles along the mean Parker spiral magnetic field, multi-spacecraft observations suggest that the cross-field propagation shapes the SEP fluxes at Earth strongly. However, adding cross-field transport of SEPs as spatial diffusion has been shown to be insufficient in modelling the SEP events without use of unrealistically large cross-field diffusion coefficients. Recently, Laitinen et al. [ApJL 773 (2013b); A&A 591 (2016)] demonstrated that the early-time propagation of energetic particles across the mean field direction in turbulent fields is not diffusive, with the particles propagating along meandering field lines. This early-time transport mode results in fast access of the particles across the mean field direction, in agreement with the SEP observations. In this work, we study the propagation of SEPs within the new transport paradigm, and demonstrate the significance of turbulence strength on the evolution of the SEP radiation environment near Earth. We calculate the transport parameters consistently using a turbulence transport model, parametrised by the SEP parallel scattering mean free path at 1 AU, λ∥*, and show that the parallel and cross-field transport are connected, with conditions resulting in slow parallel transport corresponding to wider events. We find a scaling σφ,max∝(1/λ∥*)1/4 for the Gaussian fitting of the longitudinal distribution of maximum intensities. The longitudes with highest intensities are shifted towards the west for strong scattering conditions. Our results emphasise the importance of understanding both the SEP transport and the interplanetary turbulence conditions for modelling and predicting the SEP radiation environment at Earth.

Measurement of electron energy probability function in weakly magnetized plasma

Knowledge of the real EEDF is of great importance in understanding the underlying physics of processes occurring at the magnetized plasma, such as the formation of transport barriers, cross-field diffusion coefficients and plasma–substrate interactions. In the present experiment, the application of Langmuir probe to evaluate EEPF in presence of magnetic fields within the range 594–32 G is investigated. The data recorded for EEPFs in magnetic fields and in dust is acquired using current–voltage characteristics measured in low pressure hydrogen plasma. The values of plasma density, electron temperature and EEPF are evaluated with a single cylindrical Langmuir probe at different axial positions (1 cm to 6 cm) from the magnet. From the recent EEPF observations in presence of magnetic field, it shows a bi-Maxwellian EEPF structure at different magnetic fields. But at different magnetic field, it is observed that the low energy electron population changes whereas the high-energy electron population remains almost constant. EEPF measurement shows almost identical behaviour with the unmagnetized plasma when the larmour radius of electron is greater than or equal to 10 times of the probe radius.

Vertical profiles and two-dimensional distributions of carbon line emissions from C2+−C5+ ions in attached and RMP-assisted detached plasmas of large helical device

In Large Helical Device (LHD), the detached plasma is obtained without external impurity gas feed by supplying an m/n = 1/1 resonant magnetic perturbation (RMP) field to a plasma with an outwardly shifted plasma axis position of Rax = 3.90 m where the magnetic resonance exists in the stochastic magnetic field layer outside the last closed flux surface. The plasma detachment is triggered by the appearance of an m/n = 1/1 island when the density, increased using hydrogen gas feed, exceeds a threshold density. The behavior of intrinsically existing impurities, in particular, carbon originating in the graphite divertor plates, is one of the important key issues to clarify the characteristic features of the RMP-assisted plasma detachment although the particle flux still remains on some divertor plates even in the detachment phase of the discharge. For this purpose, vertical profiles and two-dimensional (2-D) distributions of edge carbon emissions of CIII to CVI have been measured at extreme ultraviolet wavelength range, and the results are compared between attached and RMP-assisted detached plasmas. It is found that the CIII and CIV emissions located in the stochastic magnetic field layer are drastically increased near the m/n = 1/1 island O-point and in the vicinity of both inboard and outboard edge separatrix X-points during the RMP-assisted detachment, while those emissions are only enhanced in the vicinity of the outboard edge X-point in attached plasmas without RMP. The result clearly indicates a change in the magnetic field lines connecting to the divertor plates, which is caused by the growth of the m/n = 1/1 edge magnetic island. In contrast, the intensity of CVI emitted radially inside the magnetic island significantly decreases during the detachment, suggesting an enhancement of the edge impurity screening. The measured carbon distribution is analyzed with a three-dimensional edge plasma transport simulation code, EMC3-EIRENE, for the attached plasmas without RMP. It is found that the narrow strip-shaped impurity trace emitted along the edge X-point and its width are sensitive to the cross-field impurity diffusion coefficient, DZ⊥. As a result, the value of DZ⊥ of C3+ ions is evaluated to be 20 times larger than that of the bulk ions in the Rax = 3.90 m configuration, while the reason is unclear at present. The measured 2-D carbon distribution is also discussed and compared to the structure of the m/n = 1/1 magnetic island, which quickly expanded during the appearance of the plasma detachment.

Whole-machine material migration studies in the TEXTOR tokamak with molybdenum

MoF6 injection from a localised source into plasma edge in the TEXTOR tokamak was the last experiment before the final shut-down of the TEXTOR machine. During decommissioning all plasma-facing components (PFCs) became available for surface studies. Detailed mapping of Mo deposition was performed in order to determine its migration on global scale. The concentration of Mo on PFC decays exponentially with distance from the source. The decay length is of the order of 0.1m on the main PFC and 1m on the receded components. Also the decay lengths modelled with the ERO code are between 0.15–1.3m, depending on the anomalous cross-field diffusion coefficient. The inner bumper limiter is found to be the major repository for Mo. Material balance measurements show that only up to 22% of the injected Mo was detected on all the PFCs thus indicating that a large fraction of injected Mo may have been pumped out before being deposited.

Direct measurement of the plasma loss width in an optimized, high ionization fraction, magnetic multi-dipole ring cusp

The loss width of plasma in the WiPAL multi-dipole magnetic ring cusp [Cooper et al., Phys. Plasmas 21, 13505 (2014); Forest et al., J. Plasma Phys. 81, 345810501 (2015)] has been directly measured using a novel array of probes embedded in the insulating plasma limiters. The large plasma volume (∼10 m3), small loss area associated with strong rare earth permanent magnets (Bo∼2.23 kG at face), and large heating power (≤200 kW) produces a broad range of electron temperatures (2<Te<15 eV), ion temperatures (0.03<Ti<2 eV), plasma densities (3×1010<ne<2×1012 cm−3), and ionization fractions (0.05<ne/(ne+nn)<1), in both argon and helium, all of which were accurately measured. This plasma regime, accessible with high magnetic fields, differs from previous devices: the cusp loss width is much larger than the Debye length and electron gyroradius and comparable to the collision length. Plasma parameters measured at the surface of ceramic limiter tiles covering the magnets and along radial chords in the cusp magnetic field indicate that electron density and temperature are nearly constant on magnetic field lines and that the mirror forces play little role in confining the plasma other than to constrict the loss area. Particle balance modeling is used to determine the cross field diffusion coefficient base on the measured losses to the limiters. The experimentally determined cross field diffusion coefficient (which determines the cusp loss width) is consistent with ambipolar diffusion across five orders of magnitude. The ambipolar diffusion across a given field line is set primarily by the electron-neutral collisions in the region where the magnetic field is the weakest, even though these plasmas can have ionization fractions near 1.

Three-dimensional scrape off layer transport in the helically symmetric experiment HSX

The edge topology of helically symmetric experiment (HSX) in the quasi-helically symmetric configuration is characterized by an 8/7 magnetic island remnant embedded in a short connection length scrape-off layer (SOL) domain. A 2D mapping of edge plasma profiles within this heterogeneous SOL has been constructed using a movable, multi-pin Langmuir probe. Comparisons of these measurements to edge simulations using the EMC3-EIRENE 3D plasma fluid and kinetic neutral gas transport model have been performed. The measurements provide strong evidence that particle transport is diffusive within the island region and dominantly convective in the SOL region. Measurements indicate that phenomenological cross-field diffusion coefficients are low in the SOL region between the last closed flux surface and edge island (i.e. m2 s−1). This level of transport was found to increase by a factor of two when a limiter is inserted almost completely into the magnetic island. A reduction in gradients of the edge electrostatic plasma potential was also measured in this configuration, suggesting that the reduced electric field may be linked to the increased cross-field transport observed.

Dynamics of three-dimensional radiative structures during RMP assisted detached plasmas on the large helical device and its comparison with EMC3-EIRENE modeling

The resonant magnetic perturbation (RMP) island introduced in the stochastic edge of the large helical device (LHD) plasma plays an important role in the stabilization of the plasma detachment (Kobayashi et al 2013 Nucl. Fusion 53 093032). The plasma enters in the sustained detachment phase in the presence of an RMP once the line averaged density exceeds a critical value with a given input power. During detachment the enhanced radiation from the stochastic edge of the LHD undergoes several spatiotemporal changes which are studied quantitatively by an infrared imaging video bolometer (IRVB) diagnostic. The experimental results are compared qualitatively and quantitatively with the radiation predicted by the 3D transport simulation with fluid model, EMC3-EIRENE. A fair amount of qualitative agreement, before and after the detachment, is reported. The issue of overestimated radiation from the model is addressed by changing the free parameters in the EMC3-EIRENE code till the total radiation and the radiation profiles match closely, within a factor of two with the experimental observations. A better quantitative match between the model and the experiment is achieved at higher cross-field impurity diffusion coefficient and lower sputtering coefficient after the detachment. In this article a comparison, the first of its kind, is established between the quantified radiation from the experiments and the synthetic image obtained from the simulation code. This exercise is aimed towards validating the model assumptions against the experimentally measured radiation.

Parametric study of a pin-plane probe in moderately magnetized plasma

The application of a planar Langmuir probe in magnetized plasma is found to be problematic due to significant perturbation of plasma along the magnetic field lines intercepting the probe surface. This causes the Ampere–Volts ‘Ie(U)’ characteristics of the probe to deviate from its usual exponential law; in conjunction the electron saturation current Ies is significantly reduced. Moreover estimating the electron temperature Te by considering the entire semi-log plot of Ie(U) gives ambiguous values of Te. To address this problem, Pitts and Stangeby developed a formula for the reduction factor for Ies. This formula depends on a number of uncertain parameters, namely; the ion temperature T+, electron cross-field diffusion coefficient and the local potential hill Vh estimated by applying a floating pin probe in the vicinity of the planar probe. Due to implicit dependence of these parameters on Te, the resulting analysis is not straightforward. This paper presents a parametric study of different parameters that influence the characteristics of a planar probe in magnetized plasma. For this purpose a pin-plane probe is constructed and applied in the magnetized plasma column. A comprehensive discussion is presented that highlights the practical methodology of using this technique for extracting useful information of plasma parameters in magnetized plasmas.

CROSS-FIELD DIFFUSION OF ENERGETIC (100 keV to 2 MeV) PROTONS IN INTERPLANETARY SPACE

Magnetic field magnitude decreases (MDs) are observed in several regions of the interplanetary medium. In this paper, we characterize MDs observed by the Ulysses spacecraft instrumentation over the solar south pole by using magnetic field data to obtain the empirical size, magnetic field MD, and frequency of occurrence distribution functions. The interaction of energetic (100 keV to 2 MeV) protons with these MDs is investigated. Charged particle and MD interactions can be described by a geometrical model allowing the calculation of the guiding center shift after each interaction. Using the distribution functions for the MD characteristics, Monte Carlo simulations are used to obtain the cross-field diffusion coefficients as a function of particle kinetic energy. It is found that the protons under consideration cross-field diffuse at a rate of up to ≈11% of the Bohm rate. The same method used in this paper can be applied to other space regions where MDs are observed, once their local features are well known.

On the exclusion of intracluster plasma from active galactic nuclei-blown bubbles

Simple arguments suggest that magnetic fields should be aligned tangentially to the surface of an AGN-blown bubble. If this is the case, charged particles from the fully ionised intra-cluster medium (ICM) will be prevented, ordinarily, from crossing the boundary by the Lorentz force. However, recent observations indicate that thermal material may occupy up to 50% of the volume of some bubbles. Given the effect of the Lorentz force, the thermal content must then be attributed to one, or a combination, of the following processes: i) the entrainment of thermal gas into the AGN outflow that inflated the bubble; ii) rapid diffusion across the magnetic field lines at the ICM/bubble interface; iii) magnetic reconnection events which transfer thermal material across the ICM/bubble boundary. Unless the AGN outflow behaves as a magnetic tower jet, entrainment may be significant and could explain the observed thermal content of bubbles. Alternatively, the cross-field diffusion coefficient required for the ICM to fill a typical bubble is roughly 10^16 cm^2 s^-1, which is anomalously high compared to predictions from turbulent diffusion models. Finally, the mass transfer rate due to magnetic reconnection is uncertain, but significant for plausible reconnection rates. We conclude that entrainment into the outflow and mass transfer due to magnetic reconnection events are probably the most significant sources of thermal content in AGN-blown bubbles.

Compound and perpendicular diffusion of cosmic rays and random walk of the field lines: II. Non-parallel particle transport and drifts

Compound transport of energetic charged particles across the mean magnetic field due to field line random walk is investigated by means of a Chapman–Kolmogorov equation. The probability distribution function (pdf) for the particle transport across the field P⊥ is given as a convolution of the pdf for random walk of the magnetic field, PFRW, with the pdf Pp, for particle transport relative to the random walking field. The particle propagator Pp includes the effects of advection, drift, parallel diffusion and local perpendicular diffusion of particles relative to the random walking field. At early times, the particles sub-diffuse across the field due to field line random walk. At late times, the effective cross-field diffusion coefficient has the form κ⊥e = κ⊥ + κF. The diffusion coefficient κ⊥ is the local cross-field diffusion coefficient due to particle scattering in the random magnetic field. The diffusion coefficient κF is due to coherent particle advection parallel to the mean magnetic field B0 coupled with transverse random walk of the magnetic field. Estimates of cross-field diffusion due to field line random walk, advection and drift are obtained both near to the heliospheric current sheet at Earth and at higher helio-latitudes. Cross-field diffusion due to field line random walk and advection is shown to be an important transport mechanism for low-energy particles near the current sheet, where the effects of drifts are negligible. Drift effects and field line random walk are also assessed at higher helio-latitudes off the current sheet, for a model interplanetary magnetic field, with a flat current sheet in the helio-equatorial plane.

Forbush decreases and turbulence levels at coronal mass ejection fronts

Aims. We seek to estimate the average level of MHD turbulence near coronal mass ejection (CME) fronts as they propagate from the Sun to the Earth. Methods. We examined the cosmic ray data from the GRAPES-3 tracking muon telescope at Ooty, together with the data from other sources for three closely observed Forbush decrease events. Each of these event is associated with frontside halo coronal mass ejections (CMEs) and near-Earth magnetic clouds. The associated Forbush decreases are therefore expected to have significant contributions from the cosmic-ray depressions inside the CMEs/ejecta. In each case, we estimate the magnitude of the Forbush decrease using a simple model for the diffusion of high-energy protons through the largely closed field lines enclosing the CME as it expands and propagates from the Sun to the Earth. The diffusion of high-energy protons is inhibited by the smooth, large-scale magnetic field enclosing the CME and aided by the turbulent fluctuations near the CME front. We use estimates of the cross-field diffusion coefficient D ⊥ derived from the published results of extensive Monte Carlo simulations of cosmic rays propagating through turbulent magnetic fields. We then compare our estimates with the magnitudes of the observed Forbush decreases. Results. Our method helps constrain the ratio of energy density in the turbulent magnetic fields to that in the mean magnetic fields near the CME fronts. This ratio is found to be ∼2% for the 2001 April 11 Forbush decrease event, ∼6% for the 2003 November 20 Forbush decrease event and ∼249% for the much more energetic event of 2003 October 29.

Cosmic rays X. The cosmic ray knee and beyond: diffusive acceleration at oblique shocks

Our purpose is to evaluate the rate of the maximum energy and the acceleration rate that cosmic rays acquire in the non-relativistic diffusive shock acceleration as it could apply during their lifetime in various astrophysical sites, where highly oblique shocks exist. We examine numerically (using Monte-Carlo simulations) the effect of the diffusion coefficients on the energy gain and the acceleration rate, by testing the role between the obliquity of the magnetic field to the shock normal, and the significance of both perpendicular cross-field diffusion and parallel diffusion coefficients to the acceleration rate. We find (and justify previous analytical work – Jokipii 1987, ApJ, 313, 842) that in highly oblique shocks the smaller the perpendicular diffusion gets compared to the parallel diffusion coefficient values, the greater the energy gain of the cosmic rays to be obtained. An explanation of the cosmic ray spectrum in high energies, between 10 15 eV and about 10 18 eV is claimed, as we estimate the upper limit of energy that cosmic rays could gain in plausible astrophysical regimes; interpreted by the scenario of cosmic rays which are injected by three different kind of sources, (a) supernovae which explode into the interstellar medium, (b) Red Supergiants, and (c) Wolf-Rayet stars, where the two latter explode into their pre-supernovae winds.

Cosmic rays & diffusive shock acceleration at highly oblique non-relativistic shocks

Our purpose is to evaluate the rate of the maximum energy and the acceleration rate that cosmic rays acquire in the non-relativistic diffusive shock acceleration as it could apply during their lifetime in various astrophysical sites, where highly oblique shocks exist. We examine numerically (using Monte Carlo simulations) the effect of the diffusion coefficients on the energy gain and the acceleration rate, by testing the role between the obliquity of the magnetic field at the shock normal, and the significance of both perpendicular cross-field diffusion and parallel diffusion coefficients to the acceleration rate. We find (and justify previous analytical work - Jokipii 1987) that in highly oblique shocks the smaller the perpendicular diffusion gets compared to the parallel diffusion coefficient values, the greater the energy gain of the cosmic rays to be obtained. An explanation of the cosmic ray spectrum at high energies, between 10 15 eV and about 10 18 eV is claimed, as we estimate the upper limit of energy that cosmic rays could gain in plausible astrophysical regimes; interpreted by the scenario of cosmic rays which are injected by three different kind of sources, (a) supernovae which explode into the interstellar medium, (b) Red Supergiants, and (c) Wolf-Rayet stars, where the two latter explode into their pre-supernovae winds.

Studies of the particle diffusion coefficient in the fluctuating magnetic field by the direct-interaction approximation

The particle diffusion in a stochastic magnetic field is investigated by using the functional integral method. With the ensemble average of a functional representation to a kinetic equation over the fluctuating magnetic field and the random variables modeling the Coulomb collisions. a closed set of equations for an ensemble-averaged distribution function and a response function to an infinitesimal external perturbation is derived within the framework of the direct-interaction approximation (DIA). By using the Markovian approximation to the equation for the response function, the cross-field diffusion coefficients are found to be obtained from nonlinear ordinary differential equations. Explicitly calculated diffusion coefficients for various parameters are also shown in the shearless and sheared configurations.

Nonlinear excitation of coherent structures and associated cross-field transport in a magnetized plasma

Nonlinear interactions between zero-frequency electrostatic convective cells (CCs)/zonal flows (ZFs) and magnetostatic (MS) modes in a magnetoplasma are numerically investigated. These nonlinearly coupled flute-like modes can be spontaneously excited, and contribute significantly to the anomalous cross-field transport. While they are degenerate in a linear regime and form purely damped modes, their mutual nonlinear interactions give rise to large-scale coherent structures through a turbulent relaxation that leads to a self-organization via an inverse cascade. Remarkably, we find that nonlinear excitations of large-scale structures give rise to an effective cross-field diffusion coefficient that varies initially as ∼ t 1 / 2 with time, and enhances the transport level dramatically.

Study of particle behaviour at the edge in HT-7 tokamak

The cross-field diffusion coefficient (D⊥) at the edge in the HT-7 tokamak is close to the Bohm value when the line average electron density ranges from 1.5×1019 to 3.0×1019m−3. The energy profile of the particles is derived directly from the Hα(Dα) line shape; the dissociative excitation of molecules is dominating when the local electron temperature is above 10eV. By means of the Monte Carlo method the Dα line shape is also simulated. We find that the molecular dissociation contributes to 57% of neutral atoms and 53% of emission intensity in front of the limiter and 85% of neutral atoms and 82% of emission intensity in front of the wall. The influence of atomic and molecular processes on the energy balance is discussed for the scrape-off layer (SOL) and the power loss from molecular dissociation is found to be 6×104kW at the SOL. The ion Bernstein wave (IBW) can effectively suppress the magnetohydrodynamic behaviour, the fluctuation levels and the turbulence; the D⊥ in front of the limiter declines from 0.84 to 0.2m2.s−1 and the particle confinement time rises from 9 to 12ms.

Calculation of transport parameters in KT-1 tokamak edge plasma

Abstract The radial profiles of KT-1 tokamak (major radius of 27 cm, minor radius of 4.25 cm, two poloidal stainless-steel limiters) edge plasma parameters are measured using single and triple electric probes. The particle transport parameters are calculated from the measured edge plasma parameters, and the results are analyzed by the simple fluid approximations. The cross-field particle diffusion coefficient ( D ⊥ ) in the boundary plasma of the KT-1 is calculated from the density scrape-off length ( λ n ) measured by using a triple probe. The particle density and electron temperature fall exponentially in the radial direction with the e-folding length of λ n =0.13 cm and λ e =0.41 cm, respectively. From the scrape-off layer (SOL) model, the experimental values of scrape-off length ( λ n ) is used to calculate the cross-field diffusion coefficient ( D ⊥ =1.2×10 3 cm 2 /s), roughly corresponding to one third of the typical Bohm value. A simple SOL model with the contribution of recombination is introduced to evaluate the Bohm diffusion in the KT-1 tokamak edge plasma. Cross-field heat conductivity calculated from these deduced values is ∼5.2 D ⊥ in the SOL of KT-1 edge plasma. These results provide the finally certain information for edge particle transport in the KT-1 boundary plasmas.