Cross-field Diffusion Coefficient Research Articles

On the cosmic ray cross-field diffusion for solar wind turbulence

The cross-field diffusion coefficient of charged particles in the presence of pure isotropic Alfven waves, pure isotropic magnetosonic waves and their mixture is considered using Monte Carlo particle simulations. We show that the cross-field diffusion coefficient $\kappa_{\perp}$ strongly depends on the assumed spectrum and amplitude of MHD turbulence but much less on the type of waves considered. It is demonstrated that transport perpendicular to the average magnetic field is mostly determined by compound diffusion which combines the effects of scattering off magnetic irregularities with magnetic braiding. The ratio $\kappa_{\perp}/\kappa_{\parallel}D_{\rm M}\approx {\rm const.}$ is independent of rigidity over the wide range considered.

Spatial Spectrum of Artificial Ionospheric Irregularities Induced by Powerful HF Radiowaves

We present measurement results and spatial-spectrum shapes of the dependence of the relaxation time on the scale across the geomagnetic field for artificial ionospheric irregularities (AIIs) induced in the upper ionosphere by powerful HF radiation of the SURA heating facility. The irregularity diagnostics was based on observing amplitude scintillations of a 243-MHz beacon signal from a quasi-geostationary, solar-synchronous satellite and on measuring field-aligned scattering at frequencies 15 and 20 MHz. The satellite signal was received at the Kazan State University Observatory. The field-aligned scattering signals were received and analyzed by a bistatic HF radar based on the UTR-2 radio telescope located near Kharkov (Ukraine). It is shown that irregularities of the electron density, whose two-dimensional spectrum in the plane perpendicular to the geomagnetic field is the power law ae⊥-p with index p≲2, are developed in the scale range 30–60 ≲ l⊥ ≲ 200–400 m. In this case, the relative fluctuations (〈δN2〉)1/2 of the electron density increase with decreasing scale l⊥=2π/ae⊥. The estimate 〈δ N2〉)1/2 ≲ 1–1.5% is obtained for a heating power of 150 MW and irregularity scales l⊥ ∼ 30–60 m at which the fluctuations are maximum. The measured dependence of the AII relaxation time, defined as the e-folding time of the amplitude-scintillation intensity, has the form τr ∝ l⊥α. If l⊥ ≲ 30–60 m, then the index α is close to 2, whereas the effective diffusion coefficient D⊥ ≃ (2–3)· 10-1 m2/s corresponds to the ambipolar cross-field diffusion coefficient in a magnetized plasma. The time τr for scales l⊥≳ 60–100 m is independent of l⊥ and increases with decreasing velocity of regular drift of the plasma. The Doppler-spectrum broadening (〈Δν2〉)1/2 ≲ 0.6 Hz observed when receiving field-aligned scattered signals can be related to chaotic motions of plasma-density disturbances whose random drift velocities amount to (〈Δv2〉)1/2 ≃ 2–3 m/s for scales l⊥ ∼ 20 m at which the power-law index changes drastically.

Three-dimensional simulation of the electromagnetic ion/ion beam instability: cross field diffusion

Abstract. In a system with at least one ignorable spatial dimension charged particles moving in fluctuating fields are tied to the magnetic field lines. Thus, in one-and two-dimensional simulations cross-field diffusion is inhibited and important physics may be lost. We have investigated cross-field diffusion in self-consistent 3-D magnetic turbulence by fully 3-dimensional hybrid simulation (macro-particle ions, massless electron fluid). The turbulence is generated by the electromagnetic ion/ion beam instability. A cold, low density, ion beam with a high velocity stream relative to the background plasma excites the right-hand resonant instability. Such ion beams may be important in the region of the Earth's foreshock. The field turbulence scatters the beam ions parallel as well as perpendicular to the magnetic field. We have determined the parallel and perpendicular diffusion coefficient for the beam ions in the turbulent wave field. The result compares favourably well (within a factor 2) with hard-sphere scattering theory for the cross-field diffusion coefficient. The cross-field diffusion coefficient is larger than that obtained in a static field with a Kolmogorov type spectrum and similar total fluctuation power. This is attributed to the resonant behaviour of the particles in the fluctuating field.

Helium-3 transport experiments in the scrape-off layer with the Alcator C-Mod omegatron ion mass spectrometer

He 3 gas was puffed from the wall into Ohmic low confinement-mode discharges of the Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1551 (1994)] tokamak and the charged states were measured near the wall with the omegatron ion mass spectrometer. Analysis of the data shows that the concentrations of singly- and doubly-ionized helium near the wall are approximately equal. The electron temperature and density at the omegatron are too low to account for ionization of helium in the local flux tube, therefore the helium is ionized in a hotter region of the edge plasma and is transported to the omegatron. A simple one-dimensional radial transport model reproduces the observed values of charge state flux and density, but only if rapid cross-field transport is included, increasing with distance from the separatrix. A constant cross-field diffusion coefficient of order 2 m2/s and an outward convection velocity profile increasing to of order 100 m/s in the far scrape-off layer is implied.

Anomalous Cross-Field Transport of Electrons Driven by the Electron-Ion Hybrid Instability Due to the Velocity Shear in a Magnetized Filamentary Plasma

The effect of cross-field velocity shear of electrons on the plasma transport has been experimentally investigated in a steady-state filamentary plasma whose effective column radius rp is smaller than the ion Larmor radius ρi and much larger than the electron Larmor radius ρe (ρe≪rp<ρi). When the shear frequency ωS (=v0/LE, where v0 is the maximum flow velocity in the sheared flow and LE is the shear scale length), which is the measure of the strength of the velocity shear, becomes much larger than the lower hybrid frequency, electrostatic plasma fluctuations of the lower hybrid range of frequency are excited in the significantly sheared flow. It is observed that these enhanced fluctuations induce the anomalous, non-ambipolar diffusion of electrons across magnetic field lines. The estimated cross-field diffusion coefficient of electrons obeys the Bohm scaling. The observed instability can be identified as the electron-ion hybrid shear instability through comparison between experimental and numerically obtained results.

Probe measurements of electron energy distributions in a strongly magnetized low-pressure helium plasma

Electron energy distributions (EED) in strongly magnetized (∼0.3 T), low-pressure (∼0.2 Pa) helium plasmas of the toroidal device “Blaamann” [K. Rypdal et al., Plasma Phys. Controlled Fusion 36, 1099 (1994)] have been measured. In the analysis of measurements, one applies a simplified expression for the limit of a strongly magnetized plasma relating the electron energy distribution to the first derivative of electron probe current with respect to the probe potential. It is shown that for the conditions investigated this approximation gives the same electron densities and slightly lower temperatures (up to 10%) as the kinetic theory for arbitrary magnetic field strength. Cylindrical probes, which are oriented along and perpendicular to the magnetic field, are used in the measurements. It is shown that these probes give nearly identical results. However, the probe that is oriented perpendicular to the magnetic field can give the electron energy distribution in a wider energy range and with better accuracy. The cross-field diffusion coefficient of electrons near the probe is estimated and shown to be classical.

Effect of Anomalous Cross-Field Diffusion on the Field Aligned Current Generation.

First, on the basis of the satellite observations of the broadband electrostatic noise and the Alfvén wave noise in the auroral magnetosphere, within a frame of the quasi-linear theory we show that the proton (anomalous cross-field) diffusion coefficient averaged over the flux tube is likely to reach a significant fraction of the Bohm rate at least in the disturbed periods. Second, as an extension of recently proposed model that a pair of the region 1 and region 2 field-aligned currents (FACs) can be generated as a result of "natural distortion" of the hot plasma torus (HPT) in the magnetosphere under the influence of the usually prevailing convection with twin vortex cells (when the interplanetary magnetic field (IMF) is southward), we study the possible effect of the anomalous cross-field diffusion on the large-scale FACs resulting from the HPT polarization. In the magnetosphere, the hot (≥ 1 keV) plasma particles are primarily distributed in a magnetic shell which is connected to two ovals of diffuse auroras on the northern and southern polar ionospheres. Such hot plasma population is called the hot plasma torus (HPT). The numerical calculations specifically show that primary modification of the FAC pattern by this effect is the appearance of the triple FAC structure (i.e., upward FAC zone sandwiched between two downward FAC zones) in the midnight sector, which can be identified from the satellite observations at least during substorm periods. As a direct consequence of formation of such a triple FAC structure, the Harang discontinuity appears in the electric potential pattern. Thus the formation of the Harang discontinuity can be understood as a result of the HPT polarization by both effects of magnetic drift and anomalous cross-field diffusion.

Plasma and neutral dynamics in a simulated tokamak gas target divertor

A stationary, detached ionization front is observed in an experimentally simulated divertor plasma (n≤3×1019 m−3, kTe≤20 eV) interacting with a hydrogen gas target. With a neutral hydrogen density, n0≊2×1021 m−3, the electron temperature at the simulated divertor target is reduced to kTe target≊2.5 eV. Up to 97% of the electron heat flux (≤7 MW/m2) is dissipated by dissociation and ionization losses and hydrogen line radiation. The plasma pressure is observed to peak near the ionization front, and a plasma flow reversal is observed in the region of reversed pressure gradient. Classical momentum flow parallel to the magnetic field and anomalous cross-field particle transport are found. The plasma flow is strongly damped by ion–neutral collisions and is subsonic. Numerical results from a one-and-one-half dimensional (11/2-D) coupled plasma–neutral fluid model (incorporating radial particle transport, recycling, and neutral gas injection) agree well with the experimental data, and indicate that the electron heat flow is classical and well described by a harmonic flux limit. The scale length of the parallel plasma pressure gradient in a gas target is found to depend on the neutral density, the electron temperature, and the cross-field diffusion coefficient.

Confinement and turbulent transport in a plasma torus with no rotational transform

In the BLAAMANN device a weakly ionized hydrogen plasma is produced by electrons accelerated from a hot, negatively biased tungsten filament and confined in a toroidal magnetic field of strength up to 0.4 T. The plasma is turbulent, with relative fluctuation levels in ne, phi and Te of 10% or more. The time-averaged state exhibits nested toroidal surfaces of constant potential and pressure, which requires an anomalous cross-field current to remove the space-charge injected by the cathode and the charge accumulated due to the Del B- and curvature drifts. Typical plasma parameters are ne approximately 1016 m-3, Te approximately 1-20 eV, Ti approximately 1 eV. The cross-field diffusion coefficient is typically Dperpendicular to approximately 30 m2 s$ -1 approximately 104*Dperpendicular to classical approximately 101*Dperpendicular to Bohm. Evidence is presented in support of the hypothesis that the plasma goes turbulent because it needs to develop an anomalous current channel, and this turbulence in turn determines the plasma transport and the time-averaged state.

Experimental studies of the radial diffusion of energetic electrons in lower-hybrid wave heated plasmas in the Alcator-C tokamak

An upper limit for the cross-field spatial diffusion coefficient of energetic electrons in moderate density tokamak discharges has been measured. The energetic electrons were generated by square wave-modulated lower-hybrid (LH) wave injection. The decay of the fast electron population for electron energies εd≥100 keV following LH radio-frequency (RF) power shutoff was inferred from the time dependence of the radial profiles of the hard x-ray bremsstrahlung emission. The experimental results were fitted to a diffusive model that includes collisional losses and electric field acceleration. The fast electron diffusion coefficient consistent with the data is Df≤0.2 m2/s, at least in the inner half of the plasma. The corresponding global confinement time of the energetic electrons is estimated to be at least a factor of 2 greater than the energy confinement time of the bulk plasma in discharges of density n̄e=8×1019 m −3.

Interpretation of a Planar Langmuir Probe Current — Voltage Characteristic in a Strong Magnetic Field

AbstractA theory of current collection by a planar Langmuir probe in a strong magnetic field with the direction perpendicular to the probe surface based on the models of Stangeby (J. Phys. D: Appl. Phys. 15 (1982) 1007) and Stanojevic et al. (Contrib. Plasma Phys. 33 (1993) 241) is presented. Besides the possibility of deriving the plasma density, n0, the electron temperature, Te, and the cross‐field diffusion coefficient, D1, from the measured probe characteristic reported in the previous studies, experiments in a strongly magnetized D.C. discharge argon plasma showed the applicability of this theory also for deriving the ion temperature, Ti.

Calculation of observable quantities using a divertor impurity interpretive code, DIVIMP

Our picture of divertor edge plasma behaviour is largely theoretical with little experimental confirmation. Questions exist with regard to impurity production mechanisms, sputtering yields, plasma ion temperatures, parallel temperature gradients, the existence of plasma flow reversal, cross-field diffusion coefficients, etc. Spatial distributions of impurity ions of successive charge states in the edge, when interpreted with an impurity production/transport code, provide a basis for discriminating amongst the various theoretical possibilities. In this paper, for an example case, a wide range of models/assumptions about the divertor edge plasma behaviour is examined with regard to the effect on the spectroscopic intensities of C+ through C5+ in the vicinity of the divertor targets. It is shown that a single spectroscopic viewing location can be sufficient to discriminate amongst most of the models/assumptions made about the divertor plasma behaviour. More refined discrimination would require additional viewing locations and diagnostics, such as Doppler temperature measurements.

Collective scattering of electromagnetic waves and cross-B plasma diffusion

Magnetized plasmas occurring in nature as well as in fusion laboratories are often irregularly shaken by magnetic field fluctuations. The so-called 'coherent scattering' of electromagnetic waves from nonuniform, irregularly moving plasmas is investigated in the case where the scattering wavelength is large compared to the Debye length, but of the order of the irregularities correlation length. The scattered signal frequency spectrum is shown to be a transform of the plasma motion statistical 'characteristics'. When the scattering wavelength is larger than the plasma motion correlation length, the frequency spectrum is shown to be of a Lorentzian shape, with a frequency width that provides a direct measurement of the cross-B particle diffusion coefficient. This is illustrated by two series of experimental results: radar coherent backscattering observations of the auroral plasma, and far infrared scattering from tokamak fusion plasma. Radar coherent backscattering shows the transition from Gauss to Lorentz scattered frequency spectra. In infrared laser coherent scattering experiments from the Tore-Supra tokamak, a particular frequency line is observed to present a Lorentzian shape, that directly provides an electron cross-field diffusion coefficient. This diffusion coefficient agrees with the electron heat conductivity coefficient that is obtained from the observation of temperature profiles and energy balance.

Parametric Study of Biased Scrape‐Off Layer

AbstractThe particle and energy balance equations in the scrape‐off layer (SOL) plasma are solved analytically in a rectangular domain. The parallel flow is supposed to be convective, whereas the cross field flow is assumed diffusive, with modifications due to a radial E field. When the energy balance equation is neglected we get a quadratic equation for λ, the e‐folding density scale length. The normalized e‐folding scale length λ/λ0 (λ0 = λ for E = 0) is a function of single parameter α (= eEλ0/2kT, where T is the plasma temperature, e the elementary charge and k is Boltzmann's constant), and monotonically increases with α. Taking the energy balance equation into account and neglecting R1 (the ionization rate), the quadratic equation is further simplified, and λ/λ0 again depends on a single parameter, determined by Q (the input power flux), D (the cross field diffusion coefficient), γ (the sheath transmission coefficient for energy) and np (the plate density). Now λ/λ0 decreases with Q and increases linearly with D, γ and np. The variation of λ/λ0 with E is estimated for TdeV and ITER. We find that, by a proper choice of parameters, biasing may be a very valuable tool to modify the SOL properties at modest E fields, provided the heat load on the divertor plate is not excessively large.

Edge conditions and turbulent fluctuations in the HL-1 tokamak

Using a floating double probe, we have determined values for the cross-field diffusion coefficient D⊥( a) (0.2–1.0 m 2/s), the gross particle confinement time τ p (10–100 ms) and the radial particle flux Γ( a) (10 19–10 20 m −2 s −1), near the limiter radius for I p = 100 kA, ñ e = (1.0–4.5) × 10 19/m 3 and B T = 1.4–2.5 T. The parametric dependence of the edge plasma parameters on B T and line averaged density, n ¯ e , has been found to be non-linear. The turbulence characteristics have been studied using spectroscopy, microwave reflectometry, magnetic coils and an array of Langmuir probes. The experimental results indicate that turbulent diffusion plays a key role in the particle transport.

Metal impurity fluxes in the TEXTOR scrape-off layer measured by collector probes in the presence of ALT II toroidal belt limiter

Impurity fluxes of metals have been determined in the scrape-off layer of TEXTOR. Time-resolved measurements have been performed using graphite collector probes. Results were found when ALT II acted as the only limiter and were compared to earlier operational phases. Typical fluxes were (1–8)×10 18 atoms m −2 s −1. The metal density was determined to be in the range 10 15 atoms m −3, and the cross-field diffusion coefficient 6 m 2 s −1. A distinct reduction of deposited metals as well as deuterium and oxygen was found in comparison to earlier measurements performed in the presence of the poloidal and ALT I limiters. Increased fluxes were observed during auxiliary ICR heating.

Plasma edge physics in the textor tokamak with poloidal and toroidal limiters

Investigations of the plasma edge in TEXTOR are presented on the one hand by comparing results obtained with poloidal and toroidal limiters and on the other hand by discussing general problems of plasma edge physics which are independent of the limiter configuration. The characteristic properties of plasma flow to the different limiters are analyzed and show e.g. that the fraction of total ion flow to the limiter is much larger in the case of a toroidal limiter (80%). Density and heat flux profiles are presented which demonstrate that for both types of limiters a significant steepening of the scrape-off layer (SOL) occurs close to the limiter, leading to a small heat load e-folding length of 5–8 mm. The velocity distribution of recycled neutral hydrogen at a main limiter has been determined from the Doppler broadening of the H α line. The data clearly show that a large fraction of particles (30–50%) is reflected at the limiter surface having energies of about the sheath potential. Significant isotopic effects (H/D) concerning the plasma edge properties and the plasma core are presented and their relation to enhanced particle and energy transport in hydrogen compared to deuterium is discussed. A decrease of the cross field diffusion coefficient with increasing density can be deduced from density profile measurements in the SOL and a comparison with density fluctuations is given. The role of oxygen for impurity release is demonstrated. A new type of wall conditioning —boronization — is described, with two major improvements for quasi stationary conditions: reduction of oxygen and better density control. Best results with ICRH have been obtained under these conditions.

Measurements of the cross-field diffusion coefficient D⊥ in the edge plasma of JET

In relating the density scrape-off layer thickness lambda n to Dperpendicular to , account is taken of two aspects of the JET configuration: (a) the poloidally-varying cross-section of plasma flux tubes in the scrape-off layer, and (b) the different limiter configurations-discrete/continuous. Edge measurements of lambda n(0) in JET made by Langmuir probes and limiter-viewing cameras are used to deduce edge values of Dperpendicular to for ohmic discharges, over a range of conditions, Ip=1-5 MA, ne=0.7-6*1019 m-3. Generally the values are found to be close to Dperpendicular to =1019/ne m2 s-1, that is, Intor-Alcator scaling.

Investigation of the wake due to a large probe using a spatially scanning Langmuir probe

This paper describes direct experimental investigation of the region of plasma perturbed by a probe. Two adjacent probes have been mounted on the DITE tokamak. The large “disturber” probe is a rectangular graphite plate that creates the main particle flow pattern and can be biased with respect to the torus. The smaller “search” Langmuir probe is located 0.5 m away on the same magnetic field line. It can be swept back and forth mechanically through the shadow of the main probe many times during each discharge. Through measurements of ion saturation current at many distinct radii, a complete map of the perturbed region has been built up and transformed into radial and poloidal coordinates. A numerical solution of the two-dimensional diffusion equations is compared with experimental data in the limiter shadow. Two zones of substantially different interconnection length are included in the model. The assumption of equal radial and poloidal cross-field diffusion coefficients ( D ⊥ = 0.18 m 2 s −1) is found to give a good fit with the data.

Probe measurements of the density and temperature profiles in the JET plasma boundary

A series of measurements of the plasma boundary parameters have been made on JET using an array of Langmuir probes and heat flux probes. The profiles decay exponentially, with typical e-folding lengths of 30–60 mm for the density and 50–100 mm for the temperature. The cross-field diffusion coefficient estimated from these data is 0.5–1 m2·s−1. Using the particle fluxes and energies, the calculated impurity production is generally consistent with that observed spectroscopically. The measured profiles have also been used to calculate the screening of impurities from the wall due to ionization in the boundary layer. It is found that metals from the wall are ionized in the boundary layer but are likely to be deposited on the limiter from where they will be re-sputtered into the plasma. The light impurities from the wall, such as carbon and oxygen, are not well screened. From the data, estimates of the electric field in the plasma have been made which indicate significant E⃗×B⃗ drifts in the poloidal direction.