Radial Particle Transport Research Articles

First results from the multichannel interferometer system on HSX

Measuring the equilibrium electron density distribution and its response to perturbations provides important information to magnetically confined plasma research. A multichannel interferometer system is now routinely operating on the new quasihelically symmetric stellator (HSX) to measure the equilibrium profile and electron density dynamics. The interferometer system has nine viewing chords with 1.5 cm spacing. The source is a bias-tuned Gunn diode at 96 GHz with passive solid-state tripler providing output at 288 GHz (8 mW). The HSX plasma is produced by 28 GHz electron cyclotron resonance heating and first results of the interferometer measurement are reported. The density spatial distribution is reconstructed from the measured line-integrated density. At high density [n̄e>2×1012 cm−3], an m=1 density oscillation with frequency of 1–2 kHz is observed. Plans to determine the radial particle flux and transport coefficients will be discussed.

Multichannel visible spectroscopy diagnostic for particle transport studies in the H-1 heliac

A multichannel spectroscopy diagnostic has been developed to study cross-field particle transport in the radiation-dominated low-temperature plasmas (Te<100 eV) in the H-1 heliac. The optical setup covers the full plasma minor radius in the poloidal plane collecting light from ten parallel chords arranged tangentially to the flux surfaces. The light collected from the plasma is coupled into optical fibers and through interference filters into photomultipliers. Two such ten-fiber arrays are aligned parallel to one another to allow the simultaneous monitoring of two different spectral lines. The net radial electron particle flux is determined from the continuity equation by integrating over the ionization source term in the steady-state partially ionized plasma. The diagnostic measures the neutral line intensities and their ratios (in case of helium using the line ratio technique) and also measures excited neutral and ion spectral lines (in case of the argon plasma transport studies). A comparative analysis of the radial particle transport in the low- and high-confinement regimes is presented.

Effects of poloidal variation of neutral density on Pfirsch–Schlüter transport near the tokamak edge

Effects of neutral particles on plasma flows and radial transport in a collision-dominated plasma are discussed, with a particular attention given to the modifications due to a poloidal variation of the neutral density. It is found that neutrals are of no importance if the radial particle transport is on a Pfirsch–Schlüter level. If, on the other hand, anomalous effects increase this transport to the Pfirsch–Schlüter radial heat transport level or higher, neutral effects become important in determining the radial heat transport, radial electric field, and the ion parallel flow velocity.

New Insights into Hydrocyclone Operation

Hydrocyclones form an important stage within conveying systems for dewatering or size classification. Over the past few decades they have been subject to significant modeling and experimental investigations. Yet, it is only with modern developments in computational fluid dynamics (CFD) and nonintrusive measurements such as tomography and laser techniques that a proper understanding of the internal flow dynamics is being developed. This paper presents new insight into the mechanisms governing the air-core dynamics and particle separation within the hydrocyclone that have been achieved by means of CFD. In particular, the flow field is identified to be distinctly asymmetric, such that the commonly assumed deterministic and symmetric assumptions of particle separation are inaccurate. In fact, radial particle transport is identified to rely upon the positive correlation of the mean and fluctuating components of radial velocity. The mechanism for air-core development during start-up is also inferred and for the first time related to experimental observation. High-speed video and radiographic measurements have provided validation for the predicted flowfield. In addition, the potential for application of tomographic techniques to the challenging verification of high-solids CFD has been demonstrated.

Effect of aggregation and shear rate on the dispersion of red blood cells flowing in venules.

Previous in vitro studies of blood flow in small glass tubes have shown that red blood cells exhibit significant erratic deviations in the radial position in the laminar flow regime. The purpose of the present study was to assess the magnitude of this variability and that of velocity in vivo and the effect of red blood cell aggregation and shear rate upon them. With the use of a gated image intensifier and fluorescently labeled red blood cells in tracer quantities, we obtained multiple measurements of red blood cell radial and longitudinal positions at time intervals as short as 5 ms within single venous microvessels (diameter range 45-75 microm) of the rat spinotrapezius muscle. For nonaggregating red blood cells in the velocity range of 0.3-14 mm/s, the mean coefficient of variation of velocity was 16.9 +/- 10.5% and the SD of the radial position was 1.98 +/- 0.98 microm. Both quantities were inversely related to shear rate, and the former was significantly lowered on induction of red blood cell aggregation by the addition of Dextran 500 to the blood. The shear-induced random movements observed in this study may increase the radial transport of particles and solutes within the bloodstream by orders of magnitude.

Numerical simulation of phase-space flows in the Collisionless Terrella experiment

Non-Maxwellian plasmas confined in a magnetic dipole can become unstable to hot electron interchange (HEI) instability, which saturates nonlinearly exciting drift-resonant fluctuations with complex time-varying frequency spectrum. A fully self-consistent nonlinear model, which includes /spl mu/, J preserving guiding center drift Hamiltonian dynamics of hot electrons, reproduces the frequency sweeping observed experimentally, and suggests spontaneous formation and consequent inward propagation of phase-space holes- coherent structures in phase-space, that can cause particle radial transport. We present the results of the numerical simulation showing the time evolution of the phase-space.

Particle concentration and local mass flux measurements in two-phase flows with PDA. Application to a study on the dispersion of spherical particles in a turbulent air jet

The Phase Doppler Anemometry (PDA) technique is suitable for spherical particle concentration and local flux measurements in dispersed two-phase flows. When particles have three-directional paths, accurate measurements can be achieved if an integral method of calculation over the effective probe volume and an efficient auto-calibration process are employed. An experimental study is carried out on an axisymmetric two-phase jet. A post-processing of the measurements has been developed to obtain a quite complete characterisation of the particle dispersion throughout the flow. The axial local flux distribution is normalised on the transversal sections with the injected mass rate for each particle size class (by means of correction coefficients). Particle concentration and radial fluxes are calculated from the axial flux and velocity results. A balance of particles over a cylindrical volume permits to calculate further estimates of the particle radial flux, used for testing of the results. The detailed study of the spatial distribution of particles has been made up to 10 nozzle diameters (10 D) from the jet exit, in five transversal sections. The local axial flux profiles show two development sub-zones: (i) the near to nozzle zone is dominated by the exit conditions. Mainly, a wide distribution of particle path directions produces a strong radial particle transference (directional classification); (ii) the second sub-zone shows a more regular development controlled by the drag of the mean gas velocity field together with radial particle transport by gas turbulence, rebounding crashes of particles and other effects.

A non-localsynergism between electron cyclotron waves and lower hybrid waves induced by transport

In this paper, we study the effects of particle radial transport on theelectron cyclotron (EC) and lower hybrid (LH) power deposition profilesand current drive efficiency. We consider a tokamak plasma under thecombined action of LH waves, EC waves, collisions and spatial transportof electrons across the magnetic surfaces, and consider situations inwhich the spatial location of the peaks of power deposition profiles forEC and LH waves is not the same. Our results, found from numericalsolution of the diffusion equation, indicate significant modification inthe LH power deposition profile and show evidence of a non-localsynergism between LH and EC waves when transport is present, leading tostrong enhancing of RF current drive efficiency.

On guiding centre orbits of particles in toroidal systems

Passing particles in toroidal geometry are described in a Hamiltonianformalism including time-dependent electric and magnetic fields. Theseparticles are characterized by a non-vanishing toroidal velocity. Theintroduction of the toroidal angle as independent variable instead of thetime allows one to derive a map of the poloidal plane onto itself, which issimilar to the Poincaré map of magnetic field lines. In time-dependentfields the energy of the particles is not conserved leading to two coupledmaps, which is characteristic for autonomous systems with three degrees offreedom. As a result, Arnold diffusion occurs and Kolmogorov-Arnold-Moser (KAM) surfaces, which inthe case of energy conservation separate stochastic regions in phase space,can be bypassed leading to enhanced radial transport of particles. Themechanism of enhanced transport is resonance streaming along resonancelines, which constructs the complex Arnold web. The structure of this webdepends on the drift rotational transform of drift orbits and the toroidaltransit time of passing particles. Numerical examples of Arnold diffusionof test particles will be given. The theory will be applied to passingparticles in a toroidal plasma and to trapped particles in stellarators andtokamaks. Some numerical examples of Arnold diffusion of circulatingparticles will be given.

Two-Dimensional Vortex Dynamics in a Potential-Confined Electron Plasma

We study dynamics of discrete vortex strings interacting in a background vorticity distribution by using a magnetized electron plasma confined by a potential distribution in a cylindrical trap, and demonstrate relevant 2-dimensional features characterizing the incompressible dissipation-free guiding-center fluid. Some specific elementary processes are examined and compared with a recently proposed theoretical model that describes a motion of a point vortex moving up a hill of background vorticity distribution. Radial transport of particles is observed to be very limited and associated with several conserved parameters.

Investigation of Radial Particle Transport in the GAMMA 10 Tandem Mirror

Radial particle transport in GAMMA 10 was investigated under a quasi-steady state condition plasma. The transport analysis was carried out with changing the boundary conditions, in order to reconstruct the density profile which is consistent with the measured data. From the above result, the best fit profile to the measured one was obtained with the diffusivity of 0.57 m2/s. The particle diffusivity in an additional gas puffing experiment was estimated. The result of the transport analysis was also compared with the diffusion coefficient expected from classical diffusion processes.

Two dimensional modelling approach to transport properties of the TEXTOR-DED laminar zone

An important operational range for TEXTOR-DED is the case of a high ergodization at the plasma edge. Under these conditions, the edge magnetic field forms a proper ergodic layer and a laminar zone. The laminar zone is established by magnetic field lines which intersect wall elements after only a few toroidal turns (open ergodic system). For this, both the heat and particle transport in the plasma edge are dominated by the laminar zone which shows a well defined structure compared with that of the ergodic layer. For the present analysis the regions containing field lines with connection lengths corresponding to one or to two poloidal turns are of particular interest; the radial width of these regions is of the same order as the width of the unperturbed SOL of a `classical' limiter or divertor configuration. Field lines running poloidally twice around the torus introduce a particular new feature, they impose a connection between radially separated areas and thus enhance the radial temperature and particle transport. A new 2-D modelling approach code for the laminar zone of an ergodic divertor has been developed which is strongly oriented on the topology of the magnetic field lines in the plasma edge. A 2-D finite element method is used in order to model the perpendicular transport of particles and energy. For obtaining a solution of the parallel transport, an analytical model is discussed providing expressions for averaged particle and energy sources. By considering the topological properties of the magnetic field and corresponding assumptions in the code, the transport calculation in the perturbed plasma edge gives a first insight into the generic transport properties of the TEXTOR-DED laminar zone. As an important application for later experiments the power fluxes to the wall elements are estimated. They show a strong variation perpendicular to the perturbation coils and a medium variation over the helical divertor footprints.

Particle transport in a parallel-plate semiconductor reactor: Chamber modification and design criterion for enhanced process cleanliness

Convective, diffusive, and thermophoretic particle transport in a parallel-plate semiconductor reactor is investigated. Measurements that illustrate particle transport in the reactor are presented and a Eulerian continuum particle transport formulation is used to quantitatively explain the measurements. Experimental and numerical results show that particles formed in the parallel-plate region are confined in a thin sheath (∼2 cm) between the “hot” wafer and “cold” showerhead inlet. This sheath is located at the point where downward convective transport balances upward transport by thermophoresis. The particle sheath location is independent of particle size but is dependent on gas flow rates and temperature of the wafer and showerhead inlet. In addition, experimental and numerical results show that as particles exit the parallel-plate region, the radial thermophoretic particle transport can produce “ring-like” contaminant deposits on the outer wall of the reactor under certain flow conditions. We propose a simple reactor design modification and an analytic design criterion to avoid particle deposition on the chamber walls.

Self‐consistent quasi‐static parallel electric field associated with substorm growth phase

A new approach is proposed to calculate the self‐consistent parallel electric field associated with the response of a plasma to quasi‐static electromagnetic perturbations (ω < k‖vA, where vA is the Alfvén velocity and k‖ the parallel component of the wave vector). Calculations are carried out in the case of a mirror geometry, for ω < ωb (ωb being the particle bounce frequency). For the sake of simplification the β of the plasma is assumed to be small. Apart from this restriction, the full Vlasov‐Maxwell system of equations has been solved within the constraints described above (ω < k‖vA and ω < ωb) by [Le Contel et al., this issue] (LC0, hereafter), who describe self‐consistently the radial transport of particles during the substorm growth phase. LC00 used an expansion in the small parameter Te/Ti (Te/Ti is typically 0.1 to 0.2 in the plasma sheet) to solve the quasi‐neutrality condition (QNC). To the lowest order in Te/Ti < 1, they found that the QNC implies (1) the existence of a global electrostatic potential Χ0 which strongly modifies the perpendicular transport of the plasma and (2) the parallel electric field vanishes. In the present study, we solve the QNC to the next order in Te/Ti and show that a field‐aligned potential drop proportional to Te/Ti does develop. We compute explicitly this potential drop in the case of the substorm growth phase modeled as in LC000. This potential drop has been calculated analytically for two regimes of parameters, and ( being the bounce averaged magnetic drift frequency equal to , where ky is the wave number in the y direction and the bounce averaged magnetic drift velocity). The first regime ( ) corresponds to small particle energy and/or small ky, while the second regime ( >) is adapted to large energies and/or large ky. In particular, in the limit and , where uy is the diamagnetic velocity proportional to the pressure gradient, we find a parallel electric field proportional to the pressure gradient and directed toward the ionosphere in the dusk sector and toward the equator in the dawn sector. This parallel electric field corresponds to a potential drop of a few hundred volts that can accelerate electrons and produce a differential drift between electrons and ions.

Effect of the radial electric field on the fluctuation-produced transport in the H-1 heliac

Highly coherent low-frequency fluctuations are studied experimentally in the low electron temperature plasma in the H-1 toroidal heliac. The fluctuations, presumably pressure-gradient-driven resistive MHD modes, produce considerable radial particle transport. A build-up of strong sheared radial electric field leads to dramatic modifications in the fluctuation-driven transport. These modifications correlate with sudden changes in the plasma confinement, resembling low-to-high transitions in other machines. Strong negative shear in the radial electric field eventually leads to the suppression of the fluctuations, while the onset of the strong positive shear correlates with the reversal of the fluctuation-driven particle flux, leading to the inward-directed pinch. It is concluded that the radial electric field modifies radial profiles of the fluctuation propagation velocity due to the Doppler shift, and it is this velocity shear which is important for the transport modifications.

Theory of advanced stellarators

The main features of advanced stellarators are the optimized coil system which can be extrapolated to reactor size, improved properties of plasma equilibrium with reduced Shafranov shift and a stability limit which is sufficient to meet the requirements of a commercial fusion reactor. The key element to achieve these goals is the proper shape of the magnetic surfaces and minimization of the geodesic curvature of magnetic field lines. As a consequence, Pfirsch-Schlüter currents and radial particle transport are reduced. Neoclassical transport becomes small enough so that ignition is not endangered. The theoretical basis of the advanced stellarator is a systematic procedure to compute plasma equilibria with reduced Pfirsch-Schlüter currents. The close relation between neoclassical transport and viscous damping indicates that a reduction of geodesic curvature not only reduces radial transport but also leads to a reduction of viscous damping, and thus, facilitates the rotational spin-up of the plasma. For this reason achievement of shear flow and reduced anomalous transport may be expected in advanced stellarators. The paper discusses the various aspects of advanced stellarators and describes their basic properties.

Anomalous impurity transport: charge-state diffusion due to atomic processes in tokamak plasmas

A new interpretation of anomalous impurity transport in tokamak plasmas is presented. An alternative (compared with conventional) approach reveals the relative importance of the transport of impurity particles and the diffusion of impurity charge states due to ionization and recombination processes. The set of coupled transport equations is reduced to a novel kinetic equation which is analysed in terms of charge-state transport including both the transport of particles and charge-state diffusion due to atomic processes. From the analysis of this equation and from available spectroscopic data the relationship between diffusion coefficients of these types of transport is found. It is concluded that charge-state diffusion exceeds the radial diffusion of particles significantly. Hence, the conventional empirical coefficients of anomalous diffusion DA and convective velocity VA mainly model charge-state diffusion rather than radial transport of impurity particles. A simple model is developed to describe the diffusion of impurity charge states with ionization rates enhanced by non-thermal effects of electron energy distribution and with recombination rates dominated by charge exchange of impurities on hydrogen atoms. The model is tested by comparing the simulated and measured radial profiles of line emission from oxygen, scandium and iron impurities taken from the TFR and PLT tokamaks. The radial profiles of neutrals and of superthermal electrons are obtained by modelling of spectroscopic data instead of the conventional empirical coefficients DA and VA.

Effects of radial particle diffusion on the electron cyclotron absorption coefficient in tokamak plasmas in the presence of lower hybrid waves

In this paper we study the effects of particle radial transport on the electron cyclotron absorption coefficient. We consider a tokamak plasma under the combined action of lower hybrid waves, electron cyclotron waves, collisions and spatial transport of electrons across magnetic surfaces. Our results, found from the numerical solution of the diffusion equation, indicate a significant modification in the profile of the electron cyclotron absorption coefficient around the resonant surface when transport is taken into account relative to the situation when transport is absent.

Neoclassical Aspects of Transport in ITER Plasmas with High Axial Safety Factors

The neoclassical bootstrap current, parallel electrical resistivity and radial particle and heat transport properties are examined for a reference ITER low current plasma with elevated axial safety factor, q(0), and reverse shear, q′ < 0. The results are compared with two other reference cases at full current and differing plasma profiles. In each of the cases it is found that higher Z impurities are fairly robustly expelled from the core by ion temperature gradient screening, although the screening is weaker in the high q(0) plasma because of its lower collisionality. The bootstrap current is strongly enhanced in the high q(0) case as expected. Potato orbits do not significantly modify the results.

Investigation of oscillations and anomalous transport in a hydrogen hollow cathode discharge by a spatially three-dimensional two-fluid model

A spatially three-dimensional two-fluid model for electrons and ions has been developed in order to describe the plasma state of a magnetized hollow cathode arc burning in hydrogen at low pressure. In this direct current (DC) supplied discharge strong self-excited periodical oscillations have been observed previously, where a helically shaped plasma column rotates eccentrically around the magnetic field axis. The theoretical description of this plasma is based on the system of two-fluid equations formulated by Braginskii. After some estimations and approximations derived from the experimental results and by limiting the discussion to stationary and low-frequency phenomena, the system of equations can be reduced and a second-order differential equation of elliptic type for the plasma potential is derived. Using the measured spatial distributions of time resolved electron density and temperature as input data, this differential equation is solved numerically and the spatial distributions of the electric field, drift velocities, current densities and other quantities can be calculated. The results of our calculations show that an eccentrically rotating minimum of the plasma potential exists, while the arc current is concentrated in an annular region of maximum electron temperature. The magnitude of the radial particle transport coefficient is found to be in the order of the Bohm diffusion coefficient, which is about one order of magnitude larger than the classical diffusion coefficient. The measured oscillation frequencies can be explained by the drift frequency.