Radial Particle Transport Research Articles

Radial transport processes as a precursor to particle deposition in drinking water distribution systems

Various particle transport mechanisms play a role in the build-up of discoloration potential in drinking water distribution networks. In order to enhance our understanding of and ability to predict this build-up, it is essential to recognize and understand their role. Gravitational settling with drag has primarily been considered in this context. However, since flow in water distribution pipes is nearly always in the turbulent regime, turbulent processes should be considered also. In addition to these, single particle effects and forces may affect radial particle transport. In this work, we present an application of a previously published turbulent particle deposition theory to conditions relevant for drinking water distribution systems. We predict quantitatively under which conditions turbophoresis, including the virtual mass effect, the Saffman lift force, and the Magnus force may contribute significantly to sediment transport in radial direction and compare these results to experimental observations. The contribution of turbophoresis is mostly limited to large particles (>50 μm) in transport mains, and not expected to play a major role in distribution mains. The Saffman lift force may enhance this process to some degree. The Magnus force is not expected to play any significant role in drinking water distribution systems.

Plasma transport in stochastic magnetic field caused by vacuum resonant magnetic perturbations at diverted tokamak edge

A kinetic transport simulation for the first 4 ms of the vacuum resonant magnetic perturbations (RMPs) application has been performed for the first time in realistic diverted DIII-D tokamak geometry [J. Luxon, Nucl. Fusion 42, 614 (2002)], with the self-consistent evaluation of the radial electric field and the plasma rotation. It is found that, due to the kinetic effects, the stochastic parallel thermal transport is significantly reduced when compared to the standard analytic model [A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett. 40, 38 (1978)] and the nonaxisymmetric perpendicular radial particle transport is significantly enhanced from the axisymmetric level. These trends agree with recent experimental result trends [T. E. Evans, R. A. Moyer, K. H. Burrell et al., Nat. Phys. 2, 419 (2006)]. It is also found, as a side product, that an artificial local reduction of the vacuum RMP fields in the vicinity of the magnetic separatrix can bring the kinetic simulation results to a more detailed agreement with experimental plasma profiles.

Overview of Studies on Energetic‐Ion‐Driven MHD Instabiities in Stellarator/Helical Plasmas and Comparison with Tokamaks

AbstractSuppression of anomalous radial transport of alpha particles and beam ions due to energetic ion driven MHD in‐stabilities is one of the critical issues toward D‐T burning plasma experiments in toroidal magnetic confinement devices such as tokamaks and stellarator/helical devices. This paper reports the characteristics of energetic ion driven MHD modes such as Alfvén eigenmodes (AEs) and their effects on transport of energetic ions and bulk plasma in the Large Helical Device (LHD) and some different types of stellarator/helical devices. Beneficial impacts of AEs on toroidal plasma confinement are also included. These experimental results on AEs are compared with those in tokamaks, and the important similarities and differences are pointed out that can lead to better understanding of AEs in toroidal plasmas (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Use of a Gold Neutral Beam Probe to Study Fluctuation Suppression During Potential Formation in the GAMMA 10 Tandem Mirror

In the tandem mirror GAMMA 10, plasma confinement is achieved not only by the magnetic mirror configuration but also by the high potentials at both end regions. Before applying plug–electron cyclotron resonance heating (P-ECH), drift-type fluctuations were observed in the potential and density measurements. The suppression potential and density of these fluctuations were clearly determined by using a gold neutral beam probe (GNBP) system during the potential formation by the application of P-ECH. We studied the relationship between the suppression levels of the potential fluctuations and the effects of potential produced by changing the applied electron cyclotron heating power. Moreover, the particle-flux-related values obtained by examining the phase difference between the potential and density fluctuations were measured by using the GNBP. We clearly show that radial anomalous transport induces radial particle transport, which decreases the stored energy of the plasma.

Advanced tokamak research with integrated modeling in JT-60 Upgrade

Researches on advanced tokamak (AT) have progressed with integrated modeling in JT-60 Upgrade [N. Oyama et al., Nucl. Fusion 49, 104007 (2009)]. Based on JT-60U experimental analyses and first principle simulations, new models were developed and integrated into core, rotation, edge/pedestal, and scrape-off-layer (SOL)/divertor codes. The integrated models clarified complex and autonomous features in AT. An integrated core model was implemented to take account of an anomalous radial transport of alpha particles caused by Alfven eigenmodes. It showed the reduction in the fusion gain by the anomalous radial transport and further escape of alpha particles. Integrated rotation model showed mechanisms of rotation driven by the magnetic-field-ripple loss of fast ions and the charge separation due to fast-ion drift. An inward pinch model of high-Z impurity due to the atomic process was developed and indicated that the pinch velocity increases with the toroidal rotation. Integrated edge/pedestal model clarified causes of collisionality dependence of energy loss due to the edge localized mode and the enhancement of energy loss by steepening a core pressure gradient just inside the pedestal top. An ideal magnetohydrodynamics stability code was developed to take account of toroidal rotation and clarified a destabilizing effect of rotation on the pedestal. Integrated SOL/divertor model clarified a mechanism of X-point multifaceted asymmetric radiation from edge. A model of the SOL flow driven by core particle orbits which partially enter the SOL was developed by introducing the ion-orbit-induced flow to fluid equations.

Power balance and wall erosion measurements in a helicon plasma

The power balance measurements in a 1 kW argon helicon plasma discharge are demonstrated. The quantitative wall heat flux measurements using nonintrusive infrared imaging of the glass tube surface, along with data from bolometric probes and calibrated photodiodes to measure heat flux from the rest of the plasma, are shown. For the cylindrical discharge, with radius much less than the axial length, approximately 15% of 1 kW input power is lost in the transmission lines and matching network, 54% is lost through radial particle transport to the walls, 16% is lost through radiation, and 8% is lost through ion impact in the vicinity of the antenna. Wall erosion of the confining glass tube occurs due to sputter etching by ions accelerated in the electrostatic fields produced by the antenna. Wall etch rate measurements are used to quantify particle fluxes to the wall, which are in rough agreement with particle fluxes calculated from thermal flux.

Correlation between Low-Frequency Fluctuations and Plasma Stored Energy in GAMMA 10

The instabilities observed in many magnetic confinement devices induce radial particle transport. Density and potential fluctuations were measured using a gold neutral beam probe in GAMMA 10. The plasma stored energy repeatedly increases and decreases during ioncyclotron range of frequency heating. A drift-type fluctuation was observed in both the density and the potential as the plasma stored energy decreased. These results indicated a correlation between the radial particle transport induced by drift-type fluctuations and decreasing plasma stored energy.

Study of Fluctuation Suppression during Potential Formation in the Tandem Mirror GAMMA 10

In the tandem mirror GAMMA 10, plasma confinement is achieved by not only a magnetic mirror configuration but also high potentials in both end regions. Before plug electron cyclotron resonance heating (P-ECH) was applied, drift-type fluctuations were observed in potential and density measurements. Potential and density fluctuation suppression during potential formation by the application of P-ECH was clearly observed using a gold neutral beam probe (GNBP) system. We study the relationship between the suppression levels of potential fluctuations and the effects of the produced potentials by varying the applied ECH power. Moreover, the particle-flux-related values obtained by the phase difference between the potential and density fluctuations are measured using the GNBP. We can clearly show that radial anomalous transport induces radial particle transport, which decreases the plasma stored energy.

Toroidal flow and radial particle flux in tokamak plasmas

Many effects influence toroidal flow evolution in tokamak plasmas. Momentum sources and radial plasma transport due to collisional processes and microturbulence-induced anomalous transport are usually considered. In addition, toroidal flow can be affected by nonaxisymmetric magnetic fields; resonant components cause localized electromagnetic toroidal torques near rational surfaces in flowing plasmas and nonresonant components induce “global” toroidal flow damping torque throughout the plasma. Also, poloidal magnetic field transients on the magnetic field diffusion time scale can influence plasma transport. Many of these processes can also produce momentum pinch and intrinsic flow effects. This paper presents a comprehensive and self-consistent description of all these effects within a fluid moment context. Plasma processes on successive time scales (and constraints they impose) are considered sequentially: compressional Alfvén waves (Grad–Shafranov equilibrium and ion radial force balance), sound waves (pressure constant along a field line and incompressible flows within a flux surface), and ion collisions (damping of poloidal flow). Finally, plasma transport across magnetic flux surfaces is induced by the many second order (in the small gyroradius expansion) toroidal torque effects indicated above. Nonambipolar components of the induced particle transport fluxes produce radial plasma currents. Setting the flux surface average of the net radial current induced by all these effects to zero yields the transport-time-scale equation for evolution of the plasma toroidal flow. It includes a combination of global toroidal flow damping and resonant torques induced by nonaxisymmetric magnetic field components, poloidal magnetic field transients, and momentum source effects, as well as the usual collision- and microturbulence-induced transport. On the transport time scale, the plasma toroidal rotation determines the radial electric field for net ambipolar particle transport. The ultimate radial particle transport is composed of intrinsically ambipolar fluxes plus nonambipolar fluxes evaluated at this toroidal-rotation-determined radial electric field.

Study of Radial Particle Flux due to Phase Difference Between Potential and Density Fluctuations

There is a radial particle transport as the loss induced by the fluctuations. It is possible to measure the potential and density fluctuations at the arbitrary point simultaneously by using gold neutral beam probe, and their phase difference between them. The radial particle transport induces the decreasing of the plasma stored energy. This phenomenon is estimated the theoretically-predicted loss process induced by the radial transport due to the phase difference between the potential and density fluctuations.

Particle confinement control with resonant magnetic perturbations at TEXTOR

Two very contrary particle confinement stages were obtained at TEXTOR-DED by application of resonant magnetic perturbations. On the one hand a spontaneous build up of the total number of particles N tot with correlated increase in the particle confinement time τ p was observed and on the other hand a controlled decrease of N tot and τ p – the so called stochastic particle pump out is seen. Numerical analysis of the perturbed magnetic field topology shows that both domains can be distinguished by the ratio of short connection length field lines touching a specific resonant flux surface (here the q = 5 / 2 surface) to the complete perturbed layer width. During improved particle confinement, the hyperbolic fixed points (X-points) of the pitch resonant islands are directly connected to the DED target followed by an ≲ 40 % increase in τ p . The subsequent increase in the E × B shear rate Ω E × B at the q = 5 / 2 surface and a steepening of ∇ n e ( r ) suggests a reduction of the radial particle transport. On the opposite, complete stochastisation of this island chain, i.e. a predominant diffusive field line characteristics, causes a ≲ 30 % decrease of τ p with a reduction in Ω E × B at the q = 5 / 2 surface and ∇ n e ( r ) indicating enhanced effective outward particle transport.

Analysis and modeling of edge fluctuations and transport mechanism in the Maryland Centrifugal Experiment

The Maryland Centrifugal Experiment [R. F. Ellis et al., Phys. Plasmas 12, 055704 (2005)] is a mirror machine designed to have a plasma axially confined by supersonic rotation and dominantly interchange stable by the radial shear in the azimuthal velocity. Nevertheless, residual fluctuations still persist. To investigate the presence of such fluctuations, an azimuthal array of 16 magnetic pickup coils at the edge region of the plasma has been employed. A comprehensive analysis of the magnetic fluctuations reveals that, under the imposed shear flow, only m=0 and m=2 modes are dominant; yet, the observed frequency spectrum is broadband. Using higher order spectral analysis, clear evidence of nonlinear mode coupling is detected. It is also observed that the amplification of magnetic fluctuations leads to enhanced transport consistent with the drop of the plasma density and voltage. As a result, the magnetic fluctuations start to decrease in amplitude as the central plasma pressure drops. In return, the anomalous radial particle and momentum transport are reduced; thus, the plasma confinement improves. As the plasma pressure starts to build up, the plasma voltage increases, destabilizing the m=2 interchange mode. The cycle of enhanced transport and intermittent fluctuations repeats itself. A two-dimensional magnetohydrodynamics code in slab geometry is employed to investigate the dynamics of the primary interchange instability and to assess the level of transport. For very low sheared rotation, a broad spatial spectrum of unstable modes is obtained. As the sheared rotation is increased, the high mode numbers become stabilized and low mode numbers dominate the spectrum. Both the experimental data obtained from the azimuthal array probes and the simulations in case of parabolic shear flow show clear evidence of nonlinear mode coupling, explaining the broadband frequency spectrum for low mode numbers. A detailed comparison of spatiotemporal dynamics of simulations with the experimental data is presented.

Measurement of magnetic fluctuation-induced particle flux (invited)

Magnetic field fluctuation-induced particle transport has been directly measured in the high-temperature core of the MST reversed field pinch plasma. Measurement of radial particle transport is achieved by combining various interferometry techniques, including Faraday rotation, conventional interferometry, and differential interferometry. It is observed that electron convective particle flux and its divergence exhibit a significant increase during a sawtooth crash. In this paper, we describe the basic techniques employed to determine the particle flux.

Escape patterns of chaotic magnetic field lines in a tokamak with reversed magnetic shear and an ergodic limiter

The existence of a reversed magnetic shear in tokamaks improves the plasma confinement through the formation of internal transport barriers that reduce radial particle and heat transport. However, the transport poloidal profile is much influenced by the presence of chaotic magnetic field lines at the plasma edge caused by external perturbations. Contrary to many expectations, it has been observed that such a chaotic region does not uniformize heat and particle deposition on the inner tokamak wall. The deposition is characterized instead by structured patterns called magnetic footprints, here investigated for a nonmonotonic analytical plasma equilibrium perturbed by an ergodic limiter. The magnetic footprints appear due to the underlying mathematical skeleton of chaotic magnetic field lines determined by the manifold tangles. For the investigated edge safety factor ranges, these effects on the wall are associated with the field line stickiness and escape channels due to internal island chains near the flux surfaces. Comparisons between magnetic footprints and escape basins from different equilibrium and ergodic limiter characteristic parameters show that highly concentrated magnetic footprints can be avoided by properly choosing these parameters.

Current drive by EC waves in the presence of magnetic islands and transport

In this paper we address the problem of current drive by electron cyclotron (EC) waves in the presence of magnetic islands and transport. Our approach makes use of quasilinear theory by numerically solving the Fokker–Planck equation in cylindrical geometry. We take into account the actual geometry of the islands along the calculations as well as the changes in the plasma density profile due to the action of the radial particle transport. The particle transport is supposed to have a magnetic origin. The waves are assumed to be launched and propagated in the equatorial plane of the tokamak, as in the slab geometry. Our results show that the use of equilibrium profiles as usually done in the studies on neoclassical tearing mode control may not be a better choice and point to the need for taking into account the actual island geometry.

Chaotic transport in reversed shear tokamaks

For tokamak models using simplified geometries and reversed shear plasma profiles, we have numerically investigated how the onset of Lagrangian chaos at the plasma edge may affect the plasma confinement in two distinct but closely related problems. Firstly, we have considered the motion of particles in drift waves in the presence of an equilibrium radial electric field with shear. We have shown that the radial particle transport caused by this motion is selective in phase space, being determined by the resonant drift waves and depending on the parameters of both the resonant waves and the electric field profile. Moreover, we have shown that an additional transport barrier may be created at the plasma edge by increasing the electric field. In the second place, we have studied escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall, when there are resonant modes due to the action of an ergodic magnetic limiter. A non-monotonic safety factor profile has been used in the analysis of field line topology in a region of negative magnetic shear. We have observed that, if internal modes are perturbed, the distributions of field line connection lengths and magnetic footprints exhibit spatially localized escape channels. For typical physical parameters of a fusion plasma, the two Lagrangian chaotic processes considered in this work can be effective in usual conditions so as to influence plasma confinement. The reversed shear effects discussed in this work may also contribute to evaluate the transport barrier relevance in advanced confinement scenarios in future tokamak experiments.

Spatiotemporal temperature fluctuation measurements by means of a fast swept Langmuir probe array

Stationary Langmuir probe measurements of ion saturation current and floating potential in a plasma cannot give direct information on density and plasma potential fluctuations in the presence of temperature fluctuations. This problem can be avoided if the probe bias voltage is continuously swept faster than the fluctuation time scale, recording the current-voltage characteristic. This article reports the development of a spatiotemporal highly resolving Langmuir probe array with 15 fast swept tips, operating in the strongly magnetized, collisionless edge plasma of the Wendelstein 7-AS stellarator [Plasma Phys. Controlled Fusion 31, 1579 (1989)]. The probe tips are aligned in the poloidal direction, the tip spacing is 2 mm, and the sweeping frequency is 1.4 MHz. Current and voltage data are sampled with 50 MHz. The high bandwidth of the measurement is achieved by placing miniaturized differential amplifiers close to the probe tips in order to do an impedance transform. The surface-mounting technology and an additional inverse feedback module are utilized, allowing for an input voltage range of +/-100 V, and a common mode rejection rate of 55 dB at 4 MHz, which is sufficient to resolve the nonlinear probe characteristic. For the evaluation of the data, a fit model for stationary probes is employed and found adequate. Changes of the plasma parameters during one voltage sweep are taken into account by a linear interpolation of the fit parameters. Spatio-temporal fluctuation data gained by a fast swept Langmuir probe array, which can be relevant for the turbulent radial transport of particles and energy, are presented.

Transition from Bohm to classical diffusion due to edge rotation of a cylindrical plasma

The outer region of the plasma column of a large, linear plasma device is rotated in a controlled fashion by biasing a section of the vacuum chamber wall positive with respect to the cathode (Er<0). The magnitude and temporal dependence of the observed cross-field current, produced when the bias voltage is applied, is consistent with ion current arising from ion-neutral collisions. Flow speeds in the outer regions of the plasma column exceed the local sound speed. In the nonrotating plasma column, cross-field, radial particle transport proceeds at the Bohm diffusion rate. Rotation, above a threshold bias voltage, reduces cross-field transport from Bohm to classical rates, leading to steeper radial density profiles. Reduction of particle transport is global and not isolated to the region of flow shear. The transition from the nonrotating to the rotating plasma edge in the linear plasma column is similar to the low confinement to high confinement mode transition observed in tokamaks when Er<0.

Observation of Radial Particle Transport Induced by the Fluctuation Measured with a Gold Neutral Beam Probe

The radial particle flux induced by the fluctuation is measured by a Gold Neutral Beam Probe. Then the transient transport phenomenon induced by the fluctuation is investigated in the tandem mirror GAMMA 10. When the drift wave is excited at the central cell, the density near the center is reduced and the divergence of the flux becomes similar to the time derivative of the electron density. It shows that the density reduction is caused by the flux induced by the drift wave. After the density reduction, the drift wave is saturated and comes to the steady state because the density reduction accompanies the reduction of density gradient. Therefore, the transport phenomenon accompanying the growth and saturation of the drift wave is observed experimentally. In the steady state, the phase difference obeys the boltzman relation including the electron non-adiabatic term.

Simulating radial diffusion of energetic (MeV) electrons through a model of fluctuating electric and magnetic fields

Abstract. In the present work, a test particle simulation is performed in a model of analytic Ultra Low Frequency, ULF, perturbations in the electric and magnetic fields of the Earth's magnetosphere. The goal of this work is to examine if the radial transport of energetic particles in quiet-time ULF magnetospheric perturbations of various azimuthal mode numbers can be described as a diffusive process and be approximated by theoretically derived radial diffusion coefficients. In the model realistic compressional electromagnetic field perturbations are constructed by a superposition of a large number of propagating electric and consistent magnetic pulses. The diffusion rates of the electrons under the effect of the fluctuating fields are calculated numerically through the test-particle simulation as a function of the radial coordinate L in a dipolar magnetosphere; these calculations are then compared to the symmetric, electromagnetic radial diffusion coefficients for compressional, poloidal perturbations in the Earth's magnetosphere. In the model the amplitude of the perturbation fields can be adjusted to represent realistic states of magnetospheric activity. Similarly, the azimuthal modulation of the fields can be adjusted to represent different azimuthal modes of fluctuations and the contribution to radial diffusion from each mode can be quantified. Two simulations of quiet-time magnetospheric variability are performed: in the first simulation, diffusion due to poloidal perturbations of mode number m=1 is calculated; in the second, the diffusion rates from multiple-mode (m=0 to m=8) perturbations are calculated. The numerical calculations of the diffusion coefficients derived from the particle orbits are found to agree with the corresponding theoretical estimates of the diffusion coefficient within a factor of two.