Strong Radial Electric Field Research Articles

Characteristic length scales and formation of vortices in the Ginzburg-Landau-Higgs model in the presence of a uniform background charge

In this brief report we consider a non-local Abelian Higgs model in the presence of a neutralizing uniform background charge. We show that such a system possesses vortices which key feature is a strong radial electric field. We estimate the basic properties of such an object and characteristic length scales in this model.

Optimized confinement discharges in the stellarator W7-AS

In addition to the well known H-mode, other types of discharges with enhanced core energy confinement can be observed in the stellarator W7-AS. In this contribution, the properties of some particular examples of those optimized confinement (OC) discharges are presented. These are characterized, besides improved core energy confinement, by strong negative radial electric fields and high ion temperatures in the gradient region, steep density profile gradients and a high penetration depth of neutrals, and small edge electron densities. The role of these plasma parameters for the OC discharges is investigated quantitatively by a numerical model.

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.

Confinement in W7-AS and the role of radial electric field and magnetic shear

Improved neoclassical electron confinement in the centre of low-density ECRH plasmas has been observed in the presence of a strong positive radial electric field, which resembles the electron root solution of the neoclassical ambipolarity condition but is obviously driven by the loss of ECRH-generated suprathermal electrons. At higher densities and with NBI heating, a high confinement regime substantially above the ISS95-scaling and different from the H-mode is established with a strongly sheared negative radial electric field at the boundary. The application of plasma-current induced magnetic shear reveals that confinement in W7-AS is essentially determined by perturbations at high-order rational surfaces. For optimum confinement, these resonances have either to be avoided in the boundary region or magnetic shear must be sufficiently large. Independent of its sign, magnetic shear can reduce electron energy transport which is enhanced in the presence of such resonances to the neoclassical level.

Bootstrap current and neoclassical transport in tokamaks of arbitrary collisionality and aspect ratio

A multi-species fluid model is described for the steady state parallel and radial force balance equations in axisymmetric tokamak plasmas. The bootstrap current, electrical resistivity, and particle and heat fluxes are evaluated in terms of the rotation velocities and friction and viscosity coefficients. A recent formulation of the neoclassical plasma viscosity for arbitrary shape and aspect ratio (including the unity aspect ratio limit), arbitrary collisionality, and orbit squeezing from strong radial electric fields is used to illustrate features of the model. The bootstrap current for the very low aspect ratio National Spherical Torus Experiment [J. Spitzer et al., Fusion Technol. 30, 1337 (1996)] is compared with other models; the largest differences occur near the plasma edge from treatment of the collisional contributions. The effects of orbit squeezing on bootstrap current, thermal and particle transport, and poloidal rotation are illustrated for an enhanced reverse shear plasma in the Tokamak Fusion Test Reactor [D. Meade and the TFTR Group, Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. I, p. 9]. Multiple charge states of impurities are incorporated using the reduced ion charge state formalism for computational efficiency. Because the force balance equations allow for inclusion of external momentum and heat sources and sinks they can be used for general plasma rotation studies while retaining the multi-species neoclassical effects.

Influence of Biased Electrode on Plasma Confinement in the Tohoku University Heliac

Observations of an increase in electron density triggered by electrode biasing are reported in the Tohoku University Heliac (TU-Heliac). The biased electrode, which is located deep inside the plasma, induces a strong positive radial electric field, after which the line density increases by a factor of 2, the electron density profile steepens and the fluctuation level drops. We estimate the damping force opposing poloidal rotation experimentally and compare it with various versions of the neoclassical theory. The experimental results agree in that the measured damping force has a local maxima at |M p|=1–2 and tends to be proportional to M p in the high speed region (|M p|>3–6), where M p is the poloidal Mach number. For |M p|<1–2, however, the dependence of the measured damping force on M p differs a little from theoretical predictions.

Effect of plasma radial electric field on motional Stark effect measurements and equilibrium reconstruction

The motional Stark effect (MSE) has become the leading diagnostic technique for measurement of the internal poloidal field profile in neutral beam heated tokamak plasmas. The technique relies upon the measurement of the polarization angle of Stark broadened neutral beam Dalpha emission due to the strong E= nu b*B motional electric field. In many recently discovered enhanced confinement regimes in tokamaks, a strong radial electric field Er is also present in the plasma. It is shown that in these cases, the effect of Er on the interpretation of MSE measurements is significant and cannot be neglected. The importance of this effect is illustrated with the analysis of the q profile in a high performance discharge from the DIII-D tokamak

Tandem mirror experiments in GAMMA 10

Confinement of ion cyclotron resonance heating (ICRH) plasmas in the GAMMA 10 tandem mirror [Phys. Rev. Lett. 55, 159 (1985)] has been investigated. Magnetohydrodynamic (MHD) stability is provided by the axisymmetrized minimum-B system. Ion confining and thermal barrier potentials are produced only by electron cyclotron resonance heating (ECRH). Ions are heated to several keV and hot ion modes, where Ti/Te≳(mi/me)1/3, are produced. Ion pressure in the central cell increases approximately linearly both with the power radiated from the antennas and with the magnetic field. A record ion temperature of about 10 keV is obtained at the maximum magnetic field (∼0.57 T). Thermonuclear fusion neutrons are detected in a deuterium/hydrogen mixture plasma for the first time in a tandem mirror. In typical GAMMA 10 operations, strong radial electric fields are naturally produced, and density fluctuations are suppressed. Axial confinement of the core plasma is consistent with the classical potential confinement, indicating radial confinement is better than axial confinement.

Turbulent edge transport in the Princeton Beta Experiment-Modified high confinement mode

The first probe measurements of edge turbulence and transport in a neutral beam induced high confinement mode (H-mode) are reported. A strong negative radial electric field is directly observed in H-mode. A transient suppression of normalized ion saturation and floating potential fluctuation levels occurs at the low confinement mode to high confinement mode (L–H) transition, followed by a recovery to near low mode (L-mode) levels. The average poloidal wave number and the poloidal wave-number spectral width are decreased, and the correlation between fluctuating density and potential is reduced. A large-amplitude coherent oscillation, localized to the strong radial electric field region, is observed in H-mode but does not cause transport. In H-mode the effective turbulent diffusion coefficient is reduced by an order of magnitude inside the last closed flux surface and in the scrape-off layer. The results are compared with a heuristic model of turbulence suppression by velocity-shear stabilization.

The physics of transport barrier formation in the PBX-M H-mode

Measurements of edge profiles, turbulence, and turbulent-driven transport were made inside the last-closed flux surface (LCFS) and in the scrape-off layer (SOL) of PBX-M L-mode and H-mode plasmas using a fast reciprocating Langmuir probe diagnostic. Direct measurements of the potential profile confirm the generation of a strong inward radial electric field (Er approximately -100 V/cm) just inside the LCFS in H-mode. Density and potential fluctuation levels are reduced at the L-H transition, resulting in significantly lower turbulent transport. The edge density gradient then steepens in response to the reduced cross-field transport. After a stable H-mode edge equilibrium is formed, the fluctuation amplitudes recover back to nearly L-mode values. The poloidal wavenumber spectrum is narrowed in the transport barrier, and the density and potential fluctuations are decorrelated. The reduction in turbulent transport occurs across the LCFS and SOL regions and is not localized to the region of strong radial electric field.

Stability of cylindrical Couette flow of a radially polarised dielectric liquid in a radial temperature gradient

A linear stability analysis is used to predict the onset of convective instability in an annulus of a pure dielectric liquid between two long coaxial cylinders. The liquid experiences a radial temperature gradient and a strong radial ac electric field. When the two cylinders are stationary our analysis gives reasonable agreement with experiment data on silicone oils. If the central cylinder is warmer and is allowed to rotate, the stability of the Couette flow is predicted to vary with the temperature difference Δ T between the cylinders in a manner that depends markedly on the gap to radius ratio δ = ( r 2 − r 1)/ r 1 where r 1 and r 2 are the radii of the inner and outer cylinders. When δ < 10 −4 the critical Taylor number is relatively insensitive to Δ T but when δ ⩾ 10 −1 a very small temperature difference can completely destabilize the Couette flow.

Measurement of the radial electric field in the ASDEX tokamak

Estimates of the radial electric field Er at the plasma periphery are obtained by measuring the drift velocities of low-Z impurity ions (He II, B IV, C III). The drift velocities are determined from the differential Doppler shift of visible line emission observed along opposite viewing directions. The principle of the measurement, including contributions from the diamagnetic drift, as well as radial gradients in the excitation rate and the effect of integrating along the line of sight are discussed in detail. The measured line of sight averaged drift velocities can be strongly influenced by the location and shape of the Er profile, especially if, as measured on other tokamaks, it is localized to a narrow region just within the separatrix. Values of Er estimated by assuming a constant radial profile underestimate maximum local values. During the H*-phase, however, high line of sight averaged perpendicular drift velocities of the B IV ions of a least 15 km/s in the electron diamagnetic drift direction are observed. From this, the presence of a strong negative radial electric field of at least 25 kV/m in the plasma edge region is inferred. Values of the B IV ion poloidal drift velocity calculated from an appropriate neoclassical theory are in the same direction as those measured. However, the calculated line of sight averaged values are much smaller than the measured ones. This reinforces the conclusion that a strong negative radial electric field is present just within the separatrix during the H-mode

Multidimensional and Multifluid Plasma Edge Modelling: Status and New Directions

AbstractThe plasma boundary in magnetic confinement devices is observed in experiments and in computations to contain radial and poloidal variations in plasma potential, strong radial electric fields and large poloidal drift flows in addition to the parallel flow toward the plasma sheath boundaries and the particle recycling from the walls. The global power balence is largely influenced by impurity radiation and thus by impurity transport in the edge region. The behavior of the edge region is related to global confinement in ways not yet fully known and motivates further improvements in edge plasma modelling.General multifluid transport equations are reviewed in the context of the current status of plasma edge modelling. It is assumed that the macroscopic transport in the plasma edge region is suitable for a moments description, or fluid model. Progress is well established in computational treatments of the standard paradigm including classical parallel and anomalous cross‐field flux coupled to neutrals in analytic or Monte Carlo steady state computations. Formulation of momentum diffusivities and curvature drift in toroidal coordinates are considered. New directions include defining the dominant influence of drifts and non‐ambipolar flows, improving coupled plasma‐neutral transport calculations, and treating impurity flow in full multifluid models. Calculation of the plasma potential driving the E × B drift in the scrape‐off layer can be extended inside the last closed flux surface by conserving the divergence of the plasma currents. Coupled plasma‐neutral fluids using a neutral diffusion approximation show promise for recycling calculations. Impurity transport based on full multifluid treatment along the field lines has shown good agreement with divertor experiments.Advanced topics for the near future include plasma core‐edge transport coupling and eventually the direct solution of coupled momentum equations rather than the presently assumed cross‐field ‘anomalous’ flux functions. In the edge region, plasma sheath boundary conditions are a significant sink for plasma particles and heat; a small coupling between the momentum components in the plasma edge can be sufficient to drive an ‘anomalously’ large efflux from the core plasma.

High-resolution simulation of field emission

High-resolution simulations of field emission electron sources have been made using the electron optics program EGN2. Electron emission distributions are made using the Fowler-Nordheim equation. Mesh resolution in the range of 1-5 {angstrom} is required to adequately model surface details that can result in emission currents in the range found experimentally. A typical problem starts with mechanical details with dimensions of about 1{mu}. To achieve high resolution a new boundary is defined by the tip, a nearby equipotential line, and a pair of field lines. The field lines (one of which is normally the axis of symmetry) define Neumann boundaries. This new boundary is then used by the boundary preprocessor POLYGON to create an enlarged version of the problem, typically by a factor of ten. This process can be repeated until adequate resolution is obtained to simulate surface details, such as microprotusion, that could sufficiently enhance the surface electric fields and cause field emission. When simulating experimental conditions under which emission of several microamperes per tip were observed, it was found that both a locally reduced work function and a surface protrusion were needed to duplicate the experimental results. If only a local region of reduced work function is used,more » the area involved and the extent of the reduction both need to be very large to reproduce the emission. If only a surface protrusion is used, it is possible to get the observed emission current with a reasonable protrusion of length a few times radius, but then the resulting beam spreads over a very large solid angle due to the strong local radial electric fields. 8 refs., 14 figs., 1 tab.« less

Properties of dc helicity injected tokamak plasmas

Several dc helicity injection experiments using an electron beam technique have been conducted on the Current Drive Experiment (CDX) [Phys. Rev. Lett. 59, 2165 (1987)] and the Continuous Current Tokamak (CCT) [Phys. Rev. Lett. 63, 2365 (1989)]. The data strongly suggest that tokamak plasmas are being formed and maintained by this method. The largest currents driven to date are 1 kA in CDX (qa =5) and 6 kA in CCT (qa =3.5). An initial comparison of discharge properties with helicity theory indicates rough agreement. Current drive energy efficiencies are 9% and 23% of Ohmic efficiency in two cases analyzed. Strong radial electric fields are observed in these plasmas that cause poloidal rotation and, possibly, improved confinement.

Injection and propagation of a nonrelativistic electron beam and spacecraft charging

Two‐dimensional numerical simulations have been carried out in order to study the injection and propagation of a nonrelativistic electron beam from a spacecraft into a fully ionized plasma in a magnetic field. Contrary to the earlier results in one dimension, a high‐density electron beam whose density is comparable to the ambient density can propagate into a plasma. A strong radial electric field resulting from the net charges in the beam causes the beam electrons to spread radially, reducing the beam density. When the injection current exceeds the return current, significant charging of the spacecraft is observed along with the acceleration of the ambient electrons back to the spacecraft. As a result, a beam current much larger than the thermal return current can be injected into space. Recent data on the electron beam injection from the Spacelab 1 (SEPAC) are discussed.

Radial ion transport due to unstable double layers in a plasma

A motion of ions perpendicular to the magnetic field is observed experimentally during a large amplitude potential oscillation caused by the formation and disruption of moving double layers in a plasma. This radial motion is closely related to an appearance of the strong radial electric field formed between a high potential plasma composing the double layer and a wall surrounding the plasma column. The field accelerates the ions outwards from the plasma and gives rise to an ion transport towards the wall.

The role of fluctuation-induced transport in a toroidal plasma with strong radial electric fields

Previous work employing digitally implemented spectral analysis techniques is extended to demonstrate that radial fluctuation-induced transport is the dominant ion transport mechanism in an electric field dominated toroidal plasma. Such transport can be made to occur against a density gradient, and hence may have a very beneficial effect on confinement in toroidal plasmas of fusion interest. It is shown that Bohm or classical diffusion down a density gradient, the collisional Pedersen-current mechanism, and the collisionless electric field gradient mechanism described by Cole (1976) all played a minor role, if any, in the radial transport of this plasma.

Fluctuations and turbulence in an electric field bumpy torus plasma

In this experiment, strong radial electric fields were imposed along the minor radius of a steady-state bumpy torus plasma by biasing it with electrodes maintained at kilovolt potentials. Digitally implemented spectral analysis techniques were used to experimentally investigate the characteristics of the fluctuations of plasma number density and electrostatic potential below the ion plasma and ion cyclotron frequencies. The dispersion relation between ω and k for azimuthally propagating waves was determined experimentally, and, when linear, was consistent with the E/B drift velocity. Above 100 kHz, the power spectra of both density and potential fluctuations obeyed a power law of the form P(ω) α ω−p. The spectral index p of this plasma turbulence assumed values which varied with operating conditions. The fluctuations of density and potential ranged from highly coherent rotating spokes, to highly turbulent conditions with a Gaussian distribution in amplitude.

Lower Hybrid Drift Instability Driven by Cross-Field Electron Current and Ion Heating

A strong radial electric field E r is produced in an inhomogeneous plasma column under a weak magnetic field B by applying a dc voltage between a cathode and a heating anode of hollow cylindrical type. Then, the lower hybrid drift instability is excited by a cross-field current due to E r × B drift of electrons. Experimental results of the instability are explained by the dispersion equation, where a negative energy wave of a drifting electron beam interacts with the lower hybrid wave in the background plasma. As the instability is developed, the radial electron current increases and hot ions up to 1 keV are produced.