Radial Currents Research Articles

Equilibrium of current driven rotating liquid metal

In view of great importance of magneto-rotational instability (MRI) as a fundamental mechanism for angular momentum transfer in magnetized stellar accretion disks, several research centers are involved in experimental study of MRI under laboratory conditions. The idea of the experiment is to investigate the rotation dynamics of well conducting liquid (liquid metal) between two cylinders in axial magnetic field. In this Letter, an experimental scheme with immovable cylinders and fluid rotation driven by radial current is considered. The analytical solution of a stationary flow was found taking into account the external current. Results of axially symmetric numerical simulations of current driven fluid dynamics in experimental setup geometry are presented. The analytical solution and numerical simulations show that the current driven fluid rotation in axial magnetic field provides the axially homogeneous velocity profile suitable for MRI study in classical statement.

Current driven vortex dynamics in the Corbino disk

To study the shear rigidity of vortex systems, we simulate the radial current driven vortex dynamics in the two-dimensional Corbino disk geometry of type-II superconductors. The radial currents in the disk induce the spatially inhomogeneous Lorentz force, yielding the local shear stress to the vortex lattice. Molecular dynamics simulations of a point vortex model demonstrate that (1) at low currents the vortices rotate as a rigid solid, (2) at large currents the vortices move freely as a liquid, (3) at intermediate currents the complicated plastic slippage of neighboring annular section of the vortex array occurs, and (4) temperature effects enhance the plastic slippage events.

One-dimensional spherical elementary current systems and their use for determining ionospheric currents from satellite measurements

Abstract The method of 1D spherical elementary current systems (SECS) is a new way for determining ionospheric and field-aligned currents in spherical geometry from magnetic field measurements made by a low-orbit satellite. In contrast to earlier methods, the full ionospheric current distribution, including both divergence-free and curl-free horizontal currents, as well as field-aligned currents, can be determined. Placing infinitely many 2D SECSs of identical amplitudes at a constant latitude results in two types of 1D SECSs, which are independent of longitude, and by superposition can reproduce any ionospheric and field-aligned current system with the same property. One type of the 1D SECSs is divergence-free and toroidal with a poloidal magnetic field, and the other type is curl-free and poloidal. Associated with the divergence of the curl-free type are radial currents. The magnetic field of the combined curl-free 1D SECS and field-aligned currents is toroidal and restricted to the region above the ionosphere. Ionospheric currents are determined by placing several 1D SECSs at different latitudes and choosing their amplitudes in such a way that their combined magnetic field as closely as possible fits the one measured by the satellite. The 1D SECS method has been tested using both modeled and real data from the CHAMP satellite, and found to work excellently in 1D cases.

Particle pinch mitigated by radial currents in the electric tokamak

A dominant particle pinch is observed in Ohmic plasmas of the electric tokamak (ET) associated with enhanced poloidal rotation. The density increases dramatically, with strong profile peaking. In pinch dominated particle transport, the pinch velocity profile is determined from the Thomson density profile data. The pinching rate is controlled with soft gas puffing. Hard puffing produces inverted density profiles that do not pinch due to the MHD instabilities. The build-up time of the density is typically 1 s. Due to density accumulation in the absence of significant core fuelling, the characteristic Troyon limit (βN = βaB/I ∼ 3,%, m, T, MA) is reached even in Ohmic plasmas. Density ramps are terminated by internal disruptions due to beta collapse without any significant radiative energy loss. The loop voltage remains low (0.4 V) during the ramp. Prior to, and during the ramp, we observe no reduction in the electrostatic fluctuations in the present experiments. Electrode biasing, using the J × B force, shows that the density accumulation can be reduced and even stopped through slowing the poloidal rotation (reducing the magnitude of the background negative Er). This observation is consistent with the presence of a ‘viscous’ pinch driven by the dominance of the radial electric field through ion mobility. Other neoclassical pinch mechanisms (i.e. Ware and thermoelectric) contribute to the density accumulation and are shown to be secondary effects as revealed by the radial current modulation effects. The easily achieved thermal Mach numbers are ±0.15 for poloidal and ±0.2 for toroidal rotation using the present biaser. There is no significant spontaneous toroidal rotation. The spontaneous poloidal rotation seen in Ohmic plasmas has the thermal Mach number Mp ∼ 0.15 across the measured profile where r/a > 0.5. This rotation is sufficient to account for the observed radial pinch velocity.

On neutral-beam injection counter to the plasma current

It is well known that when neutral beams inject ions into trapped orbits in a tokamak, the transfer of momentum between the beam and the plasma occurs through the torque exerted by a radial return current. It is shown that this implies that the angular momentum transferred to the plasma can be larger than the angular momentum of the beam, if the injection is in the opposite direction to the plasma current and the beam ions suffer orbit losses. On the Mega-Ampere Spherical Tokamak (MAST) [R. J. Akers, J. W. Ahn, G. Y. Antar, L. C. Appel, D. Applegate, C. Brickley et al., Plasma Phys. Controlled Fusion 45, A175 (2003)], this results in up to 30% larger momentum deposition with counterinjection than with co-injection, with substantially increased plasma rotation as a result. It is also shown that heating of the plasma (most probably of the ions) can occur even when the beam ions are lost before they have had time to slow down in the plasma. This is the dominant heating mechanism in the outer 40% of the MAST plasma during counterinjection.

Observation of Centrifugally Driven Interchange Instabilities in a Plasma Confined by a Magnetic Dipole

Centrifugally driven interchange instabilities are observed in a laboratory plasma confined by a dipole magnetic field. The instabilities appear when an equatorial mesh is biased to drive a radial current that causes rapid axisymmetric plasma rotation. The observed instabilities are quasicoherent in the laboratory frame of reference; they have global radial mode structures and low azimuthal mode numbers, and they are modified by the presence of energetic, magnetically confined electrons. Results from a self-consistent nonlinear simulation reproduce the measured mode structures.

ELECTROMAGNETIC EFFECTS IN SUPERCONDUCTORS IN STATIONARY GRAVITATIONAL FIELD

The general relativistic modifications to the resistive state in superconductors of second type in the presence of a stationary gravitational field are studied. Some superconducting devices that can measure the gravitational field by its red-shift effect on the frequency of radiation are suggested. It has been shown that by varying the orientation of a superconductor with respect to the earth gravitational field, a corresponding varying contribution to AC Josephson frequency would be added by gravity. A magnetic flux (being proportional to angular velocity of rotation Ω) through a rotating hollow superconducting cylinder with the radial gradient of temperature ∇rT is theoretically predicted. The magnetic flux is assumed to be produced by the azimuthal current arising from Coriolis force effect on radial thermoelectric current. Finally the magnetic flux through the superconducting ring with radial heat flow located at the equatorial plane interior of the rotating neutron star is calculated. In particular it has been shown that nonvanishing magnetic flux will be generated due to the general relativistic effect of dragging of inertial frames on the thermoelectric current.

Excitation of the centrifugally driven interchange instability in a plasma confined by a magnetic dipole

The centrifugally driven electrostatic interchange instability is excited for the first time in a laboratory magnetoplasma. The plasma is confined by a dipole magnetic field, and the instability is excited when an equatorial mesh is biased to induce a radial current that creates rapid axisymmetric plasma rotation. The observed instabilities appear quasicoherent in the lab frame of reference; they have global radial mode structures and low azimuthal mode numbers, and they are modified by the presence of energetic, magnetically confined electrons. The mode structure is measured using a multiprobe correlation technique as well as a novel 96-point polar imaging diagnostic which measures particle flux along field lines that map to the pole. Interchange instabilities caused by hot electron pressure are simultaneously observed at the hot electron drift frequency. Adjusting the hot electron fraction α modifies the stability as well as the structures of the centrifugally driven modes. In the presence of larger fractions of energetic electrons, m=1 is observed to be the dominant mode. For faster rotating plasmas containing fewer energetic electrons, m=2 dominates. Results from a self-consistent nonlinear simulation reproduce the measured mode structures in both regimes. The low azimuthal mode numbers seen in the experiment and simulation can also be interpreted with a local, linear dispersion relation of the electrostatic interchange instability. Drift resonant hot electrons give the instability a real frequency, inducing stabilizing ion polarization currents that preferentially suppress high-m modes.

Wavelet Mie Representations for Solenoidal Vector Fields with Applications to Ionospheric Geomagnetic Data

A wavelet technique, the wavelet Mie representation, is introduced for the analysis and modeling of the earth's magnetic field and corresponding electric current distributions from geomagnetic data obtained within the ionosphere. The considerations are essentially based on two well-known geomathematical keystones, (i) the Helmholtz decomposition of spherical vector fields and (ii) the Mie representation of solenoidal vector fields in terms of poloidal and toroidal parts. The wavelet Mie representation is shown to provide an adequate tool for geomagnetic modeling in the case of ionospheric magnetic contributions and currents which exhibit spatially localized features. An important example is ionospheric currents flowing radially onto or away from the earth. To demonstrate the functionality of the approach, such radial currents are calculated from vectorial data of the MAGSAT and CHAMP satellite missions.

Semiconductor Crystal Growth by Modified Vertical Gradient Freezing with Electromagnetic Stirring

This paper presents a numerical model for the unsteady transport of a dopant during the VGF process by submerge d heater growth with a steady axial magnetic field and a steady radial electric current. Electromagnetic (EM) stirring can be induced in the gallium antimonide melt just above the crystal growth interface by applying a small radial electric current in the melt together with an axial magnetic field. The application of EM stirring provides a significant convective dopant transport in the melt so that the crystal solidifies with relatively good radial homogeneity. Dopant distributions in the crystal and in th e melt at several different stages during growth are presented.

Rotation dynamics and stability of collisional edge layers in tokamak plasmas

An earlier neoclassical transport theory for a collisional edge layer with steep radial gradients in the toroidal damping timescale is extended, to include also the faster poloidal damping timescale. In order to determine the stability behaviour of poloidal and toroidal rotations in a tokamak plasma, a two-timescale analysis is applied. It is observed that the poloidal and toroidal spin-up tendencies are strongly coupled by nonlocal interactions, although these evolve essentially on different timescales. Effects of charge exchange interactions, neutral beam injection, and a radial polarization current on both rotation speeds are consistently included in the model.

The electroviscous force between charged particles: beyond the thin-double-layer approximation

We have investigated the hydrodynamic drag force between charged particles in electrolyte solutions, specifically the electroviscous force that arises from the distortion of the electrical double layers by the flow field. We report an improvement on the thin-double-layer theory (S.G. Bike, D.C. Prieve, J. Colloid Interface Sci. 136 (1990) 95–112), using a more accurate boundary condition for the radial charge current. The differences become important when the double layers start to overlap. We have found that nonlinear hydrodynamic effects are small, whereas nonlinear electric effects can be significant, in some instances leading to qualitatively different behavior. If the ion diffusivities are highly asymmetric, the electroviscous force can be reduced by an order of magnitude when there is an excess of the mobile ions in the double layer. The common supposition that there are substantial differences in the electroviscous force predicted by constant-charge and constant-potential boundary conditions is incorrect; our calculations show that it is an artifact introduced by the Debye–Hückel approximation.

Instability versus collapse in a flow driven by the radial electric current

A flow of an electrically conducting fluid induced by a spherically symmetric current (discharging from a point source located on the fluid free surface) has a striking feature. As increasing total current J reaches a threshold, a jet propagating from the source along the axis of symmetry collapses, i.e., velocity becomes unbounded on the axis. It is shown here that the flow becomes unstable at J smaller than the threshold. For a flow in a conical region, θ<θcone (θ is the polar angle from the axis of symmetry), the instability leads to either a time-oscillating or steady-swirling flow depending on θcone. In a half-space, θcone=90°, the instability is oscillatory. The steady swirl first develops as J increases in a cone with θcone<85°.

On the impossibility of measuring a galvano-gravitomagnetic effect with current carrying semiconductors in a space-based experiment

In this paper we investigate the feasibility of a recently proposed space-based experiment aimed to detect the effect of the Earth's gravitomagnetic field in space-borne semiconductors carrying radial electric currents and following identical, in principle, circular equatorial orbits along opposite directions. Identical voltages of gravitomagnetic origin would be induced across the orbiting semiconductors, while equal and opposite gravitoelectric larger voltages would be generated. It turns out that the deviations from the proposed idealized orbital configuration due to the unavoidable orbital injection errors would make impossible the measurement of the gravitomagnetic voltage of interest.

Decay of enhanced density and damping of plasma flows after the electrode biasing termination on the CASTOR tokamak

Electrode biasing is a standard tool for modification of both edge and global plasma parameters on the CASTOR tokamak (R=0.4 m,a=85 mm,BT=1.3 T,Ip1≈9 kA,qa≈10). During a steady state phase of a discharge, a polarization voltage is applied on an electrode immersed into the edge plasma. This voltage causes radial currents that create radial electric field and, due to theE×B drift, they cause an enhanced rotation. Then, as a consequence, the interaction with walls decreases and particle confinement and density increase. Recently, the decay of plasma density and plasma flows after the termination of the biasing period was investigated on the CASTOR tokamak. These observations are linked to processes and mechanisms that control generation of radial electric fields in plasmas and damping ofE×B sheared flows and that therefore represent a key issue for understanding the transition to improved confinements modes. In the contribution, measured time scales of the transition to the ohmic regime after the biasing termination will be shown. Further, possible consequences of these measured scales for the valuation and explanation of important processes in the plasma will be discussed.

Experimental study and two-dimensional modelling of the plasma dynamics of magnetically driven shock waves in a coaxial tube

Plasma shocks can be magnetically driven during high current discharges in low-pressure gases, induced by an external electric circuit. Radial currents between two coaxial electrodes can be accelerated to velocities of the order of 10 cm µs−1, thus being an effective method to transform potential energy in kinetic energy. A series of experiments were conducted using a low energy plasma focus device to measure the dynamics of plasma shocks in coaxial tubes. The radial position of the current sheath near the closed end of the electrodes was determined by means of a magnetic probe. The pinching time at the open end of the electrodes was measured using a Rogowski coil. Both, the movement and shaping of the plasma sheath were modelled by means of finite elements. The sheath was represented by coupled conical segments carrying current, mass, internal energy and momentum. The Lorentz force accelerates each element in its normal direction, which leads to the continuous reshaping of the sheath. The numerical results are compared against the experimental data showing good agreement.

Vertical gradient freezing of doped gallium–antimonide semiconductor crystals using submerged heater growth and electromagnetic stirring

An investigation of the melt growth of uniformly doped gallium–antimonide (GaSb) semiconductor crystals as well as other III–V alloy crystals with uniform composition are underway at the US Air Force Research Laboratory at Hanscom Air Force Base by the vertical gradient freeze (VGF) method utilizing a submerged heater. Stirring can be induced in the GaSb melt just above the crystal growth interface by applying a small radial electric current in the liquid together with an axial magnetic field. The transport of any dopant and/or alloy component by the stirring can promote better melt homogeneity and allow for more rapid growth rates before the onset of constitutional supercooling. This paper presents a numerical model for the unsteady transport of a dopant during the VGF process by submerged heater growth with a steady axial magnetic field and a steady radial electric current. As the strength of the electromagnetic (EM) stirring increases, the convective dopant transport increases, the dopant transport in the melt reaches a steady state at an earlier time during growth, and the top of the crystal which has solidified after a steady state has been achieved exhibits axial dopant homogeneity. For crystal growth with stronger EM stirring, the crystal exhibits less radial segregation and the axially homogeneous section of the crystal is longer. Dopant distributions in the crystal and in the melt at several different stages during growth are presented.

A simulation study of currents in the Jovian magnetosphere

We have used a global magnetohydrodynamic simulation of the interaction of Jupiter's magnetosphere with the solar wind to investigate the effects of the solar wind on the structure of currents in the jovian magnetosphere. A thin equatorial current sheet with currents flowing around Jupiter dominates Jupiter's middle magnetosphere. However, in our simulations this current is not uniform in azimuth. It is weaker on the day side than the night side with local regions where the current density decreases by more than 50%. In addition to this ring current the current sheet contains strong radial “corotation enforcement” currents. Outward radial currents are found at most local times but there are regions with currents directed toward Jupiter. The current pattern is especially complex in the local afternoon and evening regions. In the near equatorial magnetosphere the field-aligned current pattern also is complex. There are regions with currents both toward and away from Jupiter's ionosphere. However, when we mapped the currents from the inner boundary of the simulation to the ionosphere we found a pattern more like that expected for the ionosphere to drive corotation with currents away from Jupiter at lower latitudes and currents toward Jupiter at higher latitudes. Since upward field-aligned currents are associated with aurora at the Earth they may be associated with aurora at Jupiter. The upward field-aligned currents map to larger distances on the night side (40 R J to 60 R J) than on the day side (20 R J to 30 R J). In the simulations changing the solar wind dynamic pressure did not make major changes in the current sheet or field-aligned currents (both were slightly stronger for higher pressures). The interplanetary magnetic field had a stronger effect on the currents with the strongest currents for northward IMF. However, it took a very long time for the magnetosphere to respond to the changes in the IMF.

Numerical simulation of plasma profile changes in TEXTOR by externally driven radial polarization currents

An improved version of the 2D multifluid code TECXY is used to simulate polarization or biassing experiments on TEXTOR tokamak. In the numerical model the condition of globally ambipolar radial transport in the transition layer is replaced by externally driven radial polarization currents. They are produced by inserting and biassing an electrode with its tip a few centimeters inside the separatrix. The ensuing additional potential drop in the transition layer and the concomitant plasma profile changes are calculated for both signs of polarization. A comparison of modelling results with experimental measurements is presented. The fluid model reproduces some features of the L–H-like transition, but not the locally very high electric fields after bifurcation which are probably related to kinetic effects at very low collisionality.

Formation and Dynamics of Very Deep Negative Potential Well in the Small Tokamak Device CSTN-IV

We achieved a potential well more than fifty times deeper than the plasma electron temperature, down to -0.3 kV with the electrode biasing, by the cross-field radial arcing current of up to 150 A which flows between the small electron-emitting electrode (LaB6) inserted to the plasma center and the stainless-steel wall of vacuum chamber. The empirical scaling of the radial resistance of plasma Rr on the radial arcing current Ib and the toroidal magnetic field BT is found to be Rr ∼ Ib-1.2BT1.0. Structural dynamics of negative potential well formation is observed: the potential dip propagates from the plasma core to the periphery. The ion saturation current also increases, starting from the inner region. The fluctuation frequency in Isat changes abruptly from 200 kHz to 30 kHz in a time of around 0.25 ms after negative biasing.