Transport of the ion bounced by the plug potential caused by radial electric field in the tandem mirror

In the tandem mirror, plug potentials are created in the plug/barrier cells by microwave injection, and also anchor cells with a minimum B magnetic field configuration are installed in order to reduce the MHD instability. Existence of the ion bounced by the plug potential (PP-bounced ion) is essential for the ion confinement in the tandem mirror. We study the transport of the PP-bounced ion on the assumption that the cross-sectional shape of the magnetic flux tube is slightly different from the cross-sectional shape of the equi-potential surface at the mirror throats of the anchor cell as small deviation from the equilibrium state. The radial-potential profile of the core plasma is adjusted by controlling the electrostatic potentials of the coaxially separated end plates. We find that the spread type of radial-potential profile is effective for the confinement of the plug-potential-bounced ion.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

MM-4U中等离子体约束位形和不稳定性的实验研究

给出了MM-4u中等离子体约束位形和不稳定性的实验结果。测得的等离子体电位轴向分布表明,该装置中能够建立起负电位轴对称串级镜约束位形;测得的密度分布与电位分布有相似形式。初步探索了等离子体参数与工程参数的关系。实验还发现在低密度情况下存在低频振荡。通过对振荡信号进行线性相关分析,根据扰动的振荡和传播特性,推断出这种振荡为离子声不稳性。不稳定性产生的可能机制是由于电子束穿过低密度本底等离子体的漂移速度超过离子声速而激发起来的。 关键词：     

Manipulation of cold atoms by an adaptable magnetic reflector

Adaptive optics for cold atoms has been experimentally realized by applying a bias magnetic field to a static magnetic mirror. The mirror consist of a 12-mm-diameter piece of commercial videotape, having a sine wave of wavelength 25.4 μm recorded in a single track across its width, curved to form a concave reflector with radius of curvature R=54 mm. We have studied the performance of the mirror by monitoring the evolution of a 24 μK cloud of ⁸⁵Rb atoms bouncing on it. A uniform static external magnetic field was added to the mirror field causing a corrugated potential from which the atoms bounce with increased angular spread. The characteristic angular distribution of the surface normal is mapped at the peak of the bounce for atoms dropped from a height of R/2 and at the peak of the second bounce for a drop height of R/4. In a second experiment a time-dependent magnetic field was applied and the angular distribution of the cloud was measured as a function of field frequency. In this scheme we demonstrate a corrugated potential whose time-dependent magnitude behaves like a diffraction grating of variable depth. Finally a rotating field was added to generate a corrugated potential that moves with a velocity given by the product of the external field rotation frequency and the videotape wavelength. This travelling grating provides a new method of manipulation as cold atoms are transported across the surface by surfing along the moving wave. Two theoretical methods have been developed to predict the behaviour of atoms reflecting from these stationary, variable magnitude and moving corrugated potentials. A simple analytic theory provides excellent agreement for reflection from a stationary corrugated potential and gives good agreement when extended to the case of a travelling grating. A Monte Carlo simulation was also performed by brute force numeric integration of the equations of motion for atoms reflecting from all three corrugated potential cases. Received: 1 December 1999 / Revised version: 3 February 2000 / Published online: 5 April 2000     

Modelling of Lévy walk kinetics of charged particles in edge electrostatic turbulence in tokamaks

We model and discuss the possible types of motion that charged particles may undergo in a stationary and spatially periodic electrostatic potential and a homogeneous magnetic field. The model is considered to be the simplest approximation of more complex phenomena of plasma edge turbulence in tokamaks. Therein, low frequency turbulence appears in the plasma edge, resulting in a fluctuation of the electron density, and also in the generation of a turbulent electrostatic field. Typical parameters of this turbulent electrostatic field are an electrical potential amplitude of 10–100 V and wave numbers k≈10³ m^-1. In our model, we consider these regimes, together with a homogeneous magnetic field with a magnitude of 1 T. We investigate the dynamics of singly-ionized carbon ions – a typical plasma impurity – with kinetic energies on the order of 10 eV. Besides the obvious Larmor and drift motions, a motion of random-walk and of Lévy walk character appear therein. All of these types of motion can play an important role in the modelling of the anomalous diffusion of particles from the plasma edge turbulence region. The dynamics mentioned will cause an inevitable escape of energetic particles and thus of power loss from the thermonuclear reactor. Moreover, Lévy walk kinetics represents a very interesting kind of kinetics, currently of great interest, which was previously not so often discussed.     

Radial drift invariant in long-thin mirrors

In omnigenous systems, guiding centers are constrained to move on magnetic surfaces. Since a magnetic surface is determined by a constant radial Clebsch coordinate, omnigeneity implies that the guiding center radial coordinate (the Clebsch coordinate) is a constant of motion. Near omnigeneity is probably a requirement for high quality confinement and in such systems only small oscillatory radial banana guiding center excursions from the average drift surface occur. The guiding center radial coordinate is then the leading term for a more precise radial drift invariant I _r , corrected by oscillatory “banana ripple” terms. An analytical expression for the radial invariant is derived for long-thin quadrupolar mirror equilibria. The formula for the invariant is then used in a Vlasov distribution function. Comparisons are first made with Vlasov equilibria using the adiabatic parallel invariant. To model radial density profiles, it is necessary to use the radial invariant (the parallel invariant is insufficient for this). The results are also compared with a fluid approach. In several aspects, the fluid and Vlasov system with the radial invariant give analogous predictions. One difference is that the parallel current associated with finite banana widths could be derived from the radial invariant.     

A Tandem Mirror Coil Design to Reduce Radial Losses

A simple modification of a standard tandem mirror coil design is shown to significantly improve the radial confinement of particles without sacrificing interchange stability. In the new design, the local departure of the particle drift surfaces from the vacuum flux surface is small everywhere, thereby reducing radial particle losses. This is achieved by adjusting the coil parameters to approximate the transport-minimizing magnetic field profiles of Myra et al. near the magnetic axis. Using this technique as a guide, a family of coil configurations is studied. It is shown that reducing the elliptical fanning of the flux surfaces on the inboard side of each quadrupole anchor leads to a great reduction in the radial transport.     

Effect of E × B electron drift and plasma discharge in dc magnetron sputtering plasma

Study of electron drift velocity caused by Etimes B motion is done with the help of a Mach probe in a dc cylindrical magnetron sputtering system at different plasma discharge parameters like discharge voltage, gas pressure and applied magnetic field strength. The interplay of the electron drift with the different discharge parameters has been investigated. Strong radial variation of the electron drift velocity is observed and is found to be maximum near the cathode and it decreases slowly with the increase of radial distance from the cathode. The sheath electric field, E measured experimentally from potential profile curve using an emissive probe is contributed to the observed radial variation of the electron drift velocity. The measured values of the drift velocities are also compared with the values from the conventional theory using the experimental values of electric and magnetic fields. This study of the drift velocity variation is helpful in providing a useful insight for determining the discharge conditions and parameters for sputter deposition of thin film.     

Diagnostics for radial electric field measurements in hot magnetized plasmas

Measurements of the radial electric field profile in magnetically confined plasmas have yielded important new insights in the physics of L-H transitions, edge biasing and/or the active control of Internal and Edge Transport Barriers. The radial electric field is not an easy plasma parameter to diagnose. Techniques to measure the radial electric field in the plasma core are the Heavy Ion Beam Probe and the Motional Stark Effect. An indirect method that is quite often applied is to derive the electric field from measurements of the poloidal and toroidal rotation velocities via the radial ion force balance. This paper will first briefly explain the need for detailed measurements of the radial electric field profile. Subsequently, the various diagnostics to measure this parameter will be reviewed. The emphasis will be especially put on recent trends, rather than on an exhaustive overview. Presented at 5th Workshop “Role of Electric Fields in Plasma Confinement and Exhaust”, Montreux, Switzerland, June 23–24, 2002. Partner in the Trilateral Euregio Cluster     

Vacuum Arc Plasma Centrfuge for Element and Isotope Separation

Vacuum arcs have been studied extensively in the past several decades with applications primarily in the areas of switching, vacuum remelting, and vapor deposition. Application of the vacuum arc for element and isotope separation has been studied recently and is reviewed in this paper. An arc was produced in a 30-cm-diameter 4-m-long cylindrical chamber with coaxially mounted electromagnets providing a 2.6-m-long constant axial magnetic field of up to 6 kG. The vacuum discharge between a solid cathode and a mesh anode was triggered electrically. A pulse-forming network (PFN) of 70-m? impedance provided nearly constant-current discharge pulses of several kiloamps and 6-12-ms duration. The magnetized plasma column, flowing axially from the anode with a typical velocity of 106 cm/s, rotated nearly as a solid body. This rotation was due to the E × B drift, produced by the axial magnetic field and the radial electric field across the column. A typical rotation frequency was 105 rad/s. The centrifugal effect due to the rotation caused a radial redistribution of ions within the plasma column, thereby producing elemental and isotope enrichment. The separation was observed to increase exponentially with the square of the radius. Enrichments of up to 300 percent were measured in a Cu-Zn plasma. The radial plasma density profile was found to be roughly Gaussian, with central electron densities of about 1013 cm-3. The radial potential profile across the column was measured and found to be parabolic with radius.     

Radial Distributions of Dusty Plasma Parameters in a DC Glow Discharge

A non‐stationary non‐local kinetic model for radial distributions of dusty plasma parameters based on the solution of Boltzmann equation for electron energy distribution function is presented. Electrons and ions production in ionizing collisions and their recombination on dust particle surface were taken into account. The drift‐diffusion approximation for ions was used. To obtain the self‐consistent radial distribution of electric potential the Poisson equation was used. It is shown that at high dust particle density the recombination of electrons and ions can exceed their production in ionization collisions in the region of dusty cloud. In this case the non‐monotonous radial distribution of the electric field is formed, the radial electric field becomes reversed and the radial electron and ion fluxes change their direction toward the center of the tube (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Formation of steep gradients with plasma detachment at grazing B-field incidence at a plasma-wall transition

We use an Eulerian Vlasov code to study the problem of the formation of a plasma sheath with plasma detachment (i.e. no plasma transport to the wall) at a plasma-wall transition, in front of an absorbing wall. The ions are described by a kinetic equation in the full velocity space which integrates exactly the ion orbits. We consider a one-dimensional slab geometry, where the inhomogeneous direction is perpendicular to the wall. The electrons, assumed to only move along the magnetic field lines, are described by a parallel-B kinetic equation. The magnetized electrons are restricted to move along the magnetic field because the surface-parallel diamagnetic and electric drifts are equal and opposite. The present study shows how an ambipolar flow in the direction normal to the wall is established. For very small values of the angleα between the magnetic field and the plane of the wall, steep density and potential gradients are established in front of the plate surface with almost no plasma transport towards the wall. Presented at 5th Workshop “Role of Electric Fields in Plasma Confinement and Exhaust”, Montreux, Switzerland, June 23–24, 2002.     

A probe-based method for measuring the transport coefficient in the tokamak edge region

A new method for measuring the diffusion coefficient in the edge plasma of fusion devices is presented. The method is based on studying the decay of the plasma fluctuation spectrum inside a small ceramic tube having its mouth flush with a magnetic surface and its axis aligned along the radial direction. The plasma fluctuations are detected by an electrode, radially movable inside the tube. In the experiment described herein, which was performed in the edge region of the CASTOR tokamak, the electrode measured the floating potential. The experimental arrangement is the same used for the direct plasma potential measurements according to the “Ball-pen probe” [1], the design of which is based on the Katsumata probe principle. When the electrode protrudes from the tube, the measured signal shows the floating potential fluctuations of the plasma. Retracting the electrode into the tube, the signal power spectrum displays a decay. This decay is different for different frequencies, and is exponential. Assuming a mainly diffusive behaviour of the plasma inside the tube, the spectrum decay length can be used to derive a value of the diffusion coefficient. The measurement were performed at different radial positions in the CASTOR edge region, so that a radial profile of the diffusion coefficient was obtained. Typical values ofD are of (2–3) m²/s, consistent with expectations from the global particle balance. The radial profile shows a tendency of the diffusion coefficient to increase going deeper into the plasma.     

Magnetic Coil Optimization for Quadrupole-Stabilized Mirror Systems

A numerical technique is presented to optimize the design of quadrupole magnetic coil systems, such as presently used in tandem mirror fusion experiments. The optimization is carried out with respect to various plasma physics properties (e.g., MHD stability and reduced radial transport of particles) which depend on the magnetic field geometry. The coils are treated as filaments of infinitesimal thickness and the magnetic field is computed in the paraxial limit. Constraints on the coil shape and on the magnetic geometry can be incorporated into the method. It is demonstrated that coil solutions can be found which match given paraxial field profiles or which directly minimize a scalar functional of these profiles. As an interesting application of the latter technique, a filamentary coil design for a nearly omnigenous anchor is obtained.     

Effective interaction potential and ordered structures of dust particles in a gas-discharge plasma

An effective potential is proposed for the interaction between dust particles in a gas-discharge plasma which takes account of the following physical factors: the spatial dependence of the particle charges on the floating potential of the plasma, anisotropy of the interaction, resulting from focusing of the negatively charged particles of the drift ion current, and aspects of screening of the dust particles by plasma electrons and ions which interact strongly with them and recombine faster in their vicinity and on their surface. Monte Carlo calculations explain the formation of threadlike structures of dispersed particles, and also “transverse crystallization” of these “threads” in a stratified gas-discharge plasma. Zh. éksp. Teor. Fiz. 115, 819–836 (March 1999)     

Impact of fast vertical and radial plasma movement on type-I ELMs in ASDEX upgrade

For the ITER project it is clear that steps have to be taken in order to avoid or mitigate type-I ELMs when operating in the standard H-mode scenario. Otherwise, divertor power loads induced by intrinsic ELMs will result in an intolerably short divertor life time. Amongst others, “magnetic triggering” based on a fast vertical movement of the plasma column has proven its ability to achieve ELM frequency control and hence mitigation by locking the ELM frequency to the imposed motion. Here, we report on an attempt to widen this approach by applying a cyclic radial plasma shift. Although motional cycle amplitudes sufficient for ELM frequency locking were achieved even easier than in the vertical case, no ELM control was established for the radial case. Analysis of this different behaviour can allow for better insight into underlying ELM release mechanisms and might potentially be a useful tool for mapping out ELM stability boundaries. Presented at the Workshop “Electric Fields, Structures and Relaxation in Edge Plasmas”, Roma, Italy, June 26–27, 2006.     

Internal transport barriers in plasmas with reversed plasma flow

Evidences of internal particle transport barriers have been observed in plasma discharges with reversed plasma flow. To investigate the influence of the radial electric field profile on these barriers, we apply a drift wave map that describe the plasma particle transport and allows the integration of particle drift in the presence of a given electrostatic turbulence spectrum. With this procedure we show that transport barriers due to the shearless flow invariant lines are created inside the plasma. Moreover, by varying the radial electric field profile, we observe the formation and destruction of internal transport barriers constituted by shearless invariant lines, as well as its effects on the transport in the map's phase space. Applicability of our results are discussed for the Texas Helimak, a toroidal plasma device in which the radial electric field can be changed by application of bias potential.     

Simulation of plasma flow in toroidal solenoid filters

An improved drift approximation model with an added radial electrostatic field has been successfully developed. Our model provides a computationally efficient way of quantitatively describing the plasma motion and predicting the plasma behavior in the toroidal solenoid in a filtered cathodic vacuum arc (FCVA) system. Storer's (1989) experimental results have been successfully simulated by this model. A good quantitative fit is obtained for our simulation results to the measured ion currents versus distance along the torus for various B field strengths, the attenuation length, and the wall current. The model describes the change of plasma density along the torus and provides the value of the electron-ion collision frequency at various conditions. The effect of the magnetic field and radial electric field on the plasma transportation can be assessed by the simulation and various plasma parameters can be determined. It is found that the radial electric field confines the 3-directional drift of the ions and is one of the most important parameters in determining the ion throughput. For any given B field strength and plasma parameters, there is a peak ion output corresponding to an optimal potential difference which can be obtained by the simulation. Over three times more ion output can be achieved when the torus wall is appropriately biased     

Observation of Radial Propagation of Electrostatic Fluctuations in Edge Plasma of the Sino United Spherical Tokamak

Radial propagation of electrostatic fluctuations in the edge plasma of Sino-United Spherical Tokamak (SUNIST) has been measured using Langmuir probes. The propagation characteristics of the floating potential fluctuations are analysed by the two-point correlation technique. The results show radially outward propagation of the turbulent fluctuations at all measured radial positions. The power-average wavenumber profile is approximately constant in plasma edge region and suddenly increases to the limiter. These results are in good agreement with the model predictions proposed by Mattor which suggests that the drift wave propagation may be a source of edge turbulence.     

Potential formation and high density plasma production on the tandem mirror GAMMA 10

GAMMA 10 experiments have advanced in high density experiments after the last EPS Workshop where we reported high density plasma production by using an ion cyclotron range of frequency heating at a high harmonic frequency and neutral beam injection in the central cell. Recently a high density plasma was obtained with much improved reproducibility than before and without degradation of diamagnetic signal. The high density plasma was attained by adjusting the spacing of the conducting plates installed in the anchor transition regions. Dependencies of particle confinement time, ion energy confinement time and plasma confining potential on plasma density were obtained for the first time in the high density region. Presented at 5th Workshop “Role of Electric Fields in Plasma Confinement and Exhaust”, Montreus, Switzerland, June 23–24, 2002.     

Experimental studies on E×B drift rotational transform andconfinement in the bumpy torus NBT-1M

Experimental studies on E×B drift rotational transform for toroidal plasma confinement were carried out using a bumpy torus NBT-1M. An inward radial electric field was observed, which induced E×B poloidal precession and formed closed drift surfaces in a conventional ECH configuration. However, the confinement was degraded by the plasma convective loss due to the asymmetric potential profile and core electrostatic fluctuations. By the use of a combination of two frequencies for ECH (18 GHz and 8.5 GHz), we could reduce both the potential asymmetry and the fluctuation. In this operation, the plasma confinement by E×B drift rotational transform was demonstrated more clearly than that in the conventional single frequency operation