Roles of electric field on toroidal magnetic confinement

Theoretical research on the influence of electric field on toroidal magnetic confinement is surveyed. The static electric field is first described. A physical picture of the radial electric field generation and its influence on confinement are shown. Neoclassical effects as well as the non-classical processes are discussed. Emphasis is made on the connection with improved confinement. Convective cells with a nonuniform potential on the magnetic surface are also discussed. The roles of the fluctuating electric field are then reviewed. Recent progress in anomalous transport theory is addressed. Through these surveys, the impact of experiments using the heavy ion beam probes on modern plasma physics is illustrated     

A planar Penning trap

We present a new concept for a Penning trap, which is planar and allows for the implementation of novel confinement techniques. The trap provides confinement perpendicular to its plane by an electric potential minimum while a superimposed magnetic field provides radial confinement. Both the axial position and the depth of the potential minimum can be controlled by the applied voltages. The device is scalable in the sense that an arbitrary number of planar traps can be embedded in one plane thus representing a multitrap array which can be used for particle interaction studies. Switches between different traps in the planar array allow for controlled interactions between the single stored particles.     

Time-dependent nested-well plasma trap

When arranged in a nested-well configuration, plasma traps of the Penning/Malmberg type become potentially suitable for confining neutral plasmas. The nested-well configuration allows confinement of overlapping electron and ion plasmas. With an ion plasma overlapped by an equal-charge-density electron plasma, the ion density can exceed the severe ion density limit which occurs within traditional single-well plasma traps. With a nested-well configuration which is time dependent, overlapping electron and singly charged-ion plasmas can be confined at the same temperature. Possible uses of thermal neutral plasmas confined within time-dependent nested-well plasma traps include basic plasma science studies and plasma processing applications     

DC column plasma kinetics in a longitudinal magnetic field

The cylindrical column plasma of a neon dc glow discharge under the influence of a weak longitudinal magnetic field is studied. An extended, fully self-consistent model of the column plasma has been used to determine the kinetic quantities of electrons, ions and excited atoms, the radial space charge field, and the axial electric field for given discharge conditions. The model includes a nonlocal kinetic treatment of the electrons by solving their spatially inhomogeneous kinetic equation, taking into account the radial space charge field and the axial magnetic field. The treatment is based on the two-term expansion of the velocity distribution and comprises the determination of its isotropic and anisotropic components in the axial, radial, and azimuthal direction. A transition from a distinctly nonlocal kinetic behavior of the electrons in the magnetic-field-free case to an almost local kinetic behavior has been found by increasing the magnetic field. The establishment of the electron cyclotron motion around the column axis increasingly restricts the radial electron energy transport and reduces the radial ambipolar current. The complex interaction of these transport phenomena with the alterations in the charge carrier production leads finally to a specific variation of the electric field components. The axial field increases by applying weak magnetic fields, however, decreases with increasingly higher magnetic fields. At higher magnetic fields, the radial space-charge field is considerably reduced     

Influence of radial electric field on trajectories of plug potential bounce ion in the tandem mirror

Bouncing ions between the plug potentials play an important role in improvement of the axial confinement in the tandem mirror. We examined the influence of the radial electric field on the trajectories of the ions passed through the anchor cell with nonaxisymmetric magnetic configuration on the assumption that the shape of the magnetic flux tube was shifted from the shape of the equipotential surface of the plasma at the mirror throats of the anchor cells. The discrepancy between the shapes enhanced the radial drift of the bounce ion. Radial potential profile of the core plasma was controlled by adjustment of the radially separated endplate potentials, and it was found that the flattened radial potential profile was effective for the decrease of the radial drift. Presented at 5th Workshop “Role of Electric Fields in Plasma Confinement and Exhaust”, Montreux, Switzerland, June 23–24, 2002.     

Quadrupole-induced resonant-particle transport in a pure electron plasma

Small transverse magnetic quadrupole fields sharply degrade the confinement of non-neutral plasmas held in Malmberg-Penning traps. For example, a quadrupole magnetic field of only 0.02 G/cm doubles the diffusion rate in a trap with a 100 G axial magnetic field. Larger quadrupole fields noticeably change the shape of the plasma. The transport is greatest at an orbital resonance. These results cast doubt on plans to use magnetic quadrupole neutral atom traps to confine antihydrogen atoms created in double-well positron/antiproton Malmberg-Penning traps.     

Two-dimensional structure and particle pinch in tokamak H mode

Two-dimensional structures of the electrostatic potential, density, and flow velocity near the edge of a tokamak plasma are investigated. The model includes the nonlinearity in bulk-ion viscosity and turbulence-driven shear viscosity. For the case with the strong radial electric field (H mode), a two-dimensional structure in a transport barrier is obtained, giving a poloidal shock with a solitary radial electric field profile. The inward particle pinch is induced from this poloidal asymmetric electric field, and increases as the radial electric field becomes stronger. The abrupt increase of this inward ion and electron flux at the onset of L- to H-mode transition explains the rapid establishment of the density pedestal, which is responsible for the observed spontaneous self-reorganization into an improved confinement regime.     

先进磁镜装置中径向电场对高能粒子的约束性能研究

本文运用Boris算法对紧凑型聚变反应装置(compact fusion reactor, CFR)中高能a粒子的运动轨道进行了数值模拟,分析了高能a粒子在不同径向电场作用下运动轨道的差异性;探究了不同径向电场对CFR装置中不同位置处a粒子约束性能的影响.研究结果表明,当正、负径向电场强度达到一定临界值时,都能够使高能a粒子很好地约束在CFR装置内部,但不同位置处径向电场强度临界值与a粒子初始条件有关.     

Effect of resonant magnetic perturbations on edge plasma parameters in the STOR-M tokamak

Edge plasma properties have been modified in the Saskatchewan Torus-Modified tokamak by means of resonant magnetic perturbations (RMP). It has been found that the radial profiles of ion saturation current and floating potential in the edge region can be modified by an externally applied static (m?=?2, n?=?1) RMP field. An increase in the pedestal plasma density (n) and more negative electric field (E_r) have been observed in the plasma edge region. It is believed that the RMP field altered the plasma transport in the edge and scrape-off layer regions, leading to a higher density pedestal and a potential drop in some cases. During the enhanced confinement phase, it is possible to identify a region where intermittent transport events, the so-called blobs, are created and the holes of lower density left behind.     

The Influence of Stochastic Layers of Magnetic Field Lines on Transport Barrier Formation in a Stellarator System

The results of local measurements of RF discharge plasma parameters in the process of internal transport barriers (ITB) formation in the vicinity of rational magnetic surfaces in the Uragan-3M torsatron are presented. The following phenomena were observed in the process of ITB formation: widening of the radial density distribution, formation of plateaus on radial density and electron temperature distributions, formation of regions with high shear of poloidal plasma rotation velocity and radial electric field in the vicinity of stochastic layers of magnetic field lines, decrease of density fluctuations and their radial correlation length, decorrelation of density fluctuations, and increase of the bootstrap current.After the ITB formation, the transition to the improved plasma confinement regime takes place. The transition moves to the beginning of the discharge with the increase of heating power. The possible mechanism of ITB formation near rational surfaces is discussed.     

The Current Distribution and the Magnetic Pressure Profile in a Vacuum Arc Subject to an Axial Magnetic Field

The steady-state electric-current distribution and the magnetic pressure in a uniform conducting medium, flowing in a cylindrical configuration between two circular electrodes, was determined by solving the magnetic field transport equation with a superimposed axial magnetic field. This medium models the interelectrode plasma of the diffuse mode metal vapor vacuum arc. The results show the following. a) The electric current and the flux of the poloidal magnetic field are constricted at the anode side of the flowing plasma. Most of the constriction takes place within a boundary layer, with a characteristic length of 1/Rme, where Rme is the magnetic-Reynolds number for axial electron flow. b) The electric-current constriction inversely depends on K?, where K? is the azimuthal surface current density which produces the axial magnetic field. c) The magnetic-pressure profile shows a radial pinch force in most of the interelectrode region, but in the anode boundary layer it is axially directed, thus retarding the plasma flow. d) The peak of the magnetic pressure is at the anode, and its amplitude directly depends on K?. As K? increases, the peak location moves toward the anode center.     

Dynamic transport simulation code including plasma rotation and radial electric field

A new one-dimensional transport code named TASK/TX, which is able to describe dynamic behavior of tokamak plasmas, has been developed. It solves simultaneously a set of flux-surface averaged equations composed of Maxwell’s equations, continuity equations, equations of motion, heat transport equations, fast-particle slowing-down equations and two-group neutral diffusion equations. The set of equations describes plasma rotations in both toroidal and poloidal directions through momentum transfer and evaluates the radial electric field self-consistently. The finite element method with a piecewise linear interpolation function is employed with a fine radial mesh near the plasma surface. The Streamline Upwind Petrov–Galerkin method is also used for robust calculation. We have confirmed that the neoclassical properties are well described by the poloidal neoclassical viscous force. The modification of density profile during neutral beam injection is presented. In the presence of ion orbit loss, the generation of the inward radial electric field and torque due to radial current is self-consistently calculated.     

磁边界效应对径向磁场中等离子体束流运动轨迹的影响

根据离子与径向磁场的约束关系，用面向对象的单元粒子法模拟了极向偏转器中等离子体束流在均匀和非均匀径向磁场中的运动情况，得到了在磁边界效应下极向偏转器内部畸变电场的分布，分析了对质量分离的影响。模拟成果对质量分离器、质谱分析仪及材料提纯等装置的研制、特殊位形电磁场控制多质量束流等相关领域的研究有参考价值。     

Instationary Electric Fields,Ion Transport and Strong Density Fluctuations in Tokamaks with Dominant Anomalous Electron Transport

A common explanation is given for ion transport and strong broadband density fluctuations in tokamaks as a result of large anomalous electron transport near dominant magnetic surfaces (resp. in small magnetic islands). The main mechanism is local density flattening connected with an anomalous electron transport induced instationary radial electric field, which forces the ions via polarization drift to follow the electrons. For the density flattening process an exact solution of the time-dependent diffusion equation for a linear initial profile over the island width is used. From this we also derive an expression for a temporal growing radial electric field. This positive field reaches its maximum at the density plateau. Strong viscous diffusion or instability-induced transport between high and low electric field regions may now reverse the density flattening. Therefore relaxation oscillations result which may also explain the observed strong density and potential fluctuations in tokamaks. Several details of recent measurements of impurity ion behaviour and density fluctuations in tokamaks may be better explained with the theory given here.     

Magnetic Vortex Tubes in Astrophysics

The viscous forces on electrons and ions in a differentially rotating plasma drive an azimuthal current density j?, with axial magnetic field Bz which is shown to be proportional to plasma vorticity. Field strengths in agreement with those observed for both stars and galaxies are obtained, assuming that reactive forces prevent radial drifts of electrons or ions. Hierarchical vorticity is required in order to reconcile the small-scale length required for field changes with the large-scale length of observed fields. A vortex tube with magnetic field (magnetic vortex tube-MVT) becomes the basic entity for the origin of magnetic fields. Twisting of field lines by differential rotation causes (1?,Bz,) ?(jz, B?,). When jzB?, > j?, Bz the MVT suffers magnetic pinch, and the axial current in the pinch flows through a cylindrical sheath with a radial electric field due to plasma polarization. An instability of drift velocity denudes a length R of the current channel of free charges, and the inductively maintained current then requires a displacement current in R and hence a growing axial electric field Ez, Ez is limited by transfer of the energy in B?, to Ez, and thereafter the energy oscillates between the fields. On the stellar scale, evidence for polar MVT's comes from young stars with bipolar outflows of gas and jets. It is argued that end-on viewing of polar MVT's accounts for the kilogauss fields of Ap stars and the 1-100-MG fields of magnetic white dwarfs.     

A wire trap for neutral atoms

We present new ways of trapping a neutral atom with static electric and magnetic fields. We discuss the interaction of a neutral atom with the magnetic field of a current carrying wire and the electric field of a charged wire. Atoms can be trapped by the 1/r magnetic field of a current-carrying wire in a two-dimensional trap. The atoms move in Kepler-like orbits around the wire and angular momentum prevents them from being absorbed at the wire. Trapping was demonstrated in an experiment by guiding atoms along a 1 m long current-carrying wire. Stable traps using the interaction of a polarizable atom with the electric field of a charged wire alone are not possible because of the 1/r ² form of the interaction potential. Nevertheless, we show that one can build a microscopic trap with a combination of a magnetic field generated by a current in a straight wire and the static electric field generated by a concentric charged ring which provides the longitudinal confinement. In all of these traps, the neutral atoms are trapped in a region of maximal field, in theirhigh-field seeking state.Dedicated to H. Walther on the occasion of his 60th birthday     

Beam Probe Space-Potential Measurement in a Minimum-B Field

A measurement of plasma space potential in a minimum-B magnetic field has been made with a particle beam probe. The diagnostic technique is an extension of conventional heavy ion beam probing in that, among other features, the probing beam is neutral rather than ionized cesium and the parallel-plate electrostatic energy analyzer is fully characterized in a new manner which permits its use in complex magnetic confinement geometries.     

A steadily rotating plasma disk

A homogeneously rotating plasma disk can be formed in a radially directed Ar-arc discharge at reduced pressure with an externally applied axial magnetic field. The radial pressure distribution is measured, as well as the emitted continuum radiation and the arc voltage. With these experimental values profiles of temperature, radial and azimuthal current density, and flow velocity in the disk are evaluated. Viscosity determines the flow pattern essentially. The effects of magnetic field and rotational motion on the discharge are investigated. The disk exhibits at nonrigid rotation a strong centrifugal force and a minor Coriolis force. A weak double vortex is found to develop in the meridional plane. The electric field in the discharge is altered by the azimuthal plasma flow.     

Plasma Modelling for the PSI Linear Plasma Device

Deuterium discharges in the PSI device have been modelled using the coupled package of the B2 hydrodynamic plasma code and the Eirene Monte‐Carlo neutral code. Radial and axial plasma profiles have been calculated for different magnetic field configurations, various radial diffusion laws and for different values of the flux limiter in the parallel electron heat conduction law used in the B2 code. The results are compared with experimental findings. The axial variation of the magnetic field strength is found to have an important influence on the plasma state via the axial plasma flow which closely resembles the neutral gas streaming through a series of laval nozzles. For particular magnetic field configurations, an appropriate ansatz for the parallel electron heat conduction turns out to be a crucial point for the applicability of hydrodynamic models to linear devices like the plasma generator PSI. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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