Volume 7, Issue 4, April 2000
 LETTERS


Superballistic transport in tearing driven magnetic turbulence
View Description Hide DescriptionIon transport is studied in a magnetic field reversal with a constant electric field and with a model tearing driven magnetic turbulence. Superdiffusive and superballistic transport regimes are found for the mean square displacements in the plane of the current sheet, with anomalous diffusion exponents up to 4. It is shown that the jump length scales as with the jump duration and and that can be interpreted in terms of the Klafter, Blumen, and Shlesinger model [Phys. Rev. A 35, 3081 (1987)] for continuous time random walk. Since velocity increases with the length of the free path, we have accelerated Lévy flights.

Electric fieldinduced plasma convection in tokamak divertors
View Description Hide DescriptionMeasurements of the electric fields,E in the DIIID tokamakdivertor region [J. C. Luxon and L. G. Davis, Fusion Technology 8, Part 2A, 441 (1985)] are quantitatively consistent with recent computational modeling establishing that circulation is the main cause of changes in divertor plasmas with the direction of the toroidalmagnetic field, Extensive twodimensional measurements of plasma potential in the DIIID tokamakdivertor region are reported for the first time. The resulting drift particle flux is calculated for standard (ion drift toward divertorXpoint) and reversed direction and for low (L) and high (H) confinement modes. Perpendicular field strengths of up to E∼5 kV/m are observed at the separatrix between the divertor private region and the scrapeoff layer (SOL). The drift, which reverses with reversal of creates a poloidal circulation pattern in the divertor that convects 25%–40% of the total ion flow to the divertor target. The circulation strongly couples the various regions of the divertor and SOL and fuels the Xpoint region. An outward shift of the profiles is seen in reversed

Vertical stability in a currentcarrying stellarator
View Description Hide DescriptionAn analytic stability criterion is derived for the vertical mode in a large aspect ratio stellarator with uniform current density profile. The effects of vacuum magnetic field generated by helical coils are shown to be stabilizing due to enhancement of field line bending energy. For a wall at infinite distance from the plasma, the amount of external poloidal flux needed for stabilization is given by where is the axisymmetric elongation and f is the ratio of vacuum rotational transform to the total transform.

Liquid metal flow encasing a magnetic cavity
View Description Hide DescriptionA stationary equilibrium of a liquid metal flowing past a cylindrical magnetic cavity is presented. The cavity has an azimuthal magnetic field and can also have an axial field. The liquid metal flow can be maintained by a sufficiently high pressure head. The scheme could be used to support a flowing liquid wall for systems producing high heat fluxes.

Transport due to front propagation in tokamaks
View Description Hide DescriptionA lowdimensional transportmodel which emphasizes the competition between two turbulent relaxation mechanisms, namely profile relaxation and nonlinear mode coupling, is proposed. When decreasing the relative weight of this mode coupling, transport exhibits a transition from diffusive to avalanchelike regimes. The latter plasma turbulenttransport can prove to be very powerful in describing experimental evidence, especially concerning transient dynamics.

A theoretical model for the generation of cocurrent rotation by radio frequency heating observed on Alcator CMod
View Description Hide DescriptionA theoretical model is presented which shows generation of a cocurrent directional central toroidal rotation by a nondirectional onaxis ion cyclotron heating in the Lowmode plasmas of Alcator CMod tokamak [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)]. It is shown that a netinward nonambipolar transport of resonant ions can induce such a rotation. The netinward transport is a result of the passing ion dominant transport process in Alcator CMod. The opposite horizontal orbit shift between co and counterpassing ions makes the wave absorption asymmetric in
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Acoustic modes in a collisional dusty plasma: Effect of the charge variation
View Description Hide DescriptionThe dispersion relation for the acoustic modes in a collisional dusty plasma is derived, taking into account the particle charge variation and ionization. Short and long wavelengths are considered separately. It is shown that the coupling between the shortwavelength branches is weak, and for sufficiently small dust fraction they can be treated independently, as in the case of a fixed charge. In the longwavelength limit, the dustion acoustic (DIA) and dust acoustic (DA) branches interact “through” the dust charging (DCh) branch, unlike the direct coupling obtained in the absence of charge variations.

Covariant formulation of the Fokker–Planck equation for moderately coupled relativistic magnetoplasma
View Description Hide DescriptionThe covariant approach of using the Fokker–Planck equation to treat large angle as well as small angle ion–electron collisions in a magnetoplasma is formulated. It includes third term velocity differential coefficients relevant for moderately coupled plasma valid for large Coulomb logarithm The kinetic equation is derived from first principle; the collision integral is formulated, including the appropriate Chapman–Enskog type of approximation in order to facilitate further evaluations of diffusion and transport coefficients.
 Nonlinear Phenomena, Turbulence, Transport

Anisotropies in magnetic field evolution and local Lyapunov exponents
View Description Hide DescriptionThe natural occurrence of small scale structures and the extreme anisotropy in the evolution of a magnetic field embedded in a conducting flow is interpreted in terms of the properties of the local Lyapunov exponents along the various local characteristic (un)stable directions for the Lagrangian flow trajectories. The local Lyapunov exponents and the characteristic directions are functions of Lagrangian coordinates and time, which are completely determined once the flow field is specified. The characteristic directions that are associated with the spatial anisotropy of the problem, are prescribed in both Lagrangian and Eulerian frames. Coordinate transformation techniques are employed to relate the spatial distributions of the magnetic field, the induced current density, and the Lorentz force, which are usually followed in Eulerian frame, to those of the local Lyapunov exponents, which are naturally defined in Lagrangian coordinates.

Electromagnetic iontemperaturegradient modes and anomalous transport in a nonuniform magnetized plasma with equilibrium flows
View Description Hide DescriptionThe linear and nonlinear properties of electrostatic and electromagnetic waves in the presence of iontemperature gradient, magneticfield gradient, density gradient, and velocity gradients are examined. In the linear limit, a dispersion relation is obtained that admits new instabilities of drift waves. It is found that parallel velocity shear couples the electrostatic and magnetostatic modes and can cause an instability. An estimate of the anomalous ion energy transport and particle flux on the basis of mixing length hypothesis is made and the results are discussed for some interesting limiting cases. Furthermore, stationary solutions of the nonlinear equations without dissipation are also presented. The findings of the present investigation should be useful in understanding fluctuations and transport phenomena in space and laboratory plasmas.

Electromagnetic effects on toroidaliontemperaturegradient modes and associated nonthermal crossfield transports
View Description Hide DescriptionThe electromagnetic effects are incorporated in the study of toroidaliontemperaturegradient(ITG) modes in a nonuniform magnetoplasma. For this purpose, dispersion relations have been derived by employing the fluid and gyrokinetic responses for the ions, as well as the fluid electron response along with Ampère’s law. The dispersion relations are numerically analyzed and results for the real and imaginary parts of the ITGwave frequencies are displayed for different values of (where and are the characteristic scale lengths of the density and magnetic field gradients, respectively) and where is the parallel component of the wave vector and is the collisionless ion skin depth. It is found that electromagnetic effects are stabilizing. Furthermore, also presented are brief calculations of particle as well as ion thermal transports in the presence of nonthermal electromagnetic fluctuations. The relevance of this investigation to the plasma confinement in tokamaks is discussed.

A kinetic magnetohydrodynamic energy integral in three dimensional geometry
View Description Hide DescriptionRecent observations of Alfvén wave excitations in stellarator geometry and their successful description by the global magnetohydrodynamic(MHD)stability code CAS3D (Code for the Analysis of the MHDStability of 3D Equilibria) [C. Nührenberg, Phys. Plasmas 6, 137 (1998)] have raised the question of to what extent a fast particle population may destabilize such modes. In answering this question a theoretical basis must be developed through which the influence of fast particles upon global MHD modes in realistic threedimensional geometries can be investigated. As a first step towards this goal, a linearized driftkinetic equation for electromagnetic perturbations is derived and solved. It is furthermore shown that a generalized kinetic MHDenergy integral exists which is nonlinear with respect to the mode frequencies. This energy integral agrees with previous less general results in their limits.

The roles of shear and crosscorrelations on the fluctuation levels in simple stochastic models
View Description Hide DescriptionHighly simplified models of random flows interacting with background microturbulence are analyzed. In the limit of very rapid velocity fluctuations, it is shown rigorously that the fluctuation level of a passively advected scalar is not controlled by the rms shear. In a model with random velocities dependent only on time, the level of crosscorrelations between the flows and the background turbulence regulates the saturation level. This effect is illustrated by considering a simple stochasticoscillator model, both exactly and with analysis and numerical solutions of the directinteraction approximation. Implications for the understanding of selfconsistent turbulence are discussed briefly.
 Magnetically Confined Plasmas, Heating, Confinement

Axial length and separatrix radius behavior of fieldreversed configuration plasma in dynamic compression of mirror distance
View Description Hide DescriptionThe axial magnetic compression experiment of the fieldreversed configuration (FRC) plasma is reported. The FRC produced in the thetapinch system is translated into the confinement region. The separatrix length of the translated FRC is decided by the mirror distance. The compression is done in a manner as shortening the distance in time. The compression coil is installed inside the chamber to raise the strength of the confinement field at the neighborhood of the mirror. The mirror distance is compressed to be 70% of the original one. The increment of the separatrix radius is observed to be 14%. This is nearly consistent with the adiabatic calculation. The decay rate of the radius has a constant value. From the line integrated density signal measured by the interferometer, no rotational instability is observed even in the case of the compression.

Nonlinear stability limit in high tokamaks
View Description Hide DescriptionLinearly unstable high tokamak equilibria are shown to be nonlinearly stabilized by an axisymmetric flow containing both toroidal and poloidal components. As fingers of hot plasma produced by pressure driven ballooning instabilities start to convect out towards the bounding wall, an axisymmetric flow is selfconsistently generated and opposes the growth of the fingers, maintaining confinement. However, as increases the growth rate of the fingers increases until there is insufficient time for the developing axisymmetric flow to halt their rapid progress to the wall, and confinement is lost. The ultimate stability of a tokamakplasma is determined by a nonlinear stability limit in

Global drift wave map test particle simulations
View Description Hide DescriptionGlobal drift wave map equations that allow the integration of particle orbits on long time scales are implemented to describe transport. Ensembles of test particles are tracked to simulate the lowconfinement mode/reversed shear/enhanced reversed shear plasmas in the TokamakFusion Test Reactor (TFTR) tokamak and the Optimized Shear plasma in the Joint European Torus (JET) tokamak. The simulations incorporate a radial electric field, obtained from a neoclassical calculation [Zhu et al., Phys. Plasmas 6, 2503 (1999)] and a model for drift wavefluctuations that takes into account change in the mode structure due to [Taylor et al., Plasma Phys. Controlled Fusion38, 1999 (1996)]. Steady state particle density profiles along with two different measures of transport, the diffusion coefficient based on a running time average of the particle displacement and that calculated from the mean exit time, are obtained. For either weak or reversed magnetic shear and highly sheared particle transport barriers are observed to be established. In the presence of such a transport barrier, it is shown that there is, in general, a difference between the two measures of transport. The difference is explained by a simple model of the transport barrier.

The Hurst exponent and longtime correlation
View Description Hide DescriptionThe rescaled range statistics (R/S) method is applied to the ion saturation current fluctuationsmeasured by the Langmuir probe at the edge of Tore Supra [Equipe Tore Supra, in Proceedings of the 13th International Conference on Plasma Physics and Controlled Nuclear Fusion, Washington, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 549] to evaluate the Hurst exponent. Data block randomization is carried out to the data sets in order to investigate the relationship between the Hurst exponent and longtime correlation. It is observed that H is well above 0.5 in the longtime selfsimilar range. However, it is found that the information which leads to is totally contained in the shorttime correlation and no link to long times is found.

Impact of E × B drifts on impurity distribution in the scrapeoff layer of a tokamak
View Description Hide DescriptionAs shown in recent years, a strong electrostatic field exists in the tokamak ScrapeOffLayer (SOL) and divertor zone. In the present paper it is demonstrated that the drifts resulting from it, compete with the impurity velocities caused by friction with the main ions, as well as with thermal forces. This effect can redistribute impurity flows significantly. Particularly, it may lead to impurity flow reversal. Fluid equations for the test impurities are derived using the two most representative ionization states model. As shown to first approximation, impurity motion does not depend on the ionization state. For a favorable magneticfield direction, when the ion drift is directed towards the Xpoint, in the private region the impurities flow from the outer to the inner divertor plate. On the contrary, in the SOL the impurity flow is directed from the inner to the outer plate. Significant impurity velocity shear exists near the separatrix, and creates the effect of flow reversal. Diffusion across the flux surfaces transports impurities flowing away from the divertor plates to regions with the opposite flow direction. A reduced visual model is presented.

Stability and transport of parallel velocity shear driven mode with negative magnetic shear
View Description Hide DescriptionThe linear and quasilinear behavior of the driftlike perturbation with a parallel velocity shear is studied in a sheared slab geometry. Full analytic studies show that when the magnetic shear has the same sign as the second derivative of the parallel velocity with respect to the radial coordinate, the linear mode may become unstable and turbulent momentum transport increases. On the other hand, when the magnetic shear has opposite sign to the second derivative of the parallel velocity, the linear mode is completely stabilized and turbulent momentum transport reduces.

Applicability of the ballooning transform to trapped ion modes
View Description Hide DescriptionIn the scope of the study of lowfrequency electrostaticmicroinstabilities in tokamakplasmas, attention has been focused on the effect of trapped ions. The ballooning transform has been applied to the gyrokineticequation, for the case of a large aspect ratio plasma with circular magnetic surfaces. A new eigenvalue code has been developed to solve the resulting integral equation, for the case of adiabatic electrons and full ion dynamics, thus taking into account both circulating and trapped ions. The goal has been to assess the validity of the ballooning transform for trapped ion modes. A scan over the parameter has been carried out to determine a lower threshold for applicability of the ballooning representation. Illustrative results of trapped ion modes (TIM) are presented, together with the comparison with the ones obtained using a global gyrokinetic code, for low toroidal wave numbers, and a local kinetic dispersion relation.