Index of content:
Volume 9, Issue 5, May 2002
 LETTERS


Laminar plasma dynamos
View Description Hide DescriptionA new kind of dynamo utilizing flowing laboratory plasmas has been identified. The conversion of plasma kinetic energy to magnetic energy is verified numerically by kinematic dynamo simulations for magnetic Reynolds numbers above 210. As opposed to intrinsicallyturbulent liquidsodium dynamos, the proposed plasma dynamo corresponds to laminar flowtopology. Modest plasma parameters (1–20 eV temperatures, densities in 0.3–1.0 m scalelengths driven by velocities on the order of the Alfvén critical ionization velocity) selfconsistently satisfy the conditions needed for the magnetic field amplication. Growth rates for plasma dynamos are obtained numerically with different geometry and magnetic Reynolds numbers. Magneticfieldfree coaxial plasma guns can be used to sustain the plasma flow and the dynamo.

 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Generalized plasma dispersion function for a plasma with a kappaMaxwellian velocity distribution
View Description Hide DescriptionA generalized plasma dispersion function has previously been obtained for waves in plasmas with isotropic kappa distributions for arbitrary real kappa [Mace and Hellberg, Phys. Plasmas 2, 2098 (1995)]. In many instances plasmas are found to have anisotropic powerlaw distributions, and hence a similar dispersion function for electrostatic waves in plasmas having a onedimensional kappa distribution along a preferred direction in space, and a Maxwellian distribution perpendicular to it has now been developed. It is used to study the effect of superthermal electrons and ions on ionacoustic waves propagating at an angle to a magnetic field. This dispersion function should find application to wave studies both in space plasmas, where the magnetic field defines a preferred direction, and in dusty plasma crystal studies, where the ion flow direction is unique.

Numerical study of pair creation by ultraintense lasers
View Description Hide DescriptionNow that intensity of lasers has reached electron–positron pairs can be created by the irradiation of such ultraintense lasers on a thin gold foil. The energy of electrons produced by ultraintense lasers reaches more than several tens of MeV. Such high energy electrons become a source for creating electron–positron pairs via interaction with nuclei. There are a few processes that create electron–positron pairs in this situation. Two processes, call the trident process and the Bethe–Heitler process, are considered in this study. A numerical simulation code based on a relativistic Fokker–Planck equation is developed for studying the hot electrontransport. The equation is solved by assuming onedimensional real space and twodimensional momentum space with axial symmetry. It is found that the total positron yield increases logarithmically with the increase of the laser intensity, and the resultant energy distribution of the created positron is found to have a peak near the energy of 1–2 MeV.

General parametric analysis of the linear twostream instability
View Description Hide DescriptionA complete and systematic picture of the different forms of the linear twostream instability is presented. It is based in an asymptotic study of the general solution of the dispersion relation, in terms of the three dimensionless parameters characterizing the steady state of a twospecies plasma. In a zero temperatureratio limit, the parametric regions of dominance of different acoustic, Langmuir, and reactive types of the instability are determined, and analytical expressions of the maximum growth rate for all types are derived. The continuous transition between different types and the main topological changes of the unstable branch, as the parametric space is covered, are discussed. For the small temperatureratio case, new analytical expressions for the instability threshold are derived.

Linear coupling of electromagnetic and Jeans modes in selfgravitating plasma streams
View Description Hide DescriptionA new mechanism of linear coupling between electromagnetic (nonpotential) and gravitational disturbances is found for oblique propagation relatively to particle streams. The general dispersion law is derived and applied to the case of two countersteaming dust beams of equal strength and quiasiperpendicular propagation. It reveals a strong linear coupling between the lowfrequency aperiodically unstable electromagnetic (AEM) and the Jeans (JM) modes. The coupling is of a mode conversion type, resulting in a frequency gap in the dispersion, and thus significantly modifies the instability criteria. It is shown that, in contrast to the electrostatic case, AEM and JM coupling in streaming selfgravitating plasmas can actually appear even if the plasma frequencies of the dust species greatly exceed the corresponding Jeans frequencies.

Generalized lowerhybrid drift instabilities in currentsheet equilibrium
View Description Hide DescriptionA class of drift instabilities in onedimensional currentsheet configuration, i.e., classical Harris equilibrium, with frequency ranging from low ion–cyclotron to intermediate lowerhybrid frequencies, are investigated with an emphasis placed on perturbations propagating along the direction of crossfield current flow. Nonlocal twofluid stability analysis is carried out, and a class of unstable modes with multiple eigenstates, similar to that of the familiar quantum mechanical potentialwell problem, are found by numerical means. It is found that the most unstable modes correspond to quasielectrostatic, shortwavelength perturbations in the lowerhybrid frequency range, with wave functions localized at the edge of the current sheet where the density gradient is maximum. It is also found that there exist quasielectromagnetic modes located near the center of the current sheet where the current density is maximum, with both kink and sausagetype polarizations. These modes are lowfrequency, longwavelength perturbations. It turns out that the currentdriven modes are loworder eigensolutions while the lowerhybridtype modes are higherorder states, and there are intermediate solutions between the two extreme cases. Attempts are made to interpret the available simulation results in light of the present eigenmodeanalysis.
 Nonlinear Phenomena, Turbulence, Transport

Effects of ion temperature gradients on the formation of driftAlfvén vortex structures in dusty plasmas
View Description Hide DescriptionA set of equations describing the nonlinear dynamics of driftAlfvén waves in a dusty plasma accounting for the nonzero ion temperature gradients is derived. It is shown that these new equations yield a solution in the form of twoscale dipolar vortex structures propagating with velocities close to the iondrift velocity in a narrow cone centered around the direction perpendicular to both the external magnetic field and the plasma gradient directions. The typical scales, characteristic vortex velocities as well as the relevant conditions for their existence are discussed. It is shown that nonzero ion temperature gradients substantially enlarge the range of possible propagation directions and characteristic scales of the vortex structures.

Nonlinear evolution of the lower hybrid drift instability: Current sheet thinning and kinking
View Description Hide DescriptionThrough numerical plasma simulations using the implicit code CELESTE3D [G. Lapenta and J. U. Brackbill, Nonlinear Processes Geophys. 7, 151 (2000)], the development of kink modes in a Harris current sheet is investigated, and their possible nonlinear interaction with the lower hybriddrift instability (LHDI) is considered. Consistent with earlier work, the rapid development of a short wavelength LHDI is observed, followed by the slow development of long wavelength current sheet kinking. The growth of kink modes is in agreement with the linear theory for the drift kink instability only at very small mass ratios At more realistic mass ratios, the growth rate exceeds that predicted by linear theory. A thorough investigation of the dependence of current sheet kinking on ion/electron mass and temperature ratios, and current sheet thickness reveals that the growth of kink modes is unaffected by current sheet thinning, but is strongly dependent on the ion/electron temperature ratio. The saturation amplitude of the LHDI increases with decreasing electron temperature, as do the nonlinear modifications of the initial equilibrium. In particular, the ion diamagnetic drift velocity of the ions decreases sufficiently on the flanks of the current sheet to support a Kelvin–Helmholtz instability, especially with cold electrons, whose properties are completely consistent with the kink modes observed in the simulations.

Numerical solution of the Fokker–Planck equation of fully ionized magnetized plasmas and classical transport coefficients
View Description Hide DescriptionA new numerical approach to solve the linear integrodifferential Fokker–Planck equation (FPE), which describes a collisional and magnetized plasma, is presented. For this purpose, the FPE is reduced to a simple set of ordinary differential equations, which can be easily solved, with the use of standard numerical methods. The transport coefficients induced by the first anisotropicdistribution function computed by Braginskii [Reviews of Plasma Physics (Consultants Bureau, New York, 1965), Vol. 1] and improved by Epperlein and Haines [Phys. Fluids 29, 1029 (1986)], have been recovered. The viscosity coefficients are computed for arbitrary atomic numbers and arbitrary magnetic field strength and are compared to the results reported in the literature.

Instability of convective cells in ion temperature gradient turbulence
View Description Hide DescriptionIt has been demonstrated using numerical simulation of twodimensional ion temperature gradient(ITG) equations that a periodic array consisting of large scale convective cells is subject to shear flow instability. A dynamically global and selfconsistent evolution of linearly unstable modes, close to marginal instability, leads to the formation of poloidal shear flow through the process of peelinginstability. The saturated state thus comprises radially localized and polloidally extended length scales, namely, zonal flows. The zonal flows are predominantly led by the perturbed shear flow, whose growth rate is larger than the linear ITGinstability.

Controlling chaos in the currentdriven ion acoustic instability
View Description Hide DescriptionControl of intermittent chaos caused by the currentdriven ion acoustic instability is attempted and the controlling mechanism is investigated. When a small negative dc voltage is applied to the chaotic system as a perturbation, the system changes from a chaotic state to a periodic state while maintaining the instability, indicating that the chaotic state caused by the ion acoustic instability is well controlled by applying a small negative dc voltage. A hysteresis structure is observed on the curve of the mesh grid to which the negative dc voltage to control is applied. Furthermore, when a negative dc voltage is applied to the state which shows a laminar structure existing under same experimental conditions, the system becomes chaotic via a bifurcation. Drivenchaos is excited when a negative dc voltage is applied to the laminar state. Applying a small negative dc voltage leads to controlling intermittent chaos while exciting drivenchaos.

Transonic and subsonic dynamics of the currentvortex sheet
View Description Hide DescriptionSimulations of the magnetohydrodynamic(MHD) dynamics of a currentvortex sheet for low values of the Alfvén number in both the subsonic and transonic regimes are described. It is shown that, in agreement with previous linear results, the shear layer is unstable for all values of the sonic Mach number (M). However, the subsonic and transonic disturbances which develop differ significantly in many of their properties. In the subsonic case the evolution of the system is similar to the incompressible one since the growing perturbation is symmetric and evanescent in the cross stream direction. The inclusion of compressible effects mainly permits the study of its thermodynamic behavior. In the transonic case the growing perturbation appears to be overstable, asymmetric, oscillatory, and weakly evanescent in the cross stream direction. In their nonlinear evolution such modes, which we identify as fast MHD waves, lead to the formation of shocks and to a very different dynamics of the currentvortex system.

Ambipolar diffusion in an inhomogeneous dusty plasma
View Description Hide DescriptionThe ambipolar diffusion of plasma particles in a column of inhomogeneous plasma containing dust grains is investigated analytically as well as numerically. The grains act as charge sinks and behave like an immobile but chargevarying negative background. They can lead to significant depletion of the electron density and decrease the diffusion scale length. The theoretically obtained election density distribution agrees well with that from experiment.
 Magnetically Confined Plasmas, Heating, Confinement

Ideal magnetohydrodynamic equations for lowfrequency waves in toroidal plasmas
View Description Hide DescriptionReduced linear equations of magnetohydrodynamics in highaspectratio toroidal devices are derived, which are intended, first of all, for studying the Alfvén eigenmodes in stellarators and tokamaks. The equations take into account the effects of the plasma pressure and compressibility, which are known to be of importance for toroidicityinduced Alfvén eigenmodes, and are applicable to perturbations with arbitrary perpendicular wavelength. The reduction consists in eliminating highfrequency fast magnetoacoustic waves from the system and is shown not to affect the continuous spectrum of Alfvén and slow magnetoacoustic waves, which, to a large extent, determines the behavior of the waves of interest.

The role of clustering effects in interpreting nondiffusive transport measurements in tokamaks
View Description Hide DescriptionRecent measurements in tokamak plasmas provide clear evidence for rapid nondiffusive transport and nonGaussian fluctuations, and have been widely interpreted in terms of the sandpile and selforganized criticality(SOC) paradigms. Many of the statistical physics inferences that can be drawn from observations of, for example, avalanching transport remain to be explored. This paper will show that the statistical characterization of both experimentally observed and simulated avalanching transport phenomena reveals several points of contact with existing stochastic process models that have seldom been deployed in a plasma physics context. It will be shown that statistical physics techniques developed to model clustering of events can be used to characterize microscopic fluctuations in both local density and flux, as well as the global transport properties to which they give rise. This provides a fresh interpretation for some of the key aspects of observed critical gradientdriven transport phenomenology in tokamaks. In particular it provides new evidence for scalefree correlations in the fluctuations which drive the transport, and quantifies their distribution in terms of fewparameter nonGaussian models. The correlation properties of density fluctuations can be interpreted in terms of random walk models, whereas flux fluctuations cannot: instead they can be described by the discrete negative binomial distribution, which again indicates clustering. Some of the spatio–temporal correlations considered emulate multichannel measurements in tokamaks, and it is shown how these can be used to characterize the transport of naturally arising coherent structures.

Effect of combined triangularity and ellipticity on the stability limit of the ideal internal kink mode in a tokamak
View Description Hide DescriptionThe effect of combined triangular and elliptical shaping of the plasma cross section on the stability limit of the ideal, internal kink mode in a tokamak is analyzed by means of a computer algebraexpansion of the magnetohydrodynamic equations. The work extends the result of a previous investigation of the effect of ellipticity alone on this mode in toroidal plasmas [Wahlberg, Phys. Plasmas 5, 1387 (1998)]. It is shown that, in contrast to the strongly destabilizing effect of (positive) ellipticity alone, the effect of combined positive ellipticity and positive triangularity is stabilizing. The effect is of the same importance as the effect of ellipticity alone if the triangularity of the q=1 surface is of the same order of magnitude as the inverse aspect ratio. When the safety factor at the magnetic axis is close to (but below) unity, the geometrical factor governing the stability of the ideal, internal kink mode is found to be the same as the corresponding factor in the Mercier criterion for shaped tokamaks.

Comparision of neoclassical rotation theory with experiment under a variety of conditions in DIIID
View Description Hide DescriptionA neoclassical theory of gyroviscous radial momentum transport and poloidal and toroidal rotation has been compared with experiment in DIIID [Luxon, Anderson, Batty et al., Plasma Physics and Controlled Nuclear Fusion Research 1986 (IAEA, Vienna, 1987), Vol. 1, p. 159] discharges in different confinement regimes, with a range of neutral beam powers and with co and counterinjection, and with various types of dominant impurity species present. Calculated central toroidal rotation velocities and momentum confinement times agreed with experiment over a wide range of these conditions, with one notable exception in which a drift correction may be needed to reduce the gyroviscous toroidal force. Radial distributions of toroidal and poloidal rotation velocities and radial electric field, calculated using the radial distribution of toroidalangular momentum input density, agreed with measured distributions for the one time in an Lmode discharge that was examined in detail.

A comparison of drift wave stability in stellarator and tokamak geometry
View Description Hide DescriptionThe influence of plasma geometry on the linear stability of electrostaticiontemperaturegradient driven drift modes (ITG or modes) is investigated. An advanced fluid model is used for the ions together with Boltzmann distributed electrons. The derived eigenvalueequation is solved numerically. A comparison is made between an H–1NF [Fusion Technol. 17, 123 (1990)] like stellarator equilibrium, a numerical tokamak equilibrium and the analytical equilibrium. The numerical and the analytical tokamak are found to be in good agreement in the low inverse aspect ratio limit. The growth rates of the tokamak and stellarator are comparable whereas the modulus of the real frequency is substantially larger in the stellarator. The threshold in for the stellarator is found to be somewhat larger. In addition, a stronger stabilization of the ITG mode growth is found for large in the stellarator case.

Drift wave instability near a magnetic separatrix
View Description Hide DescriptionIt is well known that the pure driftAlfvén wave (DW) (i.e., in the absence of curvature and toroidal coupling effects) is stabilized by magnetic shear in circular flux surface geometry when the drift frequency is constant radially [P. N. Guzdar, L. Chen, P. K. Kaw, and C. Oberman, Phys. Rev. Lett. 40, 1566 (1978)] as is implicit in a local ballooning analysis. In the edge plasma near a magnetic separatrix, Xpoint geometry is important and the circular flux surface model does not apply. Using several numerical codes and analytical models, it is found that the DW is robustly unstable in this case. Physically, instability is driven by wave reflection from the steep profile of near the Xpoints, due to magnetic shear and the local minimum of the poloidal magnetic field. It is concluded that a complete set of dimensionless parameters describing edge turbulence must include DW parameters that embody the physics of Xpoint effects and plasma shaping.

Consideration of multifaceted asymmetric radiation from the edge (MARFE) as a dissipative structure
View Description Hide DescriptionMultifaceted asymmetric radiation from the edge (MARFE) is considered as an example of dissipative structures which develop under critical conditions in different physical and technical systems. The model proposed results in a system of algebraic equation including a relation similar to Maxwell’s Rule that determines such characteristic parameters as the plasma temperature in MARFE, its extent in poloidal and radial directions. Predictions of this approximate approach are compared with the results of one and twodimensional numerical simulations.