Volume 12, Issue 2, February 2005
 LETTERS


Observation of the low to high confinement transition in the large helical device
View Description Hide DescriptionThe low to high confinement transition has been observed on the large helical device [A. Iiyoshi, A. Komori, A. Ejiri et al., Nucl. Fusion39, 1245 (1999)], exhibiting rapid increase in edge electron density with sharp depression of emission. The transition occurs in low toroidal field discharges and are heated by high power neutral beam injection. The plasma thus has a relatively high value of the volume averaged value. The electron temperature and density profiles have steep gradients at the edge region which has high magnetic shear but is at a magnetic hill. Formation of the edge transport barrier leads to enhanced activities of the interchange type of modes with ( are the poloidal and toroidalmode numbers) in the edge region. At present, these magnetohydrodynamic activities limit the rise of the stored energy; the resultant increment of the stored energy remains modest.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Helical rays in twodimensional resonant wave conversion
View Description Hide DescriptionThe process of resonant wave conversion (often called linear mode conversion) has traditionally been analyzed with a spatially onedimensional slab model, for which the rays propagate in a twodimensional phase space. However, it has recently been shown [E. R. Tracy and A. N. Kaufman, Phys. Rev. Lett.91, 130402 (2003)] that multidimensional rays have a helical structure for conversion in two or more spatial dimensions (if their dispersion matrix is generic). In that case, a onedimensional model is inadequate; a correct analysis requires two spatial dimensions and, thus, fourdimensional phase space. A coldplasma model is introduced in this paper which exhibits ray helicity in conversion regions where the density and magnetic field gradients are significantly nonparallel. For illustration, such regions are identified in a model of the poloidal plane of a deuteriumtritium tokamakplasma. In each conversion region, characterized by a sixsector topology, rays in the sector for incident and reflected magnetosonic waves exhibit significant helicity. A detailed analytic and numerical study of helical rays in this sector is developed for a “symmetricwedge” model.

Stopping power for arbitrary angle between test particle velocity and magnetic field
View Description Hide DescriptionUsing the longitudinal dielectric function derived previously for charged test particles in helical movement around magnetic field lines, the numerical convergence of the series involved is found and the double numerical integrations on wave vector components are performed yielding the stopping power for arbitrary angle between the test particle velocity and magnetic field. Calculations are performed for particle Larmor radius larger and shorter than Debye length, i.e., for protons in a cold magnetized plasma and for thermonuclear particles in a dense, hot, and strongly magnetized plasma. A strong decrease is found for the energy loss as the angle varies from 0 to . The range of thermonuclear particles as a function of the velocity angle with respect to the magnetic field is also given.

Dust particle alignments and confinement in a radio frequency sheath
View Description Hide DescriptionStability of vertical and horizontal confinement of dust particles levitating in a rf sheath was studied experimentally. The experiments were carried out in an argon plasmadischarge with micronsized dust particles. Disruptions of particle arrangements were triggered by changing the discharge controlling parameters (pressure and peaktopeak voltage) as well as by applying an additional bias to the confining electrode. Where the transition was triggered by changes of the discharge parameters, the transition from the horizontal to the vertical alignment has been found to be more pronounced than the reverse one. Clear hysteretic phenomena were observed for the transition triggered by changes of the confining voltage.

Covariant kinetic dispersion theory of linear waves in anisotropic plasmas. II. Comparison of covariant and noncovariant growth rates of the nonrelativistic Weibel instability
View Description Hide DescriptionAperiodic solutions to the covariant and noncovariant dispersion relations of transverse oscillations in unmagnetized anisotropic biMaxwellian plasmas of arbitrary composition are investigated in the case of nonrelativistic plasma temperatures. With numerical solutions and analytical approximations it is demonstrated that the covariant and noncovariant aperiodic solutions are practically identical.

Magnetohydrodynamic twotemperature equations for multicomponent plasma
View Description Hide DescriptionThe physics of plasmas of mixed composition is of increasing importance both in laboratory experiments and in space plasmas. This work is devoted to constructing from first principles a set of magnetohydrodynamic equations for a multicomponent plasma of arbitrary concentrations, overcoming some limitations of the classical system by S. I. Braginskii [Sov. Phys. JETP6, 358 (1958)]. A procedure applicable when the ion species have very different atomic masses is developed and applied to produce a full set of transport coefficients. Our approach permits us to explain the discrepancy between Braginskii results and results obtained by direct numerical solution of the electron kinetic equation by E. M. Epperlein and M. G. Haines [Phys. Fluids.29, 1029 (1986)].

Wave packet in a twodimensional hexagonal crystal
View Description Hide DescriptionThe propagation of a nonlinear wave packet of dust lattice waves(DLW) in a twodimensional hexagonal crystal is investigated. The dispersion relation and the group velocity for DLW are found for longitudinal and transverse propagation directions. The reductive perturbation method is used to derive a dimensional nonlinear Schrödinger equation (NLSE) that governs the weakly nonlinear propagation of the wave packet. This NLSE is used to investigate the modulational instability of the packet of DLW. It is found that the instability region is different for different propagation directions.
 Nonlinear Phenomena, Turbulence, Transport

The scaling properties of dissipation in incompressible isotropic threedimensional magnetohydrodynamic turbulence
View Description Hide DescriptionThe statistical properties of the dissipation process constrain the analysis of large scale numerical simulations of threedimensional incompressible magnetohydrodynamic(MHD)turbulence, such as those of Biskamp and Müller [Phys. Plasmas7, 4889 (2000)]. The structure functions of the turbulent flow are expected to display statistical selfsimilarity, but the relatively low Reynolds numbers attainable by direct numerical simulation, combined with the finite size of the system, make this difficult to measure directly. However, it is known that extended selfsimilarity, which constrains the ratio of scaling exponents of structure functions of different orders, is well satisfied. This implies the extension of physical scaling arguments beyond the inertial range into the dissipation range. The present work focuses on the scaling properties of the dissipation process itself. This provides an important consistency check in that we find that the ratio of dissipation structure function exponents is that predicted by the She and Leveque [Phys. Rev. Lett72, 336 (1994)] theory proposed by Biskamp and Müller. This supplies further evidence that the cascade mechanism in threedimensional MHDturbulence is nonlinear random eddy scrambling, with the level of intermittency determined by dissipation through the formation of current sheets.

Statistics of particle transport in a twodimensional dusty plasma cluster
View Description Hide DescriptionStatistical analysis is performed on long time series of dust particle trajectories in a twodimensional dusty plasmacluster. Particle transport is found to be superdiffusive on all time scales until the range of particle displacements approaches the size of the cluster.Analysis of probability distribution functions and rescaled range analysis of the position increments show that the signal is nonGaussian selfsimilar with Hurst exponent , indicating that the superdiffusion is caused by longrange dependencies in the system. Investigation of temporal and spatial characteristics of persistent particle slips demonstrates that they are associated with collective events present on all time scales and responsible for the nonGaussianity and longmemory effects.

Vorticity probes and the characterization of vortices in the Kelvin–Helmholtz instability in the large plasma device experiment
View Description Hide DescriptionA new fivepin probe design called the vorticity probe is presented that explicitly measures the vorticity in the flow from floating potentials, independent of any absolute calibration errors. The five Tantalum probe tips are arranged in a diamond pattern with tip spacing. The fluctuating floating potential at each tip is measured and used to compute a finitedifference approximation of the vorticity. The probe is tested in the large plasma device (LAPD) [W. Gekelman et al., Rev. Sci. Instrum.62, 2875 (1991)], operated with a variable bias between the anode and the chamber wall that creates a sharply localized profile at from the axis of the diameter chamber. The fluctuations are peaked in the shear flow layer and are correlated with theoretical calculations of the Kelvin–Helmholtz instability for this plasma. The spectrum at matches the theoretical prediction from the measured gradient that reaches in the axial magnetic field.

Ion acoustic solitary waves in a dusty plasma obliquely propagating to an external magnetic field
View Description Hide DescriptionThe nonlinear ion acoustic solitary wave in a magnetized dusty plasma, obliquely propagating to the embedding external magnetic field, is revisited. It is found that when the charge density of dust particles is high, the Sagdeev potential needs to be expanded up to near . In this case, it is shown that there could exist rarefactive ion acoustic solitary waves as well as the kinktype double layer solutions, in addition to the conventional humptype ones found in the expansion. The amplitude variations of ion acoustic solitary waves in a magnetized dusty plasma are also examined with respect to the change of the dust charge density and the wave directional angle.

Gyrokinetic simulations of ion and impurity transport
View Description Hide DescriptionA systematic study of turbulent particle and energy transport in both pure and multicomponent plasmas is presented. In this study, gyrokinetic results from the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys.186, 545 (2003)] are supplemented with those from the GLF23 [R. E. Waltz, G. M. Staebler, W. Dorland et al., Phys. Plasmas4, 2482 (1997)] transport model, as well as from quasilinear theory. Various results are obtained. The production of a particle pinch driven by temperature gradients (a thermal pinch) is demonstrated, and further shown to be weakened by finite electron collisionality. Helium transport and the effects of helium density gradient and concentration in a deuterium plasma are examined. Interestingly, it is found that the simple (diffusion versus convective velocity) model of impurity flow is consistent with results obtained from nonlinear gyrokinetic simulations. Also studied is the transport in a 5050 deuteriumtritium plasma, where a symmetry breaking is observed indicating the potential for fuel separation in a burning plasma. Quasilinear theory together with linear simulations shows that the symmetry breaking which enhances the tritium confinement arises largely from finiteLarmorradius effects. To justify the numerical methods used in the paper, a variety of linear benchmarks and nonlinear grid refinement studies are detailed.

Soliton perturbation theory for Alfvén waves in plasmas
View Description Hide DescriptionThe solitonperturbation theory is used to study the Alfvén waves in plasmas that are governed by the derivative nonlinear Schrödinger’s equation. The adiabatic parameter dynamics of the solitons in presence of the perturbation terms are obtained. In particular, the nonlinear gain (damping) and the coefficient of finite conductivity are treated as perturbation terms.

Twofluid magnetic island dynamics in slab geometry. I. Isolated islands
View Description Hide DescriptionA set of reduced, twodimensional, twofluid, driftMHD (magnetohydrodynamical) equations is derived. Using these equations, a complete and fully selfconsistent solution is obtained for an isolated magnetic island propagating through a slab plasma with uniform but different ion and electron fluid velocities. The ion and electron fluid flow profiles around the island are uniquely determined, and are everywhere continuous. Moreover, the island phase velocity is uniquely specified by the condition that the islandinduced modifications to the ion and electron velocity profiles remain localized in the vicinity of the island. Finally, the ion polarization current correction to the Rutherford island width evolution equation is evaluated and found to be stabilizing provided that the anomalous perpendicular ion viscosity significantly exceeds the anomalous perpendicular electron viscosity.

Twofluid magnetic island dynamics in slab geometry. II. Islands interacting with resistive walls or resonant magnetic perturbations
View Description Hide DescriptionThe dynamics of a propagating magnetic island interacting with a resistive wall or an externally generated, resonant magnetic perturbation is investigated using twofluid, drift(magnetohydrodynamical) (MHD) theory in slab geometry. In both cases, the islandequation of motion is found to take exactly the same form as that predicted by singlefluid MHD theory. Three ion polarization terms are found in the Rutherford island width evolution equation. The first is the driftMHD polarization term for an isolated island, and is unaffected by the interaction with a wall or magnetic perturbation. Next, there is the polarization term due to interaction with a wall or magnetic perturbation which is predicted by singlefluidMHD theory. This term is always destabilizing. Finally, there is a hybrid of the other two polarization terms. The sign of this term depends on many factors. However, under normal circumstances, it is stabilizing if the noninteracting island propagates in the ion diamagnetic direction (with respect to the wall or magnetic perturbation) and destabilizing if it propagates in the electron diamagnetic direction.

Dressed particle simulation of dusty plasmas
View Description Hide DescriptionA dressed particle approach to numerical simulation of dusty plasmas is presented. Since the dust grains in the laboratory are usually immersed in a streaming plasma, their interaction potential has a complex spatial structure which can be computed within the framework of linear response theory. For typical experimental parameters the twobody force is sufficiently shortranged to make molecular dynamics techniques feasible. As an application of this approach, the formation of twodimensional clusters is investigated and compared with experimental results.

Investigations of shortscale fluctuations in a helicon plasma by crosscorrelation enhanced scattering
View Description Hide DescriptionCorrelation enhanced scattering (CES) near the upper hybrid resonance has been applied for studying smallscale plasma densityfluctuations excited by the rf fields in a helicon discharge. The turbulent fluctuations are diagnosed for conditions where the electron plasma frequency exceeds the electron cyclotron frequency considerably. The frequency and wave number spectra of the fluctuations are measured both in the plasma core as well as in outer region of the helicon discharge. The spectral measurements evidence the shortscale fluctuations to originate from a parametric decay instability. The lowfrequency fluctuations obey the ionsound dispersion relation while the lower sideband of the helicon wave frequency satisfies the Trivelpiece–Gould wave dispersion relation. In order to gain more insight in the experimental results and, in particular, to estimate the fluctuation level the backscattering process is analyzed both numerically and analytically for highdensity plasma conditions. A fully electromagnetic model was developed that takes into account the radial density distribution of the plasma column as well as the antenna diagram of the rectangular emitting/receiving horn. Using this model the relative amplitude of ionsound density fluctuations in the core of the helicon discharge is estimated as 11%. The role of nonlinear effects on formation of the scattering spectra due to the high fluctuation level in the plasma center is discussed. The findings also demonstrate that the CES diagnostic can be applied to diagnose fluctuations in spherical tokamak plasmas where the probing conditions resemble those of highdensity helicon discharges.

Nonlinear evolution of the modulational instability and chaos using onedimensional Zakharov equations and a simplified model
View Description Hide DescriptionNonlinear evolution of modulational instability by using the nonlinear Schrödinger equation in one dimension reveals a periodic reoccurrence of initial conditions. The nonlinear Schrödinger equation is the adiabatic limit of Zakharov equations, which couples the electrostatic electron plasma wave and ionacoustic wave propagation. In the present paper nonlinear evolution of modulational instability is investigated by using onedimensional Zakharov equations numerically. A simplified model is predicted that establishes the fact that the effect of relaxing the condition of adiabaticity is drastic on the nonlinear evolution patterns of modulational instability. These evolutions are quite sensitive to initial conditions, Fermi–Pasta–Ulam recurrence is broken up and a chaotic state develops. Next, quantitative methods like calculation of Lyapunov exponents and their variation with wave number is used to study spatial and temporally chaotic behavior. It is shown that regular patterns with a periodic sequence in space and time and spatiotemporal chaos with irregular localized patterns are formed in different regions of unstable wave numbers.
 Magnetically Confined Plasmas, Heating, Confinement

Stabilization of sawtooth oscillations by the circulating energetic ions
View Description Hide DescriptionThe influence of the wellcirculating energetic ions on the ideal kink instability and the tearing instabilities (collisionless and semicollisional modes) is studied. It is found that the precession of these ions can be by an important stabilizing factor, especially when the balanced tangential neutral beam injection is used and/or in the presence of fusionproduced particles.

Short wavelength ion temperature gradient instability in toroidal plasmas
View Description Hide DescriptionSeries of ion temperature gradient(ITG or ) driven modes in the short wavelength region, , are investigated with a gyrokinetic integral equation code in toroidal plasmas. These instabilities exist even if electrons are assumed adiabatic. However, nonadiabaticelectron response can influence these short wavelength ITG (SWITG) modes, especially the fundamental mode. At typical parameters, excitation of the mode requires that both and exceed thresholds, while the and modes with higher harmonic eigenfunctions persist unstable even at . Dependence of the SWITG modes on other parameters is also investigated. The mode with an odd potential eigenfunction grows faster than the mode and may be dominant in low , high , weak positive magnetic shear, and/or weak toroidicity regions.