Volume 12, Issue 4, April 2005
 LETTERS


Relationship between density peaking, particle thermodiffusion, Ohmic confinement, and microinstabilities in ASDEX Upgrade mode plasmas
View Description Hide DescriptionNew experimental results obtained in ASDEX Upgrade [O. Gruber, H.S. Bosch, S. Günter et al., Nucl. Fusion39, 1321 (1999)] plasmas in low confinement mode with central electron cyclotron heating are presented in which transitions in both the particle and electron heat transportproperties have been observed. A comprehensive albeit qualitative explanation for both the transport channels is provided in the framework of the theory of ion temperature gradient and trapped electron mode microinstabilities. The different transport behaviors are related to the dominant instability at play and to the collisionality regime. In particular, central electron heating induces a flattening of the density profile when the dominant instability is a trapped electron mode, and density peaking is observed to increase with decreasing collisionality.

Angular dependence of imprinting levels in lasertarget interactions on planar CH foils
View Description Hide DescriptionImprinting of laserbeam modulations at various angles of incidence is measured for the first time in planar CH foils. The imprinted target modulations were seeded by special probe beams at a spatial wavelength of and subsequently amplified by five drive beams. The measured imprint efficiency decreases by a factor of 3 as the angle of incidence of the probe beam is increased from 20° to 60°, as predicted by theoretical modeling. The imprinting is very sensitive to the relative arrival time of the probe and drive beams.

Suppression of rotating external kink instabilities using optimized mode control feedback
View Description Hide DescriptionRotating external kink instabilities have been suppressed as well as excited in a tokamak using active magnetic coils that directly couple to the plasma through gaps in passive stabilizing conducting shells that surround the plasma. The kink instability has a complex growth rate, approximately , and is near the ideal wall stability limit when discharges are prepared with a rapid plasma current ramp and adjusted to have an edge safety factor near 3. The active control coils are driven by a digital mode control feedback system that uses multiple fieldprogrammable gate arrays to analyze signals from 20 poloidal field sensors and achieve highspeed feedback control. The feedback coil geometry used was designed to optimize feedback effectiveness. Signal processing is of critical importance to optimize phase transfer functions for control of rotating modes.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Linear analysis of magnetic and flow shear stabilization of Zpinch instabilities
View Description Hide DescriptionA global normal mode stability analysis on the effect of radially sheared azimuthal flow and radially sheared magnetic fields on magnetohydrodynamic (MHD) instabilities in Zpinchplasmas is presented. A linearized set of ideal MHD equations allows the investigation of plasmas with both magnetic shear and flow shear included in the plasma equilibrium. The stabilizing effects of sheared azimuthal flow and sheared axial magnetic field are presented. Here we show that radial shear in the functional form of a vortex is particularly efficient at reducing instability growth rates.

Ion drag on dust grains in electronegative plasmas
View Description Hide DescriptionThe electric and the positive and negativeion drag forces on a dust grain in an electronegative complex plasma are investigated. It is shown that the number of locations where the drag forces balance the electric force is considerably larger than that in an electropositive plasma. The balance occurs in the socalled oscillation regime where the electric field oscillates in space. The effect of the negativeion drag force on the dust grain can be substantial in a certain parameter range.

Drift waves in a highdensity cylindrical helicon discharge
View Description Hide DescriptionA lowfrequency instability is investigated in a helicon plasma, which is characterized by comparably high plasma and high collision frequencies. Single movable Langmuir probes and a poloidal probe array are used for studies of spatiotemporal dynamics and for characterization of the background plasma parameters. All experimentally observed features of the instability are found to be consistent with drift waves. A linear nonlocal numerical model for drift modes, based on the twofluid description of a plasma, is used for comparison between the experimental observations and theory. Comparing numerical and experimental frequencies, it is found that the experimentally observed frequencies are consistent with drift waves. The numerical results show that the high electron collision frequencies provide the strongest destabilization mechanism in the helicon plasma.

Formation and rotation of twodimensional Coulomb crystals in magnetized complex plasma
View Description Hide DescriptionThe formation and rotation of twodimensional (2D) dust Coulomb crystals with finite number of particles are simulated in a selfconsistent manner, based on a dynamical model for radiofrequency sheath over a concave electrode with an axial magnetic field. The dust particles are initially placed at random positions inside the sheath, and then their motions are tracked by a moleculardynamics method until stable, ordered 2D structures are formed, which rotate in a plane perpendicular to the magnetic field, driven by the azimuthal ion flow due to the effect. The rotation patterns are found to depend, in a complex way, on the particle number, the crystal structure, and the discharge parameters, such as the discharge pressure and the magnetic field. In particular, a rigid rotation is typically observed for those clusters with high symmetry structures, for example, the cluster 19 (1,6,12), with the rotation angular frequency of the order of , which is proportional to the magnetic field magnitude, but decreases with the increasing discharge pressures. However, the intershell rotations are also observed for those structures of the dust crystals with less symmetry, e.g., 20 (1,7,12), especially for strong magnetic fields.

Hybrid magnetohydrodynamickinetic electron closure methods and shear Alfvén waves in nonuniform plasmas
View Description Hide DescriptionTwo hybrid magnetohydrodynamickinetic electron models of shear Alfvén waves with different closure schemes involving the assumption of quasineutrality are compared. One method assumes quasineutrality directly while the other allows for a nonzero that produces a “correcting” electric field. The interpretation of the different closure schemes is discussed and the two methods are shown to yield consistent results for both the cases of a constant and variable density along the field line. In the variable density case the hybrid system with and without a shear Alfvén wave perturbation is also contrasted. In the latter case, static parallel electric fields that increased with the plasma temperature were generated to support the density gradients. When the system was perturbed, a time dependent parallel electric field contribution oscillated around the static field structure needed to support the profile. Landau damping effects were also investigated and the energy invariant for the systems derived.

Effect of shear flow and magnetic field on the Rayleigh–Taylor instability
View Description Hide DescriptionThe effects of sheared equilibrium flow and magnetic field on the Rayleigh–Taylor instability(RTI) are investigated and the linear growth rate is obtained analytically in the presence of a sharp interface. It is shown that the shear flow acts as a driving force and is the dominating drive when Atwood number , wave number , flow shear , and gravitational acceleration satisfy . As increases growth rate increases first and then falls down if is satisfied, and otherwise it rises monotonically. When magnetic stabilizing effect governs, RTI only occurs in the long wave region and not only the permitted band, , is extended but the instability is enhanced as increases or the reduced Alfvén speed decreases. For regime governed by the destabilizing effect of shear flow, growth rate increases as and increase.

Displacement eigenmodes for coldfluid and warmfluid magnetized plasma oscillations
View Description Hide DescriptionColdfluid and warmfluid electrostatic plasma modes of magnetized nonuniform plasmas are determined as eigenfunctions of an integral equation describing the perturbed fluid displacement. The frequencies of these displacement eigenmodes are always real. In some cases, the modes are singular and form a continuous spectrum, and this causes spatially Landaudamped quasimodes to appear in the response to initial perturbations. In other cases the spectrum is discrete. Finitetemperature frequency shifts, of interest as a temperature diagnostic, are evaluated and compared to analytic theory.

Effective plasma inductance computation
View Description Hide DescriptionThe calculation of the resistive wall modes and their feedback stabilization is greatly simplified by splitting the plasma response from that of the external conductors. Existing calculations either consider highly simplified models of the external conductors or assume the plasma response can be approximated by a single rigid mode. The full response of an ideal, nonrotating plasma to perturbations that evolve slowly compared to the Alfvén time is contained in the matrix for the effective plasma inductance. This matrix can be used in a code that accurately calculates the effects of the external conductors to obtain an essentially complete description of both plasma and the conducting structures. Calculations of for a number of tokamak equilibria are given together with an explanation of how the calculations are made and why they are important.

Suppression of low frequency plasma instabilities in a magnetized plasma column
View Description Hide DescriptionThis paper reports on a new experimental observation of the suppression of both naturally occurring and driven oscillations in a magnetized, linear plasma column. Detailed measurements are made of the potential structure, density profiles, and wave propagation using Langmuir and emissive probes. These measurements indicate that the decrease in the level of plasma oscillations (by factors of 10 or greater) is related to the direction of the radial electric field, but may also be connected to a combination of transverse and parallel flows in the plasma.

Magnetodynamics of a multicomponent (dusty) plasma. I. Rotation waves near lowfrequency cutoff in a homogeneous medium
View Description Hide DescriptionBy considering one of the species of a twoion species plasma to be massive charged dust particles, the origin of the lowfrequency cutoff in a multispecies plasma is found to be a fluid rotation of the light component with a characteristic frequency, , where and are densities of the heavy component and electrons, respectively, is the charge state of the heavy component, and is the light ion cyclotron frequency. A fluidresonance at modifies the properties of plasma oscillations in the vicinity of the cutoff and gives rise to the rotation waves in a manner similar to the cyclotron waves. The presence of a heavy component leads to the nonlinear Schrödinger equation for the system. The nonlinear dynamics of such a system consists of a combination of strong and weak turbulence with strong turbulence dominating in the long wavelength and the weak turbulence dominating in the short wavelength.

Magnetodynamics of a multicomponent (dusty) plasma. II. Magnetic drift waves in an inhomogeneous medium
View Description Hide DescriptionThe electromagnetic oscillations near the lowfrequency cutoff (the rotation waves) and their stability and nonlinear state, analyzed in the companion paper [G. Ganguli and L. Rudakov, Phys. Plasmas12, 042110 (2005)] for a homogeneous plasma, are generalized to include inhomogeneity in the equilibrium density and magnetic field. It is shown that in the forbidden frequency band below the cutoff the magnetic drift waves appear, which can exist even in a cold plasma. The magnetic drift wave and nonlinear structures associated with it are analyzed and their relevance to astrophysical plasmas are discussed. It is found that in an inhomogeneous plasma the rotation wave packets can couple to the magnetic drift waves. The behavior of such structures is governed by nonlinear Schrödinger equation. The spatial scale of the nonlinear structures due to the magnetic drift waves in astrophysical plasmas such as dense molecular clouds, which are the regions of star creation, is estimated to be around 10 a.u.

Toroidal flowcaused change in magnetic topology of equilibrium eigenstates
View Description Hide DescriptionEquilibrium eigenstates of an axisymmetric magnetically confined plasma with toroidalflow are investigated by means of exact solutions of the ideal magnetohydrodynamic equations. The study includes “compressible” flows with constant temperature , but varying density on magnetic surfaces and incompressible ones with constant density , but varying temperature thereon [the function is the poloidal magnetic flux function with cylindrical coordinates]. These variations are necessary for the existence of tokamak steady states with flow. The “compressible” and incompressible solutions are associated with the ansatz and , respectively, where is the rotation frequency. In both cases eigenfunctions of the form describe configurations with magnetic axes. A connection between multitoroidal configurations and reversed magnetic shear is also identified. Owing to the flow, the respective eigenvalues can be considered in two alternative ways: either as floweigenvalues, and , which depend on a pressure parameter or as pressure eigenvalues, which depend on the flow parameters, or . In the context of the latter consideration when the flow parameters are varied continuously there are transition points, and , at which an additional magnetic axis is formed. This flowcaused change in magnetic topology is possible solely in the presence of toroidicity because in the limit of infinite aspect ratio the axial flow does not appear in the equilibrium equation. Also, the lower the aspect ratio the smaller and . In addition, the effects of the flow and the aspect ratio on the Shafranov shift are evaluated along with the variations of density and temperature on magnetic surfaces.

Flux amplification in helicity injected spherical tori
View Description Hide DescriptionAn important measure of the effective current drive by helicity injection into spheromaks and spherical tori is provided by the flux amplification factor, defined as the ratio between the closed poloidal flux in the relaxed mean field and the initial injector vacuum poloidal flux. Flux amplification in magnetic helicity injection is governed by a resonant behavior for Taylorrelaxed plasmas satisfying . Under the finite net toroidal flux constraint in a spherical torus(ST), the constrained linear resonance is upshifted substantially from the primary Jensen–Chu resonance that was known to be responsible for flux amplification in spheromak formation. Standard coaxial helicity injection into a ST operates at large , with the characteristic dimensionless parameter defined as the ratio between the toroidal flux in the discharge chamber and the injector poloidal flux. Meaningful flux amplification for ST plasmas is limited by a critical at which edge toroidal field reverses its direction. The is downshifted from by a small amount inversely proportional to . The maximum flux amplification factor scales linearly with . At the other end of , substantial flux amplification becomes available for that scales inversely proportional to , a significant departure from that in spheromak formation. These important parameters follow the inequality. Even though is greater than in a typical ST, detailed profile considerations further constrain the maximum useful flux amplification factor in a ST to be smaller than . The scaling laws are given analytically in the asymptotic limit of , but numerical solutions indicate that they are useful even for .
 Nonlinear Phenomena, Turbulence, Transport

Critical density solitary waves structures in a hot magnetized dusty plasma with vortexlike ion distribution in phase space
View Description Hide DescriptionThe nonlinear properties of solitary waves structures in a hot magnetized dusty plasma consisting of isothermal hot electrons, nonisothermal ions, and high negatively charged massive dustgrains are reported. A modified Korteweg–de Vries (modified KdV) equation, which admits a solitary waves solution, for small but finite amplitude, is derived using a reductive perturbation theory. A nonisothermal ion distribution provides the possibility of existence of rarefactive solitary waves. On the other hand, the dynamics of solitary waves at a critical ion density is governed by KdV equation. The modification in the amplitude and width of the solitary waves structures due to the inclusion of obliqueness and external magnetic field are also investigated.

Stimulated Raman scattering of relativistic laser beam in plasmas
View Description Hide DescriptionThis paper presents the stimulated Raman scattering(SRS) of relativistic laser beam in unmagnetized plasma. The effect of the relativistic electron mass nonlinearity and the relativistic selffocusing of the pump laser on the SRS process is studied. The effect of nonlinear coupling between the pump laser and scatteredlaser beam has been incorporated. Semianalytical solution for the back reflectivity for SRS has been obtained. For a typical laser wavelength , intensity , and a plasma having density , the back reflectivity comes out to be .

Basis function multifield bispectral deconvolution analysis
View Description Hide DescriptionA different procedure for calculating linear and nonlinear coefficients of model systems for fully developed turbulence is derived. This procedure can be applied to systems with multiple interacting fields; in the singlefield case the linear coefficients consist of mode frequencies and growth rates. This method differs from previous methods in the use of a limited set of functions or basis set from which the nonlinear terms in the turbulenceequation are approximated in a series expansion. The algorithm is derived from this assumption using a least squares approach. This approach has been tested on simulations of fully developed twodimensional turbulence and compared to previous methods. It is able to reconstruct coefficients with several significant figures precision and offers excellent noise rejection capabilities, and is moreover able to operate using tiny data sets compared to those required by previous methods.

Shock wave in magnetized dusty plasmas with dust charging and nonthermal ion effects
View Description Hide DescriptionThe effects of the external magnetized field, nonadiabatic dust charge fluctuation, and nonthermally distributed ions on threedimensional dust acoustic shock wave in dusty plasmas have been investigated. By using the reductive perturbation method, a Korteweg–de Vries (KdV) Burger equation governing the dust acoustic shock wave is derived. The results of numerical integrations of KdV Burger equation show that the external magnetized field, nonthermally distributed ions, and nonadiabatic dust charge fluctuation have strong influence on the shock structures.