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Volume 4, Issue 7, July 1997

Confinement of a neutral plasma using nested electric potential wells
View Description Hide DescriptionA selfconsistent, twodimensional analysis is presented on confining a region of neutral plasma with a Penning/Malmberg type plasma trap using a nested well configuration. It is found that a neutral plasma region having disparate electron and ion temperatures or having high charge state ions can be confined with static fields. For confining a neutral region comprised of electrons and equal temperature low charge state ions, a quasistatic approach appears promising.

Enhanced reverse shear bifurcation in tokamak
View Description Hide DescriptionA transport bifurcation model for enhanced reverse shear (ERS) mode recently observed in tokamaks is given. The model includes effects due to evolution of magnetic shear and bootstrap current. It is shown that these effects substantially reduce the power threshold for ERS transition.

Crossedfield secondary emission electron source
View Description Hide DescriptionA novel crossedfield secondaryemission (CFSE) electron source that is capable of producing highcurrent tubular electron beams is described. This new electron source is based on the mechanism of secondaryemission multiplication of electron current in a magnetronlike device having smooth cylindrical electrodes. The input electron current may be as low as a few mA. The multiplication process starts at the negative slope of an applied voltage pulse. After initiation, the current is extracted from the diode region with no regard to the voltage pulse shape and as a consequence, the CFSE electron source can operate in a long pulse mode. At the diode voltage of for a diode gap of the output current reaches a value of more than 100 A.

Linear stability of the collisionless, large Larmor radius Zpinch
View Description Hide DescriptionThe Vlasov fluid model is used to study the and internal and free boundary modes in a collisionless, large Larmor radius Z pinch. Two methods (initial value and variational) are employed, and give good agreement. The growth rate can be reduced from its zero Larmor radius value by a factor of up to 10 for and up to 3 for Stability thresholds and the role of resonant ions are discussed.

Dust acoustic waves in a direct current glow discharge
View Description Hide DescriptionAn experimental investigation of dust acoustic (DA) waves in a dc glow discharge plasma is described. The glow discharge is formed between a 3 cm anode disk and the grounded walls of a 60 cm diameter vacuum chamber which is filled with nitrogen gas at a pressure of about 100 mTorr. Dust located on a tray in the chamber is attracted into the plasma where it is trapped electrostatically. The dust acoustic waves were produced by applying a modulation signal (5–40 Hz) to the anode. The wavelength of the DA waves was measured from single frame video images of scattered light from the dust grains. The measured dispersion relation is compared with theoretical predictions.

Impulsive and transient excitation of Bohm–Gross waves in a dissipative plasma
View Description Hide DescriptionBased on the resolution of the partial differential equation describing the external excitation of the Bohm–Gross longitudinal wave, analytical expressions for causal responses of a dissipative macroscopic plasma are derived. Both impulsive and harmonic solutions representing the spatial Green’s functions of the radiation problem are given. These exact responses of the plasma, expressed in terms of twovariable Lommel functions, are then used to gain some better understanding of the excitation and dynamics of the wellknown thermal wave. Special attention is paid to the resonant excitation case. Intrinsic characteristics of the secular behavior of the radiated signal are illustrated and analyzed. It is shown that the proffered algebraic solutions constitute a generalization of previous results inferred from an asymptotic representation of the Green’s functions, or from the familiar steady state harmonic approach.

Plasma equations in general relativity
View Description Hide DescriptionVlasov’s equation and the ideal multifluid equations are considered in manifestly covariant form. In the latter case, a thermodynamic closure (locally the first law of thermodynamics) leads to a generalized Kelvin/Helmholtz theorem. In the former case, the local dispersion relation for Langmuir waves in a strong gravitational field is derived and solved.

A model for particle acceleration in lower hybrid collapse
View Description Hide DescriptionA model for particle acceleration during the nonlinear collapse of lower hybridwaves is described. Using the MusherSturman wave equation to describe the effects of nonlinear processes and a velocity diffusion equation for the particle velocity distribution, the model selfconsistently describes the exchange of energy between the fields and the particles in the local plasma. Twodimensional solutions are presented for the modulational instability of a plane wave and the collapse of a cylindrical wave packet. These calculations were motivated by sounding rocket observations in the vicinity of auroral arcs in the Earth’s ionosphere, which have revealed the existence of largeamplitude lowerhybrid wave packets associated with ions accelerated to energies of 100 eV. The scaling of the sizes of these wave packets is consistent with the theory of lowerhybrid collapse and the observed lowerhybrid field amplitudes are adequate to accelerate the ionospheric ions to the observed energies.

Stochastic particle transport in a magnetic island due to electrostatic drift waves
View Description Hide DescriptionThe effect of poloidally mode coupled, ballooning type electrostaticdrift waves on a magnetic island has been studied both analytically and numerically. It has been shown quantitatively that particle orbits become stochastic and their behavior can be a possible candidate for the radial plasma transport across a magnetic island of a tokamak. The transport is significant in that it takes place even when the flux surface is not destroyed. The mechanism of the stochasticity generation is understood as an overlapping of secondary islands caused by resonance between periodic particle motions in the magnetic island and Fourier modes of E×B drift due to the electrostaticdrift waves. The diffusion process perpendicular to magnetic surface has been analyzed by approximating the distribution to the Gaussian type. In addition, local diffusion process in the vicinity of Kolmogorov, Arnold, and Moser surfaces has been discussed.

Twodimensional plasma flow past a laser beam
View Description Hide DescriptionAnalytical results are presented for laser beam deflection rate due to plasma flow when the ponderomotive force (PMF) is static and given. Explicit expressions are obtained in various parameter regimes including that of weak PMF for the case of a coherent (diffraction limited) beam and a beam whose fluctuations are spatially homogeneous, as in the case of a model random phase plate beam. When the Landau damping coefficient, , is negligible and the beam is either coherent and cylindrically symmetric, or random with isotropic fluctuations, the deflection rate is obtained as a closed form function of plasma flowMach number,M. For finite damping, results are expressed in terms of a universal, one dimensional integral parameterized by M and . For arbitrary PMF and M small, the problem is identified with one in the theory of random dielectric media.

Nonlinear dynamics of an elliptic magnetic stagnation line
View Description Hide DescriptionThe nonlinear evolution of the kink instability of a plasma with an elliptic magnetic stagnation line is studied by means of an amplitude expansion of the ideal magnetohydrodynamic(MHD)equations. A cylindrically symmetric plasma with circular field lines is used to model the magnetic field geometry close to the stagnation line. Due to the symmetry with respect to the linear stability problem of such a system has a twofolded degeneracy, with equal eigenvalues for helical kink perturbations with positive and negative polarization. It is shown that, near marginal stability, the nonlinear evolution of the instability can be described in terms of a twodimensional potential where and represent the amplitudes of the perturbations with positive and negative helical polarization. The potential is found to be nonlinearly stabilizing for all values of the polarization. Furthermore, in addition to the equilibrium point the nonlinear potential has eight equilibrium points in the plane, four corresponding to helical polarization ( or ) and four to plane polarization The latter equilibria have the lowest energy, indicating that plane kinks preferably should be formed as the stagnation line instability evolves. The equilibria with helical polarization agree with the bifurcated Zpinch equilibria obtained by means of a different method in a previous paper [Plasma Phys. Controlled Fusion 35, 551 (1993)].

Van der Pol behavior of virtual anode oscillations in the sheath around a grid in a double plasma device
View Description Hide DescriptionExperiments are reported on oscillations that arise in a double plasma device when plasma production is restricted to the source chamber and the separating grid between the two chambers is biased negatively. The free oscillating system shows periodic pulling which is a typical behavior of driven van der Pol type oscillators. The second interacting frequency is identified to be half the ion plasma frequency at the sheath edge on the source side. With the help of particle in cell simulations the concept of virtual anodeoscillations (VAO’s) as the underlying oscillation mechanism is investigated and the van der Pol character of these is revealed. When applied to the experimental conditions, the VAOmodel predicts correct oscillation frequencies. It gives a new interpretation of the scaling of these with plasma density and grid bias, and is compatible with earlier findings.

Quasilinear theory of collisionless electron heating in radio frequency gas discharges
View Description Hide DescriptionOn the basis of quasilinear kinetic theory, the electron heating of rf discharges is treated for characteristic scale lengths of the heating field much shorter than the electron mean free path. The analysis considers plasmas bounded by walls providing specular reflection. The expressions for the coefficients of electron diffusion in energy space are obtained and analyzed for inductively and capacitively coupled plasmas. Accounting for the oscillatory spatial structure of the penetrating electric field in the regime of anomalous skin effect leads to a decrease of the diffusion coefficient for high, and an increase for low, energy electrons. It is shown that the presence of a second boundary in the case of collisionless plasma slabs results in a similar effect. The formation of energy distribution functions in various regimes of collisionless heating is discussed. The diffusion coefficients are presented taking into account ambipolar electric fields.

Solution of the drift kinetic equation in the regime of weak collisions by stochastic mapping techniques
View Description Hide DescriptionA new method for solving the drift kinetic equation applicable for nonintegrable particle motion is presented. To obtain this goal, the general form of the drift kinetic equation is reduced to a stochastic mapping equation which is valid in the weak collisions regime. This equation describes the evolution of the distribution function on Poincaré cuts of phase space. The proposed Monte Carlo algorithm applied to the stochastic mapping equation turns out to solve the drift kinetic equation much faster than a direct integration of stochastic orbits. It can be applied to study quasilinear effects of radio frequency heating and transport in systems with complex magnetic field geometries such as stellarators,tokamaks with toroidal magnetic field ripples, or ergodic divertors. For systems with axial space symmetry the stochastic mapping equation is shown to reduce to the wellknown canonical (bounce) averaged equation. For nonaxisymmetric magnetic fields the bounce averaged equation for trapped particles is recovered.

Ion acoustic soliton excitation using a modulated highfrequency sinusoidal wave
View Description Hide DescriptionExperiments on the excitation of ion acoustic solitons using a fine mesh grid in a normal two component plasma are described. The excitation is novel in that a modulated highfrequency sinusoidal wave voltage signal is applied to the grid. The carrier frequency of the highfrequency sinusoidal wave is above the ion plasma frequency. An interpretation of the velocity modulation and bunching of free streaming ions that pass through the grid to which the signal is applied is given.

Numerical measurement of turbulent responses in driftAlfvén turbulence
View Description Hide DescriptionA driftAlfvén magnetoturbulence model that augments reduced magnetohydrodynamics with evolution of electron density under parallel compression and fluid advection has been studied numerically. In the Alfvénic regime, measurement of spectral transfer rates, frequency spectra, energy partitions, and the ensembleaveraged turbulent response reveals both Alfvénic and hydrodynamic characteristics. The rms turbulent frequency is Alfvénic, the energies are equipartitioned, and there is a fast, Alfvéntime scale relaxation in the turbulent response. The mean frequency is hydrodynamic, with diamagnetic and eddy straining signatures, and there is an eddy straining decorrelation appearing as a distinct, long time scale branch in the turbulent response. The decay rates and relative fluctuation strengths associated with fast and slow time scale decorrelation are in good agreement with theoretical predictions that posit a Kolmogorov spectrum in the Alfvénic regime.

The magnetized RayleighTaylor instability with a temporally variable gravity
View Description Hide DescriptionHybrid simulations with kinetic ions and massless fluid electrons are used to investigate the linear and nonlinear behavior of the RayleighTaylor instability in a collisionless, magnetized plasma in slab geometry with the plasma subject to a time varying gravity. In particular, cases where the sign of gravity is reversed for some time interval are compared with the corresponding case with constant gravity. Consistent with simple theory, the effect of the gravity reversal is to stop the growth of the instability. And when the gravity is restored to its initial direction, the instability resumes at a rate that is commensurate with its earlier value. Several ways to estimate the rate of growth of the thickness of the mixing layer when is not constant are suggested and compared with the simulations.

Expansion of the relativistic FokkerPlanck equation including nonlinear terms and a nonMaxwellian background
View Description Hide DescriptionThe relativistic FokkerPlanck collision term in Braams and Karney [Phys. Fluids B 1, 1355 (1989)] is expanded using Cartesian tensors (equivalent to associated Legendre spherical harmonics) retaining all nonlinear terms and an arbitrary zeroth order distribution background. Expressions are given for collision terms between all harmonics and the background distribution in terms of the and functions in Braams and Karney. The results reduce to Braams and Karney for the first order harmonic term with a Maxwellian background and to those given by Shkarofsky [Can. J. Phys. 41, 1753 (1963)] in the nonrelativistic limit. Expressions for the energy and momentum transfer associated with relativistic Coulomb collisions are given. The fast two dimensional FokkerPlanck solver in Shoucri and Shkarofsky [Comput. Phys. Commun. 82, 287 (1994)] has been extended to include the second order harmonic term.

A gyroLandaufluid transport model
View Description Hide DescriptionA physically comprehensive and theoretically based transportmodel tuned to threedimensional (3D) ballooning modegyrokinetic instabilities and gyrofluid nonlinear turbulence simulations is formulated with global and local magnetic shear stabilization and rotational shear stabilization. Taking no fit coefficients from experiment, the model is tested against a large transport profile database with good agreement. This model is capable of describing enhanced core confinement transport barriers in negative central shear discharges based on rotational shear stabilization. The model is used to make ignition projections from relative gyroradius scaling discharges.

On the Bernstein–Landau paradox
View Description Hide DescriptionThe essence of the Bernstein–Landau paradox is that in a stable unmagnetized plasma electrostatic waves exhibit collisionless Landau damping, while in a magnetized plasma the Bernstein modes, perpendicular to the magnetic field, are exactly undamped, independent of the strength of the magnetic field. This problem is the subject of the present study. An analytical solution of the initial value problem for perturbations perpendicular to the magnetic field is given, which is a generalization of the wellknown Landau work to magnetized plasmas. By introducing, according to Plemelj’s prescription, plus and minusfunctions, having unique analytical properties, the character of the shortterm and longterm plasma response is revealed, showing in the small magnetic field limit Landau damping in the first gyroperiod, followed by recurrence, and exhibiting irregular behavior with no damping at large times. The initial damping rate is seen to be close to the commonly used Landau damping rate for unmagnetized plasmas, however with a significant systematic deviation. A corrected expression for the Landau damping rate is found which yields a perfect description of the initial damping of oscillations perpendicular to a weak magnetic field. An alternative approach, expansion over Bernstein modes, is also employed. It is found that a zerofrequency (convective) mode, revealed earlier in particle simulations, is included in the complete linear treatment.