Volume 11, Issue 11, November 2004
 LETTERS


Twostream stability for a focusing charged particle beam
View Description Hide DescriptionThe growth of the twostream instability in onedimensonal (1D) spherical geometry is analyzed using Laplace and Fourier transforms. An analytic expression for the asymptotic growth is obtained and compared to the wellknown planar formula. Stronger linear growth is predicted for a converging beam than for its corresponding 1D planar counterpart at the same initial density. Calculations based on the analytic model are compared to 1D particleincell simulations and excellent agreement is obtained.
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 ARTICLES

 Lasers, Particle Beams, Accelerators, Radiation Generation

Excitation of “monotron” oscillations in klystrons
View Description Hide DescriptionA general method for calculations of starting currents of modes in klystron cavities is developed. This method allows one to determine the threshold for excitation of socalled monotron oscillations in klystrons having an arbitrary geometry of cavities and an arbitrary cross section of an electron beam. The method is used for evaluating the starting currents of monotron oscillations in a sheet beam, band klystron, which is currently in the design state at Calabazas Creek Research Inc.
 Basic Plasma Phenomena, Waves, Instabilities

Surface wave propagation in an ideal Hallmagnetohydrodynamic plasma jet in flowing environment
View Description Hide DescriptionThe behavior of the Hallmagnetohydrodynamic (HallMHD) sausage and kink waves is studied in the presence of steady flow. The influence of the flow both inside and outside the plasma slab is taken into account. The plasma in the environment is considered to be cold and moves with the different flow velocity outside the slab. In the limit of parallel propagation, dispersion relation is derived to discuss the propagation of both the modes. Numerical results for the propagation characteristics are obtained for different Alfvénic Mach number ratios inside and outside the slab. It is found that the dispersion curves for both surface modes, namely, the sausage and kink ones in cold plasma show complexities in their behavior in terms of multivalued portions of the curves. These multivalued portions correspond to the different normalized phase velocities for the same value of Alfvénic Mach number. In contrast to the conventional MHDsurface waves which are assumed to be pure surface waves or pseudosurface waves,surface waves are obtained which are bulk waves for very small dimensionless wave numbers, then turn to leaky waves and finally transform to pure surface waves for values of dimensionless wave number greater than one.
 Inertially Confined Plasmas, Dense Plasmas, Equations of State

Use of linear wire array pinches to examine plasma dynamics in high magnetic fields
View Description Hide DescriptionPlanar arrangements of tungsten wires, with a flat, closely positioned current return surface, were driven by the Magpie generator [I. H. Mitchell et al., Rev. Sci. Instrum. 67, 1553 (1996)]. This “linear array” configuration was expected to increase the magnetic field and forces experienced by the wires to the same level as created in experiments at the Z facility. The wires in the linear array ablated, on average, faster than in cylindrical array experiments—consistent with the expected increase in force at the wires. Streams of coronal plasma flowed from the wires to form a precursor column offset from the plane of the linear array. The dynamics of the column suggested that a much larger fraction of current flowed through it than in cylindrical array experiments ( cf. ). Inductance determined the division of current between the wires of the array; the lower inductance edge wires experienced higher currents and magnetic fields than the center wires, further increasing the ablation rate of the edge wires, resulting in an earlier start to their implosion. Timing of the implosion provided evidence that the “ablation velocity” of plasma in an array does not change with the level of drive current.
 Lowtemperature Plasmas, Plasma Applications, Plasma Sources, Sheaths

Electron crossfield transport in a low power cylindrical Hall thruster
View Description Hide DescriptionConventional annular Hall thrusters become inefficient when scaled to low power. Cylindrical Hall thrusters, which have lower surfacetovolume ratio, are therefore more promising for scaling down. They presently exhibit performance comparable with conventional annular Hall thrusters. Electron crossfield transport in a miniaturized cylindrical Hall thruster ( power level) has been studied through the analysis of experimental data and Monte Carlo simulations of electron dynamics in the thruster channel. The numerical model takes into account elastic and inelastic electron collisions with atoms, electronwall collisions, including secondary electron emission, and Bohm diffusion. It is shown that in order to explain the observed discharge current, the electron anomalous collision frequency has to be on the order of the Bohm value, . The contribution of electronwall collisions to crossfield transport is found to be insignificant.
 Basic Plasma Phenomena, Waves, Instabilities

Linear stability of static equilibrium states in the Hallmagnetohydrodynamics model
View Description Hide DescriptionThe magnetohydrodynamic(MHD) plasma model, as modified by the Hall effect, is given a Hamiltonian formulation and its stability properties are studied. It is found that, in most cases, a stable MHD plasma remains stable after the addition of the Hall effect. The most notable exceptions are when the pressure profile decreases with increasing density or when the entropy increases with density. The Hamiltonian structure of the equations enables the derivation of bounds that restrict the location of eigenfrequencies in the complex plane in some cases. The phenomenon of overstability, whereby the real part of a marginally stable eigenfrequency does not vanish, appears to be typical.
 Nonlinear Phenomena, Turbulence, Transport

Formation of nonlinear magnetic islands via trapped electrons in the lowerhybrid range
View Description Hide DescriptionCoherent nonlinear stationary state is studied in the frequency and spatial domain of electromagnetic lowerhybrid waves in a beamplasma configuration that is subjected to the oblique linear Buneman instability. In the presence of magnetic shear, a solution is found in the form of a nonlinear chain of magnetic islands. Such equilibrium may represent the saturated state of fast collisionless magnetic reconnection that is reached after the reconnection has ended. It is demonstrated that the topological constraints that hamper the reconnection of magnetic field lines in the fluid representation are efficiently removed by the nonlinear currents and space charges of trapped electrons. Two distinct trapping mechanisms are distinguished. Besides the electrostatic trapping of particles in the selfconsistent minima of potential energy, a different type of magnetic trapping is identified that is responsible for the creation of thin current sheets at the separatrices between open and closed magnetic field lines. Combined effects of the resulting two types of nonlinear phasespace vortices provide for a topological transformation of a sheared magnetic field into a single chain of magnetic islands coupled with a double chain of hydrodynamic vortices.
 Ionospheric, Solarsystem, and Astrophysical Plasmas

Suppression of convective cell generation by Alfvén waves in the ionospheric auroral cavity
View Description Hide DescriptionA theory for the parametric interaction of inertial Alfvén wave(IAW) packets with largescale convective cells accounting for the nonzero ratio of the Alfvén and light velocities is presented. It is shown that in the auroralplasma cavity where the Alfvén velocity has its maximum value, the parametric interaction of IAWs with convective cells is substantially reduced. In this region the Alfvén velocity is comparable to the speed of light and thus the displacement current cannot be neglected. This current plays a stabilizing role and results in a decline of the parametric instability growth rate. On the contrary, the incorporation of the finite width of the IAW packet leads to increase in the convective cell growth rate. A compact expression for the instability growth rate and the optimal conditions for the fastest growing convective mode are derived. The relevance of the theory to recent spacecraft measurements in the Earth’s ionosphere is pointed out.
 Basic Plasma Phenomena, Waves, Instabilities

A kinetic model for an argon plasma containing dust grains
View Description Hide DescriptionA complex lowpressure argon discharge plasma containing dust grains is studied using a Boltzmann equation for the electrons and fluid equations for the ions. Local effects, such as the spatial distribution of the dust density and external electric field, are included, and their effect on the electron energy distribution, the electron and ion number densities, the electrontemperature, and the dust charge are investigated. It is found that dust particles can strongly affect the plasma parameters by modifying the electron energy distribution, the electrontemperature, the creation and loss of plasma particles, as well as the spatial distributions of the electrons and ions. In particular, for sufficiently high grain density and/or size, in a lowpressure argon glow discharge, the Druyvesteynlike electron distribution in pristine plasmas can become nearly Maxwellian.Electron collection by the dust grains is the main cause for the change in the electrondistribution function.
 Ionospheric, Solarsystem, and Astrophysical Plasmas

Study of high Mach number laser driven blast waves
View Description Hide DescriptionThe study of blast waves produced by intense lasers in gases is motivated by the desire to explore astrophysically relevant hydrodynamic phenomena in the laboratory. A systematic scan of laser produced blast waves was performed and the structure of blast waves was examined over a wide range of drive laser energy. Lasers with energies ranging from illuminated a pin target in either xenon or nitrogen gas, creating a spherical blast wave. A strongly radiating blast wave in xenon gas is observed while blast waves in nitrogen more closely approximate a pure Taylor–Sedov wave. It is also found that at all laser energies, blast waves traveling through xenon gas had their hydrodynamic evolution significantly affected by the passage of illumination laser.
 Magnetically Confined Plasmas, Heating, Confinement

Nonlinear elongation of twodimensional structures in electron temperature gradient driven turbulence
View Description Hide DescriptionThe nonlinear evolution of the electron temperature gradient (ETG) driven mode can be described with a simple, twodimensional reduced fluidmodel, similar to that used for the thermal Rossby wave system. Consistent with ballooning mode structure, primary instability drive with a strong anisotropy in wave number (i.e., ) is considered for the inviscid limit of the ETG model. The amplitude equation, describing the initial envelope modulations of this system, is derived using reductive perturbation methods. The dynamics of the intensity field variance in radial and poloidal directions, i.e., the two diagonal elements of the covariance tensor), which follow from the amplitude equation, are investigated in an attempt to determine the basins of attraction for forming zonal flow and streamer secondary structures. It is found that the focusing (or diffracting) effect of Reynolds stress is essentially stronger in the radial direction than it is in the poloidal direction. Further analysis of the structure in the radially elongated limit of the amplitude equation yields interesting results, such as a poloidally localized sheared soliton solution. The approach used here is broadly applicable.

Ballooning mode stability in high tokamaks with a magnetic island
View Description Hide DescriptionThe secondary stability of ballooning modes in a high tokamak plasma with a magnetic island is calculated numerically. As the island grows, the temperature gradient around the point of the island steepens. Resistive ballooning modes grow more rapidly in the presence of the island, but ballooning modes are unstable even in the absence of the island. When the safety factor at the magnetic axis and the width of the island is equal to the radius of the flux surface, the ballooning mode growth rate is twice as large as the growth rate in the absence of the island. The connection length along a magnetic field line from the outside of the torus, where the magnetic curvature is unfavorable for stability, to the inside of the torus, where the curvature is favorable, is shorter when is smaller. The shorter connection length at smaller provides greater stability at than at larger , and somewhat mitigates the effect of the steep temperature gradient generated at the point of the magnetic island.
 Lasers, Particle Beams, Accelerators, Radiation Generation

Ionhose instability growth and saturation for counterstreaming electron and ion beams in an applied magnetic field
View Description Hide DescriptionThe growth and saturation of the ionhose instability in an applied axial magnetic field is examined. This dipole streaming instability is an important factor in determining the timeintegrated electron beam spot size for highpower electron beam accelerators and diodes. Threedimensional particleincell simulations are used to characterize the growth and saturation of this instability for the case of counterstreaming electron and ion beams in an applied axial magnetic field. The simulation results are compared with a detailed spreadmass model. For the parameters considered here, the simulations show that the ion beam distribution evolves as the beam propagates, deviating significantly from the injected Gaussian profile. The combined modeling results elucidate the critical role of this evolving ion beam distribution on the saturation amplitude of the instability.
 Magnetically Confined Plasmas, Heating, Confinement

Analytical solution of the diffusion equation in a cylindrical medium with steplike diffusivity
View Description Hide DescriptionThe exact analytical solution of the onedimensional diffusion equation in a cylinder has been found, for a medium characterized by a diffusion coefficient with steplike and/or monomial variations, in addition to a constant damping term. This type of equation has important applications in the field of magnetically confined plasmas, in the presence of a transport barrier. A sharp variation of the heat diffusivity can also result from the microturbulence that develops whenever the temperature gradient exceeds a critical value. This analytical solution can be used to model the evolution, in space and time, of the electron temperature of a plasma heated up by an external source, the step in the heat diffusion coefficient being related to the space location of the critical temperature gradient. The general properties of the solution and its application to the analysis of perturbative electron heating experiments are discussed.
 Inertially Confined Plasmas, Dense Plasmas, Equations of State

Efficient electron beam deposition in the gas cell of the Electra laser
View Description Hide DescriptionExtensive research has been performed to elucidate the transport of electron beamenergy from a vacuum diode, through a foil support structure (hibachi), and into the Electra laser cell. Measurements and simulations of the energydeposition in the cell are reported for various krypton/argon mixtures, gas pressures, and the thickness and material of the hibachi foil. Two hibachi and several cathode configurations are investigated and electron energydeposition efficiencies into the gas of up to 75% have been achieved with a , full width at half maximum diode pulse. The experimental data are compared with one, two, and threedimensional Monte Carlotransport calculations and particleincell simulations. The importance of electron backscattering,radiation effects, and power deposition uniformity in the laser gas are discussed.
 Lowtemperature Plasmas, Plasma Applications, Plasma Sources, Sheaths

Improved model for multipactor in low pressure gas
View Description Hide DescriptionThe effect of electronneutral collisions on the multipactor threshold in a low pressure gas is analyzed using a model that takes into account the friction force from the electron impacts with the neutrals, the thermalization of the electrons, as well as the contribution from impact ionization to the total number of electrons. It is found that the friction force is most important for firstorder multipactor for materials with a low first crossover energy and leads to an increased threshold. For higherorder modes with the same material, the thermalization effect dominates and results in a lowered threshold. The contribution to the total number of electrons from impact ionization for such materials is insignificant, but for materials with a high first crossover energy this contribution dominates the behavior and a decreased threshold is obtained for all orders of multipactor.
 Magnetically Confined Plasmas, Heating, Confinement

On the probability distribution function of particle density at the edge of fusion devices
View Description Hide DescriptionThe probability distribution function of the particle density at the edge of several magnetic fusion devices, including tokamaks,stellarators, and linear devices, is known to be strongly nonGaussian. In this paper experimental results from RFX reversed field pinch(RFP) [G. Rostagni, Fusion Eng. Des. 25, 301 (1995)] are presented, confirming the universal shape of also for RFP’s. An explanation for the form of is attempted, on the basis of simple conservation equations. The model result is shown to fit fairly well empirical data in a few different experimental scenarios.
 Inertially Confined Plasmas, Dense Plasmas, Equations of State

Selfconsistent determination of Rayleigh–Taylor growth rates and ablationfront density in planar targets accelerated by laser light
View Description Hide DescriptionA technique to provide a selfconsistent determination of Rayleigh–Taylor (RT) growth rates along with ablationfront density from measured opticaldepth growth of preimposed, twodimensional sinusoidal modulations is presented. The RT growth rates of ablationfront amplitude along with ablationfront density were determined using the opticaldepth modulation ratios of the fundamental wavelength to the secondharmonic amplitudes.
 Magnetically Confined Plasmas, Heating, Confinement

Magnetic mirror minimum field with optimal ellipticity
View Description Hide DescriptionClosed form expressions for the ellipticity and the magnetic field of a conventional mirror machine, constrained to fulfill a minimum stability criterion, are derived. The best result for zero plasmas is obtained with a marginally stable magnetic field, and the ellipticity is 13.9 with the representative value 4 for the mirror ratio. The gyro centers move on a single filed line, and thereby the perpendicular drift is zero and the radial transport is minimized. The flux tube has quadrupolar symmetry with straight (nonparallel) field lines in the confinement region.
 Nonlinear Phenomena, Turbulence, Transport

Ponderomotive barrier as a Maxwell demon
View Description Hide DescriptionThe possibility of efficient ponderomotive current drive in a magnetized plasma was reported recently in [N. J. Fisch, J. M. Rax, and I. Y. Dodin, Phys. Rev. Lett. 91, 205004 (2003)]. Precise limitations on the efficiency are now given through a comprehensive analytical and numerical study of singleparticle dynamics under the action of a cyclotronresonant rf drive in various field configurations. Expressions for the particle energy gain and acceleration along the dc magnetic field are obtained. The fundamental correlation between the two effects is described. A second fundamental quantity, namely, the ratio of the potential barrier to the energy gain, can be changed by altering the field configuration. The asymmetric ponderomotive current driveeffect can be optimized, by minimizing the transverse heating.