bluuebunny/crossref_metadata_2025 huggingface dataset:
Theta-Pinch Plasma Gun for High-Beta Injection
Authors: Turner R.
Published: February 2004

A small theta-pinch plasma gun using two independently energized pinch coils has been developed to study the interaction of a high-beta plasma with magnetic fields. The gun produces a doughnutshaped puff of hydrogen plasma which, in a 2.1 kG longitudinal magnetic (Bz) field, has a density of 1−2 × 1015cm−3, a temperature of 35 eV, and a directed energy of 210 eV. The transverse energy of the puff, limited by flute instabilities during the initial compression phase and entry into the Bz field, is more than three times as large as the output from a more conventional, but comparable, conical gun. A significant amount of the directed plasma energy can be converted to transverse energy by reflecting the plasma from a magnetic barrier.
Second-Order Perturbed Distribution Associated with the Plasma Wave Echo
Authors: Nishikawa Kyoji
Published: February 2004

The perturbed distribution which contributes a plasma wave echo shows an oscillatory behavior with different phases and amplitudes before and after the echo. The difference in amplitude is found to be negligibly small except for very special cases.
Velocity Shear and Low-Frequency Plasma Instabilities
Authors: Perkins F. W. , Jassby D. L.
Published: February 2004

The effects of transverse velocity shear on the low-frequency stability of a plasma are examined theoretically for a low-β resistive plasma in a uniform magnetic field. Cylindrical geometry is used and the velocity shear is introduced by a nonuniform E × B rotation. Both numerical and analytic methods are used. The principal analytic result is a dispersion relation for instabilities caused by a thin velocity shear layer. This dispersion relation describes the Q machine edge oscillation, which is identified either as a Kelvin-Helmholtz instability or as a velocity-shear analog of the resistive drift wave, depending on the parallel wavelength. The numerical results show that properties of instabilities observed in several experiments agree reasonably well with theory. The effect of velocity shear on the drift instability is to make it into either a local or nonlocal type of normal mode.
Interaction among Three Extraordinary Waves in a Hot Electron Plasma
Authors: Das K. P.
Published: February 2004

The Krylov-Bogoliubov-Mitropolsky method is applied to the study of the interaction among three extraordinary waves propagating perpendicularly to a uniform magnetic field in a hot electron plasma. The frequency and wavenumber of the three waves satisfy the conditions ω1 + ω2 = ω3 and κ1 + κ2 = κ3. When the external magnetic field is small, the first and the third wave show a transverse character and the second wave shows a longitudinal character; in the case of a zero magnetic field, they reduce, respectively, to transverse and longitudinal waves. In the absence of a magnetic field the analysis shows a mechanism, through which the energy of a longitudinal wave may be converted into the energy of a transverse wave.
Large Amplitude Disturbances in a Positive Column
Authors: Andrews J. G.
Published: February 2004

A theory is given for treating large amplitude disturbances to ion flow in a low-pressure positive column using a characteristics method of solution.
Application of Finite Larmor Radius Equations for Collisionless Plasmas to a θ Pinch
Authors: Bowers E. , Haines M. G.
Published: February 2004

Using finite Larmor radius equations developed in an earlier paper the stability of an arbitrary β rotating θ pinch with straight lines of force in equilibrium is worked out in detail. The resulting differential equation together with boundary conditions and the specification of radial density profiles yields an eigenvalue problem which is solved with the aid of a computer. The results obtained show that an m = 1 rotational instability can occur in a θ pinch and that finite Larmor radius stabilization of this mode is present. It is also found that the rotating plasma should be stable to perturbations with an axial wavelength ≲ 1 m. This provides an explanation of why long θ pinches tend to go unstable uniformly along their length. Finite Larmor radius stabilization is critically dependent on the radial density profile, the steeper gradient favoring stability. Results are also presented showing how a large parallel temperature and shear in the axial flow can modify the rotational instability.
Average Pore Velocities in Porous Media
Authors: Guin J. A. , Kessler D. P. , Greenkorn R. A.
Published: February 2004

It is shown that for a statistical model of a porous medium with nonuniform pores, the number average pore velocity and the velocity given by the Dupuit-Forcheimer relation are equivalent only in certain limiting cases.
Reflection of Pseudowaves
Authors: Estabrook K. , Alexeff I. , Jones W. D. , Lonngren K. E.
Published: February 2004

Ion bursts (pseudowaves) in a low temperature discharge plasma are reflected from the potential barrier of a gridded energy analyzer. The energy of the reflected ions increases monotonically with the increasing potential.
Longitudinal Oscillations in Bounded Magnetoplasmas
Authors: Stenzel R. L. , Gould R. W.
Published: February 2004

Fine structure in absorption due to Buchsbaum-Hasegawa modes is observed over a wider range of magnetic fields than previously reported (ωc/ω = 0.5−0.985). The basic theory is satisfactory only near the cyclotron harmonic.
Kinetic Theory of Wave Propagation. II. Binary Gas Mixtures
Authors: Bramlette T. Taz , Huang A. Ben
Published: February 2004

Solutions to the problems of forced and free wave propagation in binary gas mixtures are presented which were obtained using the discrete ordinate method. The governing equations for the mixtures are the model equations proposed by Hamel. The solution is in excellent agreement with existing experimental data.
One-Dimensional Laser Heating of a Stationary Plasma
Authors: Steinhauer Loren C. , Ahlstrom Harlow G.
Published: February 2004

The problem of laser energy addition to a nonuniform one-dimensional plasma is considered. The object is to study plasmas which may achieve temperatures and densities of interest for application to controlled thermonuclear reactions. The advent of the nanosecond and picosecond lasers makes it possible to consider the heating of stationary, nonthermally conducting plasmas with a nonuniform density distribution in which only the electrons are heated. The solutions show that for a wide range of relevant parameters these assumptions are valid. The temperatures that can be produced are of interest in controlled thermonuclear reactions. Depending on the steepness of the density gradient, either wavelike or simultaneous heating is produced. Also, the temperature distribution is very much nonuniform and can significantly affect the subsequent dynamics of the plasma.
Flows and Wave Propagation in Ferrofluids
Authors: Curtis R. A.
Published: February 2004

The dynamic behavior of magnetically polarizable fluids (ferrofluids) is considered in two instances differing in the dependence of the fluid magnetization on temperature. When the magnetization can be regarded as temperature independent, the influence of the magnetic field on the force distribution acting on a submerged body is demonstrated, the flow pattern of the associated ordinary fluid dynamics problem remaining unaffected. In the other instance, when the temperature dependence of the magnetization must be considered, the question of thermal stability of the ferrofluid is considered and the appropriate magnetic Rayleigh number and its influence are determined. Furthermore, it is shown that small disturbances in a ferrofluid are quickly damped so that vorticity generated by the thermomagnetic interaction for such disturbances does not propagate.
Numerical Model of the Return Stroke of the Lightning Discharge
Authors: Plooster Myron N.
Published: February 2004

The numerical model of a spark discharge in air, described in the preceding paper [Phys. Fluids 14, 2111 (1971)], is used to compute the properties of the discharge channel of a lightning return stroke and its acoustic wave. Initial conditions and electric current waveforms were varied over a wide range, to correspond with the observed variability of natural lightning events. Computed temperatures, pressures, and electron densities in the discharge channel agree well with available observational data. The model predicts temperatures near the upper limit of the range of spectroscopically determined temperatures. Discharge channel radii agree well with similarity solutions for the growth of a spark channel. The energy dissipated per unit length of the discharge channel and the strength of the pressure wave lie well below most literature estimates. The computed energy inputs fall between 10 and 60 J/cm, and depend primarily on the maximum values of the discharge current.
Nonlocal Theory of Trapped Particle Instability
Authors: Bhadra Dilip K. , Liu Chuan Sheng
Published: February 2004

A nonlocal theory for the low-frequency trapped particle instability in toroidal systems has been developed in a model field. The stability of the trapped particle mode is studied by using normal mode analyses with radial boundary conditions. In the absence of magnetic shear, the finite-orbit effect is shown to be incapable of stabilizing the mode; large magnetic shear is needed for stabilization. The ratio of the localization width of the mode to the characteristic density length is of the order of (Λ/r;)1/2ε1/4 (Λ is the charactistic “banana” size, r is the characteristic density length, and ε is the aspect ratio). An estimate of the nonlinear diffusion coefficient for the mode is given.
Experimental Study of Spectral Index, Mode Coupling, and Energy Cascading in a Turbulent, Hot-Ion Plasma
Authors: Roth J. Reece
Published: February 2004

The spectrum of electrostatic potential fluctuations was measured with a capacitive probe in a steady-state, turbulent plasma confined in a magnetic mirror geometry. The plasma conditions ranged over 5×107≤ne≤5×108/cm3,8≤Te≤38eV,350≤Ti≤930eV, and Bmax = 1.0 T. When oscillation peaks were absent, the amplitude spectrum of electrostatic potential fluctuations had a power-law dependence on frequency of the form θ=θ0ν−n over the range 0.2-1.0 MHz. The value of the spectral index n depended on the probe position in the magnetic field, and, at a given position, depended on the plasma characteristics. The spectral index was generally below the value n = 2.5 predicted by some turbulence theories formulated in k space. Enhancement of the turbulent spectrum on the high-frequency side of oscillation peaks suggests that the direction of net energy flow in the turbulent spectrum is from low frequencies to high frequencies in this plasma. The effects on the amplitude spectrum of a sinusoidal external modulation of the anode voltage were assessed over the range 0-100 kHz. The spectra exhibited several mode coupling phenomena, including enhanced harmonics of the externally imposed frequency, and sideband modulation of plasma generated oscillation peaks. External excitation of the plasma at frequencies below 50 kHz resulted in only a small degree of ion heating.
Linear Conversion of Waves for Oblique Propagation
Authors: Fichet M. , Fidone I. , Granata G.
Published: February 2004

Linear conversion of waves at the upper hybrid resonance for oblique propagation is considered. The conditions for the validity of a fourth-order equation near the resonance are discussed. The cyclotron damping at ω≃2ωc for the converted plasma wave is calculated.
Propagators in Strong Plasma Turbulence
Authors: Birmingham T. J. , Bornatici M.
Published: February 2004

Straightforward relationships among Weinstock's propagator, UA, the Vlasov propagator, U, and the ensemble average Vlasov propagator, 〈U〉, are derived. U and 〈U〉 U are related to the characteristic trajectories of the Vlasov equation.
Approximate Method in the Kinetic Theory
Authors: Loyalka S. K.
Published: February 2004

An approximate method for solving the slip problems in the kinetic theory of gases is proposed, and it is shown that extremely good results can be obtained by a simple modification of Maxwell's arguments.
Postulation of the Arc Restrike Mechanisms for Exploding Wires and Tubes
Authors: Cheng Dah Yu , Loubsky William J. , Fousekis Vlasis E.
Published: February 2004

The many facets of exploding wire restrikes are studied. They are related to the cylindrical shock wave which pumps down the density of the center region of a line energy source or around the surface of the heated wire continuously to a lower density. When the density of any region is pumped down to lower than Paschen's electric breakdown criteria, restrike occurs. The cylindrical shocks occuring in exploding wires are, in general, divided into two types. In the first type the shock is generated by the wire explosion and in the second type the shock is generated by the heat conduction of the wire to the surrounding gas. Application of this mechanism to exploding tubes will enable us to create arc channels in arbitrary gaseous atmospheres with controllable plasma density with the contamination excluded. Neutral density shielded plasma experiments, therefore, can be conducted in a controllable environment.
Flame Propagation and Overdense Heating in a Laser Created Plasma
Authors: Bobin J. L.
Published: February 2004

A one-dimensional continuum hydrodynamic theory is used to investigate the structure of the deflagration wave which occurs when a laser light beam impinges on a solid target. It is shown that the nonlinear electron heat conduction is responsible for most of the structure; a region of density higher than the cutoff is strongly heated. Density and temperature profiles are calculated. An approximate solution for the thickness x of the overdense layer gives x = 45[(γ−1) / (5γ−1)](m/k)3/2A(Tc2/ρc) (m is the ion mass, k is the Boltzmann constant, A T5/2 is the nonlinear electron heat conduction coefficient, Tc is the temperature of the plasma at cutoff density ρc. The average density in the layer is about twice the cutoff density. The effects of viscosity and (since electrons are heated by the laser light) of ion-electron relaxation are evaluated.
Spreading of a Pseudowave Front
Authors: Alexeff I. , Estabrook K. , Widner M.
Published: February 2004

Using analytic, nonlinear techniques the spreading of the leading edge of a pseudowave (here assumed to be a slab of ions injected at hypersonic velocity into a dense background plasma) is computed. It is found that the front spreads due to collective effects with a characteristic velocity of 3(n20/n10)1/2va, where n20 is the initial injected ion density, n10 is the background ion density, and va is the ion-acoustic velocity. The computation also predicts a finite leading edge velocity of v0+2(n20/n10)1/2va, where v0 is the initial velocity of injection. Neither shock steepening nor an accelerating leading edge as in a free expansion of plasma is found.
Kinetic Theory of a Weakly Coupled and Weakly Inhomogeneous Gas
Authors: Øien Alf H. , Tjøtta Jacqueline Naze
Published: February 2004

A study of the evolution toward equilibrium of a weakly coupled and weakly inhomogeneous one-component gas using the multiple-time-scale method is presented here. The method is applied to the BBGKY equations and the first three hydrodynamic equations. For one special ordering between the inhomogenity parameter and the parameter associated with the weak coupling, it is found that the equation for the temperature in the Burnett approximation must be supplemented with a dissipative term describing energy conversion from kinetic energy of particles to correlational electric field energy of the gas.
Nonadiabatic Particle Motion in Cusped Magnetic Fields
Authors: Howard James E.
Published: February 2004

Analytic expressions are obtained for nonadiabatic jumps in the magnetic moment μ for particle orbits in linear and axisymmetric cusped magnetic fields, starting from an integral derived by Hastie and Taylor. The resulting formulas for Δμ/μ are found to agree to within a few percent with values derived from computed orbits. In the limit of large mirror ratios, the theoretical results confirm a semiempirical formula of Grad and van Norton.
Theory of Beam-Plasma Interaction
Authors: Kadomtsev B. B. , Pogutse O. P.
Published: February 2004

A new approach to the theoretical treatment of the cooperative phenomena at beam-plasma interaction is proposed. It takes into account the bunching effect related to trapping of the beam electrons in waves.
Structure of Turbulence in the Zeta Plasma
Authors: Robinson D. C. , Rusbridge M. G.
Published: February 2004

The structure of turbulent electric and magnetic field fluctuations is described, and the internal dynamics of the associated velocity fluctuations are compared with those of fluid turbulence. It is suggested that the plasma turbulence is qualitatively similar to fluid turbulence but with the turbulent elements elongated along the mean magnetic field to form rolls. This suggests that an appropriate comparison might be with the hypothetical two-dimensional limit of fluid turbulence, in which energy is expected to be transferred toward long wavelengths rather than to short wavelengths as for isotropic turbulence. In the plasma case, the direction of energy flow is inferred to be toward short wavelengths but the measured form of the triple correlation is close to that expected for two-dimensional turbulence; we cannot, therefore, make a clear choice between the two alternatives. Effects arising from the particle structure of the plasma do not appear to be important, except that at low pressures an increased damping occurs which may be ion Landau damping. The source of the turbulent energy is not primarily convection due to the pressure gradient but involves some mechanism of direct coupling with the plasma current associated with the “excess resistance” of the discharge.
Pulse-Stimulated Emission and Echoes at Upper Hybrid Resonance
Authors: Henderson D. M.
Published: February 2004

An experimental study of the interaction at upper hybrid resonance of high-frequency radiation with a low-temperature spatially inhomogeneous plasma is presented. This interaction is investigated through single-pulse-stimulated emission and two pulse echoes which are observed in an afterglow plasma column placed in a uniform, static magnetic field. A theoretical treatment of the linear response of a one-dimensional plasma slab in the zero-temperature approximation is given. This theory predicts that a long-lived radiation signal at the maximum upper hybrid frequency of the inhomogeneous profile is excited by a microwave pulse and decays by phase mixing. Experimental evidence to support the theory is given, especially those aspects which are essential to echo formation. Several nonlinear processes of echo formation are investigated. Based on an approximate collision model for argon, a theory is developed for upper hybrid echoes in a low-density plasma arising from velocity-dependent electron-neutral collisions. The observed echoes in argon are compared both with this theory and with the theory of Blum and Bauer for echoes from nonlinear upper hybrid oscillations. Under our experimental conditions, the collisional nonlinearity dominates.
Experimental Results on Electrostatic Stoppering
Authors: Moir Ralph W. , Barr William L. , Post Richard F.
Published: February 2004

In a pulsed experiment a magnetically guided plasma stream is reflected by a double electrode structure. Space-charge-limited densities up to 4×1011 cm−3 are calculated and verified. An application to stopper one end of a mirror fusion reactor is discussed.
Noniterative Method for Computing Rotational Temperatures from Electron Beam Excited Nitrogen Fluorescence
Authors: Schelby F. , Hill R. A.
Published: February 2004

A noniterative method for computing rotational temperatures from electron beam excited nitrogen fluorescence is described. The difference between the temperature for direct excitation (ΔK = 0) and for optical excitation (ΔK = ±1, Muntz model) is given by 2 Bv0hc/k, where Bv0 is the rotational constant.
Dissipative Effects on Nonlinear Waves in Rotating Fluids
Authors: Leibovich S. , Randall J. D.
Published: February 2004

A modification of the Korteweg-deVries equation is found to describe weak dissipation in long waves in a swirling fluid. General features of solutions are discussed, and the solution for the damping of solitary waves is presented.
Turbulent Flow Due to a Rotating Disk
Authors: Erian F. F. , Tong Y. H.
Published: February 2004

The results of an experiment, conducted to determine the turbulent structure of the flow due to a rotating disk, are presented. Mean velocities, turbulent intensities, and one Reynolds stress component are measured. A scalar eddy viscosity coefficient is calculated from the measurements and used to determine the other Reynolds stress components using Boussinesq's model. This coefficient will also permit the numerical integration of two boundary-layer-type equations describing this flow. It is shown that the eddy viscosity in the turbulent boundary layer generated by the disk rotation is substantially larger than that of the turbulent boundary layer over a flat plate.
Calculation of the Velocity Distribution Functions of Electrons in Stationary Homogeneous Cesium Plasmas
Authors: Saul Klaus G.
Published: February 2004

The velocity distribution of electrons in a plasma is calculated by solving Boltzmann's equation together with the rate equations, which describe the transition rates between the different atomic levels. The calculations are made for stationary, homogeneous, cesium plasmas immersed in uniform electric fields of the order of 20 V/m. The number density of atoms is of the order of 5×1020 m−3, and the fractional ionization ranges from zero to 10−2. The processes taken into account are: elastic collisions between electrons and atoms; collisional excitations and deexcitations of atoms; radiative deexcitations of atoms; mutual electron collisions, and elastic collisions between electrons and ions. The plasmas are assumed to be optically thick at the resonance lines if the ionization degree is above 10−4. The individual contribution of the elementary processes is shown by the calculation of some special cases. When all processes are taken into account, and the electron densities are high, the distributions are nearly Maxwellian. The calculations agree well with measurements of the electron temperature in the center of highly ionized positive columns.
Computer Calculations of Electron Cyclotron Heating in a Nonuniform Magnetic Field
Authors: Sprott J. C. , Edmonds P. H.
Published: February 2004

A computer is used to calculate the trajectories of a collection of noninteracting, nonrelativistic electrons near the axis of a spatially sinusoidal, dc magnetic field in the presence of a spatially homogeneous, perpendicular rf electric field. The computed heating rate is in good agreement with the prediction of various equivalent stochastic models for a wide variation of parameters. The distribution is approximately Maxwellian, and the particles tend to turn at the resonance surface. Departure form the stochastic theory is observed for high-energy particles that turn near the resonance surface, and a condition for stochasticity is derived. Trapping of particles initially in the loss cone is observed with strong electric fields.
Dominant Effects of Coulomb Collisions on Maintenance of Landau Damping
Authors: Johnston George L.
Published: February 2004

An analytical criterion for the maintenance, by Coulomb collisions, of the damping of a weakly damped electron wave at the rate given by the theory of Landau when nonlinear effects are present is obtained. For sufficiently small values of ν, the collision frequency, the dominant collisional effects are effects of lowest order in (ν/ka)1/3 on the linearized distribution function perturbation. The characteristics solution for the resonant component of the linearized distribution function perturbation differs from the collisionless result only in that the factor Re([−i(kv−ω)]−1) is replaced by an integral in which collisional effects are embodied in the parameter κ = ([ν/(ka)]1/3/[Im(−ω) / ka]). Neglect of the deviation of the damping of the wave from its initial value permits determination of the spatial average distribution function perturbation in the range of time ([Im(−ω)]−1)≪t≪ν−1. The principal contribution involves the resonant component of the linearized distribution function perturbation. The relative change in the slope of the spatial average distribution at v = [Re(ω) / k] is determined by inspection of the integral containing κ, as well as by approximation of this integral by the method of steepest descents, to be negligible for κ≳O(1). For this range of κ, therefore, Coulomb collisions can maintain the damping at the rate given by the theory of Landau. The physical mechanism for this effect is the inhibition by Coulomb collisions of the resonant wave-particle interaction through which nonlinear modification of the spatial average distribution function occurs.
Parallel Propagation of Nonlinear Low-Frequency Waves in High-β Plasma
Authors: Rogister André
Published: February 2004

A pair of coupled, nonlinear, partial differential equations which describe the evolution of low-frequency, large-scale-length perturbations propagating parallel, or nearly parallel, to the equilibrium magnetic field in high-β plasma have been obtained. The equations account for irreversible resonant particle effects. In the regime of small but finite propagation angles, the pair of equations collapses into a single Korteweg-de Vries equation (neglecting irreversible terms) which agrees with known results.
Collective Oscillations of a Relativistic Radiating Electron Plasma
Authors: Hakim Rémi , Mangeney André
Published: February 2004

Results obtained previously are applied to the study of the dispersion relations of a relativistic radiating electron gas. The cases of (a) supraluminous and (b) suprathermal waves are dealt with. It is found that the effect of radiation is a negligibly small damping except for longitudinal supraluminous modes which are strongly damped. The stream instability is also studied, and it is shown that the more relativistic a beam is, the more unstable it is.
Stability Equation for Viscoelastic Liquids of Arbitrary Memory
Authors: Mook Dean T.
Published: February 2004

A stability equation valid for liquids described by a general linear hereditary constitutive equation is derived by superposing an infinitesimal two-dimensional periodic disturbance on the primary flow. In the case of liquids having short memories this equation reduces to the one given by Walters.
Airborne Hot-Wire Measurements of the Small-Scale Structure of Atmospheric Turbulence
Authors: Sheih C. M. , Tennekes H. , Lumley J. L.
Published: February 2004

An experimental investigation of small-scale atmospheric turbulence is presented. Airborne measurements were made in the vicinity of the meterological tower of Brookhaven National Laboratory. Hot-wire probes mounted on the right wing tip of a Cherokee aircraft were used. The anemometer signals were recorded on an analog tape recorder in the aircraft after differentiation and filtering; they were digitized in the laboratory with a high-speed analog-to-digital converter, and recorded on magnetic tape. All data were processed with an IBM-360. A fast Fourier transform program was used to compute the spectra. The average Kolmogoroff constant computed from the small-scale spectra was α = 2.0. The cospectra and quadrature spectra of the small-scale turbulence were virtually zero. The skewness and kurtosis of ∂ui/∂x (the derivative of a velocity vector with respect to the coordinate in the direction of aircraft heading) ranged from -0.03 to -0.50 and from 4.5 to 14, respectively, at Reynolds number (Rλ) from 2280 to 5330. The spectra of (∂ui/∂x)2 were found to exhibit a -0.3 power law in the inertial subrange. The probability distribution of (∂ui/∂x)2 was nearly a straight line in log-normal coordinates.
Profile and Speed of Finite Amplitude Waves in a Falling Liquid Layer
Authors: Lin S. P.
Published: February 2004

The profiles as well as the speeds of supercritically stable surface waves are obtained for various values of surface tension, Reynolds numbers, and the angle of inclination of a falling liquid layer. The calculated values of wave speeds are in good agreement with Kapitza's measurements and the theoretically obtained wave profiles seem to resemble those appearing in his photographs. Profiles of “generalized solitary waves” which propagated at speeds several times that of the kinematic speed are also found.
Stress Induced Diffusion in Monatomic Gases and Gas Suspensions
Authors: Annis B. K.
Published: February 2004

The interaction between viscous stress and diffusion is examined through the use of the Chapman and Cowling method, and the results for a general binary mixture of monatomic gases is obtained. It is demonstrated that the kinetic theory calculation provides a first iteration to the form predicted by statistical mechanics; it also produces a modification in the barodiffusion coefficient that is in more general agreement with the results of the 13-moment method than has been shown previously. Finally, the general equations are modified to permit description of a dusty gas or aerosol of fine particles, and the result is found to differ significantly from a calculation based on the methods of stochastic processes.
Plane Poiseuille Flow of a Rarefied Gas Based on the Finite Element Method
Authors: Bramlette T. Taz
Published: February 2004

A finite element solution to the problem of a rarefied gas flowing between two parallel, infinite plates is presented. The results agree well with the numerical solution of Cercignani and Daneri, the discrete ordinate solution of Huang, Giddens, and Bagnal and the half-range moment solution of Huang and Stoy.
Stability of Normal Shock Waves with Viscosity and Heat Conduction
Authors: Morduchow Morris , Paullay Alvin J.
Published: February 2004

The stability problem, for small arbitrary one-dimensional disturbances, of a normal shock wave with viscosity and heat conduction in a thermodynamically perfect gas with a Prandtl number of 0.75 is treated, and is formulated explicitly as an eigenvalue problem involving ordinary linear differential equations with polynomial coefficients in a fixed finite domain whose end points are singular points of the differential equations. It is shown by a simple general type of mathematical argument that one possible mode shape for the perturbations is a translation of the shock structure, and that such a disturbance is neutrally stable. For the limiting case of a weak-shock structure, the equations developed here are shown to reduce systematically to a perturbed form of Burgers' equation. The weak shock structure is shown to be stable for any Prandtl number and general equation of state, and a complete solution for the disturbance eigenvalues and eigenfunctions in this case is derived and discussed.
Sheath Growth in a Low Pressure Plasma
Authors: Andrews J. G. , Varey R. H.
Published: February 2004

The limits of very slow and very fast sheath growth in a low-pressure plasma can be described by Child's law and the ion matrix model, respectively. It is shown that if the sheath edge grows with constant speed, the range between these two extremes can be treated analytically by transforming the equations to the sheath edge frame of reference. This provides a continuous transition between the two extremes which reduces to Child's law for very slow growth and to the ion matrix model for very fast growth. The theoretical expression for sheath thickness calculated from the continuous transition model is found to be in good agreement with experimental results.
Magnetic and Drift Surfaces using a New Stellarator Expansion
Authors: Dobrott D. , Frieman E. A.
Published: February 2004

A new stellarator expansion has been devised, wherein the depths of the helical and toroidal field modulations are comparable and the total rotational transform is finite. To accomplish this, we define λ = ρ/R ≪ 1 (R is the major radius, ρ is the minor radius) and choose p, the number of helical periods, to be of order λ−2/3. Detailed calculations of vacuum magnetic field properties have been carried out, including the magnetic surfaces, V″, shear, etc. For the particle surface calculations, the ratio of ion gyroradius to major radius of the torus, ε = RL/R, is chosen to be of order λ3/2. Using the same methods as for the vacuum field calculations, analytic solutions are obtained for particle drift surfaces in stellarators with finite departures from axial symmetry. These surfaces, derived from perturbation techniques, are obtained for four particle classes that are, for the first time, precisely categorized according to trapping state. Transitions between classes are interpreted. Numerical calculation of integrals is carried out for comparison with approximate results.
Nonlinear Beam-Plasma Interactions and Stochastic Acceleration
Authors: Dum Christian T. , Sudan R. N.
Published: February 2004

The development of an electron beam-plasma instability beyond the stage described by quasilinear theory has been investigated by means of kinetic equations for waves and particles which include the effects of spontaneous emission and scattering of waves. Characteristic times for the formation of a high-energy tail have been computed, which at late times may extend significantly beyond the original beam velocity. Qualitative agreement is obtained with experiments.
Two-Stream Instability in the Two Maxwellian, Resonance, and Two Pole Models for Arbitrary Stream Temperatures and Densities
Authors: Skorupski A. , Żakowicz W. , Infeld E.
Published: February 2004

The problem of stability of two hot streams of charged particles with Maxwellian distributions is solved, in principle, for arbitrary parameters. Stability limits are also found for two models often used for the velocity distributions and comparisons are made.
Dependence of Plasma Density Distribution on Local Decay Time
Authors: Uramoto Johshin
Published: February 2004

A local increase in e-folding length in a density distribution across B is not related to an increase in diffusion coefficient, if a decay time of plasma along B increases locally with reflection of the plasma on two end sheaths.
Three Wave Mode Coupling Theory of Nonresonantly Unstable Waves
Authors: Ott Edward
Published: February 2004

The usual nonlinear three wave mode coupling theory is extended to include nonresonantly unstable waves near the marginal stability limit. Both coherent and incoherent (turbulent) coupling are investigated.
Nonlinear Instability of Modulated Waves in a Magnetoplasma
Authors: Tang Ting-wei , Sivasubramanian A.
Published: February 2004

The nonlinear instability of small but finite-amplitude, modulated waves is investigated for R-, L-, O- and X-wave propagations in an electron magnetoplasma. Relativistic effects are included in the treatment.
The Darwin Model as a Tool for Electromagnetic Plasma Simulation
Authors: Kaufman Allan N. , Rostler Peter S.
Published: February 2004

The Darwin model of electromagnetic interaction is presented as a self-consistent theory, and is shown to be an excellent approximation to the Maxwell theory for slow electromagnetic waves.
Doppler Spectra in Microwave Scattering from Wind Waves
Authors: Wright J. W. , Keller W. C.
Published: February 2004

Doppler spectra in microwave scattering from wind waves have been measured at X band (3.2 cm) and K band (1.25 cm) in a short fetch wind wave tank. The scattering cross sections, mean frequency shifts, and bandwidths obtained are compared with results of measurements of the directional slope spectra, mean drift, and particle velocities of the wind waves. The scattering is attributed to low order Bragg scattering, the phase speeds of the wind waves are deduced and the dependence of the Doppler bandwidth on wind speed and Bragg wavenumber is given.
Chemical Instabilities. III. Nonlinear Stability Analysis of a Heated Horizontal Layer of Dissociating Fluid
Authors: Wollkind David J. , Frisch H. L.
Published: February 2004

The linear perturbation problem [D. J. Wollkind and H. L. Frisch, Phys. Fluids 14, 13 (1971)] is extended to include a nonlinear stability analysis of a horizontal layer of dissociating fluid, heated from above or below. This analysis deals with the simplest possible nonlinear problem, namely, a two-dimensional situation in which material property variation with temperature is neglected. The results of this analysis show that there exist finite amplitude equilibrium rolls for both the case of heating from below (at a slight departure from the critical conditions for the Bénard problem) and from above (the chemical instability). This problem having been solved, it can then be conjectured with some confidence what a fuller nonlinear analysis would reveal.
Linear and Nonlinear Collisional Processes in a Plasma
Authors: Krishan S. , Selim A. A.
Published: February 2004

Quantum techniques are used to treat the linear and nonlinear collisional processes in a uniform weakly interacting plasma near equilibrium in the absence of external magnetic field. The nonlinear collisional process consists of coupling of two particles to two waves whereas in linear collisional case only one wave is coupled to two particles. It is found that if the plasmon mode energy is below its equilibrium level, the nonlinear collisions give rise to growth and above, it contributes to damping.
Ion Heating by a Modulated Electron Beam
Authors: Haas G. M. , Eisner M.
Published: February 2004

The transfer of energy to the plasma ions in the interaction of a modulated electron beam with a beam formed plasma is found to be dependent on the square root of the plasma density, and independent of the ion species.
Longitudinal Wave Propagation in a Plasma Containing an External Time-Dependent Electric Field
Authors: Nunez Paul N.
Published: February 2004

Frequency and damping decrements for high frequency longitudinal oscillations in a plasma containing an external high frequency (Ω ≫ k υ¯_) electric field are obtained by means of a time-asymptotic solution to the linearized Vlasov equation, with an approximate collision term included. If the external field frequency is close to (ωp_2 + 3 k2υ¯_2)1/2, the contribution of the ion motion to Landau damping is significant for small external fields. The threshold field necessary to excite a high frequency instability in a plasma in which the number of a particles in a Debye sphere is very large is obtained. This problem is of interest since laser-induced instabilities may be responsible for an anomalous heating effect in the plasma.
Dynamics of Variable Wavelength in Finite-Amplitude Bénard Convection
Authors: Lipps Frank B. , Somerville Richard C. J.
Published: February 2004

The finite-amplitude Bénard convection problem is investigated by numerical integration of the rigid-boundary Boussinesq equations in two and three space dimensions. Solutions are obtained for a wide range of Prandtl numbers and at moderate Rayleigh numbers for which the flow is observed to approach a two-dimensional steady state. Detailed quantitative comparisons are made with experimental data in an effort to explain the observed increase of cell wavelength with Rayleigh number and to determine the effect of changing cell size on the heat transport. The three-dimensional model shows good evidence of being able to yield realistic values of the cell wavelength, while the two-dimensional models yield wavelengths that are much too short. These results strongly suggest that the increase in wavelength is determined by a three-dimensional transient process, while the convection tends to a two-dimensional steady state. The increase in cell size is shown to be responsible for a substantial part of the discrepancy between previous theoretical-numerical and experimental determinations of Nusselt number. It also provides a plausible explanation for the experimentally observed dependence of heat transport on Prandtl number.
Plasma Expansion into a Vacuum
Authors: Widner M. , Alexeff I. , Jones W. D.
Published: February 2004

The expansion of a semi-infinite, uniform plasma into a vacuum is studied by computer simulation. The solution resembles an analytic similarity solution except for a discontinuous front that precedes the plasma at a velocity of about 3(kT /mi)1/2. Thus, previous speculation that the initial burst of ions would be accelerated to velocities comparable to that of the thermal velocity of the plasma electrons on the basis of a fluid model alone is found to be not valid.
Stability of a Trapped Particle Equilibrium
Authors: Goldman Martin V. , Berk Herbert L.
Published: February 2004

A simple periodic Bernstein-Greene-Kruskal equilibrium is constructed, in which trapped electrons make a small contribution to the reactive part of the one-wave dispersion relation. This contribution is found to have an important effect on stability of the wave against decay into sidebands. Enhanced growth rates and frequency shifts are calculated.
Local Density Measurements by Nonlinear Mixing of Electromagnetic Waves
Authors: Cano R. , Fidone I. , Zanfagna B.
Published: February 2004

A diagnostic scheme for local measurements of the electron density in low β plasmas using the nonlinear mixing of electromagnetic waves is presented. The basic assumption is made that the three interacting waves satisfy the synchronism relations. A number of nonlinear processes are examined for different magnetic configurations. Experimental results obtained with a steady-state plasma (1010<ne<1012 cm−3) are reported to illustrate the method.
Explosive Instabilities in Simulated Plasmas
Authors: Byers J. A. , Rensink M. E. , Smith J. L. , Walters G. M.
Published: February 2004

Nonlinear instabilities arising from the interaction of two positive energy waves and one negative energy wave have been observed on a one-dimensional superparticle computer model for perpendicularly propagating, linearly stable cyclotron waves. For the case in which all three-wave amplitudes are initially equal, the theoretical predictions and experimental results on the growth of these instabilities are in good qualitative and quantitative agreement. Saturation is observed when the electrostatic energy grows to about 1% of the kinetic energy in the system, sufficient to cause significantly large changes in the equilibrium orbits. The “forward scattering” theory of Fukai, Krishan, and Harris is used to explain the qualitative behavior of the wave amplitudes and phases just prior to saturation.
Neutron Production in a Plasma Focus Discharge with and without Axial Magnetic Field
Authors: Bernstein M. J. , Hai F.
Published: February 2004

The D-D neutron emission from a 27-kJ plasma focus discharge was investigated with and without the effects of an applied axial magnetic field. With no applied field, the ratio of axial to radial neutron fluxes varied from 1.5 down to 1.2 for gas fillings of 4 to 10 Torr; the ratio of fluxes was greater for a round anode tip than for a flat end. An axial field of 1200 G (trapped flux of 57 000 Maxwells) reduced the average neutron yield from 1010 to 109, reduced the average energy of the axially emitted neutrons from 2.9 to 2.8 MeV, and caused the effective neutron source to shift away from the anode surface; the width of the neutron energy spectra remained about 500 keV. With an applied field, the ratio of axial to radial neutron fluxes increased from 1.2 early in the pulse to 1.5 at peak intensity. Streak photography with and without axial field revealed that neutron production began when the plasma column first pinched and that peak neutron emission occurred when the plasma luminosity faded; the axial field delayed the onset of peak emission by up to 80 nsec. The observations do not agree with a thermonuclear model of neutron production, but the results are consistent with a model of deuteron acceleration in crossed fields.
Upstream Growing Shear Layer in Stratified Flow
Authors: Browand F. K. , Winant C. D.
Published: February 2004

A numerical solution for an upstream growing free shear layer formed at the boundary between two uniform streams of different velocity in a strongly stratified fluid is given.
Boundary Conditions for Convective Wave Instabilities in Mirror Machines
Authors: Berk Herbert L.
Published: February 2004

Wave behavior at the ends of a mirror machine is sensitive to the shape of the electron distribution and the containment forces. However, it is shown by dimensional considerations that wave damping without reflection can be achieved experimentally.
Stochastic Equations for Fluid Mixtures
Authors: Foch J.
Published: February 2004

Recent work by Fox and Uhlenbeck, in which random fluxes were incorporated into the dissipative equations of hydrodynamics for a pure fluid, is extended to binary fluid mixtures.
Flow of Rarefied Gas over Plane Wall
Authors: Sone Yoshio , Yamamoto Kyoji
Published: February 2004

Flow of rarefied gas over an infinite plane wall on the basis of a relaxation model of the Boltzmann equation is considered. The solution is obtained in the form: Hilbert solution and boundary layer term which is appreciable only in a thin layer (with thickness of order of the mean free path) adjacent to the boundary. The Hilbert part dominates in the region away from the boundary. Using the result the asymptotic behavior (for small mean free path) of plane compressible Couette flow is investigated.
Effect of Temperature Nonuniformity on the Positive Column of a Gas Discharge
Authors: Lindgren R. G. , Gavalas G. R.
Published: February 2004

The effect of temperature nonuniformity on the voltage-current characteristic of the positive column of a gas discharge is studied theoretically. The coupled electron diffusion and neutral temperature equations are solved by perturbation and numerically. It is found that at currents corresponding to the abnormal glow and higher, the voltage drop of the positive column decreases with increasing current, but this result is quite sensitive to the experimental data. Numerical results are obtained for an H2 discharge.
Rotation of a Glow Discharge in a Homopolar Device
Authors: Diamond S. A. , Turcotte D. L.
Published: February 2004

The rotation of a glow discharge in the homopolar geometry has been studied experimentally. In helium the motion of the discharge is independent of the current level and is attributed to ion drift with the neutrals stationary. In argon at low currents the rotational speed is proportional to the current and the discharge acts like a magnetohydrodynamic pump. At higher pressure in argon the discharge contracts and the rotational speed increases by nearly an order of magnitude.
Measurements in a Nonequilibrium Plasma Boundary Layer
Authors: Brown R. T. , Mitchner M.
Published: February 2004

Measurements and related analyses of the electron temperature and electron number density in an atmospheric pressure laminar thermal boundary layer adjacent to a cooled wall are described. The analyses proceed from consideration of the coupled electron continuity and electron energy equations with boundary conditions appropriate to NaK seeded argon. It is shown that the theoretical results can be interpreted in terms of three characteristic lengths:δ, the thermal boundary layer thickness, lE, the characteristic length for electron energy exchange, and lI, the characteristic length for ionization. Electron temperature profiles were measured experimentally in the boundary layer described above using a spectroscopic technique, and electron number density profiles were measured using a small traversing probe developed by the authors. The experimental results, obtained for various values of the lengths lE and lI, were found to be in good agreement with the theory.