bluuebunny/crossref_metadata_2025 huggingface dataset:
Effect of Embedding Current-Carrying Rings in a Stellarator
Authors: Wiley David S.
Published: February 2004

Insertion of current-carrying loops, perpendicular to the field and inside the plasma region, can localize the ballooning mode in a stellarator. Estimates of the efficiency of such rings indicate that present instability concepts can be tested on existing stellarators.
Stability of Motions Involving Fluid Interfaces in Porous Media
Authors: Saville D. A.
Published: February 2004

A theory of stability is developed which accounts for the effects of fluid inertia. The inertial effects are found to stabilize certain otherwise unstable situations in a manner analogous to that discovered by Taylor.
Linearization of the Bhatnagar-Gross-Krook Equation
Authors: Su Chih-Lan
Published: February 2004

Linearization of the Bhatnagar-Gross-Krook equation with respect to an absolute Maxwellian distribution function is justified.
Viscous Fluid Motion Exterior to a Rotating Sphere in the Presence of a Toroidal Magnetic Field
Authors: Ranger K. B.
Published: February 2004

For Alfvén number unity, an exact solution is found for the steady rotation of a magnetized sphere in a viscous conducting fluid.
Circular Channel Magnetohydrodynamic Experiments in a Transverse Magnetic Field
Authors: Loeffler A. L. , Maciulaitis A. , Hoff M.
Published: February 2004

Experimental static pressure distributions and velocity profiles are reported for mercury flow through circular pipes in a transverse magnetic field. Both laminar and turbulent flows were investigated.
Effect of Electrostatic Field on Propagation of Electromagnetic Waves in an Anisotropic Plasma
Authors: Bachynski M. P. , Gibbs B. W.
Published: February 2004

A laboratory experiment has been conducted to test the theory of Hsieh relating to the effect of an electrostatic field on propagation of electromagnetic waves in an anisotropic plasma. Experiment does not support this theory.
Velocity Moments of the Linearized Vlasov Equation
Authors: Dorman G.
Published: February 2004

Using a recently obtained self-consistent solution of the Vlasov-Poisson equations for inhomogeneous plasmas, the velocity moments of the Vlasov equation are calculated to first order in temperature.
Electroacoustic Resonance Densities in Afterglow Plasmas
Authors: Lustig C. D.
Published: February 2004

The electron densities at which electroacoustic (Tonks-Dattner) resonances were excited in an afterglow plasma column were measured with a microwave cavity and compared with theoretical predictions.
Magnetic Field Corrections to the Plasma Bremsstrahlung Spectrum
Authors: Pytte Agnar , McBride John B.
Published: February 2004

The bremsstrahlung emitted in a Maxwellian plasma in a constant magnetic field is calculated. It is assumed that the wave frequency ω is large compared with the plasma frequency ωp and the electron cyclotron frequency Ωe.
Plasma Camera Observations of Electric and Pressure Drifts at the Edge of a Low-β Plasma
Authors: Cataldo Joseph C.
Published: February 2004

Plasma camera photographs show E × B driven irregularities rotating around the edge of the plasma column. Placing an artificial boundary in the core of the plasma column results in a pressure gradient that will drive the plasma in the − ∇p × B direction.
Kinetic Model of Tonks-Dattner Resonances in Plasma Columns
Authors: Baldwin D. E.
Published: February 2004

The linearized Vlasov equation is used to describe the coupling to plasma waves in bounded plasmas of externally driven quasistatic electric fields of frequency ω, treating as an example a cylindrically symmetric equilibrium. The coupling takes place at the plasma resonance, where ω equals the local plasma frequency. It is described by an asymptotic theory based upon the small parameter νT/ωL < < 1, whereνT, where is the electron thermal velocity and L the equilibrium scale length. A previously suggested mechanism based on a WKB solution of the Vlasov equation is then developed to provide trapping of the plasma waves between the plasma resonance and the wall sheath, including the effects of Landau damping. The effect of these internal resonances on the external admittance of the plasma is shown, and a numerical example containing typical experimental parameters is given. A comparision is made with previous theories which utilized a fluid model of the plasma.
Experimental Studies of Linear Beam-Plasma Instabilities in a Magnetic Field
Authors: Apel J. R.
Published: February 2004

The interactions of an electron beam with a bounded, uniform, equilibrium plasma have been studied experimentally by varying several of the physical parameters that appear in the dispersion equation. This equation (which takes into account the geometry, the magnetic field, and collisions, but which neglects temperature), is solved for complex wavenumber roots in order to compare the wave variables ω, kr, and ki with their experimental counterparts. The only instability that has been observed with certainty is a convective one having a frequency f below both fpe and fce, all of which are in the neighborhood of 1 GHz. This frequency, and the associated wavelength and axial growth rate as well, are in reasonable agreement with the calculated values, if the absolute values of the effective plasma frequency as obtained from probe measurements are correct. Data are presented on the behavior of the wave properties with time, distance, beam voltage, frequency, and plasma and cyclotron frequencies; and the existence of several nonlinear effects is noted.
Low-Frequency Waves and Instabilities on the Positive Column in a Magnetic Field. II. Study of Asymmetric Modes
Authors: Self S. A. , Crawford F. W. , Ewald H. N.
Published: February 2004

An analysis was presented previously [H. N. Ewald, F. W. Crawford, and S. A. Self, Phys. Fluids 12, 305 (1969)] for the normal modes of low-frequency wave propagation on the positive column in an axial magnetic field, and dispersion characteristics were discussed for axisymmetric (m = 0) ion-acoustic and electron wave modes. These studies are complemented with an examination of asymmetric modes (m ≠ 0). First, the stability of a low-pressure positive column without axial drift has been investigated. It is found that with increasing magnetic field, instability first occurs in high-order modes. Next, the theory has been applied to the positive column over a wide pressure range. The computed results are compared with previous approximate analyses of the current-convective instability. Finally, the specific prediction of the theory that asymmetric electron wave modes, rotating in the sense of the electron diamagnetic drift (m ≥ 1), should grow convectively for sufficiently large magnetic field has been checked experimentally. Measurements on the propagation of the m = 1 wave on a low-pressure mercury-vapor positive column are presented which support this prediction.
Some Constants of the Motion for Perturbation of Large-Amplitude Electrostatic Waves
Authors: Nakayama Toshio , Oberman Carl
Published: February 2004

It is shown that there exists a large family of global quadratic constants of motion for perturbations around the steady large-amplitude electrostatic waves of Bernstein, Greene, and Kruskal.
Normal Mode Representation of the High-Frequency Properties of an Inhomogeneous Plasma
Authors: Leavens W. M. , Love C. H.
Published: February 2004

Analysis of “exact” numerical solutions of the Vlasov equation for longitudinal perturbations of a realistic inhomogeneous plasma shows that the response Ep(x)eiwt to an externally supplied driving field Ed(x)eiwt is well described by a normal mode representation Ep(x) =  ∑ n=1N En(x)ω2 − ωn2  ∫ 0L En(x′) dx′. The free oscillation frequencies ωn and the normal modes En(x) are determined from solutions of the Vlasov equation for a δ-function driving field. The normal mode representation is then used to obtain the solution of the Vlasov equation for a uniform driving field, and the results compare well with “exact” solutions.
Stability of a Rotating Theta-Pinch Plasma
Authors: Palsedge John A.
Published: February 2004

The bounce model has been used to calculate the growth rate of the m = 1 mode of a linear θ pinch having an isotropic Maxwellian ion distribution function rotating with angular velocity ω. For short wavelength, the perturbation rotates with the ions; for longer wavelength it rotates more slowly. The plasma is unstable above a critical wavelength, with growth times τ ≈ 25 μsec for typical values of ω. This result falls between the magnetohydrodynamic result of τ = ∞ (stable) and the rigid body limit of τ ≈ ω−1. Consideration of the m = 2 mode is also included.
Ion Sound Instability in a Collisionless Shock Wave
Authors: Krall Nicholas A. , Book David L.
Published: February 2004

The nonlinear development of an ion sound instability is calculated for a case in which a diamagnetic current of electrons propagates across a magnetic field, and in which ion gyration in the magnetic field can be neglected. The energy content of the mode is calculated; the parameter range is appropriate to experiments on collisionless low-amplitude magnetic shock waves.
Continuum Theory of Cooled Spherical Electrostatic Probes
Authors: Thomas D. Lyddon
Published: February 2004

The continuum theory of Su and Lam is extended to cover the case of a probe cooler than the gas in which it is immersed. It is assumed that the equilibrium temperature distribution is set up around the probe, and that the gas properties vary as predicted by simple kinetic theory. It is found that the highly negative probe problem can be solved in a manner similar to that adopted by Su and Lam, that the effect of the temperature distribution on the current-voltage characteristics is very slight, and that an approximate expression given by Su and Lam is more accurate for a cold probe than for one at the gas temperature.
Laboratory Study of Turbulence in Collision-Free Shocks
Authors: Patrick R. M. , Pugh E. R.
Published: February 2004

In an earlier paper the authors describe a plasma wind tunnel that produces a steady collision-free flow. A shock wave standing in front of a magnetic obstacle was produced in this flow. The changes in magnitude and direction of the magnetic field across the shock wave were found to be in agreement with values predicted using the magnetohydrodynamic Rankine-Hugoniot relations. This work has been extended using electric field measurements to determine the over-all flow patterns. The electron density has been measured with a laser interferometer, and the density ratio across the shock wave has been found to be consistent with the shock wave equations. The power spectra of the magnetic and electric fluctuations have been measured. These fluctuations are consistent with whistler waves standing in the shock front. The power spectrum shows large variations with position in the shock with the highest frequencies appearing near the toe of the shock wave. The amplitude and frequency variation of the power spectrum is quite similar to space data where the latter is available. The electric field fluctuations are found to be proportional to the magnetic fluctuations with a proportionality constant equal to the flow velocity. The absolute magnitude of the magnetic turbulence is too low to absorb all of the dissipation required for the shock wave and a simple model using wave-particle interactions is suggested.
Magnetohydrodynamic Free Convection from a Horizontal Plate
Authors: Singh S. N. , Cremers C. J.
Published: February 2004

The solution for a more realistic free convection problem from a horizontal plate under the action of a uniform vertical magnetic field is presented.
Effect of Tensor Conductivity on Collisionless Magnetogasdynamic Flows
Authors: Tang J. Y. T. , Seebass R.
Published: February 2004

Steady, linearized, aligned-fields flow of a collisionless plasma past slender bodies is investigated. An approach similar to that of Chew, Goldberger, and Low is used to derive a consistent set of hydrodynamiclike equations for treating collisionless magnetogasdynamic flows in the presence of a strong magnetic field. The nature of the behavior predicted by this system of equations, in contrast to the original Chew-Goldberger-Low system, is similar to that predicted by the continuum equations of Sears and Resler. For certain specialized upstream conditions these two systems are identical. The close mathematical relationship that exists between them provides a convenient interpretation of collisionless plasmadynamic phenomena in terms of continuum variables.
Magnetohydrodynamic Flow in a Container
Authors: Ingham D. B.
Published: February 2004

A linear theory for steady rotational motions is presented under the assumptions that Rm and ε are much less than E where Rm, ε, and E are the “rotational” magnetic Reynolds, Rossby, and Ekman numbers, respectively. The effect of the “rotational magnetic force coefficient,” N2 ( = σμ2 H02/ρΩ), which is a measure of the relative importance of the magnetic forces (of order σμ2 ΩLH02) and the rotational forces (of order ρΩ2 L) is investigated. Attention is focused on the case when the direction of rotation and applied magnetic field at infinity are parallel, and all boundaries are either perpendicular or parallel to this direction. If N2< < 1, Ekman layer suction and the double structure of the vertical Stewartson layers are dominant, but if N2〉 〈 E−1/3, the magnetic forces dominate and a Hartmann-type boundary layer is present with the double structure of the vertical boundary layer disappearing and being replaced by a single layer. A solution for the complete range of values of N2 is presented.
Low Reynolds Number Instability of an Incompressible Half-Jet
Authors: Ko Sung-Hwan , Lessen Martin
Published: February 2004

The instability of the free laminar boundary layer between parallel streams is investigated for an incompressible fluid. It is found that no minimum critical Reynolds number for instability exists based on the assumption of parallel undisturbed flow. However, when the parallel flow theory is corrected for the nonparallelism that actually exists at low Reynolds numbers, the minimum critical Reynolds number for instability becomes 10.2 with the wavenumber 0.135.
Propagation Velocity of Turbulent Slugs and Streaks in Transition Pipe Flow
Authors: Lindgren E. Rune
Published: February 2004

Taking account of experimental observations on the transition process, an elementary theory is developed for estimation of propagation velocity of the rear end of turbulent slugs and streaks which constitute a major feature of the transition process in pipe flow. The theory gives a lower propagation velocity than observed experimentally within the lower range of transition Reynolds numbers while at higher Reynolds numbers the theory gives a value about 7% higher than obtained experimentally. These deviations are due to approximations in the analysis which cannot be avoided at the present level of information on the structure of turbulent shear.
Direction of Maximum Turbulent Vorticity in a Shear Flow
Authors: Deissler R. G.
Published: February 2004

An equation for the direction of maximum turbulent voricity in a turbulent shear flow is obtained. For a weak homogeneous turbulent field with a uniform transverse velocity gradient, that direction is found to be reasonably close to (but different from) the direction of maximum mean strain rate for a range of velocity gradients. The degree of alignment of the turbulent vortices is also determined.
Nonsimilar Effects in the Collapsing of an Empty Spherical Cavity in Water
Authors: Akinsete V. A. , Lee J. H. S.
Published: February 2004

The flow field behind, and the motion of an empty spherical cavity collapsing in water are calculated by means of a perturbation technique similar to Sakurai's theory for blast waves in gases. In order that the higher approximations may be uniformly valid, the radius coordinate is modified in accordance with Lighthill's principle. The present scheme applies only to the latter half of the collapse process when the cavity speed is highly supersonic and extends Hunter's self-similar solution to account for nonsimilar effects due to the finite sound speed at the interface as well as the finite cavity radius of curvature. The first-order theory is worked out for a sample cavity of initial radius 1 cm collapsing under a constant ambient pressure of 6 atm. The necessary coupling with the initial conditions is obtained from the results of some earlier numerical calculations. The present results indicate that while the nonsimilar effects modify the distributions of flow parameters, the cavity trajectory is practically unchanged from the self-similar law. Very high pressures are shown to accompany cavity collapse even at moderately high collapse speeds.
Asymptotic Theory of Nearly Free-Molecular Flows
Authors: Pao Young-ping , Willis D. Roger
Published: February 2004

An asymptotic theory for obtaining nearly free-molecular solutions which are uniformly valid throughout the flow field is proposed in the present study for the linearized Boltzmann equation. The theory is based on an integral-equation formulation of the linearized Boltzmann equation, using an inner-and-outer-expansion procedure. In the inner region the problem is simplified in that the collisional effects are only secondary. Outside of the inner region the angle subtended by the body is small so that the flow field is essentially that created by a source at the origin. The form of the source term is determined by the free-molecular solution to the problem. The drag force is obtained for two-dimensional flows. Three-dimensional flows and nonlinear problems are discussed.
Ion-Exosphere with Variable Conditions at the Baropause
Authors: Hartle R. E.
Published: February 2004

The model ion-exosphere of Eviatar, Lenchek, and Singer for a nonrotating planet with a static, centered-dipole magnetic field is generalized by permitting the density and temperature to vary over the baropause. In particular, the density and/or temperature are allowed to differ at the conjugate magnetic field points of the baropause. For this case, the ion and electron velocity-distribution functions, satisfying the Vlasov equations in the drift approximation, are constructed. Then, the species densities are determined from the distributions and compared with the corresponding results of Eviatar et al. for the case of uniform density and temperature at the baropause. In addition, the particle current densities, pressures, and temperatures are derived.
Laminar Free-Convection Heat Transfer from a Needle
Authors: Cebeci Tuncer , Na Tsung Y.
Published: February 2004

The partial differential equations for laminar free convection over a needle are reduced to ordinary differential equations by a similarity analysis, and the values of local skin friction, heat transfer for various needles are obtained.
Microwave Diagnostics of Laser Produced Aluminum Plasmas
Authors: Pack J. L. , George T. V. , Engelhardt A. G.
Published: February 2004

A focused laser beam has produced plasmas from single aluminum spheres 50-150 μ in radius. Microwave studies determined the expansion velocity at 300 nsec and the average electron density between 1 and 6 μsec.
Simple Phenomenological Theory of Turbulent Shear Flows
Authors: Nee Victor W. , Kovasznay Leslie S. G.
Published: February 2004

A rate equation is proposed to govern the variation of the effective turbulent viscosity. The effects of generation, convection, diffusion, and decay are each represented by appropriate terms leaving only two empirical constants to be determined by experiment. This rate equation together with the equations of motion form a closed system applicable to quasiparallel turbulent shear flows. For an incompressible turbulent boundary layer with zero pressure gradient, solutions were obtained by assuming local similarity and a linear growth of the boundary-layer thickness. Another problem, the turbulent-nonturbulent interface at the outer edge of the boundary layer was treated by using the further assumption that the large scale motion of the interface has no significant contribution to the Reynolds stress. It can be shown that for a nearly homogeneous domain, Prandtl's mixing length theory is a limiting case of the present theory.
Model Equation for Nonhomogeneous Turbulence
Authors: Lundgren T. S.
Published: February 2004

The equation for the one-point turbulent distribution function is closed by assuming a relaxation model for the pressure fluctuation term and several other less critical approximations. The resulting equation is solved for a class of rectilinear flows and for decay of a periodic wake. Good agreement with available experiments is found. A theory of turbulent transport coefficients is derived in a certain approximation.
Vortex Breakdown Flowfield
Authors: Bossel Hartmut H.
Published: February 2004

The Navier-Stokes equations for incompressible rotationally symmetric vortex flow at high swirl and large core Reynolds number are shown to approximate to the equation of inviscid rotating flow in regions where axial gradients are large. This equation becomes linear for flow originally near the axis, where rigid rotation results from viscous action. Series solutions at high supercritical swirl values near the critical one under the condition of flow retardation near the axis are found to exhibit the experimentally observed features of vortex breakdown flows: bulges of decelerated flow, or bubbles of recirculating fluid, with reversed axial and swirl velocities near the axis. It is concluded that the vortex breakdown in vortex tubes and on delta wings is neither due to hydrodynamic instability, nor is it a phenomenon akin to the hydraulic jump. Rather it is a regular feature of the solution of the equations of motion under the given conditions.
Onset of Convection in a Water Layer Formed Continuously by Melting Ice
Authors: Yen Yin-Chao , Galea Francis
Published: February 2004

The onset of convection, in a water layer continuously formed by melting ice from above, has been obtained by the experimental determination of the water layer depth d at which the mode of heat transfer changes from conduction to convection. This was accomplished both by determining the time at which the temperature profile of the water layer started to deviate from linear distribution and by locating the inflection point in the curve relating water-ice interface position and time. Experimental values of d (either for melting from above or below) were found with a mean deviation of 14.1% from those by theoretical analysis of a similar problem. From the present and previous investigations [Phys. Fluids 11, 1263 (1968)], it can be concluded that the critical Rayleigh number for a horizontal layer of fluid with a density inversion is not a single value as for a normal fluid with a monotonic density-temperature relationship, but varies with boundary temperatures.
Reverse Flow Solutions for Compressible Laminar Boundary-Layer Equations
Authors: Rogers David F.
Published: February 2004

Several new similarity solutions are presented for the laminar compressible boundary layer with reverse flow for Prandtl numbers of 1.0 and 0.723. New solutions without reverse flow are presented for Prandtl number equal 0.723. Wall-to-stagnation temperature ratios from 0 to 2 are considered. These solutions quantitatively show the effects of pressure gradient, and wall heat transfer on the wall shearing stress and enthalpy gradient.
Stability of Two Superposed Elasticoviscous Liquids in Plane Couette Flow
Authors: Li Chin-Hsiu
Published: February 2004

It is found that the elasticity in the liquid cannot only destabilize the flow, but it can also stabilize the flow for certain values of depth ratio, viscosity ratio, and elasticity ratio. The stabilizing or destabilizing effect of the elasticity in liquid is absent in the absence of viscosity stratification, and is only brought about when the viscosity varies.
Transport Mechanics in Systems of Orientable Particles
Authors: Condiff D. W. , Brenner H.
Published: February 2004

The phenomenological description of transport processes in a fluid composed of molecules or particles which are orientable is reformulated so as to render it capable of distinguishing between and determining the form of the distribution of orientation. With orientation variables playing the role of continuously distributed parameters suitable for tensorial labeling of multicomponent species, equations for the transport of mass, momentum, energy, and angular momentum in the position-orientation hyperspace are independently derived by continuum and statistical mechanical arguments. The selection of the point of location of a particle is shown to have an important bearing upon the transport equations of physical space obtained by orientation averaging. Linear constitutive relations are established by means of thermodynamic arguments which suggest anisotropic thermal conductivity and viscosity as well as a coupling tensor each dependent for its anisotropy upon the polyadic (polarization) moments of the distributions. The rotational and translational diffusion fluxes are predicted to be governed by rotational, translational, and coupling multicomponent diffusion tensors, thermal diffusion tensors, and by the analogous shear diffusion tensors. The special case of dilute solution theory is examined and the thermodynamic predictions of generalized transport laws reaffirmed by appeal to component (orientation specific) balances of linear and angular momentum.
Boltzmann Equation with Power-Law Interparticle Potentials
Authors: Su C. H. , Pao Young-ping
Published: February 2004

The linear Boltzmann equation for molecules with power-law potentials is considered. The contribution of small scattering-angle collisions is approximated by a Fokker-Planck operator. Within this approximation, it is shown that the spectrum of the collision operator is discrete for p > 4/3 and it contains a continuum for p ≤ 4/3, where p is the index of power-law potentials.
Continuous Supersonic Plasma Wind Tunnel
Authors: Andersen S. A. , Jensen V. O. , Nielsen P. , D'Angelo N.
Published: February 2004

The normal magnetic field configuration of a Q device has been modified to obtain a “magnetic Laval nozzle.” Continuous supersonic plasma “winds” are obtained with March numbers ∼3. The magnetic nozzle appears well suited for the study of the interaction of supersonic plasma “winds” with either material or magnetic obstacles.
Variational Principle for Stationary Magnetohydrodynamic Equilibria
Authors: Greene John M. , Karlson Erik T.
Published: February 2004

A variational principle of Hamilton's type is constructed for stationary, bounded magnetohydrodynamic flows, also known as stationary equilibria. The chief object is to find how much information must be given in order to have a well-posed problem. The results indicate, but do not rigorously prove, that five suitably chosen functions of a single variable and the location of a rigid conducting boundary defined a unique stationary flow. Comparison is made with other variational principles.
Approximate Method in Kinetic Theory. Couette Flow and the Kramers Problem
Authors: Sirovich Lawrence
Published: February 2004

An approximate method especially suited to near-continuum flows is developed. The method is applied to the case of Couette flow with arbitrary specular and diffuse reflection. The result is in very close agreement with all known limits. In the case of purely diffuse reflection the approximate theory leads to a slip coefficient which is within 112% of the exact value. The analytical behavior in the neighborhood of the walls is exactly described. The limit of purely specular reflection is exactly described by the approximation method. The method only involves elementary calculations.
Ballistic Wake of Turbulence in a Plasma Shock Wave
Authors: Krall Nicholas A. , Tidman Derek A.
Published: February 2004

The role of ballistic term in the turbulence that occurs in plasma shock waves is discussed. For electrostatic turbulence these terms are shown to give rise to a wake behind a shock wave in which the energy density in the fluctuating fields decays spatially as x−3 for a class of distribution functions including resonance functions. The importance of the ballistic transport of turbulent fields inside shocks is also pointed out. This occurs because in such structures there is usually not enough length scale for these fields to phase mix away. Thus, the use of conventional quasilinear theory (which neglects these effects) will often be inadequate to describe even weak turbulence in a shock wave.
Quantum-Mechanical Interpretation of Plasma Turbulence
Authors: Ross David W.
Published: February 2004

The matrix elements describing nonlinear effects in a weakly unstable plasma are interpreted by means of Feynman diagrams involving the shielded Coulomb potential, given by Vs(q, ω) = 4πe2/q2ε(q,ω), where ε(q, ω) is the dielectric response function. The quasiparticles or plasmons are obtained from the poles of Vs, but effects of the nonresonant parts of Vs are also retained. All the matrix elements describing interactions of Langmuir oscillations in a strong magnetic field through second order in the quasiparticle numbers are found explicitly and shown to yield the correct classical results in the limit ℏ → 0. In particular, the equations of Walters and Harris for three-wave scattering in a cold plasma are extended to finite temperatures, and the shielding or dressing of the electrons is included in the equations for the nonlinear Landau damping. The self-energy of a plasmon is also represented by diagrams and the optical theorem is used to compare the self-energy with the scattering matrices. It is found that the quantum method provides a relatively simple way of deriving and interpreting equations for the time development of the wave spectrum and particle diffusion.
Finite-Amplitude Collisional Drift Waves
Authors: Stix Thomas H.
Published: February 2004

A calculation of mode-mode coupling for collisional drift waves demonstrates several inherently nonlinear phenomena, namely, amplitude saturation, harmonic generation, frequency shift, wave-associated transport across the magnetic field, and parametric excitation of subharmonics. There is qualitative agreement with published experiments; the introduction of some additional damping mechanism into the theory could narrow the broad quantitative discrepancy between theory and experiment. The analysis uses the nonlinear ion and electron fluid equations in which ion inertia, finite ion gyroradius, perpendicular ion viscosity, and resistivity terms have retained. No cross-B transport is produced by the large-amplitude steady-state oscillations in the absence of ion viscosity; non-ambipolar transport in the pump-out direction appears when ion-ion collisions are introduced. A byproduct of the calculations is a single nonlinear scalar wave equation for the collisional drift wave. Solutions to this equation show limit-cycle behavior, i.e., periodic but nonsinusoidal finite-amplitude oscillations which are stable (or unstable) against changes of oscillation amplitude. These nonlinear solutions are described by dispersion relations containing the oscillation amplitude as one of the parameters.
Nonlinear Effects and Turbulent Behavior in a Beam-Plasma Instability
Authors: Apel J. R.
Published: February 2004

Continuing experimental studies of beam-plasma interactions in a magnetic field have shown an assortment of nonlinear effects to be present during a well-developed instability. Observations have been made of: the vanishing of the spatial growth rate; electron cross-field diffusion in synchronism with the unstable electric field; generation of harmomics of the fundamental interaction frequency up to the seventh; similarities in the spatial behavior of all seven harmonics; and the existence of a wavenumber power spectrum whose average behavior over the domain of the harmonic peaks is proportional to k−5±0.5, in agreement with certain theories of plasma turbulence. The data suggest that the large-amplitude fundamental electric field is the driving force for the nonlinearity that generates the harmonics, and that the fundamental, and the harmonics as well, represent waves traveling with a phase velocity equal to that of the slow space-charge wave on the electron beam. An interpretation is offered in terms of an approach to stationary plasma turbulence through a linear beam-plasma interaction, followed by harmonic generation, wave-wave coupling, and ultimate broadening of the emission peaks into a continuous spectrum.
Plasma Wave Regeneration in Inhomogeneous Media
Authors: Berk Herbert L. , Book David L.
Published: February 2004

The one-dimensional problem of electrons confined in a quadratic potential is solved in the WKB approximation. The unique feature of the problem is that, since particle bounce time is independent of energy, resonant particles that normally cause Landau damping periodically interact with the wave and regenerate all phase information. Because of the efficiency of the regeneration mechanism, the dielectric properties governing the system change and give rise to “regenerative modes” associated with harmonics at twice the bounce frequency. The eigenvalues calculated in this WKB approximation are in agreement with previous numerical calculations.
Computer Experiments on Plasma Instabilities due to Anisotropic Velocity Distributions
Authors: Okuda Hideo , Hasegawa Akira
Published: February 2004

Computer experiments on plasma instabilities due to anisotropic velocity distributions are made to study nonlinear phenomena as well as the validity limit of linear theory using a sheet plasma model. Three kinds of anisotropic distributions are considered; type-A, perpendicular (to an applied magnetic field) velocity distribution function having a hump at v⊥ ≠ 0, type-B, bi-Maxwellian distribution with T⊥ ≫ T‖, and type-C, loss-cone distribution. Results of the experiments show that instability due to type-A distribution is generally very strong and resembles two-beam instability. One of the characteristics of this is that the strength of the instability is relatively insensitive to the propagation angle. On the other hand, instability due to type-B distribution is quite sensitive to the propagation angle. A particular feature of the type-B instability is that, in addition to a growth that is predicted by linear theory, there exist several strong bursts which play an essential role in accelerating plasma along magnetic field lines. After the bursts, the plasma arrives at a stable state with a much reduced ratio of T⊥/T‖ compared with that at the initial state. Another interesting instability is the loss-cone instability which is caused by the type-C distribution, an inherent distribution in a mirror magnetic field. When a disturbance propagates almost perpendicularly to magnetic field, an instability is shown to develop due to a coupling of hot ions with cold electrons. With the development of the instability, ions are accelerated along the magnetic field lines and are gradually lost from the mirror field.
Collisional Absorption and Emission of Longitudinal Waves in a One-Dimensional Plasma
Authors: Dawson John M. , Shanny Ramy , Birmingham Thomas J.
Published: February 2004

Collisional absorption and emission of longitudinal waves in a one-species, one-dimensional plasma are investigated by numerical experiments. The theory of Birmingham, Dawson, and Kulsrud for longitudinal bremsstrahlung is extended to the one-dimensional case. The results of the numerical experiments are found to be in agreement with the theory. Low-frequency electric field fluctuations for long-wavelength modes are also found and are associated with the random motion of the particles.
Resonant Absorption in Zero-Temperature Nonuniform Plasma
Authors: Baldwin D. E. , Ignat D. W.
Published: February 2004

A process of aborption of energy by a cold nonuniform collisionless plasma from an externally driven electric field is described using a linearized theory. With the example of a cylindrically symmetric plasma, power is shown to be absorbed whenever the maximum plasma frequency exceeds the driving frequency. The admittance of the plasma as seen by an external circuit is developed and found to be sensitively dependent upon the equilibrium density distribution near the wall, suggesting the use of this phenomenon to examine electron sheath structure. Experimental results are presented which support the theoretical prediction. The occurrence of this absorption in the presence of a magnetic field and its effect upon the propagation of surface modes along a nonmagnetized plasma column are also indicated.
Low-β Plasma Penetration across a Magnetic Field
Authors: Fried Burton D. , Ossakow Sidney
Published: February 2004

Self-consistent solutions for the problem of a collisionless plasma streaming across a magnetic field whose dimensions are small compared to (rcerci)1/2 show that the electrons can accompany the ions across the field (over distances large compared to rce) provided ωce < α ωpe, where α ≤ 1 is a function of the electron distribution function (α = 1 when the electron thermal velocities are neglected). This appears to explain the threshold, ωce ≃ 0.9 ωpe, observed in recent experiments on plasma penetration across a radial magnetic field.
Double Vortex Flows in Plasmas Axially Traversing Multipole Magnetic Fields
Authors: Barney Gerald O. , Sprott J. C.
Published: February 2004

Detailed observations of 100-eV hydrogen plasmas moving in a linear quadrupole and a toroidal octupole magnetic field show that the plasmas polarize and that the field lines quickly become equipotentials. The plasmas E × B drift with negligible diamagnetism in double vortex flow patterns similar to the self-consistent solutions of Poukey. The agreement is not perfect presumably because the uniform field and steady state assumed in the theory are lacking in the experiments.
Beam-Injected and Lorentz-Trapped Hot Electron Plasma
Authors: Perkins W. A.
Published: February 2004

Neutral-atom injection with Lorentz trapping is one of the most popular and successful methods of forming a “hot ion plasma.” It is suggested here that one could form a “hot electron plasma” by injecting ions with megaelectron volt energies and using Lorentz trapping. For example, build-up calculations indicate that one could form in a mirror machine a 15-keV “hot electron plasma” with a density of 109 cm−3 by using a 50-μ A beam of H2+ at 60 MeV. The H2+ beam would be sent through a gas cell or foil to obtain some 30 MeV H0 atoms by dissociation. The H0 would then pass through the magnetic confinement field and some 15-keV electrons would be trapped by Lorentz ionization of excited H0. If the background gas pressure is below 10−8 Torr, electron-electron scattering will determine the containment time for n ≈ 109 cm−3. Neutralization of the hot electrons can be accomplished by ionization of the residual gas as the ionization time constant is much shorter than the gasscattering time constant. Since typical scattering times are many seconds, dc operation is preferable. If one can obtain the necessary combination of ion energy and confining magnetic field strength, Lorentz electron stripping from the H− or He− ground state can result in very high trapping efficiencies and higher plasma densities. Some advantages and uses for beam-injected and Lorentz-trapped hot electron plasmas are discussed.
Instability Phenomenon Associated with an Enclosed Rotating Disk
Authors: Macey J. P. , Wellman E. J.
Published: February 2004

An instability phenomenon in the form of a symmetrical pattern of vortices was found to exist at the edge of a rotating disk partially submerged in liquid in a vertical tank.
Influence of Low-Pass Filtering on Correlation Measurements
Authors: Stegen G. R.
Published: February 2004

The influence of low-pass filtering on measurement of odd-order correlations of non-Gaussian processes is investigated using digital harmonic analysis. These corrections are found to be negligible for the case considered.
Properties of Reversible Collision Operators
Authors: Wisnivesky D.
Published: February 2004

It is shown that the reversible part of the collision operator determines the form of the radial distribution function. An important limitation of many of the existent kinetic equations is pointed out.
Stability Limitations for Stellarators with Sharp Surfaces
Authors: Rosenbluth M. N. , Johnson J. L. , Greene J. M. , Weimer K. E.
Published: February 2004

Application of the magnetohydrodynamic energy principle to a stellarator equilibrium where the plasma pressure is constant inside a bounding magnetic surface shows that the configuration is unstable to a nearly rigid shift of the plasma column.
Transmission and Reflection of Surface Waves by a Movable Dock
Authors: Fetter Alexander L.
Published: February 2004

An integral equation is derived for the propagation of small amplitude surface waves perpendicular to a movable strip lying in the free surface. The transmission and reflection amplitudes are calculated with a variational approximation valid for long and medium wavelengths. Typical numerical results are presented.
Singular Perturbation Analysis of Acoustic-Gravity Waves
Authors: Einaudi F.
Published: February 2004

A singular perturbation analysis of acoustic-gravity waves is presented in which not only the dependent but also the independent variables are expanded in power series of a small parameter ε. The series expansion of the independent variables enables us to correct, at each stage of the expansion, the forward characteristic lines of the governing equations and in turn, to determine the crossing of adjacent characteristics, if such crossings indeed occur for the chosen initial conditions. For waves propagating upwards in the vertical z direction and satisfying the condition that at z = 0, u = u0 sin ωt, it is shown that a shock develops in the flow. The distance at which the shock takes place is given for different values of the index of refraction and the wave form obtained is compared to the usual linear solution.
Development of Shock Waves in Atmospheres with Density and Temperature Variation
Authors: Walsh E. K.
Published: February 2004

The problem of the growth or decay of second-order (acceleration) discontinuities using the theory of singular surfaces is investigated for the particular case of a medium consisting of a perfect gas exhibiting density and temperature fields which vary exponentially. Relations are derived for the amplitude of such waves as well as for the critical times for those cases where the acceleration discontinuities increase without bound, the criterion used for the development of a velocity or shock discontinuity.
Electrically Driven Blast Waves
Authors: Ferguson J. L. , Barach J. P.
Published: February 2004

Experiments in an electric shock tube operating at a few Torr have shown compression waves moving ahead of the luminous discharge plasma for Mach numbers below 12 to 15. Failure to observe this separation at higher velocities is attributed to mixing caused by a Taylor unstable density distribution and the deceleration of the flow. The unstable distribution is caused by the density rise accompanying ionization behind the shock front. A model based on these assumptions, which correctly predicts separation conditions in argon, is presented. The structure of the shock waves (pressure, flow velocity, and temperature) is approximately described by blast wave theory. The deviations are primarily due to real gas effects.
Similitude for Shock-Wave Initiated Flux Compression
Authors: NiCastro James
Published: February 2004

An investigation and extension of similarity concepts has been undertaken for describing shock-initiated flux compression devices. The similarity equations are developed for finite variable conductivities. Compatibility of an induced homology for the preshock magnetic field is seen to give rise to a flux compression constraint. This constraint relates the shock speed to the growth rate of the field and the homology characterizing preshock density gradients. Use of a nonstatic piston in similarity problems is questioned on physical grounds. Numerical examples are calculated for field compression with an infinite postshock magnetic Reynolds number in order to obtain sample postshock field profiles. Analytic solutions can be obtained when the dimensionless Alfvén velocity B2/R ≳ 1. Some flux slipping appears to be required to obtain nonsingular solutions.
Exact Solution for Rotating Bodies in a Viscous Conducting Fluid
Authors: Ranger K. B.
Published: February 2004

An exact solution is found for the motion of a conducting solid of revolution rotating in an infinite conducting viscous fluid at rest at infinity. The magnetic field is the sum of a uniform field directed parallel to the axis and an induced toroidal field. Explicit expressions for the fluid velocity, magnetic field, and couple on the solid are given for the case of a sphere.
Electrohydrodynamic Charge Relaxation and Interfacial Perpendicular-Field Instability
Authors: Melcher James R. , Smith Charles V.
Published: February 2004

The small-amplitude motions of a plane interface between two fluids stressed by an initially perpendicular electric field are investigated. The fluids are modeled as Ohmic conductors and the convection of the surface charge caused by the dynamic interplay of interfacial electric shear stresses and the viscous stresses is highlighted. The influence of viscosity on instability growth rates in the zero-shear stress limits of perfectly conducting and perfectly insulating interfaces is described and compared to cases involving electrical shear stresses. Detailed attention is given to the instability of an interface between fluids having electrical relaxation times long compared to times of interest. It is shown that, for many common liquids, even a slight amount of surface charge makes the interface unstable at a considerably lower voltage than would be expected from theories based on the dielectrophoretic limit of no interfacial free charge. Experiments, performed using high-frequency ac stresses, gradually increased dc fields, and abruptly applied dc fields, support the theoretical model. In the general case, the electric Hartmann number is identified as an index to the dominance of the electric shear stresses over the viscous shear stresses in determining the interfacial convection of free charge.
Pair Distribution Function of Charged Particles
Authors: Rio Fernando del , DeWitt H. E.
Published: February 2004

The pair distribution function for a classical one-component plasma is obtained by summing terms of the Montroll-Mayer cluster expansion of g(r) as modified by Meeron and Hirt for the Coulomb potential. A simple class of diagrams in this nodal expansion gives the asymptotic form of g(r) for long distance as a modified Debye form. We obtain results exact to O(Λ2 log Λ) where Λ = 1/4πnλD3 is the plasma parameter. The analysis shows that for Λ larger than a critical value Λc the long-distance form of g(r) changes from the Debye form to a damped oscillatory form in qualitative agreement with the Monte Carlo calculations of Brush, Sahlin, and Teller. Numerical calculations done on the simplest form of our result agree moderately well with the Monte Carlo results over the entire range of r for λ ≤ 2, and represent a substantial improvement over the nonlinear Debye-Hückel result.
Collision Operator for a Relativistic Lorentz Gas
Authors: Kelly Don C.
Published: February 2004

The elastic collision operator for a relativistic Lorentz gas is converted to differential form. The Fokker-Planck “limit” is deduced. The Fokker-Planck form is obtained for a relativistic electronion gas. Possible implications for a relativistic plasma are discussed.