bluuebunny/crossref_metadata_2025 huggingface dataset:
Numerical Study of Collisional Effects on Spatial Ion-Wave Echoes
Authors: Nishikawa Kyoji , Gould Roy W.
Published: February 2004

Collisional effects on the second-order spatial ion-wave echo are studied numerically. General agreement is obtained with the experimental results of Ikezi, Takahashi, and Nishikawa. A critical argument is raised against the validity of the small collision approximation.
Contributions to Non-Equilibrium Thermodynamics. I. Theory of Hydrodynamical Fluctuations
Authors: Fox Ronald Forrest , Uhlenbeck George E.
Published: February 2004

The velocity of a particle in Brownian motion as described by the Langevin equation is a stationary Gaussian–Markov process. Similarly, in the formulation of the laws of non-equilibrium thermodynamics by Onsager and Machlup, the macroscopic variables describing the state of a system lead to an n-component stationary Gaussian–Markov process, which, in addition, these authors assumed to be even in time. By dropping this assumption, the most general stationary Gaussian–Markov process is discussed. As a consequence, the theory becomes applicable to the linearized hydrodynamical equations and suggests that the Navier–Stokes equations require additional fluctuation terms which were first proposed by Landau and Lifshitz. Such terms and their correlation properties are presented, and these equations are then used to derive the Langevin equation for the Brownian motion of a particle of arbitrary shape.
Angular Acceleration of Liquid Helium II
Authors: Chan S. L.
Published: February 2004

Studies have been made of the processes of angular acceleration and retardation of a simply connected volume of helium II at 1.64°K using the technique of second sound attenuation. The acceleration and retardation are found to approach closely to reversibility as compared with experiments where the acceleration is more rapid. A critical velocity for bringing helium II into rotation has been found and the most reliable value for this is (0.047 ± 0.005) cm sec−1 for a cylindrical cavity of radius 2.60 cm. A relaxation time of about 103 sec is found for helium II to come into rotational equilibrium. Persistent currents of long lifetime have also been seen. The results are interpreted in terms of quantized vortices in liquid helium II.
Confined Flow Velocity Profiles in the Presence of Vortex Rings
Authors: McCormack Percival D.
Published: February 2004

Using the electromagnetic analogy, the instantanous velocity and pressure profiles due to a vortex ring confined in a cylindrical channel, are derived. The ring is considered to have been formed by an impulsive pressure at an upstream orifice. The predicted profiles resemble an experimentally determined pressure profile previously reported.
Wind-Wave Interactions
Authors: Wu Jin
Published: February 2004

A criterion proposed earlier for determining airflow separation from wind waves and a previously determined relationship between surface roughness and wind stress are herein correlated. The results indicate that the airflow boundary layer is developed due to the form drag provided by wavelets (surface roughness) superimposed on big waves. Based on the magnitudes of surface roughness, viscous-sublayer thickness and critical height, the mechanisms of wind-wave generation are discussed.
Circular-Disk Viscometer and Related Electrostatic Problems
Authors: Shaw Susann J. N.
Published: February 2004

The method of matched asymptotic expansions is applied to the problem of determining the azimuthal velocity field due to the opposing slow rotations of a pair of thin coaxial disks in a homogeneous, incompressible, viscous fluid. An asymptotic expansion for the velocity field, which is uniformly valid as the ratio ε of the separation between the disks to the disk diameter approaches zero, is given and integrated to obtain an asymptotic expansion for the turning moment which contains the full second approximation including terms of the orders ε log2ε, ε logε, and ε. Corresponding results are given for the electrostatic condenser. The plane counterparts of the circular-disk viscometer and condenser are also considered.
Electrohydrodynamic Stability of Space-Charge-Limited Currents in Dielectric Liquids. II. Experimental Study
Authors: Watson P. K. , Schneider J. M. , Till H. R.
Published: February 2004

Electroconvective effects are being studied in films of dielectric liquids, using an electron beam as an injecting electrode. The experiments are performed on a dual electron beam system in which one beam is used to charge up the free surface of a thin layer of the liquid, the other beam is directed across the surface and is used to determine the surface potential of the sample. The conduction properties of a silicone fluid (Dow Corning 703) have been determined, using this system. At low currents the conduction is space-charge-limited. Above the critical voltage, V0 = 99μη/ε, the space-charge-limited conduction becomes unstable; cellular convection motion of the liquid occurs, and there is a transition between space-charge-limited conduction and convection-enhanced conduction. Thus, the conductivity of the liquid increases due to the bulk motion of the fluid. A further effect of convection can be seen in the charging transients. For low values of current the voltage follows a charge-up curve which is characteristic of a space-charge-limited capacitor. For larger currents a well-defined peak occurs in the charging curves and this is indicative of a change in the conduction properties of the fluid. The time delay from current onset to the onset of convection has been measured as a function of current, for several sample thicknesses. These time delays are in close agreement with theoretical values calculated from a heuristic model of transient stability in space-charge-limited current flow.
Measurements of the Small-Scale Structure of Turbulence at Moderate Reynolds Numbers
Authors: Wyngaard J. C. , Tennekes H.
Published: February 2004

Measurements of probability densities and distributions, moments, and spectra obtained from the first two time derivatives of the streamwise velocity fluctuation in a mixing layer are presented. Probability distributions of squared derivatives are found to be nearly log normal. The skewness (S) and kurtosis (K) of the first derivative are compared with new atmospheric data at much higher Reynolds numbers. Reynolds-number dependence is indicated, in conflict with universal equilibrium theory. A modified theory using fluctuating dissipation predicts that S and K have power-law behavior with turbulent Reynolds number and are related by S ∝ K3/8, in general agreement with the trends of the limited data available.
Spectral Analysis of Inviscid Burgers' Model of Turbulence Using Cameron-Martin-Wiener Exact Expansion
Authors: Kahng Woo-Hyung
Published: February 2004

An exact series solution of the energy spectrum function for a Gaussian initial velocity field is obtained. It is shown that the energy spectrum function goes quickly to an algebraic form (1/kt)n, where 2 < n < 4, except in the regions of extremely small and large k, the algebraic region extending to larger k as time proceeds. The numerical value of n seems to depend on the initial energy spectrum function.
Class of Asymptotic Solutions of Relativistic Gas
Authors: Chiu H. H.
Published: February 2004

A method for obtaining asymptotic solutions for a relativistic gas or gas mixtures at high effective temperatures, subjected to a body force or no body force, is presented. The method yields the solution of the conservation equation by linear superposition of the energy momentum tensor of the electromagnetic field with or without electric charge and current. The nature of the flow field of the high temperature gas is similar to that of the photon gas within the first two asymptotic approximations.
Structure of Three-Dimensional Supersonic and Hypersonic Flow
Authors: Chong T. H. , Sirovich Lawrence
Published: February 2004

The Oseen equations in three dimensions for an arbitrary gas are considered. In particular, the cases of supersonic and hypersonic flow are studied. The asymptotic flow field displaying all the dissipative effects is found in terms of known functions. The explicit structure of the Mach cone and the wake is presented. The latter is shown to decouple, to lowest order, into a viscous and to a heat conducting wake, containing only entropy and vorticity perturbations, respectively. The above results are shown, by means of the nonlinear Navier-Stokes equations, to correctly describe the far field flow past a finite body.
Similarity Analysis of the Radiative Gas Dynamic Equations with Spherical Symmetry
Authors: NiCastro J. R. A. J.
Published: February 2004

Similarity representation of the radiative gas dynamic equations with spherical symmetry, amenable to a wide variety of radiation law, is presented. The general representation of the equations of motion is effected by the simple artifice of retaining the definitions of the radiant quantities as operators on the radiative intensity and of recognizing the variability of the index refraction. Specific constitutive forms for the radiation field manifest themselves in implied constraint conditions. Because of radiative heating, similarity structure may be prescribed for the gas on both sides of shock waves. Numerical examples are constructed for strong explosions and implosions.
Nonlinear Theory of Unstable Two-Dimensional Detonation
Authors: Erpenbeck Jerome J.
Published: February 2004

A two-dimensional theory is presented for the structure of detonations for systems whose steady-state solutions are hydrodynamically unstable. Periodic boundary conditions are imposed in the direction transverse to the steady flow. The analysis, which depends on the assumption that the steady detonation is only “slightly” unstable, permits the time-dependent, two-dimensional flow to be described by a system of two, complex, autonomous, ordinary differential equations in the time. Both traveling-wave and standing-wave solutions are found to be possible, and their significance is discussed. The theory is applied to an ideal-gas, one-reaction system and solutions of both types are found to exist and to be stable for a variety of transverse periods within the unstable regime. With increasing heat of reaction, the magnitude of the perturbations within these waves increases rapidly.
Investigation of Helium Arcs at 10 atm Pressure
Authors: Hwang C. C. , Emmons Howard W.
Published: February 2004

The measured “EI-ER” characteristics of wall-confined helium arcs at 10 atm pressure, when interpreted with the Elenbaas-Heller equation, show that the arcs are close to local thermodynamic equilibrium. A spectroscopic measurement is also made to investigate possible deviations from local thermodynamic equilibrium. The results show that, despite over-all indications of a closer approach to local thermodynamic equilibrium at 10 atm than at 1 atm, the 10 atm arcs are still not in local thermodynamic equilibrium in the region near the walls. Theoretical criteria of local thermodynamic equilibrium tend to support the above results that local thermodynamic equilibrium is approached when the arc pressure is raised, but the complete local thermodynamic equilibrium is not attained at 10 atm. It is believed that the deduced transport properties from the arc measurement with the aid of the Elenbaas-Heller equation are the first approximations. The deduced electrical conductivity and thermal conductivity agree with the theoretical prediction of Lick and Emmons within a factor of 2.
Means of Classifying Convective and Absolute Instabilities
Authors: Baldwin D. E. , Rowlands G.
Published: February 2004

A simple numerical procedure for distinguishing convective and absolute instabilities is described.
Dispersion Measurements of Electrostatic Ion Waves in a Uniform Magnetic Field
Authors: Hirose A. , Alexeff I. , Jones W. D.
Published: February 2004

The phase and group velocities of electrostatic ion waves in a uniform magnetic field have been studied experimentally, both as a function of propagation angle (θ) with respect to the field, and as a function of wave frequency. For ω ≫ ωci, the ion cyclotron frequency, the phase velocity is found to be identical to the ion acoustic velocity (KTe/M)1/2. For ω ≳ ωci, the electrostatic ion cyclotron mode has been observed. The slow mode (ω < ωci cos θ) has been observed to have a constant phase velocity (KTe/M)1/2 cos θ, in apparent contradiction to theory. The frequency gap (ohgr;ci cos θ < ω < ωci), where waves theoretically do not propagate, has been demonstrated.
Harris Instabilities in a Plasma of Finite Length
Authors: Colchin R. J. , Dunlap J. L.
Published: February 2004

The experimental observations concern particular microinstability modes found in a short, highly anisotropic (T‖/T⌋ ≈ 0.005), hot ion plasma (ωpe ≳ ωci > ω ωpi) formed by fast H0 injection into a simple magnetic mirror field. These modes were characterized by Bθ probe signals at ion gyrofrequencies and also at discrete sidebands of comparable amplitude about the gyrofrequencies. Sidebands were related to mirror bounce motions of the ions by experiments using different magnetic field gradients. The presence of high amplitude sidebands and observations of an antisymmetric axial potential distribution associated with one of the oscillations indicated that the modes were those of Harris instability rather than of negative mass. Comparisons of observations with results of numerical studies of Harris instability in infinite media and with finite length effects confirmed the assignment.
Nonlinear Decay and Instability of a Nonuniform Finite-Amplitude Plasma Wave
Authors: Porkolab M. , Chang R. P. H.
Published: February 2004

The effects of spatial nonuniformities in the amplitude of a decaying finite-amplitude plasma wave are examined. It is found that the usually neglected, but experimentally important, initial damping (or growth) of the finite-amplitude wave may have important consequences upon the decay process. The mode-coupling equations are solved for both forward-scattering and back-scattering type decay processes. The latter case is particularly interesting, since both amplification in space, and instability in time, of the perturbed waves may occur in the presence of damping mechanisms. Calculations are presented which show that longitudinal waves with frequencies in the vicinity of cyclotron harmonics may be subject to such instabilities.
Magnetohydrostatic ℓ = 1, Finite β Stellarator Equilibrium
Authors: Nührenberg Jürgen
Published: February 2004

A finite β, ℓ = 1 stellarator configuration with tightly wound helical fields and with no longitudinal current through each magnetic surface is determined using a thin-tube expansion. The independent variables are the magnetic surfaces as coordinate surfaces and the magnetic field lines and the current density lines as coordinate lines. The usual thin-tube quantities ρ, φ, and s are treated as dependent variables. The method can readily be applied to other configurations.
Correlation Effects in Semi-Infinite Plasmas
Authors: Guernsey Ralph L.
Published: February 2004

The system of a fully ionized gas combined to a half-space by a perfectly reflecting boundary is discussed. It is shown how the effect of pair correlations can rigorously be taken into account in both the equilibrium and nonequilibrium theory.
Simulation of Binary Collision Processes in Plasmas
Authors: Oliphant T. A. , Nielson C. W.
Published: February 2004

A numerical procedure for adding the effects of binary collisions to previously collisionless plasma simulation programs has been developed. It is shown that the model faithfully reproduces a numerical solution to the Fokker-Planck equation. As an illustration of the effect of collisions, a mirror mode problem is solved in θ-pinch geometry. Solutions are displayed for varying collision frequencies and qualitative as well as quantitative differences are readily apparent.
Thermal Conductivity and Low Frequency Waves in Collisional Plasmas
Authors: Tsai Shih-tung , Perkins Francis W. , Stix Thomas H.
Published: February 2004

Thermal fluctuations and heat flow terms are retained in the two-fluid equations which are used to derive a localized dispersion relation for low-frequency electrostatic waves in a nonuniform collisional plasma. A slab plasma immersed in a uniform magnetic field is assumed. The Nyquist analysis shows two unstable waves: the collisional drift instability and a new overstability of the entropy wave. The collisional drift wave is most easily excited for parallel wavenumbers given by k‖2 = 0.15 α2(me/mi)1/2 where α ≡ |≇ In n| (all quantities in cgs units). The stability condition at this k| is B/k⊥ < 104 (min/κTe|α|)1/2 G-cm. These are in markedly improved agreement with the experimental data. Heat transport reduces the maximum growth rate, especially at high density. A small equilibrium temperature gradient tends to stabilize the drift waves in the large magnetic field region. The entropywave instability propagates along ion drift direction and is found in the range 0.4 ≤ d¯ ≤ 2 with d¯ ≈ 0.15 (k⊥κ2Ti/Ωi2mi)2νiiνeime/k‖κ2Te. The maximum growth rate of entropy wave is roughly k‖(κTi/mi)1/2(k⊥κ2Te/miΩi2)(mi/me)1/4, and occurs around d¯ = 0.6 ∼ 1The ion thermal conductivity and temperature gradient are not sigificant for both instabilities.
Collisions in a Plasma of Finite-Size Particles
Authors: Okuda Hideo , Birdsall Charles K.
Published: February 2004

Collisions in one-, two-, and three-dimensional plasmas of finite-size particles, clouds, are studied from two different points of view. The first approach starts from the dynamics of binary collisions and proceeds to obtain the interaction force between two clouds including the effect of static shielding which is then used to obtain the scattering cross section. The calculation shows that cloud cross sections are reduced by orders of magnitude compared with those of point particles as the cloud radius is made comparable to the Debye length. The second approach makes use of the kinetic equations of Balescu-Lenard and Landau from which the Fokker-Planck coefficients for a test cloud in an equilibrium plasma are calculated. It is shown that the Fokker-Planck coefficients for clouds also become considerably smaller than those for point particles when the cloud radius becomes comparable to the Debye length; in addition, the velocity dependence of the coefficients for thick clouds are different from those for point particles. As an application, it is shown that the high collision frequencies encountered in computer plasma simulation (ND too small by normal plasma criteria) can be greatly reduced by use of clouds of radius comparable to the Debye length.
Interaction of Negative Mass and Loss Cone Modes
Authors: Berk H. L. , Pearlstein L. D. , Walters G. M.
Published: February 2004

The standard negative mass instability is investigated for a thin layer of charge, oriented concentrically about the axis of symmetry of the magnetic field and immersed in a plasma background. The radius of the charge layer is taken to be equal to the gyroradius of the particles forming the layer. The dispersion relation which describes the interaction of the perturbed layer charge with the plasma background is obtained. Substantial modification to the dispersion relation arises at the first cyclotron harmonic due to beam-plasma interaction. Furthermore, a stable beam mode, predicted at the hybrid frequency in the low-temperature plasma theory, does not occur in this system.
Nonlinear Evolution of Multiple-Finite Amplitude Resonant Loss-Cone Modes
Authors: Aamodt R. E.
Published: February 2004

The dynamics of hot particles moving in the presence of several finite amplitude longitudinal flute modes with frequencies near a harmonic of the cyclotron frequency are derived. It is found that, in general, such electric fields cause sizable groups of particles to lose or gain a substantial fraction of their kinetic energy. The dynamics are then self-consistently applied to the problem of determining the nonlinear evolution of the resonant hot-cold species loss-cone instabilities. For this model it is shown that nonlinear stabilization takes place through large particle excursions in velocity space and by the nonlinear detuning of the system out of resonance. An estimate of the energy exchange process shows that at any time, only a small fraction of the initial hot particle free energy is in the form of electric field fluctuations; most of the available energy is transformed into heating of the high-energy tail of the ions. The final state of this system is shown to be a stable, completely quiescent extremely hot plasma.
Echoes at Upper Hybrid Resonance. I. Measurements on Afterglow Plasma
Authors: Bauer L. O. , Blum F. A.
Published: February 2004

The two-pulse stimulated radiation from nonuniform rare gas (Ar, Ne, He) afterglow plasma columns longitudinally immersed in a uniform (one part in 104) magnetic field was studied. For microwave excitation pulses with a center frequency near the maximum upper hybrid frequency of the spatially nonuniform plasma columns, strong two-pulse echoes are observed. A detailed study of these upper hybrid echoes, using an S-band microwave apparatus, is given. At high densities strong echoes are observed shifted from free electron cyclotron resonance by as much as 20%. The conditions for maximum echo follow maximum upper hybrid resonance as the electron density is varied, but are also found to be dependent on the power and time separation τ of excitation pulses. The power and time width of the first echo are shown to have a complex, yet systematic dependence on four major parameters: electron density, magnetic field, excitation power, and τ. The observed behavior is found to be in general qualitative agreement with calculations involving a one-dimensional slab of cold nonuniform collisionless plasma. A study of the effects of neutral gas pressure on certain echo properties indicates that electron neutral collisions do not play any essential role in the echo formation process. Also, some anomalous observations at X band are reported.
Echoes at Upper Hybrid Resonance. II. Theory for a Cold Nonuniform Plasma
Authors: Blum F. A. , Bauer L. O.
Published: February 2004

The Lagrangian description of a one-dimensional slab of cold nonuniform plasma in a uniform magnetic field is used to calculate the properties of temporal echoes generated by the application of two electric field pulses. Under weak excitation, the electron plasma acts as an ensemble of uncoupled nonlinear oscillators with amplitude dependent eigenfrequencies, which are the local upper hybrid frequencies [ωc2 + ωp2(x)]1/2 in the linear approximation. The decay of the single-pulse response by phase mixing of the oscillators and the action of their nonlinear restoring forces yields, in response to two pulses, a train of echoes in the voltage across the slab. The amplitude of the first echo is studied in detail as a function of magnetic field, electron density, excitation power, and time separation of the excitation pulses. This model successfully accounts for the major features of experimental observations of echoes from afterglow plasmas in a uniform magnetic field. The theoretical echo is strongest in a narrow band of frequencies near the maximum upper hybrid frequency of the plasma slab and shows complex saturation properties in general agreement with experiment.
Dependence on Reynolds Number of High-Order Moments of Velocity Derivatives in Isotropic Turbulence
Authors: Saffman P. G.
Published: February 2004

The results of a heuristic model of the fine scale structure of homogeneous turbulence are presented. Predictions are made about the way in which flatness and skewness factors of arbitrary order depend upon the Reynolds number of the turbulence.
Stationary Convective Cells in a Streaming Plasma Column
Authors: Cataldo Joseph C.
Published: February 2004

Observations of a low-β plasma indicate that, at low magnetic fields, a distinct stationary cellular pattern sets in, resulting in a density one order of magnitude higher than that at higher magnetic fields.
Turbulent Energy Balance and Spectra of the Axisymmetric Wake
Authors: Uberoi Mahinder S. , Freymuth Peter
Published: February 2004

Axisymmetric turbulent wake behind a sphere in an incompressible fluid has been experimentally investigated from 50 to 300 diam downstream from the sphere at Reynolds numbers from 4000 to 150 000. Mean and turbulent velocity measurements show that the region of self-preservation starts 50 sphere diam downstream, and the virtual origin of the wake is 12 sphere diam downstream. Detailed measurements were made in the self-preserving region of the wake. The three components of the turbulent velocity, turbulent shear, and the mean velocity defect were measured across the wake using the hot-wire anemometer. From the measurements the turbulent energy production, dissipation, convection, and diffusion across the wake were determined. The one-dimensional energy spectra of the three components of the turbulent velocity, their dependence on distance along and across the wake and on Reynolds number have been measured. The large scale motion (low wavenumbers) is dynamically similar and the small scale motion (large wavenumbers) exhibits Kolmogoroff's universal equilibrium. The present spectral measurements are compared with other published measurements of the universal equilibrium spectra in various turbulent flows.
Indeterminacy of the Moment Problem for Intermittent Turbulence
Authors: Orszag Steven A.
Published: February 2004

It is shown that the log-normal distribution of local energy dissipation in high-Reynolds-number turbulence implies that the evolution of turbulence is not determined by specification of initial values for moments of all orders. The consequence of this indeterminacy for theories of turbulence is discussed.
Kinetic Theory of the Piston Problem by the Bhatnagar-Gross-Krook Equation
Authors: Wu Yau , Lee C. H.
Published: February 2004

The formation of shock and expansion waves by a moving piston is studied according to the kinetic theory of gases. A piston is impulsively moved at a constant but arbitrary speed with a diffuse reflection on either isothermal or adiabatic piston wall. The Bhatnagar-Gross-Krook equation has been solved by applying the numerical method proposed by Chu for the shock tube problem. The waves are developed through intermolecular collisions for various piston speeds (Mach number 0.438, 0.876, and 1.314). The properties across the shock wave agree quite well with the Rankine-Hugoniot relations. A kinetic layer of several mean free paths near the isothermal piston wall is clearly observed. A temperature jump at the isothermal wall is also developed. Solutions for the adiabatic wall with zero temperature gradient are obtained and compared very well with the gas dynamic solutions. Temperature overshoots (Tx) inside the shock waves have been observed for higher piston speeds (Mach number 0.876 and 1.314).
Evolution of Shock Waves and Thermal Disturbances Generated by a Fractionally Accommodating Surface
Authors: Kovitz A. A. , Hellman K. H.
Published: February 2004

The “piston problem” is studied numerically using the Boltzmann collision integral as the governing relation. A fractionally accommodating, impermeable piston (Maxwell boundary condition) is assumed. Mintzer's method of generalized orthogonal polynomials, together with the method of characteristics, form the basis for the computation. These results represent an extension of previous work on the piston problem to include nonlinear effects, fractionally accommodating surface, and the Boltzmann collision integral rather than other kinetic models. Early time behavior for the evolution of shock waves, both weak (M ≅ 1.13) and stronger ( M ≅ 2.9), is very dependent on the accommodation co-efficient of the piston. For a cold piston, fractionally accommodating, there always exists a layer of cool gas between the piston surface and the shocked gas. The Mach number of the fully developed shock wave (after about 60-80 collision times) for a cold piston is slightly less than the ideal value. A sudden increase in the surface temperature of a fixed piston generates a thermal disturbance. The gas temperature at the surface rises quickly at first, but then becomes imperceptibly slow before reaching the surface temperature; the major temperature rise in the gas is preceded by a precursor-like thermal pulse moving with almost sonic velocity for the example considered.
Non-Diffusive Effects in the Radiative Propagation of a Thermal Pulse
Authors: Traugott S. C.
Published: February 2004

The very early, pre-hydrodynamic transport of energy by radiation in a strong explosion is studied, taking departures from the Rosseland diffusion approximation into account. Similarity solutions exist for the plane, cylindrical, and spherical case when the grey absorption coefficient varies as a power of temperature which is 1, 12, and 13, respectively. Solutions are found for the plane and spherical case using both the technique of matched asymptotic expansions and numerical integration. These solutions allow computation of temperatures and heat flux as a function of time, distance from the center, and energy release. Non-diffusive radiation leads to a relatively cool precursor to the main portion of the thermal wave. This precursor is much less pronounced in the spherical case. It is also found possible to predict the temperature visible to a distant observer.
Experimental Study of a Plasma Flow in a Magnetic Nozzle
Authors: Kuriki Kyoichi , Okada Osami
Published: February 2004

Interaction between an axisymmetric jet of plasma and a magnetic field generated by concentric current loops is studied experimentally. With a large Hall parameter, electrons are confined to the converging-diverging lines of force. The maximum Hall parameter for electrons is greater than 30. Measurements are made of the electric potential, ion density, electron temperature, and ion velocity. The flow of charged particles is found to be aligned with the magnetic lines of force with a slip relative to neutral atoms. The ion is compressed electromagnetically and is pumped to flow over a potential barrier formed near the center of the coil. The maximum velocity of ions at the exit of the magnetic nozzle is greater than that expected from an isentropic expansion. This extraordinary speed of ions is accounted for in terms of the electrostatic acceleration. In the magnetic channel the energy equation for ions is coupled with the energy equation for electrons.
Plasma Heating by Reflected Ionizing Shock Waves
Authors: Taussig Robert T.
Published: February 2004

Ionizing shocks reflected by a transverse magnetic field “barrier” heat and compress the plasma at the barrier. Numerical results are presented for an ideal gas (typical values for hydrogen initially at 100 MTorr and room temperature). Resolution of the arbitrary discontinuity formed by the incident shock at the barrier field is discussed in detail. The recent work of Bout and Gross is extended to an additional branch of solutions corresponding to applied magnetic fields greater than their critical field. Calculations using a simplified transverse ionizing shock structure are compared to the pure gas dynamic and pure magnetohydrodynamic cases. The range of validity of the ideal gas approximation is reviewed briefly.
Oblique Shocks in Finite-Beta Plasmas
Authors: Crevier W. F. , Tidman D. A.
Published: February 2004

The structure of shock waves and solitons propagating oblique to a magnetic field in a warm plasma is analyzed. The calculations are based on two-fluid equations including resistive dissipation. A classification scheme for the various structures obtained as the shock speed and plasma parameters vary is given. The problem of high Mach number shock structure is also discussed.
Transport Coefficients of Inhomogeneous Plasmas in a Magnetic Field
Authors: Yoshikawa S.
Published: February 2004

Transport coefficients of inhomogeneous, magnetized plasmas are derived using the quasilinear approximation. It is shown that mechanisms which allow the motion of ions across the magnetic field, such as ion-neutral collisions, are essential in arriving at divergent-free, finite transport coefficients in unbounded plasmas. The transport coefficients are calculated for both unbounded and bounded plasmas. Although in toroidal plasmas the transport coefficients do not follow the 1/B law, the calculated diffusion coefficients are numerically very close to what is known as the Bohm diffusion coefficients in a number of experimental devices.
Turbulent Plasmas in a Magnetic Field—A Statistical Theory
Authors: Weinstock Jerome
Published: February 2004

A statistical theory of plasma turbulence in a magnetic field is described. This theory makes use of averaging operators to formally solve the Vlasov equation and the stochastic acceleration problem. Sets of turbulence equations are thereby derived for determining the ensemble average of the oneparticle distribution function and the electric field spectrum. The average distribution function is seen to satisfy a diffusion equation to all orders in the perturbation—even in the presence of a magnetic field. The mentioned equations are used to derive a nonlinear dispersion relation for waves in turbulent plasmas in a magnetic field. This dispersion relation is a nonlinear generalization of Bernstein's linear dispersion relation for electrostatic waves. The nonlinearity manifests itself as a damping factor proportional to mean square deviations from mean particle trajectories. A simplifying feature of the present work is the use of cumulant expansions, which also avoid certain heuristic arguments. A previous result, given by Dupree, is shown to be a special case of the present result.
Turbulent Heating Experiment
Authors: Hsieh C. L. , Lichtenberg A. J.
Published: February 2004

Results are presented of an experimental investigation of turbulent heating. A current parallel to the mirror magnetic axis, produced by discharging a capacitor, excites an interaction and, with proper conditions (plasma density, magnetic field strength for trapping), it is found that some class of turbulently heated plasma electrons can be adiabatically compressed to high temperature. In the most favorable heating conditions electrons are heated to 85 keV at 25 kG (factor of 40 in magnetic compression). This corresponds to Te ≃ 2 keV immediately after turbulent heating, which is approximately equal to the total voltage drop across the electrodes. The interaction is characterized by an anomalously high resistance, and radiation that covers a broad range up to the electron plasma frequency and including the frequency range corresponding to the electron-ion streaming instabilities. At low density (< 1012 cm−3), a sheath is generated giving rise primarily to the beam plasma interaction. In the intermediate density range 2 × 1012−1013 cm−3 the anomalous resistivity had approximately a n−1/2 dependence, characteristic of the current-convective mode. At densities over 2 × 1013, all interactions are quenched due to the voltage drop across the self-inductance of the discharge circuit including the plasma column. The results are compared with related turbulent heating experiments.
Growth Rate Calculations for Electron-Electron Modes with Pressure Anisotropy and Cold Plasma
Authors: Jacquinot J. , Leloup C.
Published: February 2004

Maximum linear growth rates of electromagnetic and electrostatic waves in an infinite homogeneous plasma are compared for a large domain of physical parameters. The analysis is restricted to frequencies just below the electron cyclotron frequency.
Density Profile Measurement Using an Electromagnetic Wave in the Extraordinary Mode
Authors: Tulle P. A.
Published: February 2004

A method is presented for the measurement of spatial distributions of electron plasma density. It is based upon the reflection of the extraordinary mode (k¯ ⊥ B¯0, E¯ ⊥ B¯0) due to cutoff which occurs for a frequency ω, satisfying (ωp/ω)2 = 1 − ωc/ωinstead of (ωp/ω)2 = 1for the ordinary mode (k¯ ⊥ B¯0, E¯ ‖ B¯0). Consequently, the principle advantages are extension of the domain of plasma density measurements for a particular microwave frequency, and determination of the complete density profile by varying the frequency within the band of a single generator. Accurate results can be obtained because relative measurements of the density profile are made. Their interpretation is accomplished with a computational aid which calculates the propagation of the wave through the nonuniform plasma.
Particle Motion in the Presence of Three-Dimensional Finite Amplitude Harmonic Cyclotron Waves
Authors: Aamodt R. E.
Published: February 2004

The motion of charged particles in six-dimensional phase space is investigated when the particles are influenced by a strong uniform magnetic field and finite amplitude electric fields with frequencies at or near a harmonic of the cyclotron frequency. In general, it is found that the particles move in a vortex filament pattern in this six-dimensional phase space. Using the constraint of this motion the amount of energy available to go into electric field energy is estimated for a loss-cone distribution function with several assumed simple types of three-dimensional wave forms. It is found that only a small fraction of the particle kinetic free energy can go into waves.
Perturbed Ion Distributions in Ion Waves and Echoes
Authors: Ikezi H. , Taylor R. J.
Published: February 2004

The perturbed part of the ion distribution function is observed experimentally when an ion wave or ion wave echo is excited in a plasma. In the case of the wave the perturbed distribution is confirmed to survive, as predicted by Landau, after the wave damps away. In the case of the ion wave echo the features of the oscillations of the distribution function in velocity space are in agreement with the prediction of the perturbation theory carried to the second order. However the second-order perturbed distribution function, which is responsible for the formation of the echo, is observed to undergo a strong reduction in amplitude after the appearance of the echo electric field.
Coupling of Transverse and Longitudinal Waves in a Drifting Magnetoplasma
Authors: Hsieh H. C.
Published: February 2004

The coupling of transverse circularly polarized electromagnetic waves and longitudinal plasma waves in a collisionless drifting magnetoplasma is studied. A quasilongitudinal propagation is considered. It is shown that the left-hand circularly polarized wave may be amplified by interacting with a slow space-charge wave, while a right-hand circularly polarized wave may be attenuated by interaction with a fast space-charge wave. The condition for amplifying the left-hand wave is given by b > 1/(1 + σ2), where b = (ωp/Ωz), σ = (u0z/c)in which ωp and Ωz are the electron plasma and electron cyclotron angular frequencies, respectively. The symbol u0z is the drift velocity of plasma and c is the speed of light in a vacuum. The variarion of the rate of growth or decay and the variation of phase velocity of the transverse electromagnetic wave with the parameters b, σ, and κ = (B0⊥/B0z) are examined in detail. B0⊥ and B0z are the normal and parallel components of magnetostatic field, respectively.
Generalized Boundary Conditions
Authors: Lindman E. L.
Published: February 2004

The concept of the generalized boundary condition is introduced, and stabilization of ion-sound waves and drift waves using such boundary conditions is demonstrated. The boundary consists of a two-dimensional, lumped-parameter transmission line in electrical contact with the plasma. A boundary dispersion relation is introduced which describes the boundary modes and their interaction with the plasma. Modes which are combinations of plasma and boundary modes are obtained which can be stabilized by appropriate choice of inactive circuit elements.
Interactions of a Plasma with a Spiraling Electron Beam
Authors: Kusse B. R. , Bers Abraham
Published: February 2004

A hollow, spiraling electron beam with energies along and across the applied magnetic field (B0) was injected into argon (7 × 10−5 Torr) to produce a plasma. With increasing plasma density oscillations were observed at frequencies above integral multiples of the electron cyclotron frequency. A theoretical study of the coupling between electrostatic plasma waves and waves on a spiraling beam is shown to predict the observed frequencies and wavelengths. The theoretical analysis accounts for the finite thickness of the beam and for finite Larmor-radius effects in the plasma. The latter are shown to explain the sudden jumps in the observed frequencies which resulted when the plasma density increased. The results show that a spiraling beam with energy across B0 is able to transfer some of this energy to the plasma even when the electrons are hot.
Steady Flow in the Axially Symmetric Torus Using the Guiding-Center Equations
Authors: Dobrott D. , Greene J. M.
Published: February 2004

General steady flow in an axially symmetric torus is investigated using the guiding-center equations. Several constants of the macroscopic and microscopic motion are obtained, and a second-order quasilinear partial differential equation is derived for the self-consistent magnetic flux function. The condition specifying that this equation be hyperbolic or elliptic is given. For the former case, jump conditions are given when weak (discontinuous) solutions are admitted.
Nonadiabatic Harmonic Oscillator
Authors: Howard James E.
Published: February 2004

Nonadiabatic changes in the action integral are estimated for the special case of even ω(t) by using a steepest-descent method to evaluate an integral of Vandervoort. The results are found to be in good agreement with a numerical example.
Plasma Loss Structure in a Linear Multipole
Authors: Palladino R. W.
Published: February 2004

The dominant losses from hot electron plasmas in the Princeton linear quadrupole device have been found to be radially outward. When this nonclassical radial loss was studied in detail, a surprising amount of variation was found in the amplitude of the loss rate as seen moving parallel to the current-carrying conductors, which led to the further discovery of spatial variations of internal plasma parameters, particulary plasma density. Efforts to correlate the anomalously large loss zones with local perturbations, obstructions, fluctuations, or variations in plasma heating and ionization were only partially successful. The periodic structure in plasma density and charged-particle loss rates apparently reflects stable, internally supported modes that have lifetimes longer than the plasma lifetime presently being considered; i.e., > 10τBohm.
Stability of Combined Heat and Mass Transfer in a Porous Medium
Authors: Wankat P. C. , Schowalter W. R.
Published: February 2004

An energy method is applied to ascertain stability criteria for combined heat and mass transfer in a fluid contained in a porous medium. In the limiting case of zero mass transfer the results differ slightly from those of Westbrook.
Nonlinear Development of the Beam-Plasma Instability
Authors: Drummond W. E. , Malmberg J. H. , O'Neil T. M. , Thompson J. R.
Published: February 2004

The nonlinear limit of wave growth induced by a low density cold electron beam in a collisionless plasma is calculated from a simple physical model. The bandwidth of the growing “noise” is so small that the beam interacts with a nearly sinusoidal electric field.
Stability and Shape of Isolated and Pairs of Water Drops in an Electric Field
Authors: Brazier-Smith P. R.
Published: February 2004

A numerical method of calculating the correct stable equilibrium shape of a conducting drop subject to electrical forces is described. Its application to the problem of the stability of an isolated water drop of undistorted radius R and surface tension T situated in an electric field E indicates that a drop is unstable if E(R/T)12 exceeds a value of 1.603 and its maximum stable deformation expressed as a/b, the ratio of the major to minor axes is 1.83. The numerical method is also applied to a study of the stability of drop pairs. The results show that the critical value of E(R/T)12 depends upon the initial separation X of the drops. For X = 0, E(R/T)12 is zero and its value increases as X increases, tending to a value of 1.603. Finally, the relevance of these results to the behavior of drops in the atmosphere is discussed.
Amplitude Limitation of a Collisional Drift Wave Instability
Authors: Hinton F. L. , Horton C. W.
Published: February 2004

A nonlinear analysis of collisional drift waves is presented in which a systematic expansion is made in powers of the wave amplitude. The two-fluid equations are used, including the effects of resistivity, viscosity, and thermal transport. The result, for the wave amplitude as a function of magnetic field in the linearly unstable region close to marginal stability, agrees reasonably well with experiment.
Chemical Instabilities: I. A Heated Horizontal Layer of Dissociating Fluid
Authors: Wollkind David J. , Frisch H. L.
Published: February 2004

An investigation is made of the stability to infinitesimal disturbances of a horizontal layer of dissociating fluid, heated from above or below. A modification of mathematical model due to Lighthill is employed. The results of the linear perturbation analysis of the normal mode resolution of the disturbances show that: (1) there is a slight departure in the onset of convective instability from the classical Bénard problem for a nonreactive fluid layer heated from below; (2) for the case of heating from above, which is stable for a nonreactive fluid, there is also an onset of instability. Such a flow situation which is stable if the fluid is not chemically reactive but can exhibit an instability if the fluid is chemically reactive (i.e., in this case a dissociating fluid) is referred to as a chemical instability.
Anomalous Plasma Resistivity at Low Electric Fields
Authors: Coppi B. , Mazzucato E.
Published: February 2004

Experiments have shown the appearance of “nonclassical” resistivity, higher than that predicted by the known transport theory based on electron-ion collisions, in magnetically confined plasmas where the electron gyrofrequency is larger than the Langmuir frequency and the electric field is well below the runaway threshold. A theoretical interpretation of the anomalous resistivity onset is proposed observing that (at long but finite mean free paths) nonresonant modes, associated with the effects of electron-electron collisions, are excited when the electron flow velocity along the magnetic field is roughly larger than the ion sound-wave velocity. The magnitude of anomalous resistivity is then discussed in relation with the nonlinear effects of resulting fluctuations and of related modes with wavelengths shorter than the mean free path. A comparison between several experiments on plasma confined in different stellarator and tokamak configurations is given. The differences in physical regimes that lead to various mechanisms for the appearance of “nonclassical” resistivity and the relationship with anomalous diffusion are pointed out.
Influence of Collisions on the Instability of Cold and Warm Electron Beams in a Plasma
Authors: Böhmer H. , Chang J. , Raether M.
Published: February 2004

The effect of Coulomb collisions on the growth of the instability of monoenergetic beams and beams of finite initial velocity spread in a plasma has been investigated experimentally. The results are compared with existing theories and with computations based on a beam with Lorentzian distribution function. It is shown that the instability is suppressed by collisions if the beam has a sufficiently large velocity spread in agreement with the prediction of Ascoli and Singhaus and that their stability criterion is valid over a larger parameter range than had previously been assumed. Evidence is presented for a self-quenching of the instability of an initially monoenergetic beam due to the combined effect of collisions and the smearing out of the beam distribution function by the unstable waves.