bluuebunny/crossref_metadata_2025 huggingface dataset:
Shock formation distance in a pressure driven shock tube
Authors: Rothkopf E. M. , Low W.
Published: March 2003

Measurements of the shock formation distance in a conventional pressure driven shock tube of 5.2 cm i.d. using two different diaphragm types and three different driver gases with a driven gas of air are presented. The shock formation distance is found to be approximately proportional to the effective opening time of the diaphragm and inversely proportional to the average speeds of sound of the driver and driven gases.
Equatorial propagation of axisymmetric magnetohydrodynamic shocks
Authors: Rosenau Philip , Frankenthal Shimshon
Published: March 2003

Self-similar solutions are presented for the equatorial propagation of axisymmetric, piston-driven magnetohydrodynamic shocks into an inhomogeneous ideal gas permeated by a current-free azimuthal magnetic field. Several regimes of magnetically dominated flow near the piston are possible, depending on the ambient density distribution of the unshocked gas. The strong hydrodynamic and magnetic gradients which permeate this flow indicate the need for a more refined treatment which will include the effects of diffusion due to dissipative phenomena. Global features of the flow are discussed and illustrated by numerical solutions. The use of reductive properties of the equations to simplify the problem in several special cases is indicated. Implications regarding the propagation of disturbances in stellar atmospheres are considered.
Theory of a cylindrical probe in a collisionless magnetoplasma
Authors: Laframboise J. G. , Rubinstein J.
Published: March 2003

A theory is presented for a cylindrical electrostatic probe in a collisionless plasma, when the probe axis is inclined at an angle ϑ to a uniform magnetic field. The theory is applicable to electron collection, and under more restrictive conditions, to ion collection. For a probe at space potential, the theory is exact in the limit when probe radius rp≪ Debye length λD. At attracting probe potentials, the theory yields an upper bound and an adiabatic limit for current collection. At repelling probe potentials, it provides a lower bound. The theory is valid if rp/λD and rp/ā, where ā is the mean gyroradius, are not simultaneously large enough to produce extrema in the probe sheath potential. The numerical current calculations are based on the approximation that particle orbits are helices near the probe, together with the use of kinetic theory to relate velocity distributions near the probe to those far from it. Probe characteristics are presented for ϑ from 0° to 90°, and for rp/ā from 0.1 to ∞. For ϑ=0°, the end-effect current is calculated separately.
Parametric instabilities with finite wavelength pump
Authors: Fried Burton D. , Ikemura T. , Nishikawa K. , Schmidt G.
Published: March 2003

The general problem of parametric instabilities driven by a finite wavelength pump is investigated. For the particular case of a Langmuir wave pump, it is shown that resonant decay instabilities (forward or backward scattering in the one-dimensional case), with thresholds which vanish in the colisionless limit, can occur only for pump wavenumber k0 greater than the critical value [(m/M)1/2/γ]kD, where m and M are the electron and the ion mass, respectively, and γ is the specific heat ratio. For smaller wavenumbers, there is always a nonzero threshold, the instability being of modulation character at long wavelengths and almost pure growing for short wavelengths. Frequency locking for small k0 and wavenumber locking for large k0 are demonstrated. The results are generalized to the case where the coupled waves satisfy arbitrary dispersion relations and simple physical interpretations of the instabilities are given.
Nonlinear evolution of the sausage instability
Authors: Book David L. , Ott Edward , Lampe Martin
Published: March 2003

Sausage instabilities of an incompressible, uniform, perfectly conducting Z pinch are studied in the nonlinear regime. In the long wavelength limit (analogous to the ’’shallow water theory’’ of hydrodynamics), a simplified set of universal fluid equations is derived, with no radial dependence, and with all parameters scaled out. Analytic and numerical solutions of these one-dimensional equations show that an initially sinusoidal perturbation grows into a ’’spindle’’ or cylindrical ’’spike and bubble’’ shape, with sharp radial maxima. In the short wavelength limit, the problem is shown to be mathematically equivalent to the planar semi-infinite Rayleigh–Taylor instability, which also grows into a spike-and-bubble shape. Since the spindle shape is common to both limits, it is concluded that it probably obtains in all cases. The results are in agreement with dense plasma focus experiments.
Numerical studies of nonlinear evolution of kink modes in tokamaks
Authors: Rosenbluth Marshall N. , Monticello D. A. , Strauss H. R. , White R. B.
Published: March 2003

A set of numerical techniques for investigating the full nonlinear unstable behavior of low-β kink modes of given helical symmetry in tokamaks is presented. Uniform current density plasmas display complicated deformations including the formation of large vacuum bubbles provided that the safety factor q is sufficiently close to integral. Fairly large m=1 deformations, but not bubble formation, persist for a plasma with a parabolic current density profile (and hence shear). Deformations for m⩾2 are, however, greatly suppressed.
Drift wave stabilization by a high frequency applied electric field
Authors: Weiss Irwin , Morrone Terry
Published: March 2003

Dispersion relations are calculated for drift waves in an inhomogeneous plasma with an oscillatory electric field which is applied perpendicular to the constant magnetic field. Use is made of the Vlasov equation to calculate drift wave frequencies and growth rates. Electron currents, density, and temperature gradients and finite/infinitesimal ion gyroradius are included. It is determined that substantial reduction in the drift wave growth rate can be achieved using the ac electric field when its frequency is equal approximately to either the ion or electron cyclotron frequency.
Ion-cyclotron waves in nonuniform plasmas and parametric instabilities
Authors: Sperling J. L. , Perkins F. W.
Published: March 2003

A general formalism for studying waves propagating in a plasma with density and magnetic field gradients in slab geometry is discussed. Specializing to electrostatic ion-cyclotron waves propagating perpendicular to the gradients, it is shown that a density profile can lead to local or nonlocal structure around points where N′ (x)/N (x) has a local maximum while inhomogeneous magnetic fields provide the wave with the profile of an Airy function. Application of the formalism to parametric instabilities driven by magnetosonic waves and with kyρi≫1 is discussed. In particular, it is concluded that density and magnetic field gradients should not be critical in the development of the cyclotron decay instability in the FM-1 (floating multipole-1), ATC (adiabatic toroidal compressor), and PLT (Princeton large torus) devices of Princeton.
Viscous effects on small-amplitude surface waves
Authors: Prosperetti Andrea
Published: March 2003

The transient behavior of small-amplitude standing waves on the plane surface of an infinitely deep viscous liquid is investigated. An integro-differential equation of motion for the free surface is derived and solved exactly. The small-time behavior of the solution agrees with that computed in the approximation of irrotational flow, and the large-time one with the results for the discrete spectrum obtained by means of the standard normal-mode analysis. In between these two asymptotic regimes, however, the exact solution is significantly different from either approximation, except when the effect of viscosity is very small.
Spatial stability of Poiseuille flow in an elastic tube
Authors: Garg V. K. , Rouleau W. T.
Published: March 2003

A study of the spatial stability of Poiseuille flow in an arbitrarily thick elastic tube to infinitesimal axisymmetric disturbances is presented. The differential equations of motion for the tube are solved analytically in terms of Bessel functions of complex arguments while those for the fluid are solved numerically by means of a power series followed by a step-by-step integration technique. The flow is found to be unstable for Reynolds numbers greater than a critical value that depends on the disturbance frequency and tube parameters. This critical Reynolds number varies almost as the square root of Young’s modulus for the tube material.
Asymptotic theory for peristaltic transport in a tube of arbitrary cross section
Authors: Shen M. C.
Published: March 2003

An asymptotic theory within the framework of long wave approximation is proposed for the study of peristaltic transport in a flexible tube of arbitrary cross section. The nonlinear problem of the three-dimensional Navier–Stokes equations is reduced to a sequence of linear boundary-value problems of the two-dimensional Laplace and biharmonic operators. Explicit expressions for the velocity profiles are obtained in terms of the solutions of the boundary value problems. Results for a tube of elliptical cross section are given.
Phenomenological theory of thermodynamic coupling in multicomponent compressible laminar boundary layers
Authors: Tambour Y. , Gal-Or B.
Published: March 2003

Thermodynamic couplings due to thermal diffusion, diffusion-thermo, and ob aliam diffusion effects in multicomponent compressible laminar boundary layers and in stagnation-point flows with blowing or suction, are analyzed and compared with other available analyses for simpler specific cases. The mathematical treatment includes new definitions of generalized Prandtl, Lewis, and Schmidt numbers for coupled heat and multicomponent mass transfer. Using matrix notation and new tranformations, the energy and the species conservation equations are decoupled and transformed into a widely useful single compact ’’energy-species’’ equation. For frozen multicomponent flows, the new ’’energy-species’’ equation is of the same form as the energy equation for single-component flows in the absence of thermodynamic coupling. Hence, solutions for generalized flows, which are presented here in transformed forms are obtainable from known solutions of ’’simpler’’ cases.
Conditional stability of shock waves—a criterion for detonation
Authors: Fowles G. R.
Published: March 2003

The stability of plane shock waves is treated by examining the amplitudes of acoustic waves reflected from shock fronts, and by methods of irreversible thermodynamics. Both approaches yield the same conditions for stability, −1⩽j2(dV/dP)H⩽1, where j2 is the negative slope of the Rayleigh line, and the derivative is taken along the Hugoniot P-V curve. The thermodynamic method indicates that instabilities are associated either with local maxima in the entropy, or shock velocity; or with local minima in the reduced internal energy, or particle velocity, along the Hugoniot curve. It is proposed that the latter case corresponds to detonation with the detonation state given by the particle velocity minimum.
Current-driven internal kink modes in cylindrical and helicoidal discharges
Authors: Edery D. , Laval G. , Pellat R. , Soulé J. L.
Published: March 2003

The stability of the internal m=1 kink mode is shown to be very sensitive to small distortions of a circular cylindrical equilibrium. Cylindrical and helicoidal m=2 distortions are destabilizing. Triangular m=3 and quadrangular m=4 distortions provide a means of stabilizing the internal kind mode.
Nonlinear skin effect of high-power microwaves and a density-rarefaction wave in a collisionless magnetoplasma
Authors: Minami K. , Mori Y. , Takeda S. , Ishii K.
Published: March 2003

Experimental results are presented which verify the nonlinear skin effect of high-power microwaves incident on a collisionless, uniform plasma having a sharp boundary. The skin depth, observed by microwave reflection techniques, increases with the incident microwave power. The results are compared with the theoretical analysis in which the radiation pressure due to the electromagnetic field is taken into account. It is also found that a density-rarefaction wave caused by an incident microwave propagates through an over-dense plasma at a velocity closer to that of the ion acoustic wave.
Radio frequency ion heating near the lower hybrid frequency
Authors: Fidone I.
Published: March 2003

Wave absorption near the lower hybrid frequency is considered. It is shown that, in a hot plasma, a slow wave appraching the hybrid layer is strongly damped by ion Landau damping.
Van der Pol’s equation and nonlinear oscillations in a beam plasma system
Authors: Walsh J. E. , Hagelin J. S.
Published: March 2003

A nonlinear dispersion relation for beam plasma oscillations is obtained by expanding the usual dispersion relation about both the most unstable root and the perturbed beam electron orbits. This procedure leads to a nonlinear rate equation similar to the van der Pol equation.
Scaling of plasma turbulence resulting from parametric instabilities
Authors: Ott Edward
Published: March 2003

Dimensional analysis is used to obtain results on the turbulent state resulting from parametric instabilities of an initially cold plasma. The results include the possibility of an applied magnetic field, multiple ion species, and arbitrary dimensionality.
Thresholds of parametric instabilities near the lower-hybrid frequency
Authors: Berger R. L. , Perkins F. W.
Published: March 2003

Resonant decay instabilities of a pump wave with frequency ω0 near the lower-hybrid frequency ϑlh are analyzed with respect to the wavenumber k of the decay waves and the ratio ω0/ωlh to determine the decay process with the minimum threshold. It was found that the lowest thresholds are for decay into an electron plasma (lower-hybrid) wave plus either a backward ion-cyclotron wave, an ion Bernstein wave, or a low-frequency sound wave. For ω0< (2ωlh)1/2, it was found that these decay processes can occur and have faster growth than ion quasi-modes provided the drift velocity (cE0/B0) is much less than the sound speed. In many cases of interest, electromagnetic corrections to the lower-hybrid wave rule out decay into all but short wavelength (kρi ≳1) waves. The experimental results are consistent with the linear theory of parametric instabilities in a homogeneous plasma.
Equilibrium theory of toroidal magnetic cusp confinement with internal circulation
Authors: Hammer J. H. , Kunkel W. B.
Published: March 2003

Plasma confined in the Tormac configuration can be made to rotate about the minor axis so that guiding-center drifts do not carry the particles to the boundary layer even in a purely toroidal field B (R). In this way the anisotropy in velocity space caused by losses at the cusps will not be rapidly communicated to the interior. Rotation can be enhanced and controlled, in principle, by neutral injection with angular momentum about the minor axis. The properties and stability characteristics of such a state are theoretically investigated in the present paper. The conditions for a stationary state are shown to require that the number of particles on a flux tube remains constant, yielding the relation n (R) R/B (R) ≈ const. The equilibrium properties of the plasma are observed with the use of two different models: (1) The plasma is treated as consisting of two fluids with negligible centrifugal effects and interspecies interactions, where electrons are considered as isotropic with the equation of state d/dt (Pen−γ) =0, while the ions are anisotropic and obey the Chew–Goldberger–Low equations. (2) The plasma is treated as a single fluid with negligible centrifugal effects and scalar pressure, i.e., obeys d/dt (Pn−γ) =0. In each case the equilibrium solutions n (R) are found to be marginally interchange-stable.
Vlasov confinement equilibria in one dimension
Authors: Hewett D. W. , Nielson C. W. , Winske D.
Published: March 2003

A method for constructing one-dimensional Vlasov equilibria from assumed macroscopic moments is described and examples are given. General properties of these equilibria, in particular, the fact that temperature anisotropy in the two directions perpendicular to the magnetic field is required, are discussed. Results of particle simulations which verify the validity of these equilibria and illustrate the effects of temperature anisotropy are presented.
Enhanced coherent Raman emission from uniform plasmas
Authors: Prasad B.
Published: March 2003

A mechanism for the coherent emission of radio and microwaves from a warm uniform plasma is proposed. The output power from this mechanism appears to have the characteristics of a classical parametric amplification process. An earlier kinetic theory model for radiation by the scattering of plasma waves in a homogeneous plasma is revamped and modified to incorporate the dominant role of longitudinal Rayleigh scattered waves which stimulate the emission of transverse combination radiation (sum and difference of impressed and natural frequencies) by the resonant Raman scattering process in the plasma. This results in intense radio or microwave radiation at approximately twice the plasma frequency, the intensity depending upon plasma parameters. This intensity, its angular pattern, and the threshold condition for its enhanced emission are calculated. Comparisons of the computed results with the laboratory observation of the radiation output from dc discharges in argon gas, and from a helium theta-pinch plasma are made. Both qualitative and quantitative agreement are found.
Rayleigh–Taylor instability of thin viscous layers
Authors: Craik A. D. D.
Published: March 2003

A ’’thin-layer approximation’’ is developed to complement Plesset and Whipple’s [M. S. Plesset and C. G. Whipple, Phys. Fluids 17, 1 (1974)] approximate analysis. Observations of instability of very thin layers reveal that the influence of molecular diffusion may be appreciable.
Excitation of ion-acoustic wave by power-modulated electromagnetic wave in a weakly ionized plasma
Authors: Yamamoto T. , Nishio Y. , Tsukishima T.
Published: March 2003

It is shown that the electromagnetic ponderomotive force fnl of a locally irradiated microwave beam is mainly responsible for the excitation of an ion-acoustic wave, even when the ionization effect is taken into consideration.
Some properties of deep water solitons
Authors: Cohen Bruce I. , Watson Kenneth M. , West Bruce J.
Published: March 2003

Envelope solitons for surface waves in deep water are studied using the coupled equation for the Fourier amplitudes of the surface displacement. Comparison is made with some wave-tank experiments of Feir. A linear stability analysis is made for an imposed transverse ripple. A slowly growing instability is found at wavelengths comparable to, or longer than, the length of the soliton. A slowly developing instability is also found for a soliton propagating through a train of waves of wavelength appreciably smaller than that of the soliton. A soliton propagating through a train of waves with wavelength much larger than that of the soliton exhibits gross distortion due to the orbital fluid velocity of the wavetrain. This distortion is to some extent reversible, as the soliton tends to ’’recover’’ when the wavetrain is damped to zero amplitude. Some comments are given concerning the statistics of a wave field containing solitons.
Turbulent self-diffusion
Authors: Lundgren T. S. , Pointin Y. B.
Published: March 2003

A method relating Lagrangian and Eulerian statistics for the diffusion of a particle in a homogeneous stationary velocity field, which was developed for plasma diffusion by Taylor and McNamara and further explained by Montgomery, is shown to be equivalent to a method proposed by Corrsin and used by Saffman. The results are compared with numerical simulations with good agreement for velocity fields which have properties similar to real turbulence.
Effect of free stream vorticity on spatial stability of incompressible boundary layers with nonparallel effects
Authors: Wazzan A. R. , Taghavi H. , Li Y. Y.
Published: March 2003

The Falkner–Skan boundary layer is perturbed by an imposed mean free-stream vorticity. The stability of the perturbed flow to Tollmien–Schlichting waves is considered within the framework of the quasiparallel approximation (boundary layer growth terms are included but the x variation of disturbance characteristics is neglected). Falkner–Skan boundary-layer flows with Hartree pressure gradient parameter β=1.0, 0.8, 0.6, 0.1, 0.0, −0.1, and −0.14 are considered. It is found that positive free-stream vorticity is stabilizing and negative free-stream vorticity is destabilizing. For positive free-stream vorticity and starting at β=−0.14, the combined effects of the nonparallel flow effects and positive free-stream vorticity on the critical Reynolds number first decreases as β becomes more positive, reaches a minimum, and then increases again. Similarly, for negative free-stream vorticity, the effect on the critical Reynolds number first decreases as β becomes more positive, reaches a minimum value, and then increases to an asymptotic value. At a given β, the critical Reynolds number increases as the free-stream vorticity parameter becomes more positive. A limited amount of computations for flat plate shows that the transition Reynolds number, as determined from Smith’s e9 method, is strongly affected by free-stream vorticity.
Second-order slip effects in Poiseuille flow
Authors: Lang H.
Published: March 2003

Plane Poiseuille flow of a rarefied gas was studied in the presence of both a pressure and a temperature gradient under near continuum conditions. Calculations are performed for general gas–gas and gas–surface interactions of the molecules. The second-order slip and the phenomenological coefficients of the symmetric Onsager matrix were explicitly calculated by variational techniques. The slip velocity and the contributions of the Knudsen layer to mass and heat flows are described by a second symmetric matrix.
Propagation of unstable waves in a random medium: Diffusive and nondiffusive effects
Authors: Coste Jean , Peyraud Jean
Published: March 2003

The propagation of unstable wavepackets (or modes) in a one-dimensional fluid is studied in the presence of space–time dependent fluctuations. It is shown that the fluctuations have two effects: They diffuse the modes in k space and they produce, through a short scale average, a renormalization of their growth rate. In a WKB approximation the evolution of the unstable spectrum is governed by equations which generalize the usual diffusion equation.
Nonlinear harmonic generation of ion-acoustic waves with dispersion
Authors: Buzzi J. M. , Hirshfield J. L.
Published: March 2003

The observation of a dispersive effect on the nonlinear generation of ion-acoustic wave harmonics is reported. This effect is a spatial beat modulation of the second harmonic with a beating length L given by the dispersion: L=2π/[K (2ω)−2K (ω)].
Ion-acoustic waves in large radio-frequency electric fields
Authors: Lee A. , Jones W. D. , Gleman S. M. , Doucet H. J.
Published: March 2003

The propagation of ion-acoustic waves in high frequency fields is experimentally studied. The resulting phase-velocity decrease and enhanced damping are observed for radio-frequency field amplitudes up to αe≃0.5, where αe=eE/(meωovc) is the normalized amplitude. Good agreement with the theory is found.
Resistive instabilities in a tokamak
Authors: Glasser A. H. , Greene J. M. , Johnson J. L.
Published: March 2003

Application of resistive instability theory shows that toroidal effects can stabilize the tearing mode in devices like the Princeton Large Torus. Contraction of the current channel is destabilizing. Finite fluid compressibility is crucial to this phenomenon.
Stability and spectra of the bumpy ϑ pinch
Authors: Cayton Thomas E. , Vahala George
Published: March 2003

Finite wavelength modes in the bumpy ϑ pinch are examined by performing perturbation expansions in the small bumpiness on the equations of ideal magnetohydrodynamics. The unstable modes are transverse and compressible. The evolution of two unstable classes of modes from a single unstable class is followed numerically as the plasma β is varied.
Effect of anisotropy and rotation on turbulence production
Authors: Ferziger Joel H. , Shaanan Shlomo
Published: March 2003

It is shown that the mechanism of turbulence production is one which requires anisotropy and simultaneously increases the anisotropy. The maximum production rate occurs when the mean flow corresponds to irrotational strain and rotation inhibits the production process.
High frequency wall-pressure fluctuations in turbulent boundary layers
Authors: Bull M. K. , Thomas A. S. W.
Published: March 2003

Directly comparable spectral measurements with piezoelectric and pinhole-microphone transducers show pinhole measurements to be significantly in error. The increase in measured rms pressure with reduction of transducer size is not nearly as dramatic as previous work has suggested.
Millikan’s argument at moderately large Reynolds number
Authors: Afzal Noor
Published: March 2003

Millikan’s overlap argument is extended to estimate the effect of moderately large Reynolds number on fully developed turbulent pipe and channel flows. The only assumption needed is that regarding the order of the higher-order effects.
Beam trapping subsequent to the parametric pump depletion saturation of a beam-plasma instability
Authors: Jones R. , Carr W. , Seidl M.
Published: March 2003

Large amplitude wave fields can stabilize by parametric decay, but the particle distribution that drives them cannot. In a beam-plasma system, it is shown that the beam traps in the potential of slower grown modes having phase velocity closer to the beam velocity.
Axisymmetric surface waves in viscous swirling flow
Authors: Shen M. C.
Published: March 2003

A nonlinear asymptotic theory is developed for the study of surface waves in a rotating viscous fluid with a cylindrical air core, and the mathematical model considered is relevant to phenomena of engineering and geophysical interest. The theory yields an asymptotic equation governing the evolution of axisymmetric waves on the cylindrical free surface of the fluid, and also a stability criterion for the wave motion.
Refraction of plane Rossby waves
Authors: Scott Wayman E.
Published: March 2003

A plane Rossby wave, propagating in an incompressible liquid of density ρ1, is incident upon the plane interface defining another incompressible liquid of density ρ2. The refraction of the wave is studied, and the results are as interesting as for the case of reflection from a plane wall. In particular, the incident and refracted wavenumber vectors, and the incident and reflected energy fluxes, satisfy the optical law of reflection; and the reflected and refracted energy fluxes are colinear but opposite directed. Most interesting of all is that, at normal incidence, there is total reflection.
Prediction of the intermittent turbulent wake of a heated cylinder
Authors: Libby Paul A.
Published: March 2003

An analysis is presented of the velocity and temperature characteristics in the turbulent wake of a heated cylinder with intermittency taken into account. Using the usual eddy transport assumption, the unconditioned velocity characteristics in the far-wake are developed systematically and are then used in the calculation of the intermittency and of the conditioned streamwise velocities, i.e., the average velocities within the turbulent fluid alone. It is shown that if intermittency is taken into account, the usual model for the dissipation in the conservation equation for turbulent kinetic energy must be modified. The unconditioned and conditioned mean temperature and temperature intensity are described. Comparison is made with available experimental data.
Wave propagation in a binary gas mixture as described by kinetic models of the Boltzmann equations
Authors: Greene David E.
Published: March 2003

The initial-value problem defined by the linear one-dimensional Oppenheim model, which qualitatively describes wave propagation in a binary gas mixture and which is representative of other kinetic models, is examined. An asymptotic study of the dispersion relation and its analytic continuation is carried out to determine the structure of the solution.
Generalized electrolytes
Authors: Cohn Jack
Published: March 2003

A previous formulation for finding the pair distribution function for arbitrary dilute homogeneous systems is modified to apply to dilute systems composed of equal numbers of oppositely charged particles. The charges, however, are generalized in that they can exert forces on each other that need not be Coulombic. The formalism is applied to a dilute strong electrolyte where the pair-potential differs slightly from the Coulomb case. A closed form solution is found and activity coefficients are calculated for such dilute solutions. The resulting non square-root limiting law is exhibited.
Parametric instabilities in density modulated relativistic electron beam plasma interaction
Authors: Basu Bamandas , Taussig R. T.
Published: March 2003

Parametric coupling between negative energy beam synchronous modes and positive energy plasma oscillation modes of a uniform beam-plasma system, due to the presence of sinusoidal density modulation in the monoenergetic, relativistic electron beam, have been theoretically investigated on the basis of linearized Vlasov–Poisson equations using a multiple-time-scale perturbation theoretical approach. It has been found that, for a given beam-to-plasma density ratio, there exists an upper limit to the initial beam energy for which the instabilities can be excited. Within the allowed range, maximum linear growth rate exhibits a minimum as the beam energy increases from its nonrelativistic value. To determine the effectiveness of the parametric interaction process, feedback effects of the instabilities on the beam-plasma distribution functions have also been considered and estimates of energy transfers have been made. For typical parameters, the beam is found to lose about 15% of its initial kinetic energy during the ’’hydrodynamic’’ stage and the time required is about 4.72 nsec.
Linear parametric instabilities at high-pump powers
Authors: Roderick N. F.
Published: March 2003

The linear parametric decay and oscillating two-stream instabilities have been studied at high-pump power for perturbations propagating oblique to the pump field. The electrostatic Vlasov–Poisson system for a homogeneous two-component plasma has been solved numerically to investigate the high-frequency branches of these instabilities. Results show that the maximum growth rate of the oscillating two-stream instability occurs oblique to the pump field for power levels above a critical value. The angular dependence of this growth rate is dependent on the electron-ion mass ratio. For these cases, the maximum value of the oscillating two-stream growth rate remains constant for increasing power above the critical level while the direction of maximum growth rate becomes more oblique to the pump field and the volume in k space of the unstable region increases. The maximum value of the parametric decay growth rate increases with increasing power level and occurs parallel to the pump field for all values of pump intensity investigated.
Electrostatic parametric instabilities arising from relativistic electron mass oscillations
Authors: Lin A. T. , Tsintsadze N. L.
Published: March 2003

The relativistic oscillation of the electron mass in very intense high frequency fields can give rise to parametric instabilities. These instabilities, whose growth rates do not depend on the electron-to-ion mass ratio, will surpass the oscillating two-stream instability and become the dominant process when the laser beam produces electron mass variations of the order of (me/Mi)1/3 or about 6.5×10−2 for deuterium. This corresponds to oscillating energies of a few ten keV. The linear and nonlinear stages of these instabilities are investigated through analytic methods and computer simulations.
Two new proofs of the test particle superposition principle of plasma kinetic theory
Authors: Krommes John A.
Published: March 2003

The test particle superposition principle of plasma kinetic theory is discussed in relation to the recent theory of two-time fluctuations in plasma given by Williams and Oberman. Both a new deductive and a new inductive proof of the principle are presented; the deductive approach appears here for the first time in the literature. The fundamental observation is that two-time expectations of one-body operators are determined completely in terms of the (x,v) phase space density autocorrelation, which to lowest order in the discreteness parameter obeys the linearized Vlasov equation with singular initial condition. For the deductive proof, this equation is solved formally using time-ordered operators, and the solution is then re-arranged into the superposition principle. The inductive proof is simpler than Rostoker’s although similar in some ways; it differs in that first-order equations for pair correlation functions need not be invoked. It is pointed out that the superposition principle is also applicable to the short-time theory of neutral fluids.
Neoclassical transport theory of a multispecies plasma in the low collision frequency regime
Authors: Hirshman S. P. , Sigmar D. J. , Clarke J. F.
Published: March 2003

A comprehensive neoclassical transport theory for a multispecies plasma in the low collision frequency banana regime is developed. A recently developed approximate collision operator is used to analytically calculate the transport coefficients in a nonisothermal, finite beta plasma for arbitrary mass ratios and all values of the aspect ratio. The physical effects of collisions in the large and small aspect ratio limits are discussed in detail. The bootstrap current is expressed in terms of the parallel friction forces, and an explicit calculation of the current is performed for the case of two ion species in which one is a heavy impurity ion.
High-beta effects and anomalous diffusion in plasmas expanding into magnetic fields
Authors: Koopman David W.
Published: March 2003

A metallic laser-produced plasma is allowed to expand transversely into an applied magnetic field, under conditions where the typical ion cyclotron radius is much larger, and the electron cyclotron radius much smaller, than the experimental dimensions. A stationary background plasma may also be present. Initially, the flow energy density exceeds B20/8π. Magnetic coil probes, Langmuir probes, and microwave diagnostics are used to study the plasma–field interaction. Field compression at the leading edge and field exclusion within the expanding plasma are seen. The diagnostic measurements and comparison with a theoretical model demonstrate plasma turbulence and anomalously high diffusion of field into the expanding plasma.
Bifurcated stability of a family of stellarator equilibria
Authors: Kappraff Jay M.
Published: March 2003

The ideal magnetohydrodynamic free boundary model is employed to study the bifurcation of a family of helically symmetric equilibria. The equilibria correspond to an L=2 stellarator. The plasma column has finite length and is surrounded by a vacuum region enclosed by an outer conductor. The stability analysis is based on a determination of the sign of the second variation of the potential energy. The column length is chosen to avoid ’’kink instabilities’’ for some range of the angular wavenumber, m, for which the theory applies. At a critical value of beta, a marginally stable state of principally m=1 long wavelength modes is determined and serves as the starting point of bifurcation. Neighboring bifurcated equilibria are found to be stable when the conducting wall is within 1.15 plasma column radii of the plasma vacuum interface. This position was not sufficient to stabilize the original equilibria.
Anomalous damping of ion-acoustic waves in the presence of strong Langmuir turbulence
Authors: Yu M. Y. , Spatschek K. H.
Published: March 2003

The damping of ion-acoustic waves in a plasma with a high level of Langmuir turbulence is investigated. The dependence of the damping rate on the turbulent energy density is given analytically.
Endloss from a slender high beta plasma column contained in a linear solenoid
Authors: Steinhauer Loren C.
Published: March 2003

A model is presented to simulate endloss from a high beta plasma contained laterally in a straight solenoid. For slender plasma columns, the plasma lifetime depends on both the acoustic transit time (time for a sound wave to traverse one-half of the plasma length), and the characteristic radial diffusion time (diffusion of plasma across the magnetic field). In the limit of strong diffusion (which occurs for narrow high beta plasma columns), the plasma lifetime equals the hybrid lifetime which is proportional to the geometric mean of the acoustic and diffusion times. This predicted behavior stands in marked contrast with conventional endloss theories which have confinement time proportional to acoustic time alone. It is also shown that the endloss process may be accelerated considerably if the ratio of plasma radius to magnet radius is not small, due to inverse mirroring effects in the streaming plasma.
Net effect of pressure gradient on a sphere
Authors: Soo S. L.
Published: March 2003

Pressure gradient in a fluid does not exert a net force on a particle in it even at large flow Reynolds number. This pressure gradient does not include the effect of gravity or other potential field.
Hollow electron column from an equipotential cathode
Authors: Driscoll C. F. , Malmberg J. H.
Published: March 2003

An unneutralized, magnetically confined electron column thermally emitted from an equipotential cathode is considered. An analytic, scaled solution of the radial Poisson’s equation indicates that the column is hollow and less than √8 central Debye lengths in radius.
Boundary value problem involving a simple Fokker–Planck equation
Authors: Stein Daniel , Bernstein Ira B.
Published: March 2003

The Fokker–Planck equation μ∂f/∂x=α∂/∂μ [(1−μ2) ∂f/∂μ], describing particles undergoing elastic small angle collisions with infinitely massive scatterers in a slab, is solved in a variety of limits by analytic and numerical means.
Cross-field energy transport by plasma waves
Authors: Rosenbluth Marshall N. , Liu C. S.
Published: March 2003

Energy transport across a magnetic field by plasma and ion waves is shown to be an important process even in thermal equilibrium, because their propagation is uninhibited by the magnetic field and their long mean free path.
Growth of thermal constrictions in a weakly ionized gas discharge in helium
Authors: Jaeger E. F. , Oster L. , Phelps A. V.
Published: March 2003

Neutral and charged particle densities, radial velocities, and temperatures are calculated as functions of time for cylindrical discharges in helium at pressures from 1 to 1000 Torr and a radius of 1 cm. Ionization, recombination, ambipolar diffusion, specific heat of the neutrals, and variation of gas pressure in space and time are included. Ionization of excited states, energy loss by radiation, and space charge sheaths are neglected. Under most conditions, increased ionization in regions of decreased gas density causes a constriction of the discharge which is accentuated at high pressures and high recombination rates. Greater circuit resistance stabilizes the discharge. At low pressures, the electron density profile expands. Initial steep gradients in electron density cause constrictions off axis.
Parametric excitation of ion density fluctuations in the relativistic beam-plasma interaction
Authors: Schamel H. , Lee Y. C. , Morales G. J.
Published: March 2003

When a weak and cold relativistic electron beam interacts with a dense plasma, it generates a nearly monochromatic wave of high intensity which triggers the growth of parametric instabilities. The present work investigates this process by using a hybrid technique in which the fully relativistic motion of the beam particles is treated numerically, while the behavior of the background plasma and the parametrically excited waves is treated analytically through appropriate linear dielectric functions. It is found that the self-consistent excitation of large ion density fluctuations leads to the decoupling of the beam from the background plasma, hence limiting the amount of energy that can be extracted from the beam. By adjusting the various parameters of the problem it is found that up to 23% of the initial beam energy can be transferred to the electrostatic waves. The large ion fluctuations responsible for decoupling the beam correspond to purely growing modes which exhibit secular growth in time.
Parametric instabilities in plasma with sinusoidal density modulation
Authors: Nicholson Dwight R.
Published: March 2003

Parametric instabilities in the presence of sinusoidal plasma density modulation are considered analytically and by numerical integration of the coupled mode equations. The density modulation tends to reduce temporal and spatial growth rates. If there is a linear density gradient in addition to the density modulation, the usual convective saturation exists for small modulation; however, above a certain threshold modulation, the convective saturation is replaced by absolute growth. This result is in qualitative agreement with earlier work on plasma with linear density gradient plus turbulence.
Atomic and ionic beam source utilizing pulsed laser blow off
Authors: Utterback N. G. , Tang S. P. , Friichtenicht J. F.
Published: March 2003

When a pulsed laser is focused on a material surface and sufficient energy is suddenly deposited in that surface, local vaporization occurs and surface material ’’blows off.’’ If this occurs in a vacuum, intense beams of even refractory materials can be formed by collimating at distances where the expanding gas bubble has become collisionless. A simple model is presented which predicts experimentally observed particle velocity distributions and angular distributions. Of particular significance is the implication from these distributions that the equilibrium temperature of the initial dense gas bubble is much lower than a cursory on-axis velocity measurement might imply. This is critical in evaluating effects due to beam particle internal energy. Laser parameters and experimental configurations determine bubble temperature and hence internal energy and in the extreme whether atoms or ions (plasma) are produced; particle velocities may be effectively varied by choosing appropriate angles and arrival times.
Delayed emission excited by a high power microwave pulse
Authors: Sasaki S. , Ohyabu N. , Kaneko O. , Kawashima N.
Published: March 2003

An experiment is performed to study the interaction of a high power microwave pulse with a magnetized dense plasma. A delayed emission appears after the complete termination of a pumping microwave pulse when the frequency of the pumping wave is equal to the harmonics of the cyclotron frequency and is near the plasma frequency. Two types of delayed emission (types I, II) are observed, depending on the experimental conditions. The type I delayed emission is characterized by the frequency spectrum with sharp peaks at cyclotron harmonics (mfce:m=1,2...), type II with broad peaks between (m+1/2) fce and (m+1) fce. The main properties of these phenomena are explained in terms of anomalous power absorption at cyclotron harmonic resonances and excitation of electron plasma waves by an anisotropic electron velocity distribution. Each type of delayed emission can be triggered artificially by a sudden decrease in cold background plasma density and is suppressed by an increase in cold plasma.
Studies of the merging of vortices
Authors: Lo Robert K. C. , Ting Lu
Published: March 2003

Finite difference equations of the two-dimensional unsteady incompressible Navier Stokes equations are constructed to study the merging of vortices. Comparison with asymptotic solutions show that the latter remain as good approximations even when the viscous cores of the vortices overlap each other.
Theoretical analysis of convective instability of a growing horizontal thermal boundary layer
Authors: Robinson J. L.
Published: March 2003

An analytic description of the development of boundary layer and interface instabilities past the initial linear stage is given. A problem with an analytic approach is that whereas the quasi-static approximation, implying the fast growth of perturbations, is made in order to freeze in the time-dependent basic temperature profile, the nonlinear analysis of Stuart and Watson is valid only for small growth rates. A model in which these two assumptions are combined does, however, successfully describe a number of features of the nonlinear behavior of the system. The dominant role of the fastest growing periodic perturbation, including a damping of other disturbances and a short-lived equilibration, together with a breakaway of plumes from the outer boundaries of the active region is indicated. The analysis is made possible by the use of a simple approximation to the velocity for the linear problem. This approximation is shown to give a good estimate of the linear growth rates, as well as permitting a straightforward treatment of nonlinear effects.
Nonlinear stability of heated parallel flows
Authors: Shulze R. C. , Carmi S.
Published: March 2003

Stability results are obtained for parallel flows driven by moving boundaries and pressure gradients and subjected to given temperature fields. The temperature profiles considered are obtained by prescribing the heat flux through the boundaries of the flow domain or by frictionally generating heat internally via a temperature dependent viscosity. An exact solution is obtained for the frictionally heated basic flow driven by a pressure gradient. Results show that internal heat generation reduces the region of certain stability while the pressure gradient has the opposite effect of increasing it.
Dissipative universal instability due to trapped electrons in toroidal systems and anomalous diffusion
Authors: Liu C. S. , Rosenbluth Marshall N. , Tang W. M.
Published: March 2003

Drift wave instabilities in toroidal systems arising from collisions of trapped electrons are analyzed including the effects of a sheared magnetic field. A maximum bound on the turbulent transport is estimated, and the theoretical predictions compared with experimental results from the Princeton FM-1 spherator.
Plasma confinement by localized cusps
Authors: Leung K. N. , Hershkowitz Noah , MacKenzie K. R.
Published: March 2003

Details of the confinement of primary ionizing electrons and plasma by multidipole fields are given. It is shown that primary electrons are very efficiently confined by the cusps, with leakage half-widths given by the electron gyroradii. Plasma is confined much more weakly. Leakage half-widths of helium, argon, and xenon plasmas are found to be twice the hydrid gyroradii. Plasma noise in the neighborhood of the hybrid frequency is observed in the cusp regions.
One-dimensional numerical study of charged particle trajectories in turbulent electrostatic wave fields
Authors: Graham Kristine N. , Fejer J. A.
Published: March 2003

The motion of a charged particle in strong turbulent wave fields is studied numerically over many trapping periods. Transitions between three velocity states, namely the trapped state, and the states of high and low velocity, characterize the motion.
Line stretching in turbulence
Authors: Dhar Deepak
Published: March 2003

An elementary proof is given that in homogeneous isotropic turbulence fluid particles on the average drift apart.