bluuebunny/crossref_metadata_2025 huggingface dataset:
The squared eigenstates of the sine–Gordon eigenvalue problem
Authors: Kaup D. J.
Published: March 2003

An analysis of the squared sine–Gordon eigenvalue problem in laboratory coordinates is presented. It is shown that unlike the unsquared laboratory coordinate eigenvalue problem, the squared laboratory coordinate eigenvalue problem may be cast into the form of a standard eigenvalue problem, wherein an eigenvalue independent operator operating on an eigenfunction generates the eigenvalue. With this form, it becomes rather elementary to obtain the squared-eigenfunction expansion of the sine–Gordon potentials as well as to demonstrate closure.
On embedded eigenvalues for the one-dimensional Schrödinger equation
Authors: Hoffmann-Ostenhof Maria , Hoffmann-Ostenhof Thomas
Published: March 2003

We consider the one-dimensional Schrödinger equation (−d2/dx2+V(x)−λ)u(x)=0 for x≥0, with Dirichlet boundary conditions, where λ≥0 and V(x) is real valued, bounded, and vanishes for x→∞. Conditions on V for the absence of non-negative eigenvalues are derived. We show for instance: Let λ>0, u≠0. If for some c>0, 0<μc+>0, with α ∈ (0,1] for λ>0, respectively, α ∈ (0,2] for λ=0.
Null infinity from a quasi-Newtonian view
Authors: Winicour Jeffrey
Published: March 2003

A scheme is elaborated which generates unique characteristic initial value data for a general relativistic fluid in terms of initial value data for a Newtonian fluid. The chief ingredient is the demand that the evolution of the general relativistic fluid yield the evolution of the Newtonian fluid as a parameter λ, corresponding to 1/c, goes to zero. The resulting gravitational null data is examined in detail to the first three nontrivial orders in λ. To this order, the data is asymptotically flat at future null infinity and appears to properly incorporate an outgoing radiation condition. The implications of these results for the calculation of gravitational radiation from quasi-Newtonian systems is discussed.
Inverse problem of image processing
Authors: Szu Harold H.
Published: March 2003

A Gel’fand–Levitan inverse problem of image processing is used to determine an optimum trade-off potential U(f) or V(f) from the knowledge of the restored object Q(f) or the output transfer function Ψ(f) and the design knowledge of the optical transfer function (OTF) S(f). Analytic examples and exact solutions are given for the coherent and incoherent image restorations. The minimum mean-square image spread (MMIS) filter is found to yield an identical minimum mean square estimation-error (MMSE) filter of Wiener in the special case, similar to the visual MTF or contrast sensitivity function, peaked at the middle band of spatial frequency channels. The trade-off potential for the linear and noisy motion-blurred image restoration is obtained. By means of the Gel’fand–Levitan inverse transform technique for the reference potential, the design of the energy constrained MMIS filter follows. Lastly, both the direct and inverse problems of incoherent imaging are simultaneously solved with a specific example of the dc incision, namely the central dark field method of Abbe and Zernike. It illustrates the main concept that a useful and efficient new approach of image processing requires a systematical design of both the imaging OTF and image restoration filters under noise.
On some general properties of the point spectrum of three particles moving in one dimension
Authors: Perez J. Fernando , Malta C. P. , Coutinho F. A. B.
Published: March 2003

The eigenstates of three particles moving in one dimension are classified according to the S3 plus parity group. The ordering of the ground state S3 band is given for a fairly general class of potentials. Sufficient conditions are given both for existence and nonexistence of bound states of a given symmetry.
On the classical part of the mean field dynamics for quantum lattice systems in grand canonical representations
Authors: Rieckers Alfred
Published: March 2003

For a class of discrete mean field models the limiting dynamics is investigated in the representations of generalized grand canonical states. It is demonstrated that for a certain form of spontaneous symmetry breakdown the W*-automorphism dynamics exhibits a uniquely determined nontrivial classical part, which is essential for the explanation of macroscopic quantum phenomena.
The direct linearization of a class of nonlinear evolution equations
Authors: Santini P. M. , Ablowitz M. J. , Fokas A. S.
Published: March 2003

The paper deals with the direct linearization, an approach used to generate particular solutions of the partial differential equations that can be solved through the inverse scattering transform. Linear integral equations are presented which enable one to find broad classes of solutions to certain nonlinear evolution equations in 1+1 and 2+1 dimensions.
On the center-of-mass motion of geometrically confined classical particles
Authors: Dullemond C.
Published: March 2003

By means of group-theoretical methods based on O(3,2) a description of center-of-mass motion is given of a set of harmonically oscillating classical particles which can attain relativistic velocities. The limitation ‖v‖<c on the velocity leads to a limitation ‖r‖<R on the amplitude, where R is related to the universal oscillator frequency ω by R=cω−1. It turns out that the center-of-mass carries out a harmonic oscillation with the same frequency ω and the same limitations, and that conditions can be formulated for the set of particles to be in its ‘‘rest system.’’ The method can be applied to hadrons considered as bags containing harmonically oscillating classical quarks.
Homogeneous canonical formulation of the nonrelativistic hydrogen atom
Authors: Grinberg Horacio , Marañon Julio , Vucetich Hector
Published: March 2003

The homogeneous canonical formulation is applied to the Hamiltonian of the nonrelativistic hydrogen atom. Its connection with the isotropic harmonic oscillator in a four-dimensional Riemann space leads to the quantum analog of the Kepler problem.
Cylindrically symmetric solitary wave solutions to the Einstein equations
Authors: Letelier P. S.
Published: March 2003

The integration of the Einstein equations for cylindrically symmetric solitary waves is reduced to a single quadrature when the ‘‘seed’’ solution is diagonal. Also in this case, explicit formulas that show the solitary wave character of the one- and two-soliton solutions are studied. A particular case of n-soliton solution is exhibited. Two theorems that show how to construct new solutions from known ones are presented.
From i ° to the 3+1 description of spatial infinity
Authors: Ashtekar Abhay , Magnon Anne
Published: March 2003

By carrying out a 3+1 decomposition of the spi framework, the expressions of the conserved quantities, defined at i ° in terms of the Weyl curvature, are recast in terms of the initial data of the physical space-time. In particular, the analysis brings out the supertranslation ambiguities in the usual 3+1 definitions of angular momentum and clarifies, within the 3+1 framework, the meaning of the stronger boundary condition needed to remove these ambiguities. The discussion is so arranged that only a minimal acquaintance with the spi framework is necessary to appreciate these issues.
Finite energy electric monopoles in an extended theory of gravitation
Authors: Kunstatter G.
Published: March 2003

We present a one-parameter family of extended Einstein–Maxwell Lagrangians in which an antisymmetric tensor field is nonlinearly coupled to both the gravitational and electromagnetic fields. We show that for arbitrary, positive values of the relevant parameter, the theory admits exact, static spherically symmetric solutions with everywhere finite electric field density and energy density. Asymptotically, the solutions are indistinguishable from the Reissner–Nordstrom solution in general relativity. In addition, we show that a corrected form of the exact solution in the nonsymmetric Kaluza–Klein theory presented in an earlier paper provides a special case of the family of solutions described above.
Kinetic potentials in quantum mechanics
Authors: Hall Richard L.
Published: March 2003

Suppose that the Hamiltonian H=−Δ+vf(r) represents the energy of a particle which moves in an attractive central potential and obeys nonrelativistic quantum mechanics. The discrete eigenvalues Enl=Fnl(v) of H may be expressed as a Legendre transformation Fnl(v)=mins≳0(s+vf̄nl(s)), n=1,2,3,..., l=0,1,2,..., where the ‘‘kinetic potentials’’ f̄nl(s) associated with f(r) are defined by f̄nl(s) =infDnl supψ∈Dnl, ∥ψ∥=1 ∫ ψ(r) f ([ψ,−Δψ)/s]1/2r)ψ(r)d3r, and Dnl is an n-dimensional subspace of L2(R3) labeled by Ylm(θ,φ), m=0, and contained in the domain 𝒟(H) of H. If the potential has the form f(r)=∑Ni=1 g(i)( f(i)(r)) then in many interesting cases it turns out that the corresponding kinetic potentials can be closely approximated by ∑Ni=1 g(i)( f̄nl(i)(s)). This nice behavior of the kinetic potentials leads to a constructive global approximation theory for Schrödinger eigenvalues. As an illustration, detailed recipes are provided for arbitrary linear combinations of power-law potentials and the log potential. For the linear plus Coulomb potential and the quartic anharmonic oscillator the approximate eigenvalues are compared to accurate values found by numerical integration.
Current sheet observations in a small theta pinch
Authors: Yarborough W. W. , Barach J. P.
Published: March 2003

Magnetic field coil measurements are taken in a small theta pinch operated in helium with a capacitor bank energy of 1500 J. The divided pinch coil was connected series antiparallel so that a cusped magnetic field was produced. Plots of current density, magnetic field, and J×B force density are obtained and interpreted via a generalized Ohm’s law. A substantial magnetic field overshoot occurs and is explained in terms of the plasma kinetic energy producing paramagnetic currents via the motional electromotive force. Force density plots of the pinch chamber exhibit a surface of shear in the magnetic force on the plasma which is unusual and suggestive.
Laminar flow behavior under slip−boundary conditions
Authors: Lugt Hans J. , Ohring Samuel
Published: March 2003

Laminar flows past bodies under slip−boundary conditions are investigated theoretically within the framework of the Navier−Stokes equations. The numerical solutions to the equations are obtained using newly developed computer programs for incompressible fluid flows past elliptic cylinders and oblate spheroids. The influence of slippage on flow separation, vorticity, and vortex shedding, as well as on the force coefficients, is discussed.
Two−dimensional hypersonic magnetohydrodynamic flow
Authors: Smith Roger
Published: March 2003

The problem of the two−dimensional, inviscid, infinitely−conducting hypersonic flow past nonconducting bodies, in the presence of near−aligned magnetic fields, is analyzed, the problem being solved by transforming from the physical plane to the stream function, magnetic stream function plane. The shock shapes and lift and drag coefficients are determined for some particular examples.
Dynamics of an ensemble of plane waves in nonlinear dispersive media
Authors: Hasegawa Akira
Published: March 2003

A statistical description of the dynamics of an ensemble of plane waves in nonlinear and strongly dispersive media is derived. A modulational instability, a second sound wave, and a localized group of waves are obtained from the description. The results apply to the dynamics of many optical waves in strongly dispersive dielectric media with the Kerr effect as well as plasma waves for which decays or the wave particle interactions are prohibited.
Interpretation of soliton formation and parametric instabilities
Authors: Manheimer Wallace M. , Papadopoulos K.
Published: March 2003

It is shown that soliton formation and the resulting plasma heating are nothing more than the description in configuration space of well-known parametric processes and quasi−linear theory.
Asymptotic method for planetary waves
Authors: Shen M. C.
Published: March 2003

An asymptotic method based upon the ray theory is extended to the study of planetary waves in a fluid of variable depth over the rotating earth. An asymptotic solution involving a phase function and an amplitude function is constructed. Application of the method to the study of wave resonance of a compressible fluid in a rotating spherical shell is considered.
Mode conversion of toroidal Alfvén waves
Authors: Swanson D. G.
Published: March 2003

The effects of electron inertia and mode conversion on the propagation of Alfvén waves in toroidal magnetic fields are considered. When electron inertia is neglected, two singularities occur in the equation determining the radial and vertical wavefield dependencies. The inclusion of electron inertia resolves one singularity and is shown to lead to linear mode conversion in either a cold electron or warm electron approximation. The Alfvén wave converts to an electrostatic wave which propagates back toward the inside of the torus in the cold electron approximation and through the ion cyclotron resonance toward the outside edge of the torus with warm electrons via the electrostatic ion cyclotron wave. Without damping, both lead to a discrete spectrum of eigenfrequencies, but with only weak damping, the electrostatic waves are absorbed and lead to a continuous spectrum of frequencies. The nature of the damping terms gives an indication of the type of energy absorption, whether Landau damping of electrons or ions or ion cyclotron damping. The second singularity in the equations is found to have only regular solutions and does not lead to mode conversion.
Two-dimensional magnetohydrodynamic simulation of toroidal pinches
Authors: Lui H. C. , Chu C. K.
Published: March 2003

Equations of dissipative magnetohydrodynamics are solved numerically for an axisymmetric toroidal pinch. A circular cross-section screw pinch is treated, although the method is general and extendable to other geometries. Calculated results are compared with experimental results of the SP-1 machine at Jutphaas. Very good agreement is attained, indicating that on short time scales, magnetohydrodynamics gives a good representation of the physical phenomena.
Theory of plasma heating by nonlinear excitation of lower hybrid resonance
Authors: Hasegawa Akira , Chen Liu
Published: March 2003

A theory of plasma heating when the lower hybrid wave is parametrically excited by an electromagnetic pump at frequency ω0 close to the lower hybrid resonant frequency ωlh (i.e., ω0<√2ωlh) is presented. In this case, the excitation is made through electron nonlinear Landau damping. The saturation level is obtained using the cascading model and the heating rate is calculated. It is shown that the heating rate may be obtained without knowing the saturation spectrum of the excited turbulence. In particular, the heating rate of ions is given by νfε0E02/2, where νf≈1/16ωlh(ωpe/ω0)2 (E0/B0ve)2.
Anomalous transport properties associated with the lower-hybrid-drift instability
Authors: Davidson R. C. , Gladd N. T.
Published: March 2003

The linear stability behavior and anomalous transport properties associated with the lower-hybrid-drift instability are studied assuming flute-like perturbations with k⋅B0=0. Primary emphasis is placed on the low-drift-velocity regime with VE≲vThi (here, VE is the cross-field electron E×B drift velocity), which pertains to the late stages of implosion and the post-implosion phase of high-density pinch experiments. Nonlinear estimates of the instantaneous heating rates and rate of momentum transfer are made, and the results are studied numerically to determine the parametric dependence on VE/vThi and the level of turbulent field fluctuation energy ℰF. It is shown that the lower-hybrid-drift instability can result in substantial resistivity and plasma heating for VE≲vThi, as well as for the large-drift-velocity regime (VE≳vThi). For example, when Ti/Te≫1 and ω2pe/ω2ce≫1, the bound on anomalous resistivity for VE≲vThi is [nan]max≃4π√π/2(VE/vThi)2 ωLH/ω2ce, where ωLH = (ωciωce)1/2 is the lower-hybrid frequency. This large value of resistivity is consistent with observations made during the post-implosion phase of the ZT-1 experiment.
Evidence that the electrostatic ion cyclotron instability is saturated by ion heating
Authors: Kelley Michael C. , Bering Edgar A. , Mozer Forrest S.
Published: March 2003

Observations have been made of electric field oscillations near the local ion gyro frequency and of an intense beam of plasma ions at the edge of an auroral arc. The observations are in good agreement with ion heating as the saturation mechanism for electrostatic ion cyclotron waves.
Structure of electron fluid dynamical plane waves. Antiforce waves
Authors: Sanmann Everett E. , Fowler R. G.
Published: March 2003

The techniques of fluid dynamics are applied to the passage of ionizing waves counter to strong electric fields. The wave is considered to be characterized by a weak discontinuity at its front, and a solution for the wave speed and structure has been found. The structure of the ionizing wave divides into two distinct regions: (1) a sheath region at the wavefront where the electric field, temperature, and velocity first attain maximum values and then the electric field decreases to zero as the electrons reach the same velocity as the ions, and (2) a quasi-neutral region. The electrons possess a large temperature at the beginning of the quasi-neutral region and ionization continues to take place until the electrons cool below the ionizing temperature. The dependence of the velocity of the ionizing wave upon the applied electric field has been found to agree well with experiment.
Thermally generated magnetic fields in laser-driven compressions and explosions
Authors: Tidman D. A.
Published: March 2003

The evolution of thermally generated magnetic fields in a plasma undergoing a nearly spherically symmetric adiabatic compression or expansion is calculated. The analysis is applied to obtain approximate results for the development of magnetic fields in a laser-driven compression and explosion of a pellet of nuclear fuel. Localized sources such as those occurring at composition boundaries in structured pellets or at shock fronts give stronger fields than those deriving from smoothly distributed asymmetries. Although these fields may approach 107 G in the late stages of compression, this is not expected to present difficulties for the compression process. Assuming ignition of a nuclear explosion occurs, the sources become much stronger and values of ≈1010 G are obtained at tamper boundaries assuming a 20% departure from spherical symmetry during the explosion.
Three-dimensional guiding-center plasmas
Authors: Knorr Georg
Published: March 2003

A three-dimensional guiding-center plasma model is derived from the Vlasov equation using a method by Frieman, Davidson, and Langdon. In two dimensions the reduction of the description to configuration space occurs only for homogeneous magnetic fields. Macroscopic equations are derived for a homogeneous magnetic field and the stability of nonneutral plasmas is investigated. Sheets consisting of magnetic field lines and charged positively show unstable behavior if k∥/k⊥<a/cs, where a is the E×B drift and cs is the ion sound velocity. k∥ and k⊥ are the wavenumbers parallel and perpendicular to the magnetic field. Sheets with electron charges are stable if the phase velocity of the disturbance along B is smaller than the electron thermal velocity.
Plasma heating by relativistic electron beams. II. Return current interaction
Authors: Thode L. E. , Sudan R. N.
Published: March 2003

The combined interactions of the relativistic two-stream instability and return current driven Buneman/ion sound instability are investigated by numerical simulation for a beam-to-plasma density ratio ≈10−1 and γ=2−8. In this regime the evolution of the two-stream instability is relatively unaffected by the return current instability. The growth rate of the Buneman instability drops sharply when trapping of plasma electrons by the unstable Buneman waves occurs, but wave growth continues at a much reduced rate until other processes, e.g.,ion acceleration, wave scattering, and nonlinear Landau damping set in. Ions are heated by the return current and this heating is almost independent of the initial beam γ for constant return current. The bulk of the electron distribution is heated, whereas in the absence of a return current the two-stream instability primarily produces only energetic tails. The total plasma electron energy after several hundred plasma periods is proportional to the beam energy. The effective collision frequency of the plasma electrons due to microturbulence is typically 0.2?0.4 ωi, where ωi is the ion plasma frequency. In the strong turbulence created by the electron beam and the return current, the wave energy spectrum scales as ‖Ek‖2≈k−2.
Plasma turbulence measurements from forbidden transitions in argon and neon
Authors: Turner James M.
Published: March 2003

Possible forbidden transitions are suggested as sources of satellites for the study of plasma turbulence. These transitions are in argon and neon and have some advantages over previously used helium lines.
Laser target model
Authors: Colombant D. G. , Whitney K. G. , Tidman D. A. , Winsor N. K. , Davis J.
Published: March 2003

A numerical simulation model is described for the dense hot plasma produced in the interaction of a focused laser pulse with a target of moderate atomic weight. Specific results are given for the line and continuum x-ray emission, together with other parameters of the plasma, for the case of an aluminum target.
Burgers’ model with a renormalized Wiener–Hermite representation
Authors: Meecham W. C. , Iyer P. , Clever W. C.
Published: March 2003

The use of the Wiener–Hermite expansion for the turbulence problem is reviewed. The expansion is known to give good results for lower Reynolds’ number flows, up to a fluctuation Reynolds’ number of 20 using more recent time-dependent bases. The use and meaning of these bases is discussed. A new development in Wiener–Hermite expansion is used to calculate Burgers’ model: It is known that these expansions are not unique; by taking advantage of this arbitrariness, a renormalization is presented and used to improve the convergence of the expansion. The procedure involves calculation for turbulence using a time-dependent base for a short time. The calculation is then stopped and the resulting functions are adjusted in such a way as to minimize the non-Gaussian part of the energy, at the same time preserving the last value of the transfer function. Following this, the calculation is resumed using these new, adjusted values for the functions; then the process is repeated. For the first time it was possible to obtain the equilibrium form k−2, of the energy spectrum for Burgers’ model of turbulence. The calculation proceeds, holding the non-Gaussian part of the energy to but a few percent. Good results are obtained up to fluctuation Reynolds’ numbers of 100.
Finite-element analysis of compressible and incompressible viscous flow and heat transfer problems
Authors: Laskaris Trifon E.
Published: March 2003

There are numerous problems of two-dimensional viscous, compressible or incompressible steady-state flows where the governing hydrodynamic equations are difficult to solve even numerically due to their elliptic-hyperbolic character and the complex geometry of the flow configuration. For such problems, a finite-element numerical technique has been developed whereby the steady-state hydrodynamic equations and the associated boundary conditions are solved taking into full account the nonlinear convective terms, viscous terms, heat conduction terms, and variable fluid properties. The numerical technique is based upon a general formulation for the system of hydrodynamic equations making use of the method of weighted residuals, applied over discrete, distorted finite elements of the flow domain where the unknown fluid variables are expressed continuously in terms of polynomial approximating functions and nodal parameters. This process results in a set of nonlinear algebraic equations for the nodal parameters which are solved iteratively by using a multi-dimensional Newton–Raphson scheme. To assess its accuracy, the method is applied to problems of compressible and incompressible viscous flow and heat transfer in diverging channels with plane walls, and also to a problem of normal shock wave in one-dimensional flow. The results in all cases are in satisfactory agreement with existing analytical solutions and experimental data. Furthermore, the numerical scheme appears to be stable.
Cross-hatching: A consequence of differential deformation of a viscous solid
Authors: Stock Hans W.
Published: March 2003

The hypothesis, proposed by Probstein and Gold, that cross-hatching results from the differential deformation of an inelastic material at its surface, has been used in this analysis. Wall pressure and wall shear stress perturbations leading to the deformation were calculated with the linearized small perturbation theory. The supersonic boundary layer was composed of an inviscid outer layer and a viscous sublayer. Both laminar and turbulent mean velocity and Mach number profiles were used in the calculation. In contrast to the work of Probstein and Gold the viscous sublayer was included and wall pressure perturbations were also considered. The essential result is the prediction of the pattern cant angle, which was not possible with the inviscid analysis. The theory qualitatively confirms the experimentally observed features of cross-hatching, similarly seen by Probstein and Gold. For instance, for cross-hatching to occur, the boundary layer must be supersonic and turbulent, whilst the inelastic body material must be of the Maxwell type. Theory and experiment also show that the pattern is charcterized by a cant angle equal to the local Mach angle, by a wavelength inversely proportional to the static pressure and directly proportional to the viscosity of the material.
Motion of a plasma column in a perturbing magnetic field
Authors: Miller G.
Published: March 2003

The motion of a plasma column acted upon by a small external magnetic field is calculated using the sharp-boundary ideal magnetohydrodynamic model. The natural oscillation frequencies of the system are obtained. For the theta pinch, simple approximate formulas useful in considering feedback and dynamic stabilization schemes are derived.
Space-time structure of ion beam-plasma turbulence
Authors: Doveil F. , Grésillon D.
Published: March 2003

The turbulence excited by an ion beam penetrating an unmagnetized plasma is investigated. One-dimensional linear kinetic theory predicts the ion acoustic mode to be driven unstable when the beam velocity vb ranges from cs to 2cs. Numerical calculations are reported for the three dimensional problem, in which attention is given to unstable waves. The direction of propagation, the phase velocities, and the growth rate contours in the (k∥, k⊥) plane, are given as a function of vb. This instability is created in a double plasma device, and investigated by means of space and time correlations. Turbulence is excited, consisting of modes propagating at a phase velocity which agrees with theory. As vb increases, an abrupt transition from one-dimensional to three-dimensional structure occurs as expected.
Anomalous electron transport and lower-hybrid wave damping
Authors: Chu C. , Dawson J. M. , Okuda H.
Published: March 2003

The transport of electrons across magnetic fields was investigated by two-dimensional computer experiments. Under the modest condition ωce≈ωpe, which occurs in many laboratory plasmas and fusion devices, it is found that the electron heat and momentum transport rates are much enhanced above the classical collisional values even for plasma very close thermal equilibrium. The enhancement is due to electron turbulent motion in the fields of thermally excited lower hybrid waves. Nonthermal plasmas could show an even larger degree of enhanced transport. Employing a fluid model which includes turbulent viscous terms in the electron momentum equation, linearized theory gives predictions which are in reasonably good agreement with the observed wave damping. The computer results throw some light on the theory of strong turbulence, comparison with such theories points up some discrepancies and indicates the proper method for including the turbulence effects. Estimates of the electron heat transport in three-dimensional thermonuclear plasmas due to this mechanism gives values comparable to those predicted by neclassical theory from thermal fluctuations alone; enhancement of the fluctuations above the thermal level will given higher transport rates. These results suggest that nonclassical effects can be very important in plasma transport and could be important for fusion plasmas.
Harmonic generation by Gould–Trivelpiece modes propagating into an axial density gradient
Authors: Hirshfield J. L. , Bernstein I. B.
Published: March 2003

Prior experiments on the propagation of electrostatic waves on a plasma column (Gould–Trivelpiece modes) have shown linear wave reflections from an adjustable axial density gradient which scaled according to the predictions of WKB theory. For finite amplitude incident waves at radian frequency ω<ωpo, we have observed strong harmonic production at frequencies nω<ωpo where n in an integer and ωpo is the mean electron plasma frequency in the axially uniform part of the column. The harmonic production appeared to originate in the axially nonuniform plasma, and decreased markedly as the gradient was reduced experimentally. No threshold for harmonic production was observed, thus suggesting that parametric effects were not important. Second-order perturbation theory based on the cold plasma equations is applied to an axially nonuniform plasma in a strong uniform axial magnetic field. The results show that nonlinear source terms enter into the governing differential equation for the second-harmonic potential which are larger than the customary nonlinear terms for an axially uniform column, by a factor as large as (ωpR/ωL)4 where R is the plasma radius and L is the scale length of the inhomogeneity. Enhancement in harmonic production predicted by this model is in quantitative agreement with the experiment.
Stimulated Compton scattering of electromagnetic waves in plasma
Authors: Lin A. T. , Dawson J. M.
Published: March 2003

The so−called stimulated Compton effect is investigated on a one−and−two−halves−dimensional electromagnetic plasma model. This effect results in a parametric instability in which an electromagnetic wave is backscattered off bunches of particles rather than off coherent plasma waves. Numerical simulations were carried out with pump frequency ranging from 1.8 ωpe to 5 ωpe. The momentum imparted by the pump wave to the plasma produces an averaged plasma drift motion in the direction of the pump wave and with velocity comparable to the electron thermal velocity (V0 ≃ VT ≃ 0.1 c). In some cases a multiple backscatter process is believed to be the saturation mechanism of the instability. Stimulated Compton scattering has been observed even for frequencies below 2 ωpe where the Raman instability cannot occur. However, in this region, a sufficiently strong pump can overcome the frequency mismatch and drive the system hydrodynamically unstable. In this situiation strong acceleration of some electrons occurs producing very energetic particles.
Equation of motion of a solid particle suspended in a fluid
Authors: Soo S. L.
Published: March 2003

Consistent approximation calls for taking into consideration the effect of inertia of the fluid in a pressure gradient thus canceling out the term due to static pressure alone. Inconsistency may lead to ill−posed formulations.
Generalized Oseen theory for heat and mass transfer: Flow past semi−infinite bodies
Authors: Hewett Thomas A. , Weinbaum Sheldon
Published: March 2003

The potential flow transformation first introduced by Boussinesq is used to transform the generalized Oseen boundary value problem for the heat or mass transfer on a semi−infinite or finite arbitrary symmetric body to an equivalent classical Oseen heat and mass transfer problem for the flow past a semi−infinite or finite flat plate. New and available solutions to this simplified boundary value problem are then used to obtain new heat and mass transfer results for more general boundary shapes. The general formulation is given and new analytic solutions presented for semi−infinite bodies which include the upstream influence of acute angle wedges and blunt half−bodies at uniform surface temperature. Finally a treatment is given of semi−infinite bodies with more varied thermal boundary conditions.
Existence of weak shock wave solutions for higher−order theories of gas dynamics
Authors: Montgomery John T.
Published: March 2003

The existence of weak shock wave solutions for the higher order theories of gas dynamics generated by the Chapman−Enskog development of Boltzmann’s equation is proved.
Kinetic theory for a discrete velocity gas and application to the shock structure
Authors: Gatignol R.
Published: March 2003

A model gas is composed of identical particles with velocities restricted to a given finite set of p vectors where only binary collisions are considered. The Boltzmann equation is replaced by a system of p nonlinear coupled differential equations. These equations possess the essential properties of the Boltzmann equation. In particular, the Chapman−Enskog method can be applied. The model with six coplanar velocities is used for the problem of shock structure: The shock structure as given by the associated Navier−Stokes equations is compared with the structure which is known for the exact system. The thickness of the shock structure profile obtained from the associated Navier−Stokes equation is smaller than the thickness obtained from exact equations. These results agree well with those found by other methods.
Variation of radiation intensity behind an attenuating shock wave
Authors: Chan S. K.
Published: March 2003

An analysis is presented relating the radiation intensity time gradient behind shock waves in air to the shock−wave attenuation rate in a shock tube and boundary−layer effects on particle flow time. The analytical results are compared with the experimental data. It is shown that the very large variation of radiation gradient with shock−wave velocity is related to the strong dependency of shocked temperature with shock velocity within the range of 0.6−1.6 cm/μsec.
Convective and absolute instabilities in beam−plasma systems
Authors: Manickam J. , Carr W. , Rosen B. , Seidl M.
Published: March 2003

The linear theory of a mono−energetic electron beam interacting with a cylindrical, homogeneous, Maxwellian magnetoplasma is investigated numerically. Using standard criteria the instability of the upper branch (ω ≳ ωce; ω ∼ kzV) is shown to be either convective or absolute depending on the specific beam and plasma parameters. In the weak beam limit, nb ≪ np, a cubic dispersion equation is derived to describe the same system. The cubic equation is analyzed to show that the instability is convective when the group velocity of the plasma wave is positive. The instability is absolute when the group velocity of the plasma wave is negative and when the beam density exceeds a threshold density.
Effect of impurities on trapped particle modes
Authors: Bhadra Dilip K.
Published: March 2003

The nature of the trapped particle modes in a toroidal geometry has been investigated in the presence of impurity ions using a model magnetic field configuration. The various trapped ion and electron modes have been studied and the condition for their stabilization derived. Existence of some new modes with impurities in the ’’banana’’ regime has been shown.
Directional mean flow measurements using a single inclined hot wire
Authors: Moussa Z. M. , Eskinazi S.
Published: March 2003

The use of a single inclined hot wire for measurments of mean flow velocity and direction in a three−dimensional turbulent flow field is presented. A constant temperature hot−wire anemometer circuit is used with and without a linearizer. The use of the linearized results were found to improve the readout ability of the instrument and also to simplify the correction for directional measurements. A study of the effect of turbulence levels on the steady calibration results has shown that if the turbulence levels and the cross correlations are known, corrections can be applied to obtain angles and velocities as reliable as those obtained from a directional pressure probe. The advantages of the use of the hot wire over a pressure probe are that the hot wire has much faster response, disturbs the flow field to a lesser degree, is easier to correct for turbulence levels, and due to its smaller dimension compared with the pressure probe is less erratic concerning mean velocity gradients. The method of measurement and correction was tested in a jet mixing with a cross wind field. The range of angles shown in the experimental graphs pertain to that of a jet mixing with a cross wind.
Partial trapping of a beam in a cold collisional plasma
Authors: Winske Dan , Jackson E. Atlee
Published: March 2003

It is shown that the nonlinear trapping of an electron beam in a cold plasma with electron−ion collisions can result in only a partial trapping of the beam. The electrons separate into two groups, one near their original velocity and the other at a lower, secularly decreasing wave velocity.
Measurements of ion wave turbulence by microwave scattering
Authors: Mase Atsushi , Tsukishima Takashige
Published: March 2003

Ion wave turbulence spontaneously excited in a current-carrying plasma is investigated by the microwave scattering method. The dispersion relation, the wavenumber spectra, and the angular spectra of the ion wave turbulence are determined from the angular distribution of the scattered wave. The wavenumber spectrum has a peak around k ≃ νin/ vp, and decreases as k−4.8±0.5 with increasing k, where νin is the ion-neutral collision frequency and vp is the phase velocity of the ion wave. The angular spectrum of the wave energy is found to broaden as the total wave energy, W, increases along the electron drift. The effective collision frequency, νf, for electrons is also measured by the rf probe method as well as the dc method. An anomalous increase in νf is observed with the increase in W along the electron drift. The present experimental results are consistent with the theory of perturbed ion orbits.
Infinite wavelength kink instabilities in uniform current cylindrical plasmas with rectangular cross sections
Authors: Rosen M. D.
Published: March 2003

The magnetohydrodynamic stability of a free-boundary straight plasma column with a slightly elongated rectangular cross section, carrying a uniform axial current, is investigated analytically. Axisymmetric modes (n = 0), for which the circular cross section case is marginally stable (m = 1), are considered. Stability is found for a rigid vertical displacement, in good agreement with numerical results. However, a vertical displacement with a small additional m = 3 like perturbation, localized near the plasma surface, leads to instability.
Stability of linear flow
Authors: Ellingsen T. , Palm E.
Published: March 2003

It is shown that a finite disturbance independent of the streamwise coordinate may lead to instability of linear flow, even though the basic velocity does not possess any inflection point.
Experiments on turbulent structure and heat transfer in a two-dimensional jet
Authors: Bashir Jawaid , Uberoi Mahinder S.
Published: March 2003

Turbulence and heat transfer were measured in a heated jet of air and development of self-similarity was determined. Temperature fluctuation balance was measured across the jet. Turbulent velocity and temperature spectra and their dependence on jet Reynolds number and location across the jet were measured. The jet nozzles with length to width ratios of 20, 40, and 140 were used and the effect of aspect ratio on turbulent structure was determined.
Rheological properties of nondilute suspensions of deformable particles
Authors: Choi Seung Jung , Schowalter W. R.
Published: March 2003

The creeping flow equations have been solved to account for effects of shear on drop shape when the influence of neighboring drops is considered. A cell model is used to account for finite concentrations of the dispersed phase. From these results a constitutive equation is derived and implications for several flows are discussed. The shape and orientation of drops are computed and compared with existing data. Finally, dynamic viscosity and rigidity are obtained for nondilute suspensions of viscoelastic particles in an oscillatory shear flow.
Theory of ion acceleration by drifting intense relativistic electron beams. I. Theory
Authors: Olson Craig L.
Published: March 2003

A theory that describes the collective acceleration of ions by an intense relativistic electron beam injected into a metallic guide tube filled with neutral gas at low pressure is presented. The acceleration mechanism is shown to be of electrostatic origin (although it is different from those employed in previous electrostatic theories), and its many parametric dependences are identified and discussed. In the theory, ion acceleration occurs in the electrostatic fields of a two-dimensional, time-dependent, potential well, which is described by the self-consistent coupling of the beam dynamics with the ionization processes of the neutral gas. The theory divides into the cases (i) I0 ≳ Il, and (ii) I0 ≪ Il, where I0 is the peak injected beam current and Il is the space-charge limiting current. For case (i), the beam initially stops at the anode and creates a deep potential well. At roughly the charge neutralization time, a nonadiabatic transition occurs, the beam begins to propagate, and an ion bunch is accelerated. At low pressures, the ion energy per ion charge may be up to three times the injected electron energy. At higher pressures, the ion energy per ion charge may exceed three times the injected electron energy. At still higher pressures, ion acceleration ceases due either to beam front runaway, ion slip-out, or charge-exchange effects. For case (ii), the beam never stops at the anode, a deep well is never created, and no accelerated ions should occur. All existing ion acceleration data is in the regime I0 ≳ Il, although this was not previously recognized. The effects of ion impact ionization, ion avalanching, and charge exchange (neglected in all previous theories) are shown to play important, and sometimes dominant, roles in the acceleration process.
Theory of ion acceleration by drifting intense relativistic electron beams. II. Comparison with experiments
Authors: Olson Craig L.
Published: March 2003

Predictions of a theory together with a detailed comparison of that theory with data obtained over the past six years at several laboratories are presented, and good agreement is shown for a wide variety of measurable quantities. This agreement includes the ion energy and its dependence on ion charge state, beam current, beam energy, neutral gas perameters, and guide tube and beam dimensions. It also includes the ion number and pulse shape and their variation with pressure; the acceleration characteristics including the delay time near the anode, the acceleration region length, and the acceleration time; and the location of the ion bunch relative to the beam front. The beam front velocity and propagating beam risetime behavior are also in agreement. Effects of an external magnetic field and a plasma-filled guide are considered. In addition, radially accelerated ions, the effects of ν/γ, and possible multiple pulse mechanisms are discussed.
Instability of two-phase flow in vertical cylinders
Authors: Esmail M. Nabil , Hummel Richard L. , Smith J. W.
Published: March 2003

The stability of two-phase flow in a vertical cylinder is considered. The liquid phase is assumed to flow past the cylinder surface in a thin layer, assuming no mixing with the core gas flow. The complete system of Navier–Stokes and continuity equations for both phases is treated analytically, using a perturbation procedure based on expansion in powers of small wavenumbers. The results of the first approximation determine the phase velocity of waves developed on the liquid-gas interface. The second approximation reveals the complete pattern of hydrodynamical stability of two-phase flow over the entire range of gas-flow velocities. The topological features of stability curves are depicted. The effects of surface tension, cylinder radius, and interface curvature on the two-phase flow stability are revealed.
Theoretical and experimental study of background gas penetration into underexpanded free jets
Authors: Brook J. W. , Hamel B. B. , Muntz E. P.
Published: March 2003

The mechanisms of penetration of single and multicomponent background gases into a free jet flowing into a stationary background are examined from theoretical and experimental points of view. The theoretical treatment is based on the asymptotic theory developed by Brook and Hamel for a spherically symmetric source flow expanding into a stationary rarefied atmosphere. Agreement between theory and experiment is reasonable; certain points of disagreement are identified for future study.
Model for the breakup rate of spherical drops in isotropic turbulent flows
Authors: Delichatsios M. A.
Published: March 2003

A new model is presented for estimating the breakup rate of drops dispersed in a continuous liquid phase under isotropic turbulent conditions.
Length of a viscous-limited Taylor column
Authors: Serotsky P. , Titman C. W.
Published: March 2003

Measurements of the length of a viscous-limited axial Taylor column show that two length scales exist. One is typical of the length of the whole of the disturbance produced in the flow, and the other determines the length of the stagnant region.
Resonant Doppler velocimeter
Authors: Miles Richard B.
Published: March 2003

Narrow linewidth tunable lasers augur a new kind of laser Doppler velocimetry employing resonant absorption and fluorescence from trace atomic species rather than scattering from particles. This technique may provide better turbulence and small volume information than present velocimetry.
Enhanced scattering inherent to ’’loss-cone’’ ion distributions— General geometry
Authors: Baldwin D. E.
Published: March 2003

The ion scattering rate due to the Post–Rosenbluth convective loss-cone instability is calculated for general geometry. Noise generated by particle discreteness is amplified by the instability, the details of which are sensitively dependent upon the spatial variation of plasma parameters. Ray equations are developed for the transport and amplification of wave energy.
Ponderomotive force exerted on a plasma by an infrared laser beam
Authors: Marhic Michel E.
Published: March 2003

The continuum and single particle approaches to the ponderomotive force in an underdense plasma are presented. The force density tends to expel the plasma out of a focused laser beam. Transient and steady-state responses of the plasma to the ponderomotive force are studied, and the importance of α = (ωp2/ω2) 〈ε0(E2/2) 〉 /2neKT is emphasized. Experimental verifications are presented, obtained with a pulsed CO2 laser-amplifier system (500 MW) irradiating an argon arc plasma (ne = 3×1014 cm−3, T=1.4 eV). Density changes are monitored by studying light emitted from the focal region, and the measured decrease in light intensity is consistent with the plasma density decrease expected for a value of α=0.37.