bluuebunny/crossref_metadata_2025 huggingface dataset:
Drag reduction of the highest molecular weight fractions of polyethylene oxide
Authors: Berman Neil S.
Published: March 2003

The analysis of drag reduction produced by high molecular weight fractions of Polyox shows that the slope of the drag reduction curve on a von Kármán plot for a narrow fraction is proportional to concentration and molecular weight. Polydisperse polymer solutions have drag reduction curves characteristic of the high molecular weight tail alone. Experimental results are presented on the shape of the distribution and the drag reduction of cumulative fractions containing the highest molecular weights.
Realizability of Reynolds-stress turbulence models
Authors: Schumann U.
Published: March 2003

It is shown that certain existing phenomenological models of turbulence in terms of differential equations for the Reynolds stresses Rαβ=〈u′α u′β〉 do not guarantee realizable solutions. The known realizability conditions are Rαβ⩾0 for α=β and Rαβ2⩾Rαα Rββ for α≠β. A stronger requirement is that the matrix Rαβ be positive semi-definite. This implies three conditions like non-negative eigenvalues or non-negative principal invariants. Conditions are given which must be satisfied by the model itself in order to guarantee realizable solutions for any realizable initial and boundary conditions. Some means are proposed which can be used to change the existing models into realizable ones.
Improved treatment of electron thermal conduction in plasma hydrodynamics calculations
Authors: Moses Gregory A. , Duderstadt James J.
Published: March 2003

The classical transport law for the hydrodynamic description of the electron heat flux breaks down in the nonequilibrium laser fusion plasma and an alternative expression for the electron heat flux vector must be used. The ad-hoc flux limit treatment used in present production level codes is analyzed and shown to provide physically plausible results but without providing any further insight into the properties of the plasma. Grad’s 13 moment method is proposed as an alternative to the conventional Fourier’s law expression for the heat flux. Numerical calculations confirm that this approach not only provides physically plausible results but provides them within a more fundamental framework than the ad-hoc flux limiting schemes and thus offers the possibility of gaining more insight into the flux limiting mechanism.
Temporal evolution of ion temperatures in the presence of ion cyclotron instabilities
Authors: Correll D. L. , Böhmer H. , Rynn N. , Stern R. A.
Published: March 2003

Spectroscopic techniques to determine the temporal evolution of the ion temperature in a collisionless barium plasma are presented. The theory of temperature relaxation in plasmas with external magnetic field is modified to include wave-induced collisions. Experiment and theory are compared. The current-driven electrostatic ion cyclotron instability is shown to be an effective method for wave heating of ions.
Nonresonant coupling of ion acoustic waves in three dimensions
Authors: Mantei T. D. , Matthieussent G.
Published: March 2003

The slow nonresonant beat disturbance (ω2−ω1, k2−k1) generated by two obliquely propagating ion acoustic waves has been observed. The beat signal wavenumber, direction, and speed agree with predicted values. The beat signal amplitude, normalized to the product of the driving wave amplitudes, exhibits a maximum when the beat signal speed is approximately equal to one-half the ion thermal speed. The energy transfer between the two driving waves has also been observed.
Shear stabilization of the purely growing trapped particle instability
Authors: El-Nadi Adel
Published: March 2003

The collisionless trapped particle instability in toroidal systems is studied as a radial boundary value problem. It is shown that in the presence of a small amount of magnetic shear, electrons can flow along the field lines to stabilize the mode.
Numerical study of two-dimensional generation and collapse of Langmuir solitons
Authors: Pereira N. R. , Sudan R. N. , Denavit J.
Published: March 2003

Numerical studies of various aspects of two-dimensional Langmuir solitons, are made, viz., (i) instability and collapse of a planar soliton perturbed in the perpendicular direction, (ii) the effect of an approximate Landau damping on the collapse, and (iii) the generation and subsequent collapse of planar solitons by an external pump field. These computations verify the flow of energy from long wavelength pump fields, through soliton formation and collapse, to shorter wavelengths, where the energy is transferred to the electrons.
Plasma effects on the absorption spectrum for the ordinary mode in a magnetized plasma
Authors: Casper T. A. , Shohet J. L. , Tataronis J. A.
Published: March 2003

The rate of energy absorption for electrons in a plasma is calculated from the emission, including plasma effects through the index of refraction. The net absorption is obtained for the case of propagation perpendicular to an applied dc magnetic field. The dispersion relation for cyclotron harmonic waves is solved numerically to obtain wavenumbers as functions of excitation frequency. This gives the index of refraction required to find the net absorption rate. Spectra for various temperatures and densities are found by integration over the electron velocity distribution.
Similarity principle for the elementary gasdynamics of real fluids
Authors: Thompson Philip A. , Sullivan Daniel A.
Published: March 2003

The one-parameter description of perfect-gas dynamics via the ratio of specific heats γ is well-known and leads to conventional gasdynamic formulae. This description can be extended to real gases and liquids via the single parameter Γ̄, which is related to the distinctive thermodynamic property Γ=c[∂ (ρc)/∂P]s. For steady isentropic flow, this implies a similarity principle, that all nondimensional flow properties can be expressed as functions of Mach number M and Γ̄. This is precisely analogous to the perfect-gas case and can be represented by simple formulae. Numerical calculations and experimental data for a variety of real substances follow the similarity principle with good accuracy. The principle is applicable to the prediction of compressible-flow properties and to the correlation of experimental data.
Properties of the Monte Carlo Lorentz collision operator
Authors: Horton Wendell , Estes R. , Choi Duk-In
Published: March 2003

The validity of the Monte Carlo collision operator for generating solutions of the reduced Fokker–Planck equation governing suprathermal ions and electrons in a target plasma is established by statistical tests.
Interchange instability with line-typing and finite Larmor radius effects
Authors: Riordan John C. , Hartman Charles W.
Published: March 2003

Finite Larmor radius and end effects are included in a treatment of the low-β interchange instability. Higher order modes are shown to be destabilized by incomplete line-tying through an external plasma.
Passage of a vortex ring through a circular aperture in an infinite plane
Authors: Miloh T. , Shlien D. J.
Published: March 2003

The largest vortex ring that can pass through a prescribed circular aperture in a thin infinite plane has been analyzed for an inviscid and incompressible fluid. A closed form solution for the velocity potential and the core velocity was obtained. Also given are typical core paths for both passing and nonpassing cases as well as a relation between the core and ring radii for the limiting case.
Isolating constants of motion in two-dimensional turbulence
Authors: Lee Jon
Published: March 2003

Under consistent truncation of the Fourier amplitude equations for the inviscid two-dimensional flow, it is shown that the class of extraneous constants of motion associated with Hald’s model examples does not appear. Hence, the conclusion that total energy and enstrophy being the only isolating constants of two-dimensional turbulence is still valid, until a new class of constants of motion is discovered.
Particle and wave dynamics in a magnetized plasma subject to high rf pressure
Authors: Gekelman W. , Stenzel R. L.
Published: March 2003

The nonlinear response of a plasma subject to an intense, spatially localized rf field has been investigated experimentally. In a uniform quiescent magnetoplasma of density ne≳109 cm−3, temperature kTe≃5 kTi≃1 eV, and magnetic field B0∼100 G, a resonance cone (ω/ωc≃0.1; where ωc is the electron cyclotron frequency) is established which converges away from a circular exciter to reach a maximum amplitude at the remote cone apex. When an rf burst of intensity ε0Erf2/nekTe≲O (1) is applied, a strong density depression (δne/ne≃40%) is formed in the focal region on a time scale (∼1 μsec) short compared with a collision time. Fast ion bursts [(1/2) mvi2≃35 eV≳100 kTi], large amplitude ion acoustic waves, but negligible electron temperature increases are observed. Density and resonance cone field interact nonlinearly and in time develop a state of turbulence. Ion heating (ΔTi/Ti≃100) dominates over electron heating (ΔTe/Te∼2). The direct measurements of the particle distributions with probes and energy analyzers are supplemented by test wave techniques. Small amplitude ion acoustic, electron plasma, and Bernstein waves are propagated through the region of high rf intensity and the perturbed plasma properties are deduced from the test wave behavior. The observed nonlinear collisionless interactions between particles and intense rf field are qualitatively explained by a model involving the ponderomotive force on electrons and acceleration of ions by space charge fields.
Accessibility of equilibria in an electron beam plasma system
Authors: Cavalli Alexander , Greenly John B. , Walsh J. E.
Published: March 2003

The behavior of a beam plasma system has been modeled with a set of nonlinear rate equations. Solutions of these equations show characteristically different multiple equilibria. The experimental behavior implied by this result is shown to be in agreement with experimental observations.
Model equations for a vibrationally relaxing gas
Authors: Brun R. , Zappoli B.
Published: March 2003

Different vibrational nonequilibrium processes are reviewed as well as the corresponding zeroth-order distribution functions and relaxation equations. Two methods for the calculation of transport coefficients are then presented. The first is based on the expansion of the first order distribution function in orthogonal polynomials thus, model equations and consequently rotational and vibrational relaxation equations can be found. In the pressure tensor, diagonal terms of relaxation pressure appear and the results of a numerical calculation of these terms are given for the case of a rapidly expanding nitrogen flow. The second method consists of using a generalized Bhatnagar–Gross–Krook–Morse method from which simpler but more tractable results are obtained.
Initial value problem with non-Hermitian radial mode equations
Authors: Horton Wendell , Kwak H. , Estes R. , Choi Duk-In
Published: March 2003

A biorthogonal set of expansion functions is introduced for the radial mode problem that occurs for drift waves and trapped particle modes in nonuniform plasmas. With a vector space representation of the eigenfunctions concise time dependent and time independent perturbation theory formulae are obtained for the system.
Computer simulation of current penetration in a plasma
Authors: Lin A. T. , Dawson J. M.
Published: March 2003

Anomalous current penetration into a plasma is a fundamental process which is important in a number of plasma situations included in which are the formation of discharges and current sheath layers. A recently developed two and one-half dimensional magnetostatic code has been applied to the simulation of this process. Many anomalous processes are involved here including anomalous resistance, anomalous heat conduction, anomalous electron viscosity, and the formation of complex magnetic structures. Of dominant importance is the anomalous resistivity. It is important to identify the instabilities and turbulent processes involved. The results show that the induced current excites lower hybrid turbulence which may be related to lower hybrid oscillations recently observed in microtor. Anomalous heating and heat transport are also observed. In some cases the magnetic field lines are observed to reconnect and form magnetic islands.
Nonlinear stabilization of the lower-hybrid-drift instability by electron resonance broadening
Authors: Huba J. D. , Papadopoulos K.
Published: March 2003

The lower-hybrid-drift instability is shown to be effectively stabilized by electron resonance broadening, especially in finite β plasmas. This saturation mechanism allows steady state turbulence to develop which is crucial to plasma phenomena such as magnetic field line reconnection and collisionless shock waves.
Resonant absorption in plasma density profiles produced by laser heating, heat flow, and hydrodynamics
Authors: Malone R. C. , Morse R. L.
Published: March 2003

Efficiency and optimum angle of incidence of combined resonant and collisional absorption of laser light are found by numerical simulation and an economical extension of ray tracing to be moderately insensitive to pulse width and peak power.
Rheology of polymer solutions in laminar capillary tube flows
Authors: Ouibrahim A.
Published: March 2003

Depending on the concentration, the capillary tube diameter influences two parameters: the apparent viscosity and the critical shear rate for which the transition from steady to unsteady flow regimes occurs. A possible length parameter, characteristic of a given polymer concentration, is defined on the basis of these two parameters.
Influence of finite ion Larmor radius effects on the ion resonance instability in a nonneutral plasma column
Authors: Davidson R. C. , Uhm Hwan-sup
Published: March 2003

The influence of finite ion Larmor radius effects on the ion resonance instability in a nonneutral plasma column aligned parallel to a uniform axial magnetic field B0êz is investigated. The analysis is carried out within the framework of a hybrid Vlasov-fluid model in which the ions are described by the Vlasov equation and the electrons are described as a macroscopic, cold fluid. Electrostatic stability properties are calculated for the case in which the equilibrium electron and ion density profiles are rectangular and the ion distribution function is specified by f0i=const×δ (H⊥−ωiPϑ−T̂i) G (vz). The resulting eigenvalue equation for the perturbed electrostatic potential φ̂l(r) is solved exactly to give a closed algebraic dispersion relation for the complex eigenfrequency ω. This dispersion relation is solved numerically, and it is shown that the growth rate of the ion resonance instability exhibits a sensitive dependence on plasma parameters. For example, finite ion Larmor radius effects can have a strong stabilizing influence for azimuthal mode numbers l⩾2, particularly when the equilibrium self-electric field is sufficiently weak. For the fundamental mode (l=1), however, stability properties are identical to those calculated from a macroscopic two-fluid model, and the growth rate is unaffected by the value of the ion Larmor radius.
A second-order theory for k∥B0 electromagnetic instabilities
Authors: Gary S. Peter , Feldman W. C.
Published: March 2003

Electromagnetic instabilities which propagate parallel to an external magnetic field in an infinite, homogeneous Vlasov plasma are considered. Linear theory is used to construct second-order expressions for the time rates of change of momentum, as well as perpendicular, parallel, and total energies of each plasma species. The results are expressed in a concise form appropriate for many instabilities of this type. The ion cyclotron (T⊥i≳T∥i) and firehose (T∥i≳T⊥i) instabilities are considered as examples.
Pseudo-three-dimensional turbulence in magnetized nonuniform plasma
Authors: Hasegawa Akira , Mima Kunioki
Published: March 2003

A simple nonlinear equation is derived to describe the pseudo-three-dimensional dynamics of a nonuniform magnetized plasma with Te≫Ti by taking into account the three-dimensional electron, but two-dimensional ion dynamics in the direction perpendicular to B0. The equation bears a close resemblance to the two-dimensional Navier–Stokes equation. A stationary spectrum in the frequency range of drift waves is obtained using this equation by assuming a coexisting large amplitude long wavelength mode. The ω-integrated k spectrum is given by k1.8(1+k2)−2.2, while the width of the frequency spectrum is proportional to k3(1+k2)−1, where k is normalized by cs/ωci. The result compares well with the recently observed spectrum in the ATC tokamak.
Effect of transonic flow in the ablation cloud on the lifetime of a solid hydrogen pellet in a plasma
Authors: Parks P. B. , Turnbull R. J.
Published: March 2003

A knowledge of solid hydrogen pellet lifetimes in a plasma is critical to the design of devices to refuel tokamak fusion reactors. When the pellet is injected into the plasma, the ablated material from the pellet undergoes a transonic flow since it is heated while it expands. Calculations are done on the behavior of the transonic flow for various plasma conditions and pellet sizes. From these calculations, the ablation rate and lifetimes of the pellet are determined. A scaling law is given which allows pellet lifetimes to be easily calculated for any plasma conditions. The results of these calculations give good agreement when compared with experiments.
Multidimensional theory of the inhomogeneous beam-plasma instability
Authors: Shanahan William R.
Published: March 2003

A combined analytic and numerical study of the effect of a plasma density gradient on the beam-plasma instability is presented. After a thorough discussion of the qualitative aspects of this problem, emphasis is placed on the development of a theory which can reveal the interplay between the gradient and the multidimensional aspects of the instability. Using fluid equations, a differential equation is derived for the electrostatic potential. An integral representation for the solution of this equation is derived and its asymptotic evaluation presented. Explicit comparison is made between this asymptotic result and a direct numerical integration of the basic equations. The predictions of the theory are presented for the two-dimensional case, both for the case in which the beam propagates along the direction of the gradient and for that in which the beam is propagating at an angle to this direction. Some brief remarks are made concerning the fully three-dimensional case.
Normal mode analysis of laser beam propagation in a plasma waveguide
Authors: McMullin J. N. , Capjack C. E. , James C. R.
Published: March 2003

Normal mode theory is used to derive the familiar oscillating Gaussian solution for a laser beam in a plasma waveguide with a quadratic index of refaction. Perturbation theory is then used to derive the unstable solution in a plasma in which the quadratic index varies sinusoidally along the axis.
Cyclotron maser instability for general magnetic harmonic number
Authors: Uhm Hwan-sup , Davidson R. C. , Chu K. R.
Published: March 2003

The cyclotron maser instability for general magnetic harmonic number transverse electric (TE) and transverse magnetic (TM) waveguide modes in a conducting cylinder of radius Rc are examined. The analysis is carried out for a hollow electron beam (radius R0) propagating parallel to a uniform axial magnetic field B0êz. It is assumed that ν/γ0≪1, where ν is Budker’s parameter and γ0mc2 is the electron energy in a frame of reference moving with the beam axial velocity βbcêz. One of the most important features of the analysis is that the instability growth rate for magnetic harmonic numbers s=2,3,... is comparable to the growth rate of the fundamental (s=1) mode, particularly for moderate electron energy [β0= (1−1/γ20)1/2≳0.4]. Moreover, it is shown that the instability growth rate can be maximized by appropriate choice of the geometric parameter R0/Rc.
Computer modeling of linear theta pinch machines
Authors: Stover Elmer K. , Klevans Edward H. , York Thomas M.
Published: March 2003

A zero-dimensional time dependent computer model is developed to describe post implosion behavior of a radially diffuse plasma column in linear theta pinch machines. The model consists of five first-order differential equations for electron temperature Te, ion temperature Ti, plasma column area Ap, magnetic field embedded in the plasma column Bi, and number of electrons in the plasma column N, and incorporates the effects of particle end loss, electron and ion thermal conduction, magnetic compression of the plasma, electron-ion energy transfer, Ohmic heating of the electrons, and magnetic field diffusion. End-on interferometric experimental data, which indicate that particle confinement time scales as L[mi/(Te+Ti)]1/2, where mi is the ion mass and L is the compression coil length, are used as a guide to the choice of an end loss parameter. Numerical predictions of on-axis density and plasma temperature are found to be in reasonably good agreement with experimental results from both the collisional Scylla I-C experiment and the hot collisionless Scylla IV-P experiment. These comparisons are used to identify important physical mechanisms characterizing the behavior of a particular machine including: the significance of thermal conduction on both plasma temperature and particle end loss; the importance of magnetic field diffusion; and the impact of using a time independent end loss scaling parameter.
Sound and Tollmien–Schlichting waves in a Blasius boundary layer
Authors: Thomas Andrew S. W. , Lekoudis Spyridon G.
Published: March 2003

Calculations are presented of the distribution of the amplitude and phase of a wave pattern, consisting of sound and Tollmien–Schlichting waves, both of the same frequency, propagating independently. The calculations agree qualitatively with measurements taken in a Blasius boundary layer.
Slip of liquid inside a channel exit
Authors: Silliman William J. , Scriven L. E.
Published: March 2003

Navier’s slip coefficient boundary condition at the channel wall reduces die swell of Newtonian liquid exiting at low Reynolds number, and appears to relieve the stress singularity associated with Stokes’ no-slip hypothesis, according to a finite element analysis.
Dilute polymer flows at high strain rates: A correlation of data
Authors: Fruman D. H. , Tulin M. P.
Published: March 2003

Two anomalous phenomena in dilute polymer solution flows are reviewed: the pressure defect in Pitot tube readings and the pressure increase in orifice flow. Re-analysis of data available in the open literature shows that anomalous effects occur beyond particular values of the strain rate (onset) and that the magnitude of the effects is proportional to the strain rate in excess of the onset value. This substantiates the hypothesis that dilute polymer solutions can be characterized by a single relaxation time and a single anomalous stress magnitude both concentration dependent, the latter proportional to concentration for dilute solutions.
Self-similar motion of laser half-space plasmas. I. Deflagration regime
Authors: Sanmartín Juan R. , Barrero A.
Published: March 2003

The one-dimensional self-similar motion of an initially cold, half-space plasma of electron density n0, produced by the (anomalous) absorption of a laser pulse of irradiation φ =φ0t/τ (0<t⩽τ) at the critical density nc(nc/n0≡ε≪1), is considered. The analysis allows for electron heat conduction and ion-electron energy exchange and retains three dimensionless numbers: ε, Zi (ion charge number), and α= (9k/4mi) (τk2n20/φ0K̄e)2/3, where k, mi are Boltzmann’s constant and the ion mass, and K̄e × (electron temperature)5/2 = heat conductivity. If α ≫ε−4/3, a deflagration wave separates an isentropic compression with a shock bounding the undisturbed plasma, and an isentropic expansion flow to the vacuum. The structures of these three regions are completely determined; in particular, the Chapman–Jouguet condition is proved and the density behind the deflagration is found. The deflagration-compression thickness ratio is large (small) for α≪ε−5/3(α≫ε−5/3). The compression to expansion ratio for both energy and thickness is O (ε1/2). For Zi large, a deflagration exists even if α∼ε−4/3. Condition α≫ε−4/3 may be applied to pulses that are not linear.
Free trajectory derivation of the (Bohm) diffusion coefficient in a magnetic field
Authors: Fowler Richard G.
Published: March 2003

A derivation of the Bohm diffusion coefficient is advanced by an extension of the method of free paths. Bohm diffusion is found as the high field limit of an expression for the diffusion coefficient which ranges from normal diffusion through the Cowling B−2 regime.
Langmuir waves in a spatially periodic potential
Authors: Baños Alfredo , Weibel Erich S. , VanDam James W.
Published: March 2003

The propagation of electrostatic waves in the presence of a spatially periodic magnetic field is studied. The magnetic field is replaced by a linear array of plane potential barriers, or ’’point mirrors,’’ equally spaced and of height (1/2) mvm2 and zero width, where vm is the critical speed that separates trapped from untrapped particles (electrons). The presence of trapped particles results in an incremental wave damping, whose value can be obtained analytically in the infinite-wavelength limit. For finite wavelengths, numerical computations show that this additional damping initially decreases as the wavenumber increase from zero, and is eventually overshadowed by Landau damping when it becomes appreciable. This new damping can be physically understood in terms of the trapped particles reflecting from the barriers thereby losing that part of their momentum which is coherent with the wave. One-dimensional particle simulation results which relate to the theory are also reported.
Limiting currents of an unneutralized magnetized electron beam in a cylindrical drift tube
Authors: Thompson J. R. , Sloan M. L.
Published: March 2003

Results of an investigation of the steady state injection of a uniform unneutralized, magnetized, relativistic electron beam into a cylindrical drift tube are presented. The space-charge-limited current and the asymptotic kinetic energy of electrons on axis is determined both numerically and analytically as a function of the input kinetic energy (γ0−1) mc2 and of the ratio of beam−to−wall radii. A previously cited ’’interpolation formula’’ is obtained in the pencil beam limit, but more accurate limiting current expressions are developed for other cases (such as the fat beam limit) where the interpolation formula is as much as 20% in error. The corresponding axial electron energy is also found to be significantly smaller than the previously cited value of (γ1/30−1) mc2 except in the strong pencil beam limit.
Kinetic theory of neutral hydrogen atoms in a bounded hydrogen plasma slab
Authors: Burrell Keith H.
Published: March 2003

The transport of neutral hydrogen atoms in a hydrogen plasma slab is considered. After making a reasonable approximation for the charge exchange rate, analytic solutions for the neutral distribution function are obtained which depend on one spatial and three velocity variables. To obtain these, a condition must be imposed that implies uniform electron and ion temperatures. Specular reflection of the neutrals at the boundaries is considered. Solutions associated with the diffusion approximation are also given and the condition for its validity is discussed. The solutions are evaluated for the case of Maxwellian ion distribution functions.
Stochastic acceleration by an obliquely propagating wave-An example of overlapping resonances
Authors: Smith Gary R. , Kaufman Allan N.
Published: March 2003

A simple problem exhibiting intrinsic stochasticity is treated: the motion of a charged particle in a uniform magnetic field and a single plane wave. Detailed studies of this wave-particle interaction show the following features. An electrostatic wave propagating obliquely to the magnetic field causes stochastic motion if the wave amplitude exceeds a certain threshold. The overlap of cyclotron resonances then destroys a constant of the motion, allowing appreciable momentum transfer to the particles. A wave of large enough amplitude would thus suffer severe damping and lead to rapid heating of a particle distribution. The stochastic motion resembles a diffusion process even though the wave spectrum is monochromatic. The methods of this paper should be useful for other problems showing stochasticity such as superadiabaticity in mirror machines, destruction of magnetic surfaces in toroidal systems, and lower hybrid heating.
Experiment on sideband dispersion
Authors: Starke T. P. , Malmberg J. H.
Published: March 2003

The dispersion of the sidebands of a large amplitude plasma wave has been measured. Sidebands propagate according to a beam-plasma type dispersion. Sideband dispersion is calculated with a quasi-linear theory using the locally measured time-averaged electron velocity distribution. This model assumes that the large wave and the sidebands interact primarily through the time average of the perturbation the large wave causes in the velocity distribution. The measured sideband dispersion agrees with the predictions of this model.
Analytic, high β, flux conserving equilibria for cylindrical tokamaks
Authors: Sigmar D. J. , Vahala George
Published: March 2003

Using Grad’s theory of generalized differential equations, the temporal evolution from low to high β due to ’’adiabatic’’ and nonadiabatic (i.e., neutral beam injection) heating of a cylindrical tokamak plasma with circular cross section and peaked current profiles is calculated analytically. The influence of shaping the initial safety factor profile and the beam deposition profile and the effect of minor radius compression on the equilibrium is analyzed.
Combined effects of pressure gradient and heating on the stability of freon-114 boundary layer
Authors: Wazzan A. R. , Taghavi H. , Hsu W.-C. , Gazley Carl
Published: March 2003

Numerical computations have been made for the laminar boundary-layer development and stability of a series of similar Falkner–Skan wedge flows in freon-114 with surface heating. The variation in physical properties (primarily viscosity) of the fluid alters the thickness and velocity profile of the boundary layers and consequently, their stability characteristics. Heating of the surface, with an accompanying reduction of viscosity close to the wall, has the qualitative effect as a more negative (i.e., more favorable) pressure gradient. The effects of various combinations of pressure gradient and heat transfer on the characteristics of these variable-property laminar boundary layers, on their neutral stability, and on the growth of disturbances by the linear stability theory are described. The minimum critical Reynolds number is presented as a function of pressure gradient, temperature difference, and free-stream temperature. The latter has an appreciable effect because of the rapid change in the temperature derivative of the viscosity with temperature level.
Effect of induced pressure and impulse on cw laser penetration of solids
Authors: Shui Ven H.
Published: March 2003

The transient behavior of the cw laser produced melt layer when subjected to an over-pressure/impulse has been analyzed. Results show that the over-pressure and impulse required for significant melt removal by individual microsecond laser pulses are very high (≳103 atm and ≳104 dyn sec/cm2, respectively) and melt removal by such pulses is unlikely to be achieved in practice. The quasi-steady-state melt removal resulting from long-duration over-pressure produced either by single long-duration pulses (≳100 μsec), by high repetition rate pulses or by the cw laser itself has also been analyzed, with results indicating the possible practical operating regimes for such a mechanism.
Theory of plasma heating by magnetosonic cavity mode absorption
Authors: Ott Edward , Wersinger Jean-Marie , Bonoli Paul T.
Published: March 2003

Absorption of magnetosonic cavity modes by excitation of the spatial Alfvén resonance and by resonant particle absorption (transit time magnetic pumping) are studied and the strengths of the two damping mechanisms compared. For the mode studied, the poloidal mode number is low. This implies that the magnetosonic turning point is close to the Alfvén resonance. To deal with the resulting differential equation an asymptotic expansion technique is utilized, first using ideal magnetohydrodynamic equations, and, subsequently, with finite ion Larmor radius effects included. The antenna impedance and cavity Q are studied as a function of plasma and antenna parameters. It is found that either Alfvén resonance or resonant particle absorption dominate depending principally on radial mode number.
Self-precession and frequency shift for two waves in a plasma
Authors: Chakraborty B. , Chandra S. K.
Published: March 2003

Two elliptically polarized waves in a cold and unmagnetized plasma are found to have self-precession and frequency shift. For one wave they depend upon the amplitudes and frequencies of both. Due to the presence of the second wave the self-precession of the first wave increases if its eccentricity is less than that of the former.
Radially resolved measurements of ’’q’’ on the adiabatic toroidal compressor tokamak
Authors: Goldston R. J.
Published: March 2003

A new technique for directly measuring the safety factor, or q, profile in a tokamak is described. A tightly collimated neutral beam capable of injecting approximately 100 mA of 30 keV deuterium atoms was mounted on the Adiabatic Toroidal Compressor tokamak. By proper tangential aiming of the beam a strong concentration of circulating fast ions was created at a chosen plasma minor radius. Through examination of the orbits of these ions with a multi-sight-line charge exchange detector, it was possible to measure the shifts of the orbits off magnetic surfaces, and thereby make local measurements of q. This experiement showed that when q on axis reached unity, strong internal turbulence began, and further lowering of q at the outer edge of the plasma did not lower q (0). A second result was that the measured q (0) was approximately 1.8 times larger than the q (0) deduced from the Te(r) profile, assuming Zeff to be independent of minor radius. This suggests a significant peaking of Zeff on axis.
Influence of axial energy spread on the negative-mass instability in a relativistic nonneutral E layer
Authors: Uhm Hwan-sup , Davidson R. C.
Published: March 2003

The influence of an axial energy spread on the negative-mass instability in a relativistic nonneutral E layer aligned parallel to a uniform axial magnetic field B0êz is investigated. The stability analysis is carried out within the framework of the linearized Vlasov–Maxwell equations. It is assumed that the E layer is thin with radial thickness (2a) much smaller than the mean radius (R0), and that ν/γ0≪1, where ν is Budker’s parameter and γ0mc2 is the mean electron energy. Stability properties are investigated for the choice of electron distribution function in which all electrons have the same value of canonical angular momentum (Pϑ=P0=const) and a step-function distribution in axial momentum pz. The negative-mass growth rate is calculated including the important stabilizing influence of axial energy spread (ΔE), and it is shown that a modest energy spread (ΔE/γ0mc2≈ a few percent) is sufficient to stabilize perturbations with axial wavenumber satisfying k2R20≳1.
Wall stabilization of a sharp boundary toroidal plasma
Authors: Kito Masafumi , Honma Toshihisa
Published: March 2003

The stability of a toroidally symmetric sharp boundary plasma is studied in a wall whose cross section is an arbitrary shape. The wall stabilization has an effect on a fat plasma. The kink mode of the plasma has two stable regions in which toroidal fields and poloidal fields are, respectively, dominant. The second harmonic plays an important role for the stability. For a fixed aspect ratio of the plasma, the stable regions increase accordingly as the plasma shifts outward. If circular walls, elliptical walls, and oval-shaped walls have the same cross-sectional area, the circular wall is the worst case for the stability.
Temporal eigenvalue spectrum of the Orr–Sommerfeld equation for the Blasius boundary layer
Authors: Antar Basil N. , Benek John A.
Published: March 2003

A search for the eigenvalue spectrum of the Orr–Sommerfeld equation for the Blasius boundary layer is conducted. The investigation is numerical involving two different numerical methods. The resulting spectrum is found to depend on the finite interval of integration chosen for the numerical scheme. This spectrum is shown to be infinite and discrete whenever it is identified with the aid of numerical integrations. The spectrum belonging to the exact semi-infinite problem is inferred from the asymptotic behavior of the same spectrum. This is shown to be comprised of a finite discrete set and a continuous portion.
A theory of spontaneous fluctuations in viscous fluids far from equilibrium
Authors: Keizer Joel
Published: March 2003

It has recently been observed that the dissipative nonlinearities for a variety of transport processes can be written in a formally identical fashion. This ’’canonical form’’ expresses the spontaneous changes of extensive variables in terms of exponentials of intensive variables and depends on the molecular processes causing the dissipation. It is shown here that the dissipative terms in Newtonian fluid mechanics can be written in canonical form. Using a postulated relationship between these dissipative terms and fluctuations, the canonical form is used to describe the molecular fluctuations in the flow of Newtonian fluids. The theory describes the effect of nonlinearities, including the streaming terms, and is consistent whenever the phenomenological equations are valid. Close to equilibrium the theory reduces to the Fox–Uhlenbeck theory of hydrodynamic fluctuations, and away from equilibrium it gives an unambiguous generalization of the Landau–Lifshitz theory.
Kinetic models for polyatomic molecules with phenomenological energy exchange
Authors: Pullin D. I.
Published: March 2003

Models of the collision integral are developed for polyatomic structureless molecules subject to certain classes of phenomenological energy exchange between internal and translational energy modes in binary collisions. The exchange is described either by a model differential cross section for energy scattering or equivalently by a set of pair pseudo-internal coordinates which correlate pre- and post- collision values of the particle energies. Restrictions placed on admissible models of the exchange process are identified and one recently proposed special model is reformulated under these conditions. Chapman–Enskog type transport properties for this model are evaluated and its behavior in the context of the Monte-Carlo direct simulation method is discussed briefly.
Motion of a strong shock wave in a medium of nonuniform density
Authors: Yousaf M.
Published: March 2003

The effect of the disturbances behind a strong shock moving in a medium of nonuniform density is considered. The similarity solution is used to find the strength of the overtaking disturbance which modifies Chisnell’s approximation to become an exact theory.
Spike solution for radially symmetric solitary waves
Authors: Cumberbatch Ellis
Published: March 2003

A Korteweg–de Vries equation appropriate to radially symmetric, focusing waves is attacked by assuming a large amplitude, small width solution. The results are compared with recent numerical work.
Test particle distribution in a partially ionized plasma
Authors: Hsu T. , Hirshfield J. L. , Bernstein Ira B.
Published: March 2003

Theory and experiments are described for the evolution of the energy distribution of a group of test electrons interacting with a background plasma through electron-electron (e-e), electron-ion (e-i), and elastic electron-neutral (e-n) collisions. The experiments were performed on the afterglow of a pulsed microwave discharge (1010<ne<1012 cm−3, Te∼0.2 eV). The test electrons (4<E<14 eV) were injected into the plasma as a feeble quasi-monoenergetic beam. For the electrons, the e-n mean-free path λ was much smaller than the length of the plasma L, while the e-e mean-free path was much greater. Nonetheless, because of the large neutral-to-electron mass ratio, the dynamic friction and smaller diffusion-in-speed were determined by Coulomb collisions, while frequent e-n collisions maintained the distribution nearly isotropic. As this distribution gradually advanced along the discharge, it was shifted downward in mean energy due to dynamic friction, and broadened because of the distribution of friction path lengths, and because of diffusion-in-energy. The Boltzmann equation governing the beam electrons was reduced, by taking advantage of the smallness of λ/L and m/M, to a simple partial differential equation for the distribution function which was solved analytically. The remarkably close agreement between experiment and theory, including the lack of sensitivity of the latter to all parameters save plasma density and initial test particle energy, suggests wide applicability for the concepts examined here.
Comparative study of the axial and azimuthal bunching mechanisms in electromagnetic cyclotron instabilities
Authors: Chu K. R. , Hirshfield J. L.
Published: March 2003

A comparative study is presented of the axial and azimuthal bunching mechanisms of the electromagnetic electron cyclotron instability. Axial bunching can be described with a nonrelativistic treatment, but azimuthal bunching is relativistic in origin. As is well known, the axial bunching mechanism drives the Weibel-type instability while the azimuthal bunching mechanism drives the electron cyclotron maser instability. For an electron ensemble of cold helical trajectories, a unified physical interpretation of both instabilities is presented. It is shown that the two bunching mechanisms are actually simultaneously present in either instability and compete with one another. As a result, the dominant mechanism determines the type of instability. A criterion for distinguishing the two types of instabilities is derived. It is shown that the energy of the electrons plays an insignificant role in the criterion and, hence, should not be a factor in the justification of a nonrelativistic treatment. Regimes of validity of nonrelativistic models are defined, however. Applications to gyrotron experiments are discussed.
Closure of second- and third-moment rate equations for diffusion in homogeneous turbulence
Authors: Deardorff J. W.
Published: March 2003

Essentially exact closures are presented for the second- and third-moment rate equations for diffusion of a pollutant released at a particular time in homogeneous turbulence. The quasi-Gaussian closure is found to require addition of a down-gradient diffusion term. Explicit dependence upon the time after release is found to be retained by the highest moment gradient term. The second- and third-moment approaches are therefore concluded to be inherently incapable of accurately solving the general problem of pollutants released at different places at different times.
Spin up of a rapidly rotating gas
Authors: Bark Fritz H. , Meijer P. Staffan , Cohen H. Ian
Published: March 2003

The linear spin up problem is solved for a rapidly rotating ideal gas of constant temperature. A perturbation solution for small Mach numbers and a numerical solution for finite Mach numbers are given. For finite Mach numbers, several unexpected phenomena occur. For instance, after some time the radial velocity reverses near the center of the container in spite of the fact that gas is sucked into the Ekman layers.
Magnetohydrodynamic spectrum of instabilities due to plasma rotation
Authors: Spies G. O.
Published: March 2003

The spectrum of frequencies and growth rates of the linearized magnetohydrodynamic motion about rotating straight theta pinch equilibria is investigated. A qualitative picture is obtained of the distribution of eigenvalues in the complex plane, and of their dependence on equilibrium parameters and the three mode numbers. A numerical procedure is described which uses this picture for computing the eigenvalue with any given triple of mode numbers. It is shown that rigidly rotating equilibria are unstable unless the mass density is an increasing function of radius; computations indicate that rotation shear (within practical limits) cannot stabilize confined equilibria.
Numerical simulations of collisionless drift instabilities for low-density plasmas
Authors: Lee W. W. , Kuo Y. Y. , Okuda H.
Published: March 2003

Nonlinear behavior of the collisionless drift instabilities are studied for the universal and current driven modes by means of electrostatic particle simulations in two-and-a-half dimensions. Realistic mass ratios of electrons to the ions are used in the simulations, where the guiding-center approximation for the electrons and the exact dynamics for the ions are employed. Several nonlinear effects including the quasi-linear diffusion of the particle density, the frequency shift due to the ambipolar field, the mode competition among the unstable waves, and the quasi-linear diffusion in the velocity space are found to be dominant mechanisms for the saturation. The stabilization of the collisionless drift instabilities by the magnetic shear has also been studied.
Effects of cross-sectional elongation on trapped electron modes
Authors: Chu K. R. , Ott Edward , Manheimer Wallace M.
Published: March 2003

The dispersion relation for the trapped electron mode in noncircular cross-section tokamaks is formulated and evaluated. It is shown that modest reductions in the growth rate result from cross-sectional elongation.
Onset of natural convection in a cylinder of water saturated porous media
Authors: Zebib A.
Published: March 2003

The onset of natural convection in a cylinder of water-saturated porous media is considered. The dependence of the critical Rayleigh number and the preferred convective motion on both the aspect ratio of the cylinder and the temperature difference is established.
Spectrum of axisymmetric torsional Alfvén waves
Authors: Sy W. N-C.
Published: March 2003

The spectrum of axisymmetric torsional Alfvén waves propagating in a cylindrical, nonuniform, resistive plasma waveguide has been analyzed by a method of singular perturbations. It is indicated why some experiments show a continuous spectrum and others a discrete spectrum.
Role of clumps in drift-wave turbulence
Authors: Dupree Thomas H.
Published: March 2003

A new model of collisionless drift-wave turbulence for k⊥ai≪1 is explored that can explain the experimentally observed spectra in a simple way. The model includes clumps on an equal footing with drift waves. The calculation is approximate but does confirm the feasibility of the model and demonstrates that clumps are likely to be an important feature of drift-wave-related turbulence.
Wall stabilization of axisymmetric modes in noncircular tokamak plasmas
Authors: Chu Ming-Sheng , Miller R. L.
Published: March 2003

The axisymmetric stability of tokamak equilibria with arbitrary cross section is studied numerically using the energy principle. The contribution to δW from the plasma region is minimized analytically with respect to displacements in the toroidal and poloidal directions. the formulation of Lüst and Martensen is used for the vacuum contribution. Bessel–Fourier and other sets of trial functions are then employed to cast the minimization of δW into a matrix eigenvalue problem. A computer code named axisym evaluates these matrix elements and solves for the eigenvalues. The code is fully toroidal and compressible mode trial functions are included. Wall stabilization is studied by placing a conducting wall around the vacuum region.