bluuebunny/crossref_metadata_2025 huggingface dataset:
Harmonic oscillating two-stream instability in lower-hybrid heating
Authors: Sperling J. L. , Harvey R. W.
Published: March 2003

The harmonic oscillating two-stream instability is a four-wave process which arises when a finite amplitude wave field with frequency ω0 destabilizes waves at harmonics of ω0. The importance of the instability arises in its ability to transfer wave energy from slow electrostatic waves near the lower-hybrid frequency to waves at higher frequencies. The harmonic oscillating two-stream instability could alleviate the condensation problem which has arisen in recent cascade theories.
Pressure anisotropy stabilization of axisymmetric mirror machines
Authors: Weitzner Harold
Published: March 2003

The stability of a two species, anisotropic pressure, axisymmetric plasma is studied using the guiding center plasma model. Successively, asymptotic expansions are applied appropriate to a long, thin plasma, and to a plasma with flux surfaces close to cylinders. The resultant stability problem may be cast as an ordinary differential equation eigenvalue problem or as a problem in the calculus of variations. It is shown that low beta plasmas cannot be confined and be stable although plasmas may be stable in which the pressure gradients are nonzero where the pressure tends to zero. Stable profiles are given; these profiles include the possibility of field reversed regions. These stable profiles require the anisotropic species to be cold near the axis. Rather than absolute stability, a weaker condition is also considered which for fixed azimuthal mode number ‖m‖ puts the point of accumulation of the spectrum of modes on the stable side. It is hoped that such a condition may yield systems stable to ‖m‖ small modes although not all values of ‖m‖. This condition is more readily satisfied and allows more reasonable profiles near the axis.
Two-dimensional magnetohydrodynamic calculations of the plasma focus
Authors: Maxon Stephen , Eddleman James
Published: March 2003

Two-dimensional magnetohydrodynamic calculations on plasma focus experiments in the Mather geometry are described. The properties of the two-dimensional numerical solutions are discussed. Detailed results are given for a specific problem which compares favorably with experiment. The numerical solution for the plasma focus previously given by Potter has been rerun with substantial disagreement. Arguments are given to show that the Potter code is incorrect.
Instability of multi-layered liquid films
Authors: Wang C. K. , Seaborg J. J. , Lin S. P.
Published: March 2003

The stability of an n-layered liquid film flowing steadily down an inclined plane is investigated using linear theory. Neutral curves of all competing modes of instability have been obtained for various ratios of viscosity, density, and thickness. The interfacial mode instability due to the local downward step increase in density is found to occur only when such a density increase is large enough to provide sufficient gravitational potential. A local downward decrease in density seems to always be unstable. The interfacial mode instability associated with the local downward increase in viscosity is found to occur only if the Reynolds number is sufficiently small. The interfacial mode instability associated with the local downward step decrease in viscosity is found to be absent if the wavenumbers of the disturbances are smaller than a cutoff wavenumber.
Initial value problem for Rayleigh–Taylor instability of viscous fluids
Authors: Menikoff R. , Mjolsness R. C. , Sharp D. H. , Zemach C. , Doyle B. J.
Published: March 2003

The initial value problem associated with the development of small amplitude disturbances in Rayleigh–Taylor unstable, viscous, incompressible fluids is studied. Solutions to the linearized equations of motion which satisfy general initial conditions are obtained in terms of Fourier–Laplace transforms of the hydrodynamic variables, without restriction on the density or viscosity of either fluid. When the two fluids have equal kinematic viscosities, these transforms can be inverted explicitly to express the fluid variables as integrals of Green’s functions multiplied by initial data. In addition to normal modes, a set of continuum modes, not treated explicitly in the literature, makes an important contribution to the development of the fluid motion.
Energy transfer for the Burgers’ equation
Authors: Rosenblatt M.
Published: March 2003

The Burgers’ equation is considered as a simple nonlinear model equation in which to investigate energy transfer in the wavenumber domain. Spatially stationary (on the real line) random solutions are considered. The first-order nonlinear term for large time relating the spectrum and bispectrum (Fourier transform of third-order moments) of the random solution is determined. This nonlinear term is obtained by making use of the Hopf solution of the Burgers’ equation.
Interaction of a strong blast wave with a free surface
Authors: Falade Adebowale , Holt Maurice
Published: March 2003

When a point source explosion is initiated at the ocean surface, the shock propagated into the water is reflected at the surface as a centered expansion wave. The solution in the neighborhood of the interaction point is obtained by writing the equations of motion in the appropriate similarity variables and then changing the independent variables to polar coordinates based at the interaction point. From the zero-order solution of the resulting equations the slopes of boundaries at the interaction point are obtained. A first-order perturbation of this solution provides more accurate representation of the flow variables and the curvature of the shock surface near the interaction point.
Surface waves generated by shallow underwater explosions
Authors: Falade Adebowale , Holt Maurice
Published: March 2003

Surface water waves generated by surface and near surface point explosions are calculated. Taking the impulse distribution imparted at the water surface by the explosion as the overriding mechanism for transferring energy of the explosive to surface wave motion, the linearized theory of Kranzer and Keller is used to obtain the wave displacement in the far field. The impulse distribution is obtain by integrating the pressure wave over an appropriate time interval on a horizontal surface just beneath the undisturbed water surface. For surface explosions, a modified form of the similarity method first used by Collins and Holt is used to obtain the flow field. In the case of submerged explosions, the flow field is estimated by making necessary modifications to Sedov’s similarity solution to account for the venting that accompanies the interaction of the leading (blast) wave with the ocean surface. Surface waves generated by a charge at six depths of placement (h1=0.15 m, 0.30 m, 0.61 m, 0.91 m, 1.37 m, 3.05 m) are considered in addition to surface explosions. The results seem to support the existence of an upper critical depth phenomenon (of the type already established for chemical explosions) for point (nuclear) explosions.
Magnetohydrodynamic diffuser flow across homogeneous magnetic field
Authors: Wilhelm H. E. , Choi S. H.
Published: March 2003

Similarity transformation and self-similar solutions are derived for the incompressible radial flow of conducting, viscous fluids across an external, homogeneous magnetic field (parallel to the apse line) in a diffuser with electrodes in the planes ϑ=±ϑ0 (cylindrical coordinate system). The conducting flow across the (axial) external and induced magnetic fields induces radial and azimuthal current densities. The azimuthal current density produces a net current flux I≠0 through the electrodes which are connected by an external circuit. The eigenvalue problems for the radial velocity and induced magnetic field amplitudes are solved analytically. The external and induced magnetic fields are shown to significantly change the pressure distribution but not the onset of flow separation. This is due to the irrotational nature of the Lorentz force, ∇× (∇×B×B) =0, in which the magnetic field B(r, ϑ) is axial (noncurved).
Equilibria of high pressure elliptic flux-conserving tokamak
Authors: Mizoguchi T. , Kammash T. , Sigmar D. J.
Published: March 2003

An analytical calculation is carried out to determine the plasma current and poloidal beta for a toroidal plasma with an elliptic cross section under the constraint of flux conservation. It is shown that the pressure buildup during heating occurs in two stages: An outward shift in the magnetic axis and an elongation in the flux surfaces. The total plasma current increases with the pressure variable more rapidly for an elliptic cross section than it does for a circular cross section. This current rise produces a rather slow rise of the poloidal beta with pressure, particularly for large elongations. The ensuing class of flux conserving equilibria is characterized by large beta but modest poloidal beta.
Effects of an axial heat flux limit in linear theta pinches
Authors: Gary S. Peter , Sgro A. G. , DeSilva A. W.
Published: March 2003

With a simple model for classical electron thermal conduction and an arbitrary axial density profile, the axial electron temperature profile T (z) and cooling time tc in a linear theta pinch may be computed. Densities that decrease with increasing axial position provide the more favorable conditions for the failure of classical heat conduction. Introduction of a heat flux limit in such a profile increases tc and reduces the gradient of T (z) over most of the plasma.
Fermi–Pasta–Ulam recurrence in the two-space dimensional nonlinear Schrödinger equation
Authors: Yuen Henry C. , Ferguson Warren E.
Published: March 2003

Numerical solutions of the two-space dimensional nonlinear Schrödinger equation with spatially periodic boundary conditions have been obtained. It has been found that the long-time evolution exhibits the Fermi–Pasta–Ulam recurrence phenomenon for a wide range of initial conditions.
Group velocity direction of unstable Cerenkov beam-plasma modes
Authors: Van Andel H. W. H. , Hirose A.
Published: March 2003

It is shown that in the cold-beam, cold-plasma approximation, the group velocity of unstable Cerenkov beam-plasma modes at maximum growth rate is not perpendicular to the phase velocity. Orthogonality of these velocity vectors only results in a cold-plasma, warm-beam approximation.
Numerical results for flow past a suddenly heated vertical plate
Authors: Ingham D. B.
Published: March 2003

Four different numerical methods are used to determine the velocity and temperature of a viscous fluid in the boundary layer on a semi-infinite vertical flat plate whose temperature is suddenly increased from that of the surrounding fluid. All the numerical results show a departure from the unsteady one-dimensional solution before the theoretically predicted time. Further, the decrease in the mesh size does not seem to show the results to be the tending to a smooth limit; rather that the time of transition from the one-dimensional unsteady solution to the steady state solution decreases and appears to be tending to zero. This suggests that the mathematical solution of the boundary layer equations may be one in which the solution changes discontinuously from the unsteady one-dimensional solution to the steady state solution.
Interaction between small-scale surface waves and large-scale internal waves
Authors: Rizk Magdi H. , Ko Denny R. S.
Published: March 2003

A two-timing perturbation technique is applied in order to investigate the mutual interaction between a Stokes wave train on the water surface and long, low-frequency, internal waves in a two-layer model. The set of equations derived conserves energy in the system of surface and internal waves. This conservation is attributable to the coupling terms that appear in both the internal-wave equations and the surface-wave equations and that describe the energy transfer between both wave families. In addition to the coupling and nonlinear effects included in the surface-wave equations (which are part of the interaction equations), a higher order, linear effect, attributable to the slow variations in surface-wave properties, is also included. Because of the availability of a rigorously ordered description of the interaction processes, it has been possible to assess the relative influence of the nonlinear, finite-amplitude terms, the coupling terms, and the higher order linear terms in the complete set of governing equations for a given set of conditions.
Over−reflection of horizontally propagating gravity waves by a vertical shear layer
Authors: Mollo-Christensen Erik
Published: March 2003

The problem of horizontally propagating gravity waves impinging on a vertical shear layer which forms the boundary between uniform currents is isomorphic to an acoustic problem solved by Miles and by Ribner. The consequences of over-reflection for a spatially growing instability are pointed out. The long wave reflection problem is solved for free surface and internal waves on a thin layer in an otherwise deep fluid. Over-reflection is found possible for Froude numbers in excess of two; infinite over-reflection will occur for certain angles of impingement.
Dynamics of transverse magnetohydrodynamic shock waves
Authors: Collins A. R. , Mathers C. D.
Published: March 2003

The development of transverse magnetohydrodynamic shock waves has been studied in an electromagnetic shock tube for both parallel and antiparallel bias shock waves. Radial magnetic field profiles indicate an essentially flat shock front is formed in both cases. The shock and piston behavior is modeled by a simple snowplow model with a resistive arc across the launching endplate of the shock tube. Mass leakage through the piston is necessary to explain the observed high shock speeds. The method of characteristics is used to compute magnetic field profiles in excellent agreement with those observed experimentally.
Damping of resonance cones in lower hybrid mode conversion
Authors: Grabbe Crockett L.
Published: March 2003

The asymptotic form of the collisional and collisionless damping of the potential for the resonance cones propagating into and out of the lower hybrid layer is obtained, and the localization of the various damping mechanisms along the cone is discussed. It is found that the damping of the incoming cone is not as large as previously predicted.
Temperature gradient and electron gyroradius effects on lower hybrid drift—Drift cyclotron instabilities
Authors: McBride J. B. , Hamasaki S.
Published: March 2003

Electron and ion temperature gradients, as well as finite electron gyroradius (kρe≳1), have been retained to analyze the stability of electrostatic drift waves in the local approximation from the lower hybrid down to the ion cyclotron frequency. The instability conditions indicate the importance of these modes over this entire frequency range in a variety of applications.
Ion temperature gradient driven drift cyclotron instabilities
Authors: Catto Peter J. , Aamodt R. E.
Published: March 2003

The role of ion temperature gradient driven drift cyclotron instabilities in both mirror machines and tokamaks is examined. For a completely filled loss cone, reversed temperature and density gradients are necessary for instabilities; however, this inverted profile requirement is relaxed as the fill of the loss cone is decreased and all profiles are unstable for an empty loss cone.
Properties of large amplitude Langmuir solitons
Authors: D’Evelyn M. , Morales G. J.
Published: March 2003

This numerical study isolates some of the experimentally interesting properties of the large amplitude spatially localized electric fields in the Langmuir frequency range which are described by the nonlinear Schrodinger equation with the full exponential nonlinearity retained. The steady state eigenvalues and wavefunctions are calculated and their properties compared with the small amplitude soliton solutions. A variety of time dependent effects are investigated in both bounded and unbounded geometries. Some of these are: the evolution of initial standing waves; the collisional properties; the pumping of stationary, moving, and colliding solitons by a uniform external electric field.
Cross field thermal transport due to ion acoustic waves in weakly magnetized plasmas
Authors: Manheimer Wallace M. , Max Claire Ellen , Thomson Jeffery
Published: March 2003

It is shown that cross field temperature gradients can drive ion acoustic waves unstable in a weakly magnetized plasma. The principal effect of the instability is an enhancement of the cross field thermal conductivity.
Properties of an rf produced magnetically confined nonneutral hot electron plasma
Authors: Luhmann N. C. , Trivelpiece A. W.
Published: March 2003

A magnetically confined, nonneutral hot electron plasma is produced by the acceleration and trapping of a low energy (approximately 1 keV) electron beam injected along the axis of an evacuated right circular cylindrical cavity resonator that is excited in the TE111 mode with up to 15 kW of rf power at 0.88 GHz. The cavity axis coincides with that of the static magnetic mirror field (B∼314 G, Rm=1.3:1). The nonneutral (for approximately 10–200 msec) hot electron plasma (We∼100 keV, Ne∼4×1011 electrons, and ne ∼4×109 cm−3) remains trapped for approximately 10 sec. There is a periodic ∇B precessional motion of the trapped electron cloud at a frequency of a few MHz.
Magnetic field generation via resonant absorption
Authors: Speziale Thomas , Catto Peter J.
Published: March 2003

A simple equation is derived describing the generation of the quasi-steady magnetic field by resonant absorption in a cold, collisionless plasma. An initial value problem is solved to ascertain the explicit time behavior of the high frequency fields due to resonant absorption. These fields are employed to obtain a fully analytic expression for the quasi-steady magnetic field. Expressions are also presented for the saturated magnetic field based on saturation times for the high frequency fields appropriate to plasma wave convection or wavebreaking. Modifications of the magnetic field structure due to plasma wave propagation are also calculated and the magnetic field is seen to convect with the plasma wave.
Magnetic fields due to laser-light absorption
Authors: Woo Wee , DeGroot J. S.
Published: March 2003

A derivation is presented of a new expression for the slowly varying (dc) magnetic field generated by the absorption of laser light. Good agreement is found between results calculated from the new expression and results from simulation calculations and experiments. When applied to the resonant absorption of high powered laser light, it is shown that mega-Gauss dc magnetic fields can extend well into the overdense region for high enough resistivity. Therefore, they can inhibit the laser heated electron thermal conductivity.
Radio-frequency plugging of a high density plasma
Authors: Watari T. , Hatori T. , Kumazawa R. , Hidekuma S. , Aoki T. , Kawamoto T. , Inutake M. , Hiroe S. , Nishizawa A. , Adati K. , Sato T. , Watanabe T. , Obayashi H. , Takayama K.
Published: March 2003

Mirror end loss can be suppressed by applying an rf field at the mirror throat through low impedance coils. This method is verified to be effective for a high density plasma up to 1014 cm−3. Experimental results show that the rf field strength required for the plugging is dependent on the plasma density. The dependence differs according to the geometry of the coil. The mechanism of giving the density dependence is theoretically clarified for each coil. Particularly, it is shown that the electric field induced in the direction of the static magnetic field is intrinsic for the result of type-III coil where its efficiency for rf plugging is insensitive to the plasma density.
Stimulated Raman scatter in laser fusion target chambers
Authors: Thomson J. J.
Published: March 2003

The target chamber of a laser fusion reactor will contain small amounts of background gases. As the beam is focused, it ionizes the gas and Raman scattering is induced. Density limits on the background gas are found in order that the laser beam not become appreciably decollimated. It is found that laser bandwidth efficiently decreases the scattering effect.
Ion fluctuations and velocity distribution in the presence of ion cyclotron waves
Authors: Böhmer H. , Fornaca S. , Rynn N. , Wickham M.
Published: March 2003

Ion density fluctuations and the ion velocity distribution function in the presence of the current-driven electrostatic ion cyclotron instability are determined using resonance fluorescence of the ions. The optical line intensity modulation shows that the ion density modulation can be as large as 90%. From the Doppler broadening of the lines it is found that the distribution function of ions heated by the unstable ion cyclotron waves is Maxwellian with an uncertainty of 5%.
Reflection and absorption of ion-acoustic waves in a density gradient
Authors: Ishihara Osamu , Alexeff Igor , Doucet H. J. , Jones W. D.
Published: March 2003

One problem with ion-acoustic waves is that sometimes they are observed to be reflected from discharge tube walls, and sometimes to be absorbed. Theoretical computation reveals that a velocity gradient produced by a density gradient plays a significant role in the reflection. The velocity gradient produces a subsonic−supersonic transition and long wavelength waves are reflected before reaching the transition while short wavelength waves penetrate over the transition and are absorbed in the supersonic flow plasma.
Nonlinear saturation of the dissipative trapped electron instability
Authors: Migliuolo Stefano , Simon Albert
Published: March 2003

The nonlinear saturation amplitude of the dissipative trapped electron instability is calculated. Comparison is made with an experiment carried out in linear mirror geometry and near threshold, with only a single mode predominating. A model in which the untrapped electrons respond in a Boltzmann fashion yields good agreement. A model in which Landau damping is included predicts saturation amplitudes much smaller than observed. The first model seems appropriate for linear geometries while the second may apply to closed devices.
Phase-locked particle motion in a large-amplitude plasma wave
Authors: Smith Gary R. , Pereira N. R.
Published: March 2003

A plasma wave with an oscillating amplitude and phase occurs in two commonly studied situations, the beam-plasma interaction and the launching of a large-amplitude wave in a Maxwellian plasma. Electron motion in such a wave is either regular or stochastic. Theoretical study shows that regular motion can exhibit a phase-locking effect, which explains the persistence of amplitude oscillations observed in simulations and experiments. An additional (’’test’’) wave of moderate amplitude can prevent phase-locking, causing stochastic motion instead, and thereby destroy the amplitude oscillations. The effects studied are also relevant to the theory of sideband instability.
Time evolution of mass flows in a collisional tokamak
Authors: Hassam Adil B. , Kulsrud Russell M.
Published: March 2003

The time evolution, due to dissipative processes, of an initial pattern of poloidal and toroidal mass flows in a tokamak is considered. The calculation is applicable to a collisional, low β, axisymmetric tokamak of arbitrary minor cross section. Time rates of change of poloidal flows which are subsonic but larger than the diamagnetic speed are given according to the magnitude of the flow and the collisionality of the plasma. Over most of parameter space for typical tokamaks, the poloidal rotation is strongly damped by magnetic pumping at the rate (l/qR)2νii, where l is the mean free path, qR is the ’’connection length,’’ and νii is the ion-ion collision frequency. At higher speeds, even stronger damping is effected by electron thermal conduction. The toroidal rotation is determined largely by the conservation of toroidal angular momentum. A heuristic explanation of the damping due to magnetic pumping is given.
Fluctuating flow due to a rotating disk
Authors: Purushothaman R.
Published: March 2003

The flow due to super-imposed torsional oscillations on a rotating disk in a semi-infinite expanse of viscous fluid is studied for the large and small frequencies separately. Analytical-numerical solutions are obtained for the oscillatory and time mean flows. Expressions for the skin friction on the disk and the axial flow in the far field are given.
Transition of the axisymmetric starting plume cap
Authors: Shlien D. J.
Published: March 2003

The beginning of a continuous buoyancy (heat) injection into a stationary fluid results in a cap of buoyant fluid followed by a steady plume. This cap undergoes a transition in which a breakup is observed at a height from the source which increases with decreasing buoyancy injection rates. Sequences of cine film frames are presented illustrating this transition. A numerical criterion for the transition was found, namely, that the product of the power injected times the time at which transition occurs is a constant (19 cal). This can be related to an effective Rayleigh or Reynolds number, but the transition mechanism remains unknown. A critical effective Rayleigh number for the thermal may be estimated from these results to be 105 which in this case represents an injected heat of 10 cal.
Cylindrical, axisymmetric magnetohydrodynamic turbulence
Authors: Vahala George
Published: March 2003

Incompressible magnetohydrodynamic turbulence is considered for an axisymmetric plasma in cylindrical geometry. The equilibrium statistical states to which the plasma evolves are examined by imposing an external constraint of constant toroidal current on the equilibrium Gibbs ensemble. Only the state with maximal magnetic helicity to energy ratio has zero-mean kinetic energy for intially quiescent systems. There is an upper bound on the toroidal current to toroidal flux ratio below which this unique stable force free state can exist and whose magnetic flux surfaces are basically concentric circles. Above this critical value, the plasma is unstable with islands present in the flux surfaces. This stability result is in sharp contrast with both the results of a linearized δW analysis as well as considering the stability of the linearized spectral coefficient evolution equations for nonforce-free states.
Existence of rarefaction shocks in a laser-plasma corona
Authors: Bezzerides B. , Forslund D. W. , Lindman E. L.
Published: March 2003

General conditions under which rarefaction shocks can exist in the expanding corona of a plasma heated by a laser are derived. In particular, for the case of a two-electron temperature isothermal plasma with temperatures Th and Tc, such a shock is shown to occur if Th/Tc≳5+√24. The case of rarefaction shocks induced by the ponderomotive force is also briefly discussed.
Quantum plasmas I: The convergence formalism
Authors: Jones Roger D.
Published: March 2003

It is shown from first principles, using the formalism of Wigner distributions, that the divergences in the plasma kinetic equation due to the long range nature of the Coulomb interaction can be eliminated even if the plasma is rapidly varying, inhomogeneous, and immersed in external fields. This is due to the fact that for plasmas which have a screening length much larger than either the electron thermal wavelength or the classical distance of closest approach there is a large region in impact parameter space in which collision terms based on binary collisions and collision terms based on small momentum transfer give the same result.
Electromagnetic wave propagation in inhomogeneous plasmas
Authors: Antonsen Thomas M. , Manheimer Wallace M.
Published: March 2003

The absorption and transformation of electromagnetic waves in the vicinity of electron cyclotron harmonics is considered. The results of a simple WKB theory and a full wave theory are compared. It is found that for waves perpendicularly incident on a resonant surface (where the wave frequency equals an integer multiple of the electron cyclotron frequency), the full wave treatment is necessary to determine reflection and mode conversion coefficients, whereas, the WKB theory and full wave theory predict the same transmission coefficient. As the angle of incidence is decreased from 90°, the reflection and mode conversion coefficients become unimportant so that the full wave theory and WKB theory agree. The relevance of these processes to the heating of toroidal plasmas with high frequency waves is discussed.
Radio-frequency plugging and heating of a magnetized sheet plasma
Authors: Uehara Kazuya , Hagiwara Shigeo
Published: March 2003

Radio-frequency plugging and heating of a magnetized sheet plasma has been studied both experimentally and theoretically. It is confirmed that a sheath resonance related to ion motion occurs at a frequency intermediate between the ion cyclotron frequency and the lower hybrid frequency, and an anti-resonance occurs at the lower hybrid frequency. The rf electric field in the plasma, which produces a ponderomotive force on the ions, is strongest at the sheath resonance, and is used for the nonadiabatic rf plugging of the magnetized sheet plasma in a mirror field. The ion heating process is explained by Joule heating due to the rf electric field.
Observation of a reflection of localized radio-frequency fields near the f
p
e layer
Authors: Ohnuma Toshiro , Lembège B.
Published: March 2003

Localized rf fields, namely, the high frequency resonance cones, were observed to be reflected near the electron plasma frequency layer in an inhomogeneous magnetized plasma. The reflection of fine structures due to electron thermal motions was also observed.
Effects of fluid inertia on particle collection
Authors: Wang C. S. , Seaborg J. J. , Lin S. P.
Published: March 2003

The significance of fluid inertia in the computation of particle collection by impaction is explained by use of a numerical example.
Nonthermal emission at the plasma frequency
Authors: Fidone I. , Ramponi G. , Brossier P.
Published: March 2003

A theoretical model of nonthermal emission of radiation at the plasma frequency in a tokamak plasma with runaway electrons is proposed. The amplitude of the radiated field resulting from the nonlinear conversion of two unstable longitudinal waves is calculated.
Plasma oscillations
Authors: Case K. M.
Published: March 2003

For a simple model of a linearized plasma the normal modes are discussed for the case when an n fold degenerate eigenvalue is imbedded in the continuum. It is found that for each such eigenvalue there are 2n generalized eigenfunctions and 2n adjoint functions. The set consisting of the continuum modes, and discrete modes of both complex and real eigenvalues are complete. Expansions are readily found using biorthogonality relations which are obtained.
New magnetohydrodynamic equilibria by secondary bifurcation
Authors: Kriegsmann Gregory A. , Reiss Edward L.
Published: March 2003

For planar fields, the Grad–Shafranov theory of magnetohydrodynamic equilibria is reduced to solving Δψ+kG (ψ) =0 for some function G (ψ), where Δ is the two-dimensional Laplacian and k is an ’’amplitude’’ of G. This equation is solved on a rectangular region of aspect ratio l, with ψ=0 on the boundary, and G satisfying the conditions, G (0) =0, G′ (0) =1, G″ (0) =0, and G‴ (0) ≠0. Since G (0) =0, the basic state, ψ≡0, is a solution for all values of the parameter λ≡ka2, where a is the x dimension of the rectangle. Other equilibria, which are called the primary states, branch from the basic state at the eigenvalues λ=λmn(l) of the linearized theory. The eigenvalues are the bifurcation points of the basic state. They become multiple eigenvalues at special values of l=l̃. A previously developed perturbation method is used to show that when l varies from l̃, the multiple eigenvalues split into their constituent simple eigenvalues, and into secondary bifurcation points on some of the primary states that branch from these simple eigenvalues. The solutions that branch from the secondary bifurcation points are the new magnetohydrodynamic equilibria. They are calculated near the secondary points, and for l near l̃, by the perturbation method.
Extension of Stokes series for flow in a circular boundary
Authors: Conway B. A.
Published: March 2003

The expansion in powers of Reynolds number for steady, viscous, incompressible flow within a circular boundary, known to eighth order from the work of Kuwahara and Imai, is extended by computer to 22 terms. An attempt is made to analyze and improve the extended series.
Spanwise structure of the plane turbulent wake
Authors: Barsoum M. L. , Kawall J. G. , Keffer J. F.
Published: March 2003

An experimental investigation of a developed plane turbulent wake has been carried out to gain some insight into the spanwise structure of the large scale intermittent turbulent bulges. The results indicate that these bulges are three dimensional, and that their extent in the spanwise direction is less than in the streamwise direction and greater than in the lateral direction. No evidence of periodicity was found.
Randomness of low-order models of two-dimensional inviscid dynamics
Authors: Kells Lawrence C. , Orszag Steven A.
Published: March 2003

A statistical analysis is performed of various low-order truncations of the two-dimensional inviscid Navier–Stokes equations. The behavior of the time-averaged enstrophy and time-correlation function of each Fourier mode is analyzed and compared to the behavior expected in a random dynamical system. Empirical evidence is presented for the randomness of all isotropically truncated models for which the wavenumber cutoff is large enough to insure that every mode is involved in nontrivial interactions. This evidence is contrasted with the apparent nonrandomness found in other special truncations. The results strengthen the evidence for the validity of statistical descriptions of two-dimensional turbulence.
Use of one-dimensional Cosserat theory to study instability in a viscous liquid jet
Authors: Bogy D. B.
Published: March 2003

The problem of the instability of an incompressible viscous liquid jet is considered within the context of one-dimensional Cosserat equations. Linear stability analyses are performed for both the infinite and semi-infinite jets. The results obtained for the inviscid case are compared with the corresponding results derived from ideal fluid equations. They are also compared with recent results by other authors obtained from a different set of one-dimensional jet equations. Solutions are also obtained, within the framework of the linearized theory, to the jet break-up problems formulated as an initial-value problem for the infinite jet and as a boundary-value problem for the semi-infinite jet.
Stark profile measurements on Lyman series lines of Al x
i
i
i
Authors: Datla R. U. , Griem Hans R.
Published: March 2003

Single shot photographic spectra of hydrogen-like aluminum Lyman series lines are obtained from a low inductance vacuum spark. Corresponding pinhole pictures yield information on the source size. The observed line profiles are found to increase in width along the series and the higher series members Lγ and Lδ can be matched with convolved Stark and Gaussian profiles. The Gaussian profile includes the effects of source size, thermal Doppler broadening, and crystal resolution. The space and time-averaged electron density determined from the profile analysis is 2.5×1021–1×1022 cm−3.
Extensions of guiding center motion to higher order
Authors: Northrop Theodore G. , Rome James A.
Published: March 2003

In a static magnetic field, some well-known guiding center equations maintain their form when extended to next order in gyroradius. In these cases, it is only necessary to include the next order term in the magnetic moment series. The differential equation for guiding center motion which describes both the parallel and perpendicular velocities correctly through first order in gyroradius is given. The question of how to define the guiding center position through second order arises and is discussed, and second order drifts are derived for one usual definition. The toroidal canonical angular momentum, Pφ, of the guiding center in an axisymmetric field is shown to be conserved using the guiding center velocity correct through first order. When second-order motion is included, Pφ is no longer a constant. The above extensions of guiding center theory help to resolve the different tokamak orbits obtained either by using the guiding center equations of motion or by using conservation of Pφ.
Theory of two-fluid equilibrium of an axially symmetric plasma
Authors: Watanabe Tsuguhiro , Nishikawa Kyoji
Published: March 2003

A new formulation for determining the two-fluid equilibrium of an axially symmetric plasma is presented. The inertial force due to plasma motion is taken into account in the form of a modified electrostatic potential (due to the centrifugal force) and a modified magnetic field (due to the Coriolis’ force). A set of partial differential equations which determines the modified flux functions and the self-consistent electric and magnetic fields is derived under the assumption that the pressure is isotropic and is a function of the density and the flux function from an equation of state. The result is also formulated in the form of a variational principle which contains no constraints and hence is useful for numerical and perturbational analyses.
Ratio of scalar and velocity dissipation time scales in shear flow turbulence
Authors: Béguier C. , Dekeyser I. , Launder B. E.
Published: March 2003

Various studies of thermal turbulence in thin shear flows are re-examined in order to evaluate the ratio of the time scale of the scalar-fluctuation field to that of the velocity-fluctuation field. In all cases considered it is found that the ratio is nearly uniform with a value close to 0.5.
Statistical formulation of one-dimensional electron fluid turbulence
Authors: Fyfe David , Montgomery David
Published: March 2003

A one-dimensional electron fluid model is investigated using the mathematical methods of modern fluid turbulence theory. Nondissipative equilibrium canonical distributions are determined in a phase space whose coordinates are the real and imaginary parts of the Fourier coefficients for the field variables. Spectral densities are calculated, yielding a wavenumber electric field energy spectrum proportional to k−2 for large wavenumbers. The equations of motion are numerically integrated and the resulting spectra are found to compare well with the theoretical predictions.
Pressure generation due to a temperature discontinuity at a liquid-liquid plane interface
Authors: Cooper Fred , Blewett Patrick
Published: March 2003

Using a simplified equation of state, an analytic solution for the temperature, pressure, velocity, and acceleration of two semi-infinite liquids initially at two distinct temperatures is obtained by ignoring the effects of the generated pressure on the temperature distribution. It is found that the pressure wave generated in the cooler medium by the temperature discontinuity develops into a shock after passing through the thermal boundary layer. The cooler material is initially accelerated into the hotter material and thus if the cooler material is lighter, the interface is Raleigh–Taylor unstable. The pressures and velocities at the interface relax with a characteristic time τ=α/c2, where α is the thermal diffusivity and c is the speed of sound. For the particular case of liquid Na in contact with liquid UO2 specific results are given. The linearized approximation is compared with exact numerical integration of the full hydrodynamic equations and reasonable agreement is found.
Observations of stimulated Brillouin backscattering from a magnetically confined plasma
Authors: Massey R. S. , Pietrzyk Z. A. , Scudder D. W.
Published: March 2003

Backscattered laser radiation has been observed from a CO2 laser-produced and heated underdense plasma in a steady solenoid magnetic field, and is attributed to the stimulated Brillouin scattering process. Spectral measurements and observations of the dependence of the backscattered intensity on laser power are presented to support this identification. Backscattered radiation, amounting to as much as 1% of the incident power, was found to be redshifted by 80–100 Å, the shift expected for stimulated Brillouin scattering from a plasma at the measured temperature Te=80±25 eV. Data are also presented on the dependence of backscattered power on the density and convergence angle of incoming radiation.
Effects of beat-wave electron trapping on stimulated Raman and Thomson scattering
Authors: Cohen Bruce I. , Kaufman Allan N.
Published: March 2003

The influence of electron trapping on a large amplitude plasma oscillation driven by the nonlinear interaction of two electromagnetic waves (stimulated Raman scattering) is studied analytically and by means of numerical simulation. When the plasma oscillation is resonantly excited to sufficiently large amplitude and electron trapping occurs, there ensues considerable modification of the electron velocity distribution function. The stimulated scattering ceases to be a resonant three-wave process but continues as induced scattering by resonant electrons (stimulated Thomson scattering). The scattering of the electromagnetic waves becomes slower, but does not terminate with the onset of particle trapping in the beat wave.
Radial normal mode calculation of warm plasma stabilization of the drift cone mode
Authors: Gerver M. J.
Published: March 2003

The fraction Δ of warm plasma needed to stabilize the drift cone mode is calculated for a loss cone plasma slab in a uniform magnetic field with Rp∼aH∼k−1, where Rp is the width of the slab (representing the radial scale length), aH is the hot ion Larmor radius, and k is the wavenumber of the mode. For 2XIIB-like parameters, a minimum Δ of 14% is needed for stability, which is consistent with experimental observations. This result is an improvement on previous calculations, which used the local approximation (assuming Rp≫aH≫k−1) and gave a minimum Δ of 10% for the same parameters. Information is also obtained on the radial location and width of the normal modes, and on the effect of varying the warm plasma radial density profile.
Magnetohydrodynamic equilibria and local stability of axisymmetric tokamak plasmas
Authors: Peng Y-K. M. , Dory R. A. , Nelson D. B. , Sayer R. O.
Published: March 2003

The Mercier stability criterion is evaluated for various axisymmetric magnetohydrodynamic equilibria in a systematic study of the effects of shaping on the plasma critical β (volume averaged pressure over the vacuum toroidal field pressure at the center of the plasma chamber). Pressure profiles that are similar to those observed in tokamak experiments are used. Equilibrium parameters of interest are elongation, σ, and triangularity, δ, of D-shaped cross sections, aspect ratio, A, poloidal beta, βp, and pressure profile width, wp. Doublet plasmas with various σ are also included for completeness. It is shown that, for fixed plasma shapes, the critical β values increase strongly with increasing wp (typically by a factor of roughly 4), while for fixed values of wp the critical β values have a weaker dependence on plasma shaping (typically by a factor of roughly 2). The effectiveness of shaping (to increase β) decreases with decreasing wp, and for experimental values of wp (≲0.5) the best critical β values so determined is less than 6%. For fixed wp in D-shaped plasmas,it is shown that the highest critical β occurs around σ=1.65 and δ=0.5. The critical β values increase strongly with decreasing A. However, if the toroidal field is fixed at the coil surface at the distance between the coils and the plasma edge is greater than half the minor radius, the highest critical pressure occurs when A≳3–4. The doublet plasmas considered here with σ=3 give critical β values that are similar to those of the optimal D-shaped plasmas, when identical values of wp are used.
Quasi-neutral particle simulation model with application to ion wave propagation
Authors: Okuda H. , Dawson J. M. , Lin A. T. , Lin C. C.
Published: March 2003

A new class of particle simulation models has been developed which eliminates the high-frequency space charge oscillations while keeping the low-frequency ion-density fluctuations unmodified. Physically, the quasi-neutrality is maintained as the adiabatic electrons follow the ion-density fluctuations so as to establish the Debye shielding. It is, therefore, possible to use an integration time step comparable to the characteristic time scale of the low-frequency oscillations so that realistic plasma parameters can be used in the present simulation model. Applications to ion sound wave propagation, ion-ion two-stream instability, and the low-frequency fluctuation spectrum in a magnetic field are given. The way in which to include the nonadiabatic electrons in the model is also discussed.
Similarity law and renormalization for Burgers’ turbulence
Authors: Mizushima Jiro
Published: March 2003

Two assumptions, a similarity in the turbulent field and an invariance of the large scale motions, are made and a renormalization technique is used for the Burgers turbulence. It turns out that the power index of the energy decay ranges continuously from −2/3 to −2, depending on the cases.
Electron Landau damping and electron collisions
Authors: Sperling J. L.
Published: March 2003

The effect of electron-electron collisions on the Landau damping of a single wave in a magnetized or unmagnetized plasma is calculated using a model Fokker–Planck operator. The resulting form of Landau damping could play a role in the saturation of some parametric and trapped-particle instabilities.
Theoretical interpretation of angle- and polarization-dependent laser light absorption measurements
Authors: Thomson J. J. , Kruer W. L. , Langdon A. Bruce , Max Claire Ellen , Mead W. C.
Published: March 2003

It is shown that recently published observations of angle- and polarization-dependent absorption of intense laser light are consistent with computer simulations of resonance absorption in a steepened plasma profile, with the additional assumption of a modestly rippled critical surface.
Approximate solutions to the Navier–Stokes initial value problem
Authors: Rosen Gerald
Published: March 2003

A Galerkin–Ritz procedure for any arbitrary system of field equations is shown to follow generically from ’’two-functional’’ variational conditions. The initial-value problem for boundary-free incompressible Navier–Stokes flow is solved analytically in the two-parameter-function approximation.
Transonic nozzle flows of real gases with nonuniform gas properties
Authors: Ishii Ryuji
Published: March 2003

The transonic flow of a vibrationally relaxing or a chemically reacting gas in a convergent-divergent nozzle is considered. The procedure used to solve the flow equations is similar to that first used by Hall, and the solution is based on a series expansion in terms of the wall geometry in the transonic region. The nonuniformities of the flow properties across the flow field are taken into consideration. Taulbee and Boraas have already solved such a problem for a frozen flow by a sort of inverse method, in which the governing equations are written with the stream function as an independent variable so as to accomodate the variations in flow properties across the flow field. The problem is solved by a direct method, in which the flow equations are written with generalized coordinates of curvilinear coordinates comprising the streamlines and the system of lines normal to the streamlines, and analytical solutions are obtained for both frozen and equilibrium flows.
Transient analysis of a laser supported detonation wave using Whitham’s rule
Authors: Jumper E. J.
Published: March 2003

Analysis is made of a laser supported detonation wave using Whitham’s rule. The C+ characteristic is developed for absorption of laser energy immediately behind a shock wave. The characteristic is then coupled with the Rankine-Hugoniot equations relating conditions across the shock. In this way an equation for predicting the transient shock strength is obtained. The result is compared to experiment and to steady state laser supported detonation theory. The result of this comparison is that the derived equation does duplicate the transient response of the experiment and (when allowed to run to steady state) it does agree with many of the characteristics of the steady state theory.