bluuebunny/crossref_metadata_2025 huggingface dataset:
Numerical calculation of gravity-capillary interfacial waves of finite amplitude
Authors: Vanden-Broeck Jean-Marc
Published: March 2003

Gravity-capillary progressive interfacial waves on the interface between two semi-infinite fluids of different densities are considered. An integro-differential equation for the unknown shape of the interface is derived. By introducing a mesh and finite difference, this equation is converted into a finite set of nonlinear algebraic equations. These equations are solved by Newton’s method. In the limiting case of pure gravity waves, the results obtained are in good agreement with previous calculations. Two continuous families of capillary-gravity waves are studied. A generalization of Wilton’s ripples for interfacial waves is presented.
Nonlinear stability of modulated finite gap Taylor flow
Authors: Tustaniwskyj J. I. , Carmi S.
Published: March 2003

The energy stability analysis for an arbitrary gap time-dependent flow is performed. The solution for the basic flow is obtained assuming that either one or both cylinders rotate with a mean and/or sinusoidal velocity. Arbitrary finite amplitude three-dimensional disturbances are considered with two-dimensional axisymmetric disturbances found to render the smallest eigenvalues. The energy stability limits are found to be strongly dependent on the gap size as well as on the modulation frequency.
General theory of kinetic ballooning modes
Authors: Frieman E. A. , Rewoldt G. , Tang W. M. , Glasser A. H.
Published: March 2003

The ’’ballooning mode formalism,’’ previously developed for the ideal magnetohydrodynamic problem, is applied to the kinetic problem in tokamaks. The general two-dimensional equation governing drift and trapped-electron eigenmodes reduces to a one-dimensional integral equation along the lines of force with the radial structure determined by a WKB procedure. Comparisons made between the present one-dimensional code and a previous two-dimensional code embodying identical physical assumptions indicate reasonable agreement. This correspondence holds both for the structure along the field line and for the radial structure in the special case of closely spaced turning points.
Collisionless drift instability and ion heating in a current-carrying inhomogeneous plasma
Authors: Hatakeyama R. , Oertl M. , Märk E. , Schrittwieser R.
Published: March 2003

Low-frequency collisionless drift waves grow intensively when electron currents parallel to a magnetic field are drawn in a single-ended Q machine. For a smaller electron drift velocity, the measured dispersion relations of the wave are consistent with the linear theory of the current-driven collisionless drift instability. The temperature of the ions is observed to increase anisotropically concomitant with the growth of the drift wave. The heating rate is found to be proportional to the wave energy estimated from the saturated frequency spectrum and its dependence on the electron drift is measured to be of the form (u/ve)4. A further increase in the electron drift results in the excitation of an ion acoustic wave and a flute-like instability.
Transient amplification of shear Alfvén waves and concomitant development of the gravitational instability
Authors: Lau Y. Y. , Davidson Ronald C. , Hui Bertram
Published: March 2003

Making use of the ideal magnetohydrodynamic description in a plasma slab model, the transient amplification of shear Alfvén waves and their concomitant development into gravitational (ballooning) instabilities as the plasma pressure is increased are studied. When applied to tokamak geometry, for β<βc/2, it is found that the curvature effect has a negligibly small influence on the evolution of the shear Alfvén waves. (Here, β is the ratio of plasma pressure to magnetic pressure, βc =Rrn/Ls2 is the critical beta, R is the major radius, rn is the plasma density length scale, and Ls is the magnetic shear length scale.) The curvature effect becomes dominant, however, for β≳(3/4)βc, and the instability exhibits very strong growth whenever β≳1.1βc.
Resistive tearing mode in weakly two-dimensional neutral sheets
Authors: Janicke Lutz
Published: March 2003

The resistive tearing mode is expected to be rather sensitive to a magnetic field component perpendicular to the singular layer (B⊥) that typically occurs in weakly two-dimensional sheets, and a stabilizing effect was suggested by previous authors. A normal mode analysis is performed by rigorous application of the singular perturbation technique, i.e., the scalings are determined from the significant degeneration of the differential operator and matching is accomplished by the overlap hypothesis. For B⊥/B0=O(ε2α), a tendency of the plasma flow to follow the (curved) field lines is demonstrated (ε is the width of the singular layer and α is the wavenumber of the perturbation, both are normalized to the thickness of the current sheet). The dispersion relation, however, derived in closed analytical form for S−2/5⩽α=O(1), shows no influence of the normal component on the growth rate (S is the magnetic Reynolds number). Thus, the classical results of Furth, Killen, and Rosenbluth are recovered and an analytical expression for their numerical results in the regime of the maximum growth rate is given.
Equilibrium and propagation of a rotating relativistic electron beam
Authors: Sethian J. D. , Gerber K. A. , Spector D. N. , Robson A. E.
Published: March 2003

An experimental and theoretical study of a charged, but not current-neutralized, hollow, rotating relativistic electron beam propagating inside a metal tube in the absence of an external magnetic guide field is described. A model has been developed in which the radial equilibrium is derived from the force balance on the beam interacting with its self-field, and the velocity of propagation of the beam is derived from the power balance. The experimental results show close agreement with the predictions of the model.
Self-similar decay of turbulent kinetic energy in a model with only local energy transfer
Authors: Kerr Robert M. , Nelkin Mark
Published: March 2003

It is shown that the cascade model of Bell and Nelkin has a second self-similar solution corresponding to decaying turbulence with an energy spectrum proportional to ks at low wavenumbers. Extension of the model to the decay of a passive scalar is discussed.
Convection in binary fluids
Authors: Knobloch E.
Published: March 2003

The equations describing thermal convection in a binary fluid driven by the Soret and Dufour effects are shown to be identical, except for a relation between the thermal and solutal Rayleigh numbers, to the equations describing thermosolutal convection. A number of results about the former problem are deduced.
Point-vortex simulation of the inverse energy cascade in two-dimensional turbulence
Authors: Siggia Eric D. , Aref Hassan
Published: March 2003

The conventional cloud-in-cell vortex representation of the two-dimensional Euler equations is modified to allow energy injection from small scales. A simulation of the inverse cascade yields an energy spectrum consistent with k−5/3 and a Kolmogoroff constant of 14.
Relativistic theory of electron cyclotron resonance heating
Authors: Bernstein Ira B. , Baxter David C.
Published: March 2003

The formal theory of the interaction of mildly relativistic electrons with a cyclotron resonant applied electromagnetic field described by geometric optics is developed. The electron distribution function is written as the sum of a quasi-static part f0 and a high frequency part f1. A quasi-linear theory is employed to describe these. The resulting transport equation f0 is written to lowest significant order jointly in the reciprocal of the gyration frequency and the bounce frequency. It includes a relativistic collision term and a drag term associated with synchrotron emission. The linearized equations for f1 are solved, and an expression for the high-frequency current is derived.
Temporal evolution of lower-hybrid waves in the presence of ponderomotive density fluctuations
Authors: Karney Charles F. F.
Published: March 2003

The propagation of lower-hybrid waves in the presence of ponderomotive density fluctuations is considered. The problem is treated in two dimensions, and in order to be able to correctly impose the boundary conditions, the waves are allowed to evolve in time. The fields are described by ivτ−ℱ vξ dζ+vζζ+‖v‖2v= 0, where v is proportional to the electric field, τ to time, and ζ and ξ measure distances across and along the lower-hybrid ray. The behavior of the waves is investigated numerically. If the amplitude of the waves is large enough, the spectrum of the waves broadens and their parallel wavelength becomes shorter. The assumptions made in the formulation preclude the application of these results to the lower-hybrid heating experiment on Alcator-A. Nevertheless, there are indications that the physics embodied in this problem are responsible for some of the results of that experiment.
Electron heating in high intensity CO2 laser-plasma interaction
Authors: Ebrahim N. A. , Joshi C.
Published: March 2003

Detailed measurements of heated electron distributions generated in a short density scale length 10.6 μm laser plasma interaction in the intensity regime 1012≲I(W cm−2)≲1014 are reported. Maximum electron energies up to 600 keV observed in this study appear to be inconsistent with characteristic maximum energies of electrons generated by resonant absorption in the warm plasma wave breaking limit. Furthermore, heated electron distributions from foils of thickness much less than the hot electron mean-free-path as well as from different Z targets suggest that reheating of very energetic electrons by multipassing through the resonant region does not occur; rather the highest-energy electrons are preferentially accelerated in the backward direction with very large single pass energies. Plasma instabilities at the quarter critical as well as those at the critical are thought to be responsible for the generation of the high-energy electron component. Finally, these studies show that the electron emission spectra are sensitive to the electrical properties of the target support structure.
Two-dimensional drops in slow viscous flow
Authors: Vanden-Broeck Jean-Marc
Published: March 2003

The distortion of a two-dimensional drop in a slow viscous flow is computed up to the limiting configuration in which opposite sides of the drop touch one another.
Internal consistency of weakly nonlinear theories of solitary waves
Authors: Joseph R. I.
Published: March 2003

The Whitham equation for the wave dispersion ω/k=(1+k2)−1 is shown to be equivalent to ut+ux−uxxt+uux−(uux)xx=0. By studying its stationary wave solutions, it is shown that there exists a critical value of the speed c(=4/3) above which this weakly nonlinear theory becomes internally inconsistent.
Breakup and reconstitution of Langmuir wave packets
Authors: Tajima T. , Goldman Martin V. , Leboeuf J. N. , Dawson J. M.
Published: March 2003

Recursive behavior has been observed in a two-dimensional electrostatic particle simulation of a coherent intense Langmuir wave packet. The recursion may be associated with the fact that the plasma frequency has a spatial variation in the density depression created by the ponderomotive force.
Evidence for multiple Brillouin modes in laser-plasma backscatter experiments
Authors: Turner Robert E. , Goldman Leonard M.
Published: March 2003

Time resolved backscatter spectra, recorded during high intensity (1016 W/cm2) irradiation of moderate density scale length plasmas, show a time-dependent mode structure.
Viscous buckling of thin fluid layers
Authors: Suleiman Shawqi M. , Munson Bruce R.
Published: March 2003

Experimental results are presented describing the buckling type of instability of thin layers of very viscous liquids subjected to linear shear flow. If the dimensionless shear stress in the layer exceeds a critical value, the layer will buckle in a manner similar to the buckling of a thin elastic plate. The stability criteria are obtained as a ratio of the destabilizing viscous stresses relative to the stabilizing surface tension and gravitational forces.
Magnetic field diffusion and dissipation in reversed-field plasmas
Authors: Drake J. F. , Gladd N. T. , Huba J. D.
Published: March 2003

A diffusion equation is derived which describes the evolution of a magnetic field in a plasma of arbitrary β and resistivity. The equation is valid for a one-dimensional slab geometry, assumes the plasma remains in quasi-equilibrium throughout its evolution (i.e., pressure balance), and does not include thermal transport. Scaling laws governing the rate of change of the magnetic energy, particle drift energy, and magnetic flux are calculated. It is found that the magnetic free energy can be substantially larger than the particle drift energy and can be an important energy reservoir in driving plasma instabilities (e.g., the lower-hybrid-drift instability). In addition, the effect of a spatially varying resistivity on the evolution of a reversed-field plasma is studied. The resistivity model used is based upon the anomalous transport properties associated with the nonlocal mode structure of the lower-hybrid-drift instability. The relevance of this research to laboratory plasmas (e.g., theta pinches, reversed-field theta pinches) and space plasmas (e.g., the earth’s magnetotail) is discussed.
Neoclassical transport in helically symmetric plasmas
Authors: Pytte A. , Boozer Allen H.
Published: March 2003

The neoclassical rate of diffusion is calculated in such a way that the result is applicable to both helically symmetric and toroidally symmetric plasmas.
Convective cell formation and anomalous diffusion due to electromagnetic drift wave turbulence
Authors: Weiland J. , Sanuki Heiji , Liu C. S.
Published: March 2003

Convective cell formation and spectral cascade processes due to gravitational drift Alfvén waves are studied using a new type of model equation. Conservation relations are derived and explosive instability is found for systems near marginal finite β stability. This instability also remains when the effects of poor as well as favorable curvature regions are included, i.e., for ballooning modes. The anomalous diffusion due to convective cells and quasi-linear effects are compared.
Generation and collapse of Langmuir solitons in a nonuniform plasma
Authors: Pereira N. R. , Morales G. J.
Published: March 2003

This numerical study considers the effect of a zero-order density gradient on the development of Langmuir wave collapse in two dimensions. Two different situations are considered; (1) an initial soliton is pertubed in a direction transverse to the density gradient, and (2) the plasma is resonantly driven by an external pump electric field in the presence of transverse density fluctuations. The principal finding is that the density gradient can inhibit the development of Langmuir collapse for both the initial soliton and the externally driven cases. Over the limited parameter space surveyed it is found that collapse occurs for values of the scaled gradient parameter g≲2.5; where g = (9/8)(M/m)3/2(λD/L), M is the ion mass, m is the electron mass, λD is the Debye length, and L is the gradient scale length. For larger values of g, collapse is not observed.
Structure functions of turbulence in an adverse pressure gradient
Authors: Azad R. S. , Hummel R. H.
Published: March 2003

Longitudinal and transverse structure functions of turbulent velocity fluctuations up to the fourth order have been measured in an adverse pressure gradient and compared with the original ideas of Kolmogoroff and with other experimental results. The results show the existence of an inertial subrange for a separation range of about one decade, and in turn the predictions of Kolmogoroff’s original theory have some validity even for a flow that is subjected to an adverse pressure gradient.
Viscous buckling of slender horizontal jets
Authors: Munson B. R.
Published: March 2003

Experimental results are presented describing the buckling type of instability in jets of very viscous liquids that flow from vertical slit-type orifices. Under certain conditions, the jet may buckle in a manner similar to the buckling of a cantilever beam. The governing dimensionless parameters are identified and their critical values determined.
Alfvén wave excitation of the magnetostatic mode
Authors: Yu M. Y. , Shukla P. K. , Spatschek K. H.
Published: March 2003

It is shown that the magnetostatic mode can be excited by kinetic Alfvén waves. The growth rates are calculated for various limits of interest in plasma diffusion studies as well as Alfvén wave plasma heating experiments.
Simple criteria for the absence of the beam-Weibel instability
Authors: Cary J.R. , Thode Lester E. , Lemons Don S. , Jones Michael E. , Mostrom Michael A.
Published: March 2003

Rigorously sufficient and approximately necessary conditions for the absence of the beam-Weibel instability are derived. These conditions include previously known stability criteria and resolve the seeming contradiction that these modes can be stabilized by beam temperature when the plasma is cold, but they cannot be stabilized by beam temperature when the plasma has infinitesimally small temperature.
Linear waves and instabilities on magnetically insulated gaps
Authors: Swegle John , Ott Edward
Published: March 2003

A linear, fully relativistic and electromagnetic analysis of waves perturbing the Brillouin flow state on planar, magnetically insulated gaps is presented. Three independent classes of waves are treated individually; transverse-magnetic waves propagating normal to the insulating magnetic field, transverse-electric waves propagating in the same direction, and a set of waves propagating along the magnetic field. Dispersion relations governing discrete modes of oscillation for each class are found and solved for some cases of interest. Only the transverse-magnetic waves are found to be unstable due to the existence of a Doppler-shifted plasma reasonance layer at frequencies above the plasma frequency. The scaling of the growth rate for this instability with respect to parameters characterizing the equilibrium state is examined. In addition to these discrete modes, spectral continua associated with localized resonance phenomena in the electron sheath bounding the cathode are described and explained.
Nonlinear saturation of the lower-hybrid-drift instability: Axis encircling model
Authors: Myra J. R. , Aamodt R. E.
Published: March 2003

The nonlinear evolution of the lower-hybrid-drift instability is considered in the guiding-centers-on-axis model. Extremely rapid radial quasi-linear diffusion of electrons leads to the buildup of a radial electric field Er. Saturation occurs when the Er×B electron drift velocity equals the local ion rotational velocity. Due to the rapid linear growth rate, the unmagnetized ions are unable to shield out Er, which becomes significant long before density profile flattening occurs.
Theory of two-point correlation function in a Vlasov plasma
Authors: Boutros-Ghali Teymour , Dupree Thomas H.
Published: March 2003

A self-consistent theory of phase-space granulations, called ’’clumps’’, has been derived. These fluctuations are produced when regions of different phase-space density are mixed by the fluctuating electric fields. The source term and turbulent scattering operator for these fluctuations are obtained through a renormalization of the one- and two-point equations for a Vlasov plasma. The proper treatment of the singular behavior exhibited by the two-point equation, coupled with the self-consistent approach leads to a number of significant changes compared with previous formulations. The case of electrostatic turbulence is considered throughout this paper. The method of solution is based on the concept of two disparate time scales which allow the treatment of the equal time two-point equation as an initial condition for its two-time counterpart. The picture of a ’’test’’ clump emerges quite naturally within such a framework. The source term for the clump correlation function is identified and certain intrinsic properties determined. Physical interpretations of the coefficients in the renormalization are given and their role in energy and momentum conservation demonstrated. The theory is reminiscent of Fokker–Planck analysis with which numerous parallels are drawn.
Cross-field diffusion and fluctuation spectra in a levitated octupole in the presence of a toroidal field
Authors: Ehrhardt A. Butcher , Garner H. R. , Navratil G. A. , Post R. S.
Published: March 2003

The diffusion coefficient D⊥ for a collisionless hydrogen plasma was measured in the levitated octupole when a weak toroidal field was added. A twenty-fold decrease in the anomalous diffusion was observed with Bt/Bp≳0.1. This reduced level of diffusion was still two orders of magnitude larger than the classical value and the residual level of convective cell activity was responsible for the enhanced transport. Locally trapped particles in the poloidal field mirrors allow the convective cell activity (f<600 Hz) to persist even when the toroidal field was added. The principal effect of the added toroidal field was observed to be a localization of the convective cells in the region where particles are trapped and a shift in the k⊥ spectrum to shorter wavelengths.
Anomalous decay of induced electron currents in field-reversed systems
Authors: Reiman A. , Sudan R. N.
Published: March 2003

Induced electron currents are studied in systems which are field-reversed due to ion currents, with no toroidal magnetic field. In such systems, electron flow is induced in the region of closed field lines, with a large velocity shear that can drive a Kelvin–Helmholtz type instability. Analysis of the nonlinear evolution suggests that the instability leads to a rapid dissipation of electron currents. Rough estimates show that the instability is likely to be of importance in field-reversed ion ring and mirror experiments.
Ion emission from laser-produced, multi-ion species, two-electron temperature plasmas
Authors: Wickens L. M. , Allen J. E.
Published: March 2003

A model for ion emission from (CH)n and (CH2)n laser-produced plasmas containing both hot and cold electron populations is presented. Computed Faraday cup current traces illustrate the point that separate C6+ and H+ ion current peaks cannot be resolved, showing that care should be excercised when interpreting the total ion current observed experimentally. The slow C6+ ions are found to carry most of the ion momentum. A small number of fast C6+ and H+ ions containing a substantial fraction of the total ion energy are produced. Fast ions, corresponding to those observed experimentally, can thus be generated without the need to invoke inhibition of heat flux into the target, as has been suggested.
Spectral energy transfer for inhomogeneous turbulence
Authors: Deissler R. G.
Published: March 2003

It is shown that even for a general inhomogeneous turbulence, certain terms in the two-point spectral equation can be interpreted as transfer terms.
An approximate method in transport theory
Authors: Loyalka S. K.
Published: March 2003

A simple improvement in the generalized Maxwell method for solving transport problems is proposed. In particular, using Milne’s problem of neutron transport as an example, it is shown that the accuracy of this method can be considerably improved by a judicious use of singular eigenfunctions.
Traveling mirror compressor delay line with nonconstant capacitance
Authors: Bellan P. M.
Published: March 2003

The scaling relations for a traveling mirror magnetic compressor [P.M. Bellan, Phys. Rev. Lett. 43, 858 (1979)] having nonconstant capacitance are derived. Varying capacitance (rather than inductance) makes possible a lower impedance device, and hence, higher field levels or faster compression times.
Further results on the thermal mixing layer downstream of a turbulence grid
Authors: LaRue John C. , Libby Paul A. , Seshadri D. V. R.
Published: March 2003

Simultaneous velocity and temperature measurements in the thermal mixing layer downstream of a partially heated turbulence grid are reported. The temperature data are in good agreement with earlier results. The velocity-temperature correlations are new and permit a systematic assessment of an earlier similarity theory for the region far downstream of the grid. By selecting the virtual origin appropriately and by reconsidering the role of scalar dissipation in that region, agreement between measurement and prediction with respect to temperature intensity and two mean lateral fluxes, that of temperature and of temperature intensity, is achieved.
Chaotic (strange) and periodic behavior in instability saturation by the oscillating two-stream instability
Authors: Russell David A. , Ott Edward
Published: March 2003

The nonlinear Schrödinger equation with linear growth and damping is truncated to three waves. The resulting system of nonlinear ordinary differential equations describes the excitation of linearly damped waves by the oscillating two-stream instability driven by a linearly unstable pump wave. This system represents a simple model for the nonlinear saturation of a linearly unstable wave. The model is examined analytically and numerically as a function of the dimensionless parameters of the system. It is found that the model can exhibit a wealth of characteristic dynamical behavior including stationary equilibria, Hopf bifurcations to periodic orbits, period doubling bifurcations, chaotic solutions characteristic of a strange attractor, tangent bifurcations from chaotic to periodic solutions, transient chaos, and hysteresis. Many of these features are shown to be explainable on the basis of one-dimensional maps. In the case of chaotic solutions, evidence for the presence of a strange attractor is provided by demonstrating Cantor set-like structure (i.e., scale invariance) in the surface of section.
Finite Larmor radius model for axisymmetric compact toroids
Authors: Seyler C. E. , Barnes Daniel C.
Published: March 2003

Stability equations for axisymmetric compact toroidal configurations without a toroidal magnetic field are derived in a variational form. The application of a particular ordering procedure gives equations which include the coupling of geometry to finite Larmor radius as well as including resonant ion effects. The equations are readily obtained by applying the ordering assumptions to a variational dispersion functional form of the Vlasov-fluid equations. Application of the dispersion functional to find necessary and sufficient conditions for stability are made for the case of small, but finite Larmor radius and for the case of zero Larmor radius. The mathematical result that the zero Larmor radius case is more optimistic is physically understood in the context of an interesting stabilizing mechanism involving parallel kinetic effects.
Plasma equilibrium with rational magnetic surfaces
Authors: Boozer Allen H.
Published: March 2003

The self-consistent classical plasma equilibrium with diffusion is studied in a toroidal geometry having a sheared magnetic field. Near each rational surface it is found that the pressure gradient is zero unless the Fourier component of 1/B2, which resonates with that surface, vanishes. Despite the resonances, the overall plasma confinement is, in practice, only slightly modified by the rational surfaces.
Currents generated by lower hybrid waves
Authors: McWilliams R. , Motley R. W.
Published: March 2003

Electron currents can be driven in a linear plasma by the absorption of lower-hybrid waves excited primarily in one direction. Current-drive has been demonstrated both for collisional and resonant-electron absorption. The magnitude of the excited current is compared with the predictions from an electron kinetic equation with a Lorentz collision operator in the regime k∥vte/ω≪1.
Cyclotron wave generation and phase velocity control on an intense relativistic electron beam
Authors: Cornet Edward , Davis H. A. , Starke T. P. , Rienstra W. W. , Uglum J. R.
Published: March 2003

The axisymmetric, negative energy branch of the Doppler-shifted electron cyclotron eigenmode has been excited on an unneutralized, 15 kA, 2.25 MV, relativistic electron beam propagating along a guide magnetic field interior to a vacuum conducting wave guide. Large amplitude waves have been generated by means of a traveling wave interaction with helical slow wave structures. The growth process has been identified as the resonant coupling of the negative energy cyclotron mode with the positive energy helix modes. The large amplitude wave produced was propagated on the beam and then identified to be the desired symmetric, negative energy cyclotron wave by direct measurement of its azimuthal symmetry, wavelength, and phase velocity direction. The on-axis axial electric field component of the wave was inferred to be in excess of 10 MV/m. Finally, as is necessary for collective ion acceleration by these waves, the cyclotron wave phase velocity has been controlled, in the range 0.20–0.06 times the speed of light, by spatially changing the guide magnetic field strength.
Relativistic plasma half-space with an external magnetic field
Authors: Imre Kaya
Published: March 2003

The boundary value problem involving a magnetized plasma half-space confined by a perfectly reflecting interface is solved using the relativistic Vlasov–Maxwell system. The external field is assumed to be constant and along the normal of the boundary, and only the linear responses to obliquely incident vacuum waves are considered. When the incidence is normal, only a pair of purely transversal modes, similar to the ordinary and extraordinary modes of the infinite systems, can be excited. When the incidence is oblique, two additional hybrid p and s modes may exist, which are decoupled into the longitudinal and transversal parts only when there is no external field. The p mode vanishes if the field at the boundary, B(0), is in the plane of incidence, and the s mode is zero if B(0) is in the plane which is perpendicular to both the interface and the plane of incidence. Reflection, transmission, and absorption coefficients are calculated for the case of normal incidence.
Anomalous heat conduction at the ends of a theta pinch
Authors: Lins G. A. W.
Published: March 2003

In a small theta pinch, a density pulse propagating to the end is found to form after the compression phase. Doppler-shift measurements of the He ii, λ = 4686 Å line indicate that axial particle flow is present only during the implosion, thermal conduction being the dominant end-loss mechanism at later times. Comparison of the actual heat flux with that expected from classical theory, the presence of an enhanced forbidden component as well as plasma satellites of the He i, λ = 4922 Å line outside the coil region, and a flat-top electron distribution function obtained by Thomson scattering, lead to the conclusion that thermal conduction is anomalous. The concept of a replacement wave is successfully applied to account for the observed phenomena.
Time-resolved measurements of the laser burn-through of thin foils
Authors: Murdoch John W. , Kilkenny J. D. , Gray D. R. , Toner W. T.
Published: March 2003

New time-and-space-resolved measurements of the burn-through of 0.05–0.34 μm thick plastic foils irradiated with 100 psec, 1.06 μm laser pulses at approximately 1016 Wcm−1 are presented. Comparison of the time history of the transparency of the foils with analytic and computational models suggests that the targets do not transmit until the density is well below the critical density. Comparison of the space-resolved burn-through measurements with an analytic model suggests that lateral thermal conduction is negligible. It is proposed that ion turbulence may be responsible for the high absorption and low thermal conductivity.
Vorticity distribution in the mixing layer
Authors: Martinez-Val Rodrigo
Published: March 2003

The experimental analysis of a turbulent mixing layer shows, by means of a simple algorithm, that the vorticity is concentrated in individual cores of (a) half the strength corresponding to the initial instability and (b) dimensions appreciably smaller than the vorticity thickness of the mixing layer.
Effect of collisions on ion gyroresonance
Authors: Shaing K. C. , Callen J. D.
Published: March 2003

The effect of collisions on ion gyroresonance in a magnetized plasma for frequencies ω≃nΩi is derived by solving the Fokker–Planck equation with a multiple-time-scale-type perturbation method. An example is given for kai≫1 with a Landau collision operator.
Expansion of electron bunches
Authors: Pereira N. R. , Hunter R. O.
Published: March 2003

The expansion of an electron bunch is solved exactly in Lagrangian coordinates, and the result is compared to a self-similar solution.
Calculations of Brillouin backscatter in laser-produced plasmas
Authors: Manheimer Wallace M. , Colombant D. G.
Published: March 2003

Brillouin backscatter is calculated in an inhomogeneous laser-produced plasma. Equations for the spatial dependence of the incident reflected and sound waves are numerically integrated through the underdense plasma. Effects investigated are those stabilizing ion heating or nonlinear sound wave dissipation, flow velocity magnitude and gradient, electron heating, and broadband incident laser light. It is found that the effect of velocity gradient and broadband light can be very important in reducing the backscatter.
A three-fluid model for critical surface structure in laser-plasma systems
Authors: Stellingwerf Robert , Longmire Conrad , Alme Marvin
Published: March 2003

A simple three-fluid model has been developed to describe the critical surface structure for cases in which an abrupt density jump causes resonant absorption to be the dominant absorption mechanism. In this model, ions, thermal electrons, and superthermal electrons interact in a rarefaction wave induced by the three-temperature equation of state and the ponderomotive force of the laser beam. Scaling laws from particle-in-cell calculations are used to simulate the effects of resonant absorption. The three temperatures characterizing the problem result in four distinct laser intensity regimes. Simple expressions are derived for the induced static potential, ion velocity, density, and temperature in three of these regimes. It is shown that these results agree with recent two-dimensional simulation studies. The model provides a critical surface momentum flux condition well-suited for implementation in a one-dimensional implosion code.
Free electron laser instability for a relativistic annular electron beam in a helical wiggler field
Authors: Uhm Han S. , Davidson Ronald C.
Published: March 2003

A free electron laser instability is investigated for a relativistic annular electron beam propagating through a helical wiggler magnetic field. It is assumed that the beam is thin, with radial thickness (2a) much smaller than the beam radius (R0), and that ν/γb≪1, where ν is Budker’s parameter. The stability analysis is carried out within the framework of the linearized Vlasov–Maxwell equations for perturbations with general azimuthal harmonic number l and radial mode number s, including the important influence of (a) finite beam geometry in the radial direction, (b) positioning of the beam radius relative to the outer conducting wall (R0/Rc), and (c) finite wiggler amplitude (δB). All of these effects are shown to have an important influence on stability behavior. Moreover, the maximum coupling between the transverse and longitudinal modes increases substantially with increasing radial mode number s. It is also found that the transverse magnetic (TM) mode has slightly larger growth rate than the transverse electric (TE) mode.
Electron and ion heating in a high-voltage toroidal theta pinch with parallel or antiparallel bias fields
Authors: Merlino R. L. , Goldenbaum G. C. , Chin-Fatt C. , Chong Y. P. , DeSilva A. W. , Griem H. R. , Hess R. A. , Murphy D. P.
Published: March 2003

Rapid heating of electrons and ions has been observed in a high-voltage toroidal theta pinch with initial bias fields either parallel or antiparallel to the fast rising toroidal field. The elimination of rapid end losses has permitted higher electron temperatures to be attained. In contrast to the results of linear theta pinches in which Te≲0.3 Ti, it is now found that Te∼Ti. The ion heating is similar to that observed in the linear case indicating that the effective microinstability heating process is maintained in a toroidal system. Higher temperatures were observed with antiparallel bias fields, but in both cases superthermal electron populations were observed indicating that the turbulent heating process involves electron tail formation.
Viscous decay of envelope solitons in water waves
Authors: Segur Harvey
Published: March 2003

The viscous decay rate of a packet of gravity-induced water waves in the form of an envelope soliton is twice the decay rate of the corresponding uniform train of infinitesimal waves.
Resonant absorption of Alfvén waves
Authors: Pritchett P. L. , Canobbio E.
Published: March 2003

The resonant absorption of Alfvén waves is investigated using a resistive magnetohydrodynamic fluid code. At very low frequencies, heating at the shear Alfvén resonance is found to be inefficient.
Diocotron instability in asymmetric beams
Authors: Poukey J. W. , Freeman J. R.
Published: March 2003

A hollow relativistic electron beam propagating in a cylindrical drift tube is subject to the diocotron instability. It is shown that if the beam is not azimuthally symmetric, then the diocotron effect can disrupt the beam in a substantially shorter time than in the symmetric case.
Reply to comments by J. A. Krommes
Authors: Catto Peter J.
Published: March 2003

A comment on the adiabatic modifications to plasma turbulence theory is presented.
Modeling of vortex-corner interaction using point vortices
Authors: Conlisk A. T. , Rockwell D.
Published: March 2003

Using point vortices, the interaction of a single vortex, as well as patterns of vortices, with a corner is examined; comparisons are made with corresponding experiments. Trajectories of a vortex swept past the corner can be well-approximated, provided that a sufficiently weak strength of the vortex is specified. Calculations show that the dimensionless amplitude of the pressure fluctuation at the corner is very sensitive to small variations of the initial position of the vortex, and relatively insensitive to variations in strength; this finding has important consequences for recently observed amplitude modulation of pressure at, and velocity near, impingement. In fact, by prescribing transversely staggered patterns of vortices upstream of the corner, determined from experimental flow visualization, the form of the time-averaged pressure and velocity spectra can be approximated. The most critical feature of these spectra, a well-defined low-frequency component(s), confirms the hypothesized mechanism associated with low-frequency modulation observed in experiments. In addition, shortcomings of this method, primarily due to distributed vorticity inherent in laboratory vortices, are pointed out.
Explosions on a gas-vacuum interface
Authors: Nutt Gerald , Klein Lewis , Ratcliffe Albert E.
Published: March 2003

A finite-difference computer code is used to calculate the time development of an explosion on a gas-vacuum interface. An analytic theory of the shape of the shock wave produced in the explosion is compared with the results of the computer simulation. The assumptions used in obtaining this analytic solution are verified, and the degree to which the variables describing the explosion are self-similar is examined. Finally, certain consistency relations among the similarity exponents are tested.
Strong evaporation in half-space: Integral transport solutions for one-dimensional Bhatnagar–Gross–Krook model
Authors: Loyalka S. K.
Published: March 2003

The strong evaporation problem in half-space for the one-dimensional Bhatnagar–Gross–Krook model is considered, and it is shown that highly accurate results in the lowest approximation can be obtained by a judicious use of two different integral transport methods. Extensions of the work to higher order kinetic models is discussed, and some comments regarding obtaining accurate results for the Boltzmann equation by use of the generalized Maxwell method are also included.
Rarefaction shocks in spherical geometry
Authors: Mitrovich Dushan
Published: March 2003

The uniform density region that develops behind a rarefaction shock in planar geometry (and attaches downstream to the outer expansion flow) is shown to be modified by geometric divergence into a region of self-similar flow with nonvanishing gradients. A single set of equations is derived that describes both shock and similarity flow. The longest gradient scale length in the transition region is shown to vary linearly with the radius at the shock.
Universal drift waves in a low-aspect-ratio spheromak geometry
Authors: Marchand R. , Guzdar P. N.
Published: March 2003

An eigenmode equation for drift waves in low-aspect-ratio spheromak geometry is derived and solved numerically. In contrast to the large-aspect-ratio tokamak limit, the strong equilibrium variation involved here, allows partially localized modes at more than one value of the poloidal angle.
Ponderomotive effects and magnetic field generation due to short-wavelength ion turbulence
Authors: Mora Patrick , Pellat René
Published: March 2003

The ponderomotive effects and magnetic field generation due to the nonlinear interaction of short-wavelength ion turbulence with an electromagnetic wave are studied using the Dawson and Oberman model, which exactly describes the electron-ion interaction in the limit of infinite ion-to-electron mass ratio. The differences from the results of the heuristic Landau model are stressed, in particular for nonthermal ion correlations and for an electromagnetic wave frequency slightly exceeding the electron plasma frequency.
Quasi-linear saturation of coherent backward ionization modes
Authors: Thieltgen A. , Leclert G. , Cussenot J. R.
Published: March 2003

Quasi-linear saturation of the amplitude of coherent backward ionization waves is studied using the slowly varying parameters or Van der Pol’s method. The result is a nonlinear Landau equation which describes the growth and saturation of the wave amplitude. The analytical expression of the most important nonlinear saturation term predicts results in accordance with earlier experimental observations.
Finite Larmor radius stabilization of ballooning modes in an axisymmetric tandem mirror
Authors: D’Ippolito D. A. , Francis G. L. , Myra J. R. , Tang W. M.
Published: March 2003

The stability of an axisymmetric tandem mirror to ballooning modes is examined including the effect of finite ion gyroradius stabilization. The central cell of the tandem mirror is treated as a long-thin system with isotropic pressure, while the end plug is modeled by a stabilizing boundary condition. For the particular equilibrium considered, the finite Larmor radius corrections to ideal magnetohydrodynamic theory indicate a strong stabilizing effect on high–n ballooning modes even for quite modest values of the gyroradius, k⊥ ρi∼a/L≪1. The dependence of βc on k⊥ ρi is computed, and physical mechanisms associated with this stabilizing influence are discussed.
Low-m ballooning stability of an axisymmetric sharp-boundary tandem mirror
Authors: D’Ippolito D. A. , Hafizi B.
Published: March 2003

A simple model of an axisymmetric tandem mirror is employed to study the stability of global (low-m) ballooning modes in the central cell. The presence of a perfectly conducting wall in the model gives an estimate of the effect of wall stabilization. The scaling of the critical β ( = 2p/B2) with mode number m, connection length Lc to the end plug, and wall position w is computed for several magnetic field profiles.
Calculation of resonant transport coefficients from mappings
Authors: Cohen Ronald H. , Rowlands George
Published: March 2003

For a two-degree-of-freedom dynamical system in which the dynamics depends on a parameter μ, the effect of an externally imposed random variation (e.g., collisions) of μ is considered. In particular, mapping equations in conjunction with particle conservation are used to directly derive transport coefficients. The analytic method and nature of the results depend on a stochasticity parameter K which describes the nonlinearity of the collision-free dynamics and a collisionality parameter σ. For large K or σ, Rechester, Rosenbluth, and White’s method of diagrams in Fourier space is used to calculate stochastic diffusion. For small K and moderate σ(≳K3/2), an expansion in powers of K is used to solve the map equations and thus obtain plateau transport coefficients. For small K and small σ, an expansion in powers of σ leads to banana transport coefficients. The results are applied to the calculation of radial resonant transport coefficients for tandem mirrors; the plateau and banana particle and energy fluxes are equivalent to those previously obtained from drift-kinetic theory, and the stochastic fluxes, not directly calculable in the drift-kinetic approach, are given explicitly.
Finite Larmor radius stabilization of diffuse profile high-beta stellarators
Authors: Schmidt Michael J. , Miller Guthrie
Published: March 2003

Finite Larmor radius effects are incorporated into near theta pinch magnetohydrodynamic theory following the method of Pearlstein and Freidberg. By a straightforward solution of the eigenvalue problem with finite Larmor radius effects included, the stability of various diffuse profile configurations has been investigated. The results differ qualitatively, as well as quantitatively, from sharp boundary theory, and it is not true, in general, that the stabilizing effect is absent for m = 1. It is found that fat plasmas can be completely stabilized by finite Larmor radius effects.
Force free equilibria in toroidal geometry
Authors: Miller Guthrie , Turner Leaf
Published: March 2003

The equation ∇×B−λB=0, where B is the magnetic field and λ is constant, is solved analytically in toroidally curved cylindrical coordinates, assuming a large aspect ratio torus.
Limit cycle behavior of the bump-on-tail instability
Authors: Janssen Peter A. E. M. , Rasmussen J. Juul
Published: March 2003

The nonlinear dynamics of the bump-on-tail instability is considered. The eigenmodes have discrete k because of finite periodic boundary conditions. Increasing a critical parameter (the number density) above its neutral stable value by a small fractional amount Δ2, one mode becomes unstable. The nonlinear dynamics of the unstable mode is determined by means of the multiple time scale method. Usually, limit cycle behavior is found. A short comparison with quasi-linear theory is given, and the results are compared with experiment.
Ballooning and interchange stability in axisymmetric field reversed equilibria
Authors: Finn John M.
Published: March 2003

The magnetohydrodynamic stability of axisymmetric field reversed equilibria (compact tori) without a toroidal magnetic field is studied. It is shown that axis encircling ions do not interact with modes having a short wavelength in the toroidal (symmetry) direction. A large toroidal aspect ratio equilibrium with nearly circular flux surfaces is found to be stable to ballooning modes if the axis encircling ions carry more than half the current. In the opposite limit, e.g., elliptical flux surfaces with aspect ratio as large as 5, ninety percent of the current must be carried by axis-encircling ions. In a thermal plasma (a reversed field theta pinch, for example) only a fraction of the outer flux surfaces are unstable if ρi/L, the ratio of ion gyroradius to scale length, is greater than 0.3, and if the flux surfaces are not too elongated.
Transport of a trace impurity in a dirty plasma in the Pfirsch–Schlüter regime
Authors: Burrell Keith H. , Wong Seung Kai
Published: March 2003

Particle transport rates for a trace impurity are calculated for a Pfirsch–Schlüter regime plasma consisting of a main ion and all the charge states of a background impurity. The main ion is taken to be much lighter than all impurities, but masses and charges are otherwise arbitrary. Qualitative trends of the transport rates with variations in the trace impurity mass and background impurity concentrations are discussed.