bluuebunny/crossref_metadata_2025 huggingface dataset:
The effect of a virtual cathode on the electromagnetic stability of high-power ion diodes
Authors: Slutz S. A. , Johnson W. A.
Published: July 2002

Previous stability analyses have shown magnetically insulated ion diode equilibria to be unstable. However, important equilibrium features such as a virtual-cathode and a charge–neutral region were not included. A stability analysis including these features is presented, which indicates that the stability behavior is strongly affected by the equilibrium model. In particular, the diocotron instability displaces the ion resonance instability found in the previous analyses. The calculated growth rates for the diocotron mode are consistent with a fast growing mode that has been observed in recently reported three-dimensional numerical simulations. These simulations exhibit a transition from the diocotron to an ion resonance mode and a subsequent increase in ion divergence due to the much lower frequency of the ion mode. The stability analysis presented in this paper demonstrates how the evolution of the electron sheath reduces the diocotron growth rate resulting in unstable ion modes, thus explaining the transition to ion modes observed in the simulations.
Wave breaking in a cold plasma with a parabolic density profile
Authors: Cros B. , Chiron A. , Matthieussent G.
Published: July 2002

The wave-breaking time of electronic plasma waves in an unmagnetized, cold plasma with a parabolic density profile is obtained analytically. The results are similar to those obtained in a linear density profile except at the top of the parabolic density profile where the wave-breaking time is shown to be proportional to E−1d instead of E−1/2d, Ed being the driving field.
Trapped structures in drift wave turbulence
Authors: Crotinger James A. , Dupree Thomas H.
Published: July 2002

The development of trapped structures in decaying and saturated drift wave turbulence is studied via computer simulation. A two-dimensional electrostatic fluid model is used. The turbulence that evolves in the pure decay runs (i.e., no nonadiabatic electrons) is characterized by tightly bound monopole vortices and a very narrow frequency spectrum. For the studies of saturated turbulence, a new nonadiabatic electron model is introduced, which gives the qualitatively correct response to a coherent trapped structure. This model takes into account the effects of broadening and shifting of the frequency spectrum. These effects are found to be quite important. Trapped structures are observed in many of the saturated simulations, even in the presence of moderately broad frequency spectra. The extent of the trapping varies dramatically, becoming a much stronger effect as the average electric field increases.
Theory of kinetic Alfvén wave helicity injection and current drive
Authors: Craddock G. G. , Diamond P. H.
Published: July 2002

Kinetic shear Alfvén wave (KSAW) helicity injection motivated by the goal of simultaneous implementation of radio frequency current and flow [Phys. Rev. Lett. 67, 1535 (1991)] drive is analyzed. The quasilinear helicity flux results in a net helicity increase only via transport through the boundaries. This, in turn, requires a compressional component at the plasma edge boundary and electron dissipation at the Alfvén resonance, as well as throughout the region, where helicity transport occurs. A comparison is made to direct KSAW current drive, which can add constructively with helicity injection by tailoring of the sign of poloidal and parallel wave numbers. The KSAW helicity flux is related to the α effect due to MHD (magnetohydrodynamic) resistive kink and shear-Alfvén-driven helicity fluxes. The helicity flux need not have a zero flux surface average. Finally, the efficiency (IpR/Pabs) of helicity injection by the KSAW is found to be significantly smaller than that by viscoresistive shear Alfvén waves, and scales as (IpR/Pabs)∼n0−3/2B03, where n0 is the density and B0 is the toroidal magnetic field. Application to edge current drive for ELM control is discussed.
Anomalous viscosity due to drift wave turbulence
Authors: Itoh Sanae-I.
Published: July 2002

The transport matrix, due to low-frequency microturbulence, is obtained for a cylindrical plasma including anomalous ion and electron viscosities. Quasilinear theory is used in the electrostatic limit. Particle, momentum, and energy fluxes are represented in terms of three thermodynamical forces, which are generated by the density gradient, the gradient of the parallel flow, the temperature gradient, radial electric field, and the convection of the wave. The characteristics of the matrix are examined. The 3×3 transport matrices for electrons and ions are symmetric but contain off-diagonal elements. In the drift wave approximation, the ion flux decouples from the thermodynamical force on the electrons, and vice versa. The ion anomalous viscosity, the heat conductivity, and the off-diagonal elements are found to be comparable. The anomalous electron viscosity due to the drift wave is calculated to be small. The transport equations of ions show that pure heat conductivity, which is the value when the net particle flux is zero, is small compared to the heat conductivity [i.e., (3,3) component of the transport matrix]. The anomalous viscosity gives rise to an additional heating on the ions because of viscous damping. The condition for a particle pinch to occur is also examined. If the convection of the wave is neglected, an inward pinch of ions against the density gradient is caused by the electric field, while that of the electrons is due to the electron temperature gradient.
Effects of electrostatic confinement fields and finite gyroradius on an instability of hollow electron columns
Authors: Smith Ralph A.
Published: July 2002

Exponentially growing diocotron instabilities with azimuthal mode number l=1 arise in hollow, cylindrical electron columns when the continuity equation includes small terms corresponding to finite gyroradius or axial variation of the radial electric field. The modes are similar in spatial form to the algebraically growing perturbations of the theory without these effects.
Diocotron instability for relativistic non-neutral electron flow in planar magnetron geometry
Authors: Ayres V. M. , Chen H. C. , Stark R. A. , Uhm H. S. , Brandt H. E.
Published: July 2002

Diocotron stability properties of relativistic non-neutral electron flow in a planar magnetron are investigated within the framework of the cold-fluid-Maxwell equations. The eigenvalue equation for the extraordinary-mode waves in a relativistic velocity-sheared electron layer is obtained, and is solved in the massless, guiding-center approximation. Approximating the electromagnetic field in the anode resonator by the lowest-order mode, the dispersion relation for the diocotron instability is obtained. Although the tenuous beam approximation is assumed, the eigenvalue equation and corresponding dispersion relation are both fully electromagnetic, and valid for relativistic electron flow. The dispersion relation is numerically investigated for a broad range of system parameters. From numerical calculations of the dispersion relation, it is shown that the typical growth rate of the diocotron instability indicates a strong instability. The early evolution of the diocotron instability as an important precursor to the evolution of the full magnetron oscillation is discussed.
Steady-state dynamo and current drive in a nonuniform bounded plasma
Authors: Mett R. R. , Taylor J. B.
Published: July 2002

Current drive due to helicity injection and the dynamo effect are examined in an inhomogeneous bounded plasma. Averaged over a magnetic surface, there is, in general, no dynamo effect independent of resistivity—contrary to the results found previously for an unbounded plasma. The dynamo field is calculated explicitly for an incompressible viscoresistive fluid in the plane-slab model. In accord with the authors’ general conclusion, outside the Alfvén resonant layer it is proportional to the resistivity. Within the resonant layer there is a contribution which is increased, relative to its value outside the layer, by a factor [ωa2/(η+ν)], where ω is the wave frequency, a is the plasma radius, η is the magnetic diffusivity, and ν is the kinematic viscosity. However, this contribution vanishes when integrated across the layer. The average field in the layer is resonance enhanced by a factor [ωa2/(η+ν)]2/3 and is proportional to the shear in the magnetic field and the cube root of the gradient of the Alfvén speed. These results are interpreted in terms of helicity balance, and reconciled with the infinite medium calculations.
Temperature anisotropy effect on the toroidal ion temperature gradient mode
Authors: Kim J. Y. , Horton W. , Choi D. I. , Migliuolo S. , Coppi B.
Published: July 2002

Using the local kinetic and fluid approaches, the effects of the anisotropies in the ion temperature and in the ion temperature gradient on the toroidal ion temperature gradient driven mode are investigated. A study of the effect of the increasing ion temperature relative to the fixed electron temperature in the peaked density limit is also made. Comparisons are given between the new toroidal results and the previous slab results.
Internal tilting instability in annular field-reversed configurations
Authors: Farengo Ricardo
Published: July 2002

The energy principle is used to show that elongated annular field-reversed configurations with a conductor linking the torus are unstable to an internal tilt mode. The critical elongation increases with the aspect ratio and the growth rate decreases with plasma length for very elongated plasmas.
Theory of drift-acoustic instabilities in the presence of sheared flows
Authors: Waelbroeck F. L. , Antonsen T. M. , Guzdar P. N. , Hassam A. B.
Published: July 2002

The stabilization of ion and electron drift-acoustic modes by sheared flows is investigated. It is found that, for a cold-ion plasma, the marginal stability criterion does not depend on the parallel component of flow shear. For tokamaks, this implies that stabilization may be achieved through purely toroidal rotation.
Ionic instability thresholds in tokamaks
Authors: Garbet X. , Laurent L. , Mourgues F. , Roubin J. P. , Samain A. , Zou X. L. , Chinardet J.
Published: July 2002

Linear ionic instability thresholds are numerically calculated for tokamaks. Proof is given that the stability domain is determined by trapped-ion modes for positive values of ηi=d(log Ti) /d(log ni). The boundary is characterized by ηi≥1 and a threshold LTi/R of order 0.2/(1+Ti/Te). This value is significantly smaller than previously predicted. Experimental temperature profiles in additionally heated discharges are usually marginal with respect to this criterion. It is also shown that marginal eigenmodes are low-frequency, low-wave-number modes, which may produce a very large transport once the ion temperature gradient threshold is reached.
Refraction and reflection of ion acoustic solitons by space charge sheaths
Authors: Nishida Yasushi , Yoshida Kazuhiko , Nagasawa Takeshi
Published: July 2002

It has been found that ion acoustic solitons tunnel through the space charge sheath in front of the reflector, without time delay, but they are absorbed resonantly when the spatial width of the wave is close to the characteristic gradient scale length of the sheath. The empirical scaling laws for the reflection and transmission rates have been obtained as functions of (i) the bias voltages on the reflector, (ii) the wave width, and (iii) the density gradient scale length. The theoretical model for interpreting the observed phenomena is discussed to show the existence of the electrostatic tunnel effect in the space charge sheath area. In this model, the absorption of wave energy by the sheath, which is strong in the present experiments, was not taken into account.
Some properties of a thermodynamic model for the equilibrium of a current-carrying quasineutral plasma
Authors: Aly J. J.
Published: July 2002

This paper establishes some general properties of a two-dimensional (z-invariant) model describing smooth equilibria of a magnetized quasineutral plasma enclosed in a finite cylindrical box of arbitrary cross section Ω and submitted to the following constraints: (i) the normal component of the magnetic field is fixed on the box boundary; (ii) the plasma is in contact with a heatbath at temperature T; (iii) the plasma carries in the z direction a current whose total intensity I is externally imposed. It is shown in particular that: (i) the free energy of the system is bounded from below if and only if the dimensionless control parameter λ≤1 (λ∝IT−1/2); (ii) a minimum free energy state (thus thermodynamically absolutely stable) exists for λ≤1 and is actually the unique equilibrium that can be achieved if λ is small enough; (iii) this state is absolutely stable with respect to all ideal magnetohydrodynamic perturbations; (iv) no equilibrium can exist if λ exceeds a critical value λc≥1 (at least in the case where Ω is ‘‘star shaped’’). The nonexistence of a minimum free energy state and even of any available regular equilibria with high current may have some consequences for understanding eruptive processes in plasmas, which are briefly discussed.
Modulational instability of Langmuir waves in dense plasmas
Authors: Vladimirov S. V. , Popel S. I. , Tsytovich V. N.
Published: July 2002

The modulational instability development of Langmuir waves is investigated in highly collisional plasmas where the characteristic frequency Ω of the modulated perturbations is much less than νeff, the effective electron collision frequency. It is demonstrated that the modulational instability for the situation considered is mostly determined by collisional effects (differential Joule heating nonlinearity), in contrast to the well-known modulational instability in collisionless plasmas (where ponderomotive force nonlinearity dominates). Rates and thresholds of the instability are found in various limits. The modulational instability is most effective when the angles between a pump wave vector and wave vectors of the modulational perturbations are of order unity.
The effects of elastic scattering in neutral atom transport
Authors: Ruzic D. N.
Published: July 2002

Neutral atom elastic collisions are one of the dominant interactions in the edge of a high recycling diverted plasma. Starting from the quantum interatomic potentials, the scattering functions are derived for H on H+, H on H2, and He on H2 in the energy range of 0.1–1000 eV following classical scattering theory and an impact parameter formulation. Potentials for both the gerade and ungerade electronic wavefunctions were included. An algorithm for the addition of these reactions to the degas [J. Comput. Phys. 46, 309 (1982)] code is presented and used to simulate three test problems: (1) the transport of neutral atoms through a dilute edge plasma, (2) the penetration of neutral atoms into a dense plasma from a divertor plate, and (3) the transmittance of neutral atoms through a pump duct. In all three cases the inclusion of elastic scattering has a significant influence on the neutral atom density, temperature, and flux to the walls.
Development of coherent x-ray lasers*
Authors: London Richard A.
Published: July 2002

Proposed x-ray laser applications such as interferometry and holography require coherent radiation. The fact that x-ray laser media are short-lived high-temperature plasmas leads to very different coherence properties from those of ordinary lasers. Research aimed at developing theoretical models and experimentally characterizing and improving x-ray laser coherence is discussed. Longitudinal coherence is already sufficient for several applications due to the narrow linewidths. However, transverse coherence is estimated to be poor for most current x-ray lasers. To quantify these estimates and to design better lasers, both wave and geometric optics propagation and coherence theories have been developed. These theories and resulting predictions of the coherence length are presented and compared. Measurements of x-ray laser beam patterns and coherence lengths are presented and compared to detailed theoretical simulations. Designs for more coherent lasers are given.
Fluctuation and modulation transport studies in the Advanced Toroidal Facility (ATF) torsatron*
Authors: Wilgen J. B. , Murakami M. , Harris J. H. , Bigelow T. S. , Dory R. A. , Carreras B. A. , Aceto S. C. , Batchelor D. B. , Baylor L. R. , Bell G. L. , Bell J. D. , Colchin R. J. , Crume E. C. , Dominguez N. , Dunlap J. L. , Dyer G. R. , England A. C. , Gandy R. F. , Glowienka J. C. , Goldfinger R. C. , Goulding R. H. , Hanson G. R. , Hidalgo C. , Hiroe S. , Hirshman S. P. , Horton L. D. , Howe H. C. , Hutchinson D. P. , Isler R. C. , Jernigan T. C. , Ji H. , Kaneko H. , Kovrizhnykh L. M. , Kwon M. , Langley R. A. , Lee D. K. , Likin K. M. , Lyon J. F. , Ma C. H. , Menon M. M. , Mioduszewski P. K. , Motojima O. , Okada H. , Paul S. , Qualls A. L. , Rasmussen D. A. , Richards R. K. , Rome J. A. , Saltmarsh M. J. , Sarksyan K. A. , Sato M. , Schwelberger J. G. , Shaing K. C. , Shats M. G. , Shepard T. D. , Simpkins J. E. , Thomas C. E. , Uckan T. , Vander Sluis K. L. , Wade M. R. , Wing W. R. , Yamada H. , Zielinski J. J.
Published: July 2002

The Advanced Toroidal Facility (ATF) torsatron [Fusion Technol. 10, 179 (1986)] has completed experiments focusing on microwave scattering measurements of density fluctuations and transport studies utilizing the modulation of dimensionless parameters. Microwave scattering measurements of electron density fluctuations in the core of low-collisionality electron cyclotron heated (ECH) plasmas show features that might be evidence of trapped electron instabilities. Starting from gyro-Bohm scaling, the additional dependence of confinement on the dimensionless parameters ν* and β (collisionality and beta) has been investigated by modulating each of these parameters separately, revealing the additional favorable dependence, τE∝τgBν*−0.18β+0.3.
Ion beam divergence from unstable fluctuations in applied-B diodes
Authors: Sudan R. N. , Longcope D. W.
Published: July 2002

An electron plasma oscillation driven unstable by ion streaming is identified with the low-frequency mode observed in quicksilver [Computational Physics, edited by A. Tenner (World Scientific, Singapore, 1991), pp. 475–482] numerical simulations. This mode heats the electrons along the magnetic field and is ultimately stabilized by the thermal spread. A quasilinear theory determines the saturation level of the fluctuations, the ion divergence, and the ion energy and momentum spread as they exit the diode. The ion divergence is predicted to be independent of the ion mass for fixed diode voltage and scales as the product of the effective gap and the ion beam enhancement factor over Child–Langmuir current.
Dielectric response and thermal fluctuations in gyrokinetic plasma
Authors: Krommes John A.
Published: July 2002

A gyrokinetic fluctuation–dissipation theorem is deduced and used to predict unusual thermal-equilibrium fluctuation spectra for both electrostatic and weakly electromagnetic gyrokinetic plasmas in the limit of weak coupling. The results are in agreement with an application of the test-particle superposition principle. They are interpreted physically in terms of the concept of the ‘‘gyrokinetic vacuum,’’ whose large (tensor) dielectric constant embodies the shielding effects of the polarization drift and the inductive electric field. The calculations are performed entirely with gyrokinetic response functions, although the relations to the conventional Vlasov dielectric are also described. The previous heuristic results of Krommes et al. [Phys. Fluids 29, 2421 (1986)] are recovered systematically. A nonrelativistic covariant formalism is used to derive the finite-β results (where β is the plasma pressure). The wave-number power spectra of the charge density, electrostatic potential, and perpendicular electric field are independent of β, while those of the parallel current, parallel vector potential, and perpendicular magnetic field are increasing functions of β. These results are derived both by exact integrations of the frequency spectra and, in the appropriate limit, by resonance integrations over weakly damped normal modes. To interpret the latter results, a new form for the unusual energy conservation law of gyrokinetic plasma is exhibited and a new formula for the gyrokinetic plasmon action 𝒩(k) valid at finite β is derived. The fluctuation spectra for the normal modes can then be derived by setting the plasmon energy ωk𝒩(k) to T/2. The power spectrum of the inductive component of the parallel electric field is dominated by high-frequency, non-normal-mode noise.
Quasilinear theory of the diocotron instability for nonrelativistic non-neutral electron flow in planar geometry
Authors: Davidson Ronald C.
Published: July 2002

A macroscopic cold-fluid model is used to investigate the quasilinear stabilization of the diocotron instability for sheared, nonrelativistic electron flow. Planar diode geometry is assumed, with cathode and anode located at x=0 and x=d, respectively. The non-neutral plasma is immersed in a strong applied magnetic field B0êz, and the electrons are treated as a massless (m→0) guiding-center fluid with flow velocity Vb=−(c/B0)∇φ×êz, where ∂/∂z=0 is assumed, and the fields are electrostatic with E=−∇φ. All quantities are assumed to be periodic in the y direction with periodicity length L. The nonlinear continuity-Poisson equations are used to obtain coupled quasilinear kinetic equations describing the self-consistent evolution of the average density 〈nb〉(x,t) and spectral energy density ℰk(x,t) associated with the y-electric field perturbations. Here, the average flow velocity in the y direction is VE(x,t)=(c/B0)(∂/∂x)〈φ〉(x,t), where average quantities are defined by 〈ψ〉(x,t)=∫L0 (dy/L)ψ(x,y,t). Several general features of the quasilinear evolution of the system are discussed, including a derivation of exact conservation constraints. Typically, if the initial profile 〈nb〉(x, t=0) corresponds to instability with γk(0)>0, the perturbations amplify, and the density profile 〈nb〉(x,t) readjusts in such a way as to reduce the growth rate γk(t) and stabilize the instability. As a specific example, the quasilinear evolution of the diocotron instability is considered for 〈nb〉(x,0) corresponding to a gentle density bump superimposed on a rectangular density profile in contact with the cathode.
Interaction of a rotating relativistic electron beam with a plasma
Authors: Peter William , Rostoker Norman
Published: July 2002

A one-dimensional model of a rotating electron beam interacting with a plasma in a conducting drift tube is presented. A constant magnetic field is assumed to exist in the axial direction. Magnetohydrodynamic-like equations describing the plasma response to the external beam current are justified and solved analytically in cyclindrical geometry. The results are compared with numerical results and actual experimental magnetic probe traces. For a long-pulse beam (T≫2π/Ωi), the energy lost by the beam is calculated to be W=(2πaI0/c)2 (1−a2/R2), where a is the beam radius, R is the radius of the conducting wall, and I0 is the current per unit length of the beam.
Lower-hybrid wave resonance cone detection via CO2-laser scattering
Authors: Wurden G. A. , Wong K. L. , Ono M.
Published: July 2002

Lower-hybrid waves are studied in the Princeton ACT-I steady-state toroidal plasma device using a radially scanning CO2 laser scattering system with both amplitude and phase sensitive detection techniques. Clearly defined resonance cones launched from external electrostatic antennas are seen to disappear as the plasma density is raised. Scaling of a lower-hybrid wave (LHW) laser signal with radio-frequency (rf) power in the presence of resonance cones shows nonlinearities associated with rf-induced changes in the effective laser scattering volume. Absolute fluctuation level estimates suggest that this occurs when eΦ/Te≥1. Wave-front curvature effects can cause a complete loss of resonance cone laser signals, even though probes indicate that cones are still present. Measurements of the wave k⊥ spectrum in the plasma show direct evidence for electron Landau filtering of the original wave k∥ spectrum launched from the antenna at the plasma edge, and strong dependence on antenna phasing. Finally, frequency shifts and loss of the resonance cone signal are associated with high levels of plasma density edge turbulence.
High Marangoni number convection in a square cavity
Authors: Zebib A. , Homsy G. M. , Meiburg E.
Published: July 2002

The steady thermocapillary motion in a square cavity with a top free surface in the absence of gravitational forces is considered. The cavity is heated from the side with the vertical boundaries isothermal while the horizontal boundaries are adiabatic. The relative change in the surface tension is very small, i.e., an appropriate capillary number tends to zero, so that the free surface is assumed to remain flat at leading order. A finite-difference method is employed to compute the flow field. Numerically accurate solutions are obtained for a range of Prandtl numbers and for Reynolds numbers Re as high as 5×104. Surface deflections are computed as a domain perturbation for small capillary number. In addition, asymptotic methods are used to infer the boundary layer structure in the cavity, in the limit of large values of the Reynolds and Marangoni numbers. For a fixed Prandtl number Pr, it is shown that the Nusselt number, liquid circulation, and maximum vorticity are asymptotic to Re1/3, Re−1/3, and Re2/3, respectively. These results are in agreement with the computed solutions. The leading-order solution for the free-surface deformation is sensitive to the value of Pr. With Pr>1, the depression near the hot corner may exceed the elevation near the cold corner, while a secondary elevation may be induced near the hot corner when Pr<1.
Nonlinear waves in superposed magnetic fluids
Authors: Kant Rama , Malik S. K.
Published: July 2002

An asymptotic weakly nonlinear wave propagation in Rayleigh–Taylor magnetic fluid flows is investigated. The waves are found to be unstable against modulation. The stability analysis reveals that there exist two regions of instabilities. The magnetic field has a stabilizing influence in one region and an opposite effect in the second region. The nonlinear cutoff wavenumber which separates the region of stability from that of instability is also obtained. The magnetic field has a destabilizing effect on the cutoff wavenumber.
Partial line-tying of the flute mode in a magnetic mirror
Authors: Vandegrift Guy , Good Timothy N.
Published: July 2002

The amount of electron emission required to partially line-tie the m=1 flute mode is measured on an axisymmetric mirror-confined plasma. The results are consistent with an ideal magnetohydrodynamic (MHD) calculation with a sheath dissipation term added. The minimum electron emission required is approximately the ion saturation current. The sheath impedance is also calculated for the case when the electron emission exceeds the threshold required for the formation of a virtual sheath.
Finite amplitude Kelvin–Helmholtz instability in magnetic fluids
Authors: Malik S. K. , Singh M.
Published: July 2002

A weakly nonlinear theory of Kelvin–Helmholtz instability for magnetic fluids is presented. The method used is that of multiple scales. The equations governing the evolution of the amplitude are derived when the difference U between the velocities of the two fluids is less than or equal to the critical velocity Uc. It is shown that for subcriticial values of U the wave train of constant amplitude is unstable against modulations whereas for the supercritical values the instability is governed by a nonlinear Klein–Gordon equation. From the latter equation, the various stability criteria are obtained.
Compressibility effects on ideal and kinetic ballooning modes and elimination of finite Larmor radius stabilization
Authors: Kotschenreuther M.
Published: July 2002

The dynamics of ideal and kinetic ballooning modes are considered analytically including parallel ion dynamics, but without electron dissipation. For ideal modes and typical tokamak parameters, parallel dynamics predominantly determine the growth rate when β is within ∼20%–40% of the ideal threshold, resulting in a substantial reduction in growth rate. Compressibility also eliminates the stabilization effects of finite Larmor radius (FLR); FLR effects (when temperature gradients are neglected) can even increase the growth rate above the magnetohydrodynamic (MHD) value. Temperature gradients accentuate this by adding a new source of free energy independent of the MHD drive, in the region of ballooning coordinate corresponding in MHD to the continuum. Analytic dispersion relations are derived demonstrating the effects above; the formalism emphasizes the similarities between the ideal MHD and kinetic cases.
Growth of a gas bubble in a viscous fluid
Authors: Chang Hsueh-Chia , Chen Liang-Heng
Published: July 2002

The cavitation pressure of spherical gas bubbles is correlated to the fluid viscosity in a theoretical investigation of the viscous Rayleigh–Plesset equation. The analysis is complicated by the absence of a first integral for the dissipative system. A qualitative normal form bifurcation analysis about a double-zero codimension 2 singularity is used to guide a quantitative estimate of the cavitation pressure by numerical and Melnikov perturbation techniques.
Intensity saturation of stimulated Raman scattering by ion-wave coupling
Authors: Heikkinen J. A. , Karttunen S. J.
Published: July 2002

Nonlinear saturation of stimulated Raman scattering caused by ion-wave coupling is investigated analytically and numerically. Various linear damping conditions for plasmons and ion-acoustic waves are included in the analysis. The main results can be summarized in terms of the normalized damping coefficient β (β=Raman gain length/plasmon absorption length), which decreases with the laser intensity I as β∼I−1/2. At low intensities (β>4) the Raman reflectivity increases according to the well-known three-wave process. At high intensities (0.2<β<2) a steady state still exists and the reflectivity is saturated as a function of the laser intensity. At very high intensities (β<0.1) temporally spiky and chaotic reflectivity is obtained. The reflectivities remain at very low levels, except for large interaction lengths.
A thick beam free electron laser
Authors: Fruchtman Amnon
Published: July 2002

A 3-D theory is presented for a free electron laser that employs an electron beam of a thickness comparable to both the wiggler wavelength and the waveguide radius. The time-independent and the linearized time-dependent cold fluid and Maxwell equations are expanded in a small parameter, which is the ratio of the perpendicular to parallel electron momentum. The stability problem is reduced to a nonlinear eigenvalue problem of a fourth-order system of linear ordinary differential equations. A perturbation method is justified and used to solve these equations. A dispersion relation is derived which results from the solvability condition for the first-order equations in the perturbation. The orders of magnitude of the beam density and wave frequency, for which the growth rate of the instability scales as in the strong-pump regime of the 1-D analysis, are determined. An equation, which the beam energy radial profile has to satisfy, is also derived.
Decay of small planar perturbations on a strong steady detonation: A differential–difference equation for the shock
Authors: Fickett Wildon
Published: July 2002

In the context of the author’s mathematical analog for reactive flow, the problem of the decay of small planar perturbations on a steady overdriven detonation wave is considered. For particular choices of the reaction rate, the analysis can be carried far enough to yield a simple differential–difference equation for the shock-state history. Analysis of this equation gives the natural frequencies and decay rates of the system and allows one to identify a ‘‘feedback length.’’ A set of sample ‘‘input’’ (applied perturbation) and corresponding ‘‘output’’ (shock-state history) signals is presented.
Electron diffusion and leakage currents in magnetically insulated diodes
Authors: Desjarlais M. P. , Sudan R. N.
Published: July 2002

The diffusion of stochastic electrons and the associated leakage current is investigated for magnetically insulated diodes and gaps. The model system is planar and periodic in the drift direction of the electrons. The stochasticity results from periodic perturbations of nonrelativistic, constant-density equilibria. When the perturbation is sufficiently large to generate a globally stochastic region containing the electron source, a leakage current is established. The steady-state Fokker–Planck equation is solved using quasilinear diffusion coefficients. The resulting distribution is normalized to the globally stochastic fraction of the equilibrium electrons to obtain the leakage current. For realistic perturbations, the analysis yields leakage current values that are in good agreement with earlier experimental results. A ‘‘supercritical’’ insulating field, which is a function of the perturbation parameters, is calculated.
Effect of streamwise vortices on Tollmien–Schlichting waves in growing boundary layers
Authors: Srivastava Krishna M. , Dallmann U.
Published: July 2002

The effect of counter-rotating streamwise steady vortices on three-dimensional Tollmien–Schlichting (TS) waves in a growing boundary layer on a concavely curved surface has been studied by using the method of multiple scales. The nonlinear evolution of the amplitudes with streamwise position has been obtained analytically. It is shown that the TS waves are amplified by the presence of streamwise vortices. The effect of combination resonance between TS waves and Goertler vortices is much more pronounced than the effect of parametric resonance between the TS waves and the periodic basic flow. The amplification rates increase with Goertler number and spanwise wavenumber.
Sawtooth stabilization through island pressure enhancement
Authors: Park W. , Monticello D. A. , Chu T. K.
Published: July 2002

Using the compressible resistive magnetohydrodynamic (MHD) equations in a finite aspect ratio cylinder, it is found that the m=1 mode (the sawtooth oscillation) can saturate when the pressure inside the magnetic island is higher than that of the original core plasma. The saturation condition is of the form Δβp≳8ε−1q=1(1−q0)2. This saturation effect can be used to actively stabilize sawteeth by heating or raising the density in the island. This mechanism, together with a stabilizing toroidal effect, may also explain recent lower-hybrid wave-driven tokamak experiments where the saturation of sawteeth has been observed.
Shock loading a rippled interface between liquids of different densities
Authors: Benjamin Robert F. , Fritz Joseph N.
Published: July 2002

Experimental results of the nonlinear growth of perturbations on a shocked interface between liquids having a density ratio of 10 are reported. After the shock passes from the higher-density liquid into the lower-density liquid, spikes of the higher-density liquid are observed to grow into the other liquid without producing severe turbulence. The measured growth is compared with analytical estimates. The time-resolved shadowgraphs provide excellent data for testing hydrodynamics models.
The ambipolar electric field and neoclassical heat and particle flows in nonaxisymmetric toroidal multispecies plasmas with sources
Authors: Coronado M. , Wobig H.
Published: July 2002

The fluid description of neoclassical transport theory is applied to a general nonaxisymmetric toroidal multispecies plasma with sources. From moment equations, expressions for plasma rotation, electric current, radial heat and particle transport fluxes, and ambipolar electric field are obtained. These expressions are valid in both the plateau and collision-dominated regimes. The effect of momentum and energy flux sources on particle and heat flows, electric current, radial transport fluxes, and on the ambipolar electric field is explicitly shown. In these calculations radial temperature gradients are taken into account.
Depression of nonlinearity in decaying isotropic turbulence
Authors: Kraichnan Robert H. , Panda Raj
Published: July 2002

Simulations of decaying isotropic Navier–Stokes turbulence exhibit depression of the normalized mean-square nonlinear term to 57% of the value for a Gaussianly distributed velocity field with the same instantaneous velocity spectrum. Similar depression is found for dynamical models with random coupling coefficients (modified Betchov models). This suggests that the depression is dynamically generic rather than specifically driven by alignment of velocity and vorticity.
Analysis of anomalous resistivity during the conduction phase of the plasma erosion opening switch
Authors: Kulsrud R. M. , Ottinger P. F. , Grossmann J. M.
Published: July 2002

During the conduction phase of the plasma erosion opening switch, the current channel width, in the body of the plasma away from the electrodes, has been observed to be many times wider than the collisionless skin depth. Anomalous collisions have been invoked to explain this discrepancy. Here the problem is analyzed using an electrostatic Vlasov approach, and an unstable ion acoustic mode is identified. The derived growth rate is fast enough and the nonlinear saturation level is high enough to explain the observed magnetic field penetration.
Microwave absorption at the fundamental electron cyclotron resonance and potential formation in a tandem mirror
Authors: Kariya T. , Saito T. , Kiwamoto Y. , Cho T. , Sugawara H. , Kondoh T. , Mase A. , Itakura A. , Miyoshi S.
Published: July 2002

Strong one-pass absorption of high-power microwaves is observed at the fundamental electron cyclotron resonance in an axisymmetric end mirror of the GAMMA 10 tandem mirror [Phys. Rev. Lett. 55, 939 (1985); Phys. Fluids 29, 2781 (1986)]. The radial profile of microwave power deposition is directly measured without the influence of wall reflection. It coincides with that of the axial flow of warm electrons driven by the fundamental heating as well as with that of the plasma potential at the resonance. This indicates that strong electron cyclotron heating largely affects the potential formation through driving an axial flow of warm electrons.
Simulation of ion-cyclotron-like modes in a magnetoplasma with transverse inhomogeneous electric field
Authors: Nishikawa K.-I. , Ganguli G. , Lee Y. C. , Palmadesso P. J.
Published: July 2002

Ion-cyclotron turbulence has been observed with shocks and double layers in the magnetosphere where strongly localized electric fields perpendicular to the magnetic field are present. Theoretical analysis suggests that electrostatic waves with frequencies of the order of the ion-cyclotron frequency can be destabilized as a result of the coupling of regions of positive and negative-energy ion waves. The nonlocal theory for a smooth profile of transverse inhomogeneous electric fields shows that localized ion waves grow in the region where the electric fields are present. Using a spatially two-dimensional electrostatic code, we investigate this instability in plasma conditions characterized by a localized transverse electric field L≪Lx, where Lx is the simulation length in the x direction; and distinguish it from the transverse kinetic Kelvin–Helmholtz instability. The simulation results show that the growing ion waves are associated with the small vortices in the linear state, which evolve into a nonlinear stage dominated by large vortices with lower frequencies.
Bifurcation in axisymmetric Czochralski natural convection
Authors: Bottaro Alessandro , Zebib Abdelfattah
Published: July 2002

Numerical simulations using a finite volume method with primitive variables formulation are presented for a natural convection flow in the Czochralski melt. In the limit of very small Prandtl numbers it is shown that unsteadiness appears in the form of regular oscillations for sufficiently high values of the Rayleigh number. Such regular oscillations are preceded by a multicell motion structure in the melt, with flow separation at the wall. The critical value of the Rayleigh number for the onset of the oscillations is determined by carrying out a series of time dependent calculations.
Modon formation in the nonlinear development of the collisional drift wave instability
Authors: Kono Mitsuo , Miyashita Eiichi
Published: July 2002

Nonlinear evolution of the collisional drift wave instability has been investigated by means of numerical simulations based on a model equation derived from a two-fluid approximation. This approximation is reduced to the Hasegawa–Mima equation when the collision and viscosity are neglected. A crucial feature is that coherent structures are formed from a turbulent state. A scenario for a path to the self-organized motion through the turbulent motion has been found as follows. The initial exponential growth of a linear instability is followed by a parametric instability that excites many modes. At the same time, the wave breaks up into small vortices. The inverse cascade of the wave energy then sets in and small vortices fuse into larger ones. A large modon is formed at the final stage of evolution.
On the Hopf bifurcation occurring in the two-layer Rayleigh–Bénard convective instability
Authors: Colinet P. , Legros J. C.
Published: July 2002

The oscillating convective structures appearing at the threshold of the two-layer Rayleigh–Bénard instability are analyzed in the nonlinear regime. By deriving the amplitude equations for left- and right-traveling waves from the infinite Prandtl number Boussinesq equations, it is shown that one of these waves should generally appear, rather than standing waves, in sufficiently large cells. Numerical results show that these waves have a limited range of existence, because a hysteretic transition to stationary convection occurs when the Rayleigh number is increased (via approach of a heteroclinic orbit for standing waves, and steady-state bifurcation for traveling waves). From numerical evidence and by comparison with similar behaviors encountered in the one-layer two-component problem, it is inferred that the overall behavior is typical of a codimension-2 Takens–Bogdanov bifurcation.
Detailed investigation of energy transfers in homogeneous stratified turbulence*
Authors: Godeferd F. S. , Cambon C.
Published: July 2002

This paper investigates some irreversible mechanisms occurring in homogeneous stably stratified turbulent flows. In terms of the eigenmodes of the linear regime, the velocity-temperature field is decomposed into a vortex and two wavy components. Using an eddy-damped quasinormal Markovian (EDQNM) closure with the axisymmetry hypothesis, an analysis of the anisotropic energy transfers between the vortex kinetic energy, the wave kinetic and potential energy is made. Within the light of triadic exchanges, and by analogy of the resonance condition for three linearly interacting gravity waves, the closure model allows one to compute the detailed transfers for eight types of interactions. Results of the calculations include time evolution plots, for the isotropic closure model as well as two different types of the anisotropic closure. The pure vortical interactions are shown to be responsible for the irreversible anisotropic structure created by stable stratification, and this structure prevents the inverse cascade of two-dimensional turbulence.
Scale dependence of the statistical character of turbulent fluctuations in thermal convection
Authors: Christie Steven L. , Domaradzki J. Andrzej
Published: July 2002

Two numerical realizations of thermal turbulence at Ra=630 000 and at the disparate aspect ratios (AR) of 3.1 and 6 were shown previously [Phys. Fluids A 5, 412 (1993)] to exhibit probability distribution functions (PDFs) of temperature flucuations (T′), which were exponential in the former case and Gaussian in the latter. Such PDFs for T′ are instrumental in definitions of hard and soft turbulence regimes. Here the same two realizations are considered, but the fields are spectrally decomposed by a horizontal scale before accumulating statistics. Within either flow field, both Gaussianity and exponentiality are present, but at differing lateral scales. The T′ distributions are seen to be Gaussian in the large scales, and the exponential at the small ones with parallel trends seen in the statistics of the velocity fields. Similarities with previous experimental and theoretical results and implications for soft/hard turbulence classification are discussed.
On the practical application of vortex breakdown theory to axially symmetrical and three-dimensional compressible flows
Authors: Keller Jakob J.
Published: July 2002

A perfect-fluid theory for axially symmetrical vortex breakdown flows by Keller et al. [Z. Angew. Math. Phys. 36, 854 (1985); 39, 404 (1988)] is extended to three-dimensional compressible flows. In a first step, an approximate theory for thin vortex cores is compared to the exact theory for axially symmetrical flows of inviscid, incompressible fluids. In subsequent steps, the approximation for thin vortex cores is extended to flows of compressible fluids that are not axially symmetrical. Finally, the various types of vortex breakdown flows and the shear layer instabilities at the surface of vortex breakdown bubbles are briefly discussed.
Corrections to Taylor’s hypothesis in a turbulent circular jet
Authors: Mi J. , Antonia R. A.
Published: July 2002

The relation between mean square values of the time derivative θ,t(≡∂θ/∂t) and the spatial derivatives θ,i(≡∂θ/∂xi; i=1, 2, 3) of the temperature fluctuation θ, obtained with the assumptions of homogeneity and independence between small scales and large scales, is experimentally verified in the self-preserving region of a circular jet where the turbulence intensity levels are relatively high. Local isotropy is approximately satisfied in the fully turbulent region of this flow and Wyngaard and Clifford’s [J. Atmos. Sci. 34, 922 (1977)] simplified relation between θ,t2 and θ,12 is shown to be quite adequate in this region.
Laminar flow past an enclosed and open backward-facing step
Authors: Barton I. E.
Published: July 2002

Numerical solutions for laminar flow past an enclosed and open backward-facing step are presented. The semi-implicit method for pressure equations (SIMPLE) methodology is used with finite volume discretization. The investigation concentrated on the differences in the lower reattachment length which are caused by the upper boundary layer. The upper boundary layer can cause three major effects; flow retardation, inhibition of perpendicular streamlines, and an upper recirculation region. These all affect the lower reattachment length.
A study of the sedimentation of noncolloidal bidisperse, concentrated suspensions by an acoustic technique
Authors: Hoyos M. , Bacri J. C. , Martin J. , Salin D.
Published: July 2002

This paper uses an acoustic technique to determine the concentration profile developing during the sedimentation of noncolloidal bidisperse suspensions of glass beads in a Newtonian fluid. Various bead diameter ratios have been used and a wide range of relative concentrations is covered. From the shock front velocities and the concentrations in different zones, the sedimentation velocities of small and large particles in a homogeneous suspension of respective concentrations cs0 and cl0 have been determined. The semidilute regime (c0=ss0+cl0<20%) has many similarities with the dilute regime, where large particles provide the dominant hydrodynamic hindrance to settling. In the concentrated regime (c0≳35%), a mutual hindrance leads to a velocity reduction of large particles and to an enhancement of small ones, as compared to a monodisperse suspension. The data clearly demonstrate that size segregation in the concentrated regime disappears at a critical concentration, which for the size ratio 1.68 is equal to c0=45%.