bluuebunny/crossref_metadata_2025 huggingface dataset:
Stability of an oscillating Kolmogorov flow
Authors: Frenkel Alexander L.
Published: July 2002

The linear stability of unidirectional flow sinusoidal both in a transverse direction and in time is considered. The problem reduces to an infinite algebraic eigenvalue problem. By using continued fractions, it is proved rigorously that the time-independent flow is unstable to perturbation modes which do not have the periodicity of the basic flow in the transverse direction. Also, instability is proved for the inviscid case, for which the proofs known before do not work even when perturbation modes have the same periodicity as the basic flow. In the case of time-dependent inviscid flow, exact solutions of a generalized Orr–Sommerfeld equation are found by the separation of continuous variables. Comparison with Galerkin solutions of the eigenvalue problem obtained by the separation of a discrete ‘‘time’’ variable leads to insights into reliability of the Galerkin results for the original, two-dimensional eigenvalue problem.
Approach of a vortex pair to a rigid free surface in viscous fluid
Authors: Saffman P. G.
Published: July 2002

The motion in a viscous incompressible fluid of a vortex pair toward a rigid plane wall on which slip is allowed is considered. It is shown that the centroids of vorticity do not approach the wall monotonically, and there is some rebound at a rate depending upon the viscosity and initial separation of the vortices.
Stability of three-dimensional supersonic boundary layers
Authors: Balakumar Ponnampalam , Reed Helen L.
Published: July 2002

A rotating cone that is located in a supersonic free stream at zero angle of attack is used as a model to investigate the stability of three-dimensional supersonic boundary layers. The boundary-layer profiles on the surface are calculated using the Cebeci–Keller box scheme. The stability equations are solved to determine the eigenvalues using a two-point fourth-order finite-difference scheme [Malik et al., Z. Angew. Math. Phys. 33, 189 (1982)]. The results show that the amplification rate of the first mode is increased by a factor of 2 to 4 due to the cross-flow, compared with a two-dimensional flow with the same streamwise profile. This increase decreases with increasing Mach number. The instability with cross-flow covers a wide range of unstable frequencies (including zero) and wave numbers. The results also show that the second mode in a three-dimensional boundary layer is oblique whereas the second mode in a two-dimensional boundary layer is two dimensional. The maximum amplification rate of the second mode decreases more slowly with increasing wave angle in a three-dimensional boundary layer than in a two-dimensional boundary layer. It is concluded that the cross-flow instability becomes important for cross-flow Reynolds number on the order of 50 for low Mach numbers and 100 for high Mach numbers, this Reynolds number range corresponds to a maximum cross-flow velocity of about 4%.
Cylindrical liquid bridges squeezed between parallel plates: Exact Stokes flow solutions and hydrodynamic forces
Authors: Davis Anthony M. J. , Frenkel Alexander L.
Published: July 2002

The problem of a dynamic liquid bridge between moving parallel plates is introduced. For the case of the Stokes flow in a cylindrical bridge driven by a slow change of the distance between the plates, an exact infinite-series solution is constructed, without invoking the lubrication approximation which was never surmounted in previous theories of dynamic liquid bridges. The boundary conditions at the free surface are fully satisfied, and the singularities of physical quantities at the moving contact line are avoided by allowing a minute but nonzero slip velocity. It is shown that, for narrower bridges, the ‘‘nonlubricative’’ contribution to hydrodynamic forces may become comparable with the force associated with the lubrication approximation.
Theoretical and experimental study of the vibration of axisymmetric viscous liquid bridges
Authors: Perales J. M. , Meseguer J.
Published: July 2002

In this paper the dynamics of axisymmetric liquid columns held by capillary forces between two circular, concentric, solid disks is considered. The problem has been solved by using a one-dimensional model known in the literature as the Cosserat model, which includes viscosity effects, where the axial velocity is considered constant in each section of the liquid bridge. The dynamic response of the bridge to an excitation consisting of a small-amplitude vibration of the supporting disks has been solved by linearizing the Cosserat model. It has been assumed that such excitation is harmonic so that the analysis has been performed in the frequency domain. The particular case of a cylindrical liquid bridge has been analytically studied and the transfer function has been calculated in the cases of oscillation of both disks (either in phase or in counterphase) or only of one of them. The resolution of the general formulation for a noncylindrical liquid bridge has been numerically made by using an implicit finite difference method. In this case, the influence of the volume of the liquid column and of the residual gravity level on the first resonance has been studied, and the results compared, for the inviscid case, with other potential models, both one and three dimensional. To demonstrate the usefulness of this theoretical model in predicting the vibrational behavior of axisymmetric viscous liquid bridges, some experiments have been performed by using the neutral buoyancy technique (also known as the Plateau technique) to simulate reduced gravity conditions, with good agreement between the results of the model and experiments.
On the universal form of energy spectra in fully developed turbulence
Authors: She Zhen-Su , Jackson Eric
Published: July 2002

Several experimentally measured energy spectra of fully developed incompressible turbulent flows with Taylor microscale Reynolds numbers ranging from 130–13 000 have been reexamined. It is shown that all spectra collapse to a universal curve after a simple rescaling of space and time. This rescaling does not involve any multifractal-type transformation, and the rescaled wave numbers scatter around the Kolmogorov dissipation wave numbers derived from experimentally measured quantities. An empirical formula for the resulting universal form is proposed, indicating a nontrivial form of the energy spectrum near the viscous dissipation cutoff.
On the Lundgren–Townsend model of turbulent fine scales
Authors: Pullin D. I. , Saffman P. G.
Published: July 2002

The strained-spiral vortex model of turbulent fines scales given by Lundgren [Phys. Fluids 25, 2193 (1982)] is used to calculate vorticity and velocity-derivative moments for homogeneous isotropic turbulence. A specific form of the relaxing spiral vortex is proposed modeled by a rolling-up vortex layer embedded in a background containing opposite signed vorticity and with zero total circulation at infinity. The numerical values of two dimensionless groups are fixed in order to give a Kolmogorov constant and skewness which are within the range of experiment. This gives the result that the ratio of the ensemble average hyperskewness S2p+1≡ (∂u/∂x)2p+1/[(∂u/∂x)2](2p+1)/2 to the hyperflatness F2p≡(∂u/∂x)2p/[(∂u/∂x)2] p, p=2,3,..., is constant independent of Taylor–Reynolds number Rλ, as is the ratio of the 2pth moment of one component of the vorticity Ω2p≡ω2px/(ω2x)p to F2p. A cutoff in a relevant time integration is then used to eliminate vortex-sheet-induced divergences in the integrals corresponding to ω2px, p=2,3,..., and an assumption is made that the lateral scale of the spiral vortex in the model is the geometric mean of the Taylor and the Kolmogorov microscales. This gives Ω2p=Ω̂2pRλp/2−3/4, F2p=F̂2pRλp/2−3/4 and S2p+1=Ŝ2p+1Rλp/2−3/4, p=2,3,..., with explicit calculation of the numbers Ω̂2p, F̂2p, and Ŝ2p+1. The results of the model are compared with experimental compilation of Van Atta and Antonia [Phys. Fluids 23, 252 (1980)] for F4 and with the isotropic turbulence calculations of Kerr [J. Fluid Mech. 153, 31 (1985)] and of Vincent and Meneguzzi [J. Fluid Mech. 225, 1 (1991)].
Nonlinear behavior of magnetohydrodynamic modes near marginally stable states. I. General formulation and application to the nonresonant kink modes in a reversed field pinch and to the quasi-interchange modes in a tokamak
Authors: Nakajima Noriyoshi
Published: July 2002

Two types of nonlinear equations describing the time development of modes near marginally stable states in an inhomogeneous medium are obtained through a general formulation that employs a perturbation expansion around the marginally stable state under the assumption of a single helicity. One type of nonlinear equation has a Hamiltonian form that may be interpreted as the equation of motion for a particle in the potential field of a central force; the other type leads to the Landau equation, which is well known in fluid dynamics. The former equation is obtained when the linear operator is degenerate at the marginally stable state, which corresponds to the case when the linear dispersion relation has a double root for the frequency at the marginally stable state, whereas the latter is obtained when the linear operator is nondegenerate, i.e., the linear dispersion relation has a single root. In the framework of magnetohydrodynamics, the former corresponds to the nonresonant ideal modes, and the latter to the resistive modes. The nonlinear behavior of the nonresonant kink modes in a reversed field pinch and of the quasi-interchange modes in a tokamak are examined with the application of the general formulation. It is shown that new stable helical equilibria bifurcate near the initial axisymmetric equilibrium, so that the plasma nonlinearly oscillates around the new bifurcated equilibrium, which leads to nonlinear saturation of the nonresonant kink modes in a reversed field pinch and of the quasi-interchange mode in a tokamak. The nonlinear stabilizing effects causing bifurcation of the equilibrium are interpreted as quasilinear effects. Compressibility reduces the nonlinear stabilizing effects through changing the quasilinear components and is important even when the modes are near marginally stable states.
Effects of kinetic damping on the ion temperature gradient mode in tokamaks
Authors: Hirose A.
Published: July 2002

Damping resulting from ion magnetic drift and Landau resonances is shown to strongly stabilize the ion temperature gradient mode in tokamaks. The instability requires a steep temperature gradient εT=LT/T ≲0.05.
Theory of magnetically insulated electron flows in coaxial pulsed power transmission lines
Authors: Lawconnell Robert I. , Neri Jesse
Published: July 2002

The Cartesian magnetically insulated transmission line (MITL) theory of Mendel et al. [Appl. Phys. 50, 3830 (1979); Phys. Fluids 26, 3628 (1983)] is extended to cylindrical coordinates. A set of equations that describe arbitrary electron flows in cylindrical coordinates is presented. These equations are used to derive a general theory for laminar magnetically insulated electron flows. The laminar theory allows one to specify the potentials, fields, and densities across a coaxial line undergoing explosive electron emission at the cathode. The theory is different from others available in cylindrical coordinates in that the canonical momentum and total energy for each electron may be nonzero across the electron sheath. A nonzero canonical momentum and total energy for the electrons in the sheath allows the model to produce one-dimensional flows that resemble flows from lines with impedance mismatches and perturbing structures. The laminar theory is used to derive two new self-consistent cylindrical flow solutions: (1) for a constant density profile and (2) for a quadratic density profile of the form ρ=ρc[(r2m−r2)/(r2m−r2c)]. This profile is of interest in that it is similar to profiles observed in a long MITL simulation [Appl. Phys. 50, 4996 (1979)]. The theoretical flows are compared to numerical results obtained with two-dimensional (2-D) electromagnetic particle-in-cell (PIC) codes.
Magnetic reconnection driven by current repulsion
Authors: Richard R. L. , Sydora R. D. , Ashour-Abdalla M.
Published: July 2002

The evolution of an equilibrium consisting of two magnetic islands with oppositely directed currents embedded in a strong magnetic field is investigated, using numerical simulation methods. The rapid development of an ideal magnetohydrodynamic instability is observed, which first rotates and then expels the islands. The growth rate is on the order of the inverse of the Alfvén transit time and is much higher than that for magnetic island coalescence. In the nonlinear stage, resistivity becomes important as the reconnection process ensues and dissipates the magnetic energy. The growth rate of the instability is a weak function of the plasma beta and other plasma parameters such as S, the magnetic Reynolds number. An energy principle analysis, based on eigenfunctions obtained from the simulation, confirms the existence of the instability.
Demonstration of electron beam self-focusing in plasma wake fields
Authors: Rosenzweig J. B. , Schoessow P. , Cole B. , Ho C. , Gai W. , Konecny R. , Mtingwa S. , Norem J. , Rosing M. , Simpson J.
Published: July 2002

In this paper, the direct observation of wake-field self-focusing of an electron beam in plasma is reported. The dynamics of beam self-pinching and the fast collisionless evolution of a Bennett-like, near-equilibrium profile are examined theoretically and computationally. The experimental results are compared to predictions of the analysis and discussed in the context of application to the plasma lens and the plasma wake-field accelerator.
Nonlinear wake-field generation and relativistic focusing of intense laser pulses in plasmas
Authors: Ting A. , Esarey E. , Sprangle P.
Published: July 2002

The generation of nonlinear plasma wake fields by an intense, short laser pulse and the relativistic optical guiding of intense laser pulses in plasmas are studied with a nonlinear, self-consistent model of laser–plasma interactions. Nonlinear steepening and period lengthening of the plasma waves are observed, and expressions are obtained for various nonlinear wake-field quantities. Relativistic focusing with the self-consistent plasma response shows that laser pulse fronts and laser pulses shorter than a plasma wavelength, 2πc/ωp, are not relativistically guided and will continuously erode due to diffraction.
The diffusion of fast ions in Ohmic TFTR discharges
Authors: Heidbrink W. W. , Barnes Cris W. , Hammett G. W. , Kusama Y. , Scott S. D. , Zarnstorff M. C. , Johnson L. C. , McCune D. , Medley S. S. , Park H. K. , Roquemore A. L. , Strachan J. D. , Taylor G.
Published: July 2002

Short duration (20 msec) neutral deuterium beams are injected into the TFTR tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1986 (IAEA, Vienna, 1987), Vol. I, p. 51]. The subsequent confinement, thermalization, and diffusion of the beam ions are studied with multichannel neutron and charge exchange diagnostics. The central fast-ion diffusion (<0.05 m2/sec ) is an order of magnitude smaller than typical thermal transport coefficients.
Statistical dynamics of dissipative drift wave turbulence
Authors: Gang F. Y. , Diamond P. H. , Crotinger J. A. , Koniges A. E.
Published: July 2002

The statistical dynamics of a two-field model of dissipative drift wave turbulence is investigated using the EDQNM (eddy damped quasinormal Markovian) closure method [J. Fluid Mech. 41, 363 (1970)]. The analyses include studies of statistical closure equations, derivation of an H theorem, and its application to formulation of selective decay hypotheses for turbulent relaxation process. The results show that the dynamics of the two-field model is fundamentally different from that of the familiar, one-field Hasegawa–Mima model [Phys. Fluids 21, 87 (1978)]. In particular, density fluctuations nonlinearly couple to small scales, as does enstrophy. This transfer process is nonlinearly regulated by the dynamics of the density–vorticity cross correlation. Since density perturbations are not simply related to potential perturbations, as is vorticity, their transfer rate is greater. As a result, turbulent relaxation processes exhibit both dynamic alignment of density and vorticity and coherent vortex formation.
Stopping and thermalization of interpenetrating plasma streams
Authors: Berger R. L. , Albritton J. R. , Randall C. J. , Williams E. A. , Kruer W. L. , Langdon A. B. , Hanna C. J.
Published: July 2002

The interpenetration of two supersonically moving plasmas is affected by both collective modes of oscillation and Coulomb collisions. Two potentially important plasma instabilities, an electrostatic ion two stream and an electromagnetic ion Weibel, are considered and shown to be stabilized if only a small fraction of ion kinetic energy is converted to heat. For low-density, highly supersonic flows, the mean free path for slowing down (dominated in most cases of interest by ion–ion collisions) can be larger than or comparable to the system size. To develop an understanding of these plasmas, a unique hydrodynamic model has been developed that allows interpenetration but explicitly converts kinetic energy into heat as the ions slow down. The model is applied to the collision of two plasmas created by heating two parallel foils.
Particle acceleration in a relativistic wave in the adiabatic regime
Authors: Mora P.
Published: July 2002

The adiabatic theory of particle acceleration in a relativistic longitudinal plasma wave of fixed phase velocity is developed. The trapping condition for a low energy particle is found to be more severe than the trapping condition previously obtained for a constant amplitude wave. Intermediate energy particles that are trapped in the wave experience the beam splitting and the beam heating effects, with most of the particles ending in the larger energy beam. The particles that are not trapped experience no acceleration at all in the adiabatic limit. The validity conditions of the adiabatic theory are given for trapped and untrapped particles. Numerical results corresponding to the UCLA (University of California at Los Angeles) beat wave experiment [R. L. Williams, C. E. Clayton, C. Joshi, T. Katsouleas, and W. B. Mori, Laser Part. Beams 8, 427 (1990)] illustrate the theory. They show the important role of the trapping condition.
Vortices associated with toroidal ion-temperature-gradient-driven fluctuations
Authors: Horton W. , Jovanović D. , Rasmussen J. Juul
Published: July 2002

The three nonlinear hydrodynamic equations for potential, parallel ion velocity and ion pressure used in simulations of the toroidal ion-temperature-gradient-driven fluctuations and transport in a shear magnetic field are analyzed for coherent vortex structures. Two types of vortex structures are found: one type for weak shear that is a generalization of the usual modon vortex construction and the second type of solution for strong magnetic shear where the convective nonlinearity in the parallel velocity field generates a cubic trapping nonlinearity in the vorticity equation. These vortex structures show the possibility of explaining the saturated states observed in the numerical simulations as self-organized nonlinear states in contrast to wave turbulence.
Initial development of ponderomotive filaments in plasma from intense hot spots produced by a random phase plate
Authors: Rose Harvey A. , DuBois D. F.
Published: July 2002

Local intensity peaks, hot spots, in laser beams may initiate self-focusing, in lieu of linear instabilities. If the hot spot power, P, contains several times the critical power, Pc, and if the plasma density, n, is small compared to the critical density, nc, then on a time scale less than an acoustic transit time across the hot spot radius, τia, the hot spot collapses, capturing order unity of the initial hot spot power. The collapse time is determined as a universal function of P/Pc and τia. The focal region moves towards the laser with an initially supersonic speed, and decelerates as it propagates. The power of this back propagating focus decreases monotonically until the critical power is reached. This limiting, shallowest, focus develops on a time scale long compared to τia and corresponds to the focus obtained in a model with adiabatically responding ions. For low-density plasma nonlinear ion effects terminate collapse and a bound on the transient intensity amplification is obtained as a universal function of the optics f/number, F, and n/nc. The boundary between thermal and ponderomotive regimes depends upon F and not the laser intensity.
Boundary effects on the nonlinear interactions of surface waves
Authors: Vladimirov S. V. , Yu M. Y.
Published: July 2002

A traditional cold-plasma boundary model is revised to allow for proper description of nonlinear effects in surface wave propagation. It is shown that induced nonlinear surface currents can exist at the boundary. As an example, the third-order ponderomotive phenomena are considered, and the effect of the boundary condition on these nonlinear interactions is examined.
Dynamics of ponderomotive self-focusing and periodic bursts of stimulated Brillouin backscattering in plasmas
Authors: Andreev N. E. , Gorbunov L. M. , Tarakanov S. V. , Zykov A. I.
Published: July 2002

The space–time evolution of ponderomotive self-focusing of electromagnetic beams in a plasma is investigated. The quasineutral, hydrodynamic plasma response to the ponderomotive force is considered. The set of coupled quasioptic and acoustic equations is solved both analytically and numerically for slab and cylindrical beams. It is shown that the transient process of self-focusing has the form of a nonlinear wave propagating along the beam axis from boundary into the interior of a plasma with velocity considerably higher than the ion-sound velocity. Mutual dynamics of self-focusing and stimulated Brillouin backscattering (SBBS) is computed. It is shown that self-focusing results in the high intensity periodical bursts of SBBS. However, the time average level of scattered radiation is quite low.
Nonconservative and reverse spectral transfer in Hasegawa–Mima turbulence
Authors: Terry P. W. , Newman D. E.
Published: July 2002

The dual cascade is generally represented as a conservative cascade of enstrophy to short wavelengths through an enstrophy similarity range and an inverse cascade of energy to long wavelengths through an energy similarity range. This picture, based on a proof due to Kraichnan [Phys. Fluids 10, 1417 (1967)], is found to be significantly modified for spectra of finite extent. Dimensional arguments and direct measurement of spectral flow in Hasegawa–Mima turbulence indicate that for both the energy and enstrophy cascades, transfer of the conserved quantity is accompanied by a nonconservative transfer of the other quantity. The decrease of a given invariant (energy or enstrophy) in the nonconservative transfer in one similarity range is balanced by the increase of that quantity in the other similarity range, thus maintaining net invariance. The increase or decrease of a given invariant quantity in one similarity range depends on the injection scale and is consistent with that quantity being carried in a self-similar transfer of the other invariant quantity. This leads, in an inertial range of finite size, to some energy being carried to small scales and some enstrophy being carried to large scales.
A nonlocal theory of counterstreaming ion instability
Authors: Wong S. K. , Krall N. A.
Published: July 2002

Spherically convergent ion focus (SCIF) devices relying on hot electrons to create the confining electrostatic well are found to be subject to a counterstreaming ion instability. Nonlocal linear stability theories in a spherical geometry are formulated and solved both analytically and numerically. The results of previous calculations of local linear theory are used for comparison. Linear growth rates of the order of the beam transit frequency are predicted. The consequence of these instabilities awaits a nonlinear treatment.
A self-consistent nonlinear theory of current modulation in relativistic klystron amplifiers
Authors: Uhm Han S.
Published: July 2002

A self-consistent nonlinear theory of the energy and current modulation in a relativistic electron beam propagating through a klystron amplifier is developed. A closed integrodifferential equation for the beam current is obtained, assuming that the beam current is a function of time t and propagation distance z. Properties of the current and energy modulation are investigated from this integrodifferential equation for a broad range of system parameters. Magnitudes of the energy and current modulation are determined in terms of the gap voltage, the cavity frequency, geometric configuration, the beam intensity, and initial kinetic energy of the beam. The modulation amplitude increases, reaches peak, and decreases slowly, as the beam propagates through the amplifier. A simple expression of scaling law for maximum current modulation is obtained. This scaling law could be useful in the design and fabrication of a high-performance klystron. Nonlinear mode evolution in current profile is also investigated by Fourier decomposing the current modulation obtained from the integrodifferential equation. The mode evolution in a long-range propagation of an electron beam exhibits various interesting physical properties. For example, the maximum amplitude of the fundamental mode (l=1) occurs at the propagation distance, where all other modes vanish or have a very small amplitude. This property ensures a monochromatic frequency.
Spectral properties of the kinetic Alfvén wave in cylindrical tokamak geometry
Authors: van Rij W. I. , Vahala G. , Sigmar D. J.
Published: July 2002

It is shown, for a tokamak-like cylindrical plasma and small poloidal and toroidal mode numbers, that the full gyrokinetic shear Alfvén spectrum is discrete when k∥≠0. Calculations of the global eigenmodes of the magnetohydrodynamic (MHD) limit, and their first-order finite Larmor radius (FLR) corrections, are presented. First-order FLR theory is found to be a good approximation to full FLR theory, even for modes with high radial node number. In the presence of a positive density gradient, such as that which may occur with pellet fueling of the plasma, the existence of global MHD eigenmodes above the Alfvén continuum is confirmed.
Influence of intense equilibrium self-fields on the cyclotron maser instability in high-current gyrotrons
Authors: Uhm Han S. , Davidson Ronald C.
Published: July 2002

The linearized Vlasov–Maxwell equations are used to investigate the influence of intense equilibrium self-fields on the cyclotron maser instability. A uniform density (n̂b) electron beam propagates parallel to an applied axial magnetic field B0êz with average axial velocity βbc. The particle trajectories are calculated including the influence of the radial self-electric field and the azimuthal self-magnetic field. Moreover, the linearized Vlasov–Maxwell equations are analyzed for body-wave perturbations localized to the beam interior, assuming electromagnetic perturbations about the equilibrium distribution function f0b=(n̂b/2pπ⊥) ×δ(p⊥−γbmV⊥) ×δ(pz−γbmβbc). Near the beam axis (ω2pbr2/c2≪1), it is found that the transverse electron motion is biharmonic, with oscillatory components at the frequencies ω+b and ω−b defined by ω±b =(ωcb/2) ×{1±[1−(2ω2pb/ω2cb) ×(1−β2b)]1/2}. Similarly, the electromagnetic dispersion relation for waves propagating parallel to B0êz exhibits two types of resonance conditions: a high-frequency resonance (HFR) corresponding to ω−kβbc=ω+b, and a low-frequency resonance (LFR) corresponding to ω−kβbc=ω−b.

Both the HFR branch and the LFR branch exhibit instability, with detailed stability properties depending on the value of the self-field parameter s=ω2pb/ω2cb. Moreover, the LFR branch is entirely caused by self-field effects, whereas the HFR branch represents a generalization of the conventional cyclotron maser mode to include self-field effects. The full dispersion relation is analyzed numerically, and the real oscillation frequency ωr=Re ω and growth rate ωi=Im ω are calculated for both types of modes over a wide range of system parameters s, β⊥, βb, and kc/ωcb. Analytic estimates are made of the cyclotron maser growth properties in circumstances where β2⊥γ2z/2 is treated as a small parameter. [Here, γz=(1−β2b)−1/2. ] It is found that the maximum growth rate is given by ωi=(2γ2z)−1 ×[s(2β2⊥γ4z−s)]1/2ωcb, which occurs for wavenumber k=km=γ2zβbωcb/c. As the beam density (s) is increased, the growth rate ωi increases to the maximum value ωmaxi =γ2zβ2⊥ωcb/2 for beam density s=sm=β2⊥γ4z. As s is increased beyond sm, the growth rate ωi decreases to zero for s=s0=2β2⊥γ4z. Similarly, the instability bandwidth Δk =(2γzωcb/c)[γ2z−β−1⊥ ×(s/2)1/2]1/2 approaches zero as s approaches s0.
Stochasticity reduction
Authors: Cary John R. , Hanson James D.
Published: July 2002

A method for finding integrable Hamiltonian systems with one and a half degrees of freedom is introduced and applied to the problem of finding vacuum magnetic fields with rotational transform and a dense set of toroidal flux surfaces. In this method, the fixed points of the return map must be located, and the values of the corresponding residues calculated. The residues, being indicators of stochasticity, are systematically reduced by variation of the parameters of the system. Application of this method to the problem of finding integrable magnetic fields shows that it is practical, and it yields substantial improvement of the configuration. In particular, this method can result in an increase of the simple equilibrium-β estimate, ι2ε, by a factor of 2 or more.
Analytic theory of the nonlinear m=1 tearing mode
Authors: Hazeltine R. D. , Meiss J. D. , Morrison P. J.
Published: July 2002

Numerical studies show that the m=1 tearing mode continues to grow exponentially well into the nonlinear regime, in contrast with the slow, ‘‘Rutherford,’’ growth of m>1 modes. A single helicity calculation is presented which generalizes that of Rutherford [Phys. Fluids 16, 1903 (1973)] to the case when the constant-ψ approximation is invalid. As in that theory, the parallel current becomes an approximate flux function when the island size W exceeds the linear tearing layer width. However, for the m=1 mode, W becomes proportional to δB, rather than (δB)1/2 above this critical amplitude. This implies that the convective nonlinearity in Ohm’s law, which couples the m=0 component to the m=1 component, dominates the resistive diffusion term. The balance between the inductive electric field and this convective nonlinearity results in exponential growth. Assuming the form of the perturbed fields to be like that of the linear mode, we find that growth occurs at 71% of the linear rate.
Spreading of two-stream supersonic turbulent mixing layers
Authors: Chinzei N. , Masuya G. , Komuro T. , Murakami A. , Kudou K.
Published: July 2002

Two-stream supersonic turbulent mixing layers with a free-stream Mach number of 2.3 on the high-velocity side are experimentally investigated. A large-scale vortical structure, which has been believed to dominate the development of incompressible mixing layers, is also observed in the present supersonic layers. The spreading rate of the layer is correlated with a velocity ratio of the free streams and a Mach number based on the velocity difference across the layer.
Turbulent stabilization of the tearing mode in tokamak plasmas
Authors: Esarey E. , Freidberg J. P. , Molvig K. , Beasley C. O. , Van Rij W. I.
Published: July 2002

The effect of turbulent electron diffusion from stochastic electron orbits on the stability of low-beta fluctuations is considered through the use of the normal stochastic approximation. A set of coupled, self-adjoint equations is derived for the fluctuation potentials φ̃ and Ã∥. Solutions to this set of equations describe both unstable finite-β drift waves when analyzed for high-m modes and the tearing mode when analyzed for low-m modes. For the tearing mode, it is shown that stability is obtained for sufficiently large values of the diffusion coefficient. Provided De∼1/n, this implies that a density threshold must be surpassed before the tearing mode is observed. Physically, turbulent electron diffusion prohibits the formation of a perturbed current within a finite region about the rational surface. At higher densities, the inclusion of a finite electrostatic potential φ̃ gives an additional stabilizing term to the dispersion relation, which physically represents ion inertial effects. This ion inertial effect implies that, in the absence of diffusion, the tearing mode is stabilized for ion betas βi above some critical value.
Measurements of the size of the secondary flow regions generated by a torsionally oscillating disk in a linearly stratified fluid
Authors: Folse R. F. , Rodrigue D. A. , Courtney D. L.
Published: July 2002

Measurements have been made of the size of the region of secondary flow in a linearly stratified fluid, with Brunt–Väisälä frequencies in the range of 0.65–3.23 rad/sec, caused by a rotationally oscillating shearing stress. The stress was generated by the surfaces of a disk of radius r=5.078 cm undergoing torsional oscillations of angular frequency ω=1.50 rad/sec inside cylindrical boundaries with radii in the range 6.95–10.75 cm. The kinematic viscosity in the vicinity of the disk was approximately constant, ν=1.08 centistokes. Several features of the flow are similar to the secondary flow described by Scranton and Lindberg [Phys. Fluids 26, 1198 (1983)] as occurring in annular tank experiments to model geophysical turbulent mixing. For constant Ekman number Ek=ν/ωr2, the size of the secondary flow region depends on the Brunt–Väisälä frequency and the boundary radius; an empirical correlation of the data is presented.
Microinstabilities in weak density gradient tokamak systems
Authors: Tang W. M. , Rewoldt G. , Chen Liu
Published: July 2002

A prominent characteristic of auxiliary-heated tokamak discharges which exhibit improved (‘‘H-mode type’’) confinement properties is that their density profiles tend to be much flatter over most of the plasma radius. Despite this favorable trend, it is emphasized here that, even in the limit of zero-density gradient, low-frequency microinstabilities can persist because of the nonzero temperature gradient.
Reply to the Comments of Amendt e
t a
l.
Authors: Yu M. Y. , Stenflo L.
Published: July 2002

Questions raised in the preceding Comments are discussed. It is shown that the assertions in the original paper [Phys. Fluids 28, 3447 (1985)] are justified.
Measurements of beam-ion confinement during tangential beam-driven instabilities in a bean tokamak experiment
Authors: Heidbrink W. W. , Kaita R. , Takahashi H. , Gammel G. , Hammett G. W. , Kaye S.
Published: July 2002

During tangential injection of neutral beams into low-density tokamak plasmas with β>1%, instabilities are observed that degrade the confinement of beam ions. Neutron, charge-exchange, and diamagnetic loop measurements are examined in order to identify the mechanism or mechanisms responsible for the beam-ion transport. The data suggest a resonant interaction between the instabilities and the parallel energetic beam ions. Evidence for some nonresonant transport also exists.
Oscillatory nonlinear electron flow in a Pierce diode
Authors: Godfrey Brendan B.
Published: July 2002

Uniform density electron beam flow in a one-dimensional Pierce diode is alternately stable and unstable as the diode width is increased. Each stability transition corresponds to an equilibrium bifurcation involving either a static nonuniform equilibrium or a steady oscillatory configuration. The static equilibria, although nonlinear, are evaluated analytically and their stability properties derived. Details of the oscillatory solutions are determined numerically from integral equations relating the transit time of electrons in the diode to the electric field at the entrance plane. As the diode width is reduced, each oscillatory solution undergoes a sequence of subharmonic bifurcations, culminating in a chaotic strange attractor. The chaotic attractor itself terminates in a crisis after a further reduction of the diode width. Unlike other electron beam nonlinear oscillations (e.g., virtual cathodes), no particle reflections are required. This behavior has intrinsic interest as a possible model for beam turbulence in more complex geometries. In addition, it may find application in microwave generation.
Hall effect on magnetohydrodynamic instabilities at an elliptic magnetic stagnation line
Authors: Spies Günther O. , Faghihi Mustafa
Published: July 2002

To answer the question whether the Hall effect removes the unphysical feature of ideal magnetohydrodynamics of predicting small wavelength kink instabilities at any elliptic magnetic stagnation line, a normal mode analysis is performed of the motion of an incompressible Hall fluid about cylindrical Z-pinch equilibria with circular cross sections. The eigenvalue loci in the complex frequency plane are derived for the equilibrium with constant current density. Every particular mode becomes stable as the Hall parameter exceeds a critical value. This value, however, depends on the mode such that it increases to infinity as the ideal growth rate decreases to zero, implying that there always remains an infinite number of slowly growing instabilities. Correspondingly, the stability criterion for equilibria with arbitrary current distributions is independent of the Hall parameter.
Collisional effects and dispersion relation of magnetic field structures
Authors: Bendib A. , Luciani J. F.
Published: July 2002

The local dispersion relation of weak magnetic modes for an arbitrary wavelength ranging from collisional to collisionless cases is derived. The convection velocity and the growth rate are explicitly computed. The convection effects are emphasized and a significant departure from collisional Nernst law is shown to occur even for rather low wavenumbers. In laser plasma experiments, this prevents the convection of intermediate scale magnetic structures generated near the critical layer toward high densities. An explicit convection velocity formula is proposed that is directly usable for numerical purposes. The mathematical tools used in this work are continuous fractions arising naturally from the Fokker–Planck equation with a Landau collisional operator, so that this method can be used to study collisional effects on other plasma modes.
Collisional-radiative coefficients from a three-level atomic model in nonequilibrium argon plasmas
Authors: Braun C. G. , Kunc J. A.
Published: July 2002

A three-level atomic model is used for determining the steady-state collisional-radiative coefficients in nonequilibrium partially ionized argon plasmas. Rate equations for populations of the atomic levels are coupled to an electron Boltzmann equation that includes inelastic processes. The solution of these coupled equations yields an analytical form for the non-Maxwellian electron distribution function. The reabsorption of radiation in the plasma is included through the use of Holstein radiation escape factors [Phys. Rev. 83, 1159 (1951)]. The cross sections in this model are included in the form of simple analytical expressions obtained from a numerical fitting of available experimental data. The results and limitations of the approach are discussed in a broad range of plasma conditions (electron temperature below 25 000 °K and atomic density of 1014–1018 cm−3).
Time dependent Z-pinch equilibria
Authors: Coppins M. , Culverwell I. D. , Haines M. G.
Published: July 2002

Two classes of self-similar time dependent Z-pinch equilibria (in which pressure balance is maintained while the internal energy is rising) are described. In the first class the total current is rising and the pinch is stationary, in the second the total current is falling and the pinch is expanding. It is found that, in contrast to the steady state case, both gas embedded and thermally isolated equilibria can be obtained at low (I≪1 MA) currents by varying the pinch parameters. Furthermore, a skin current can be maintained during the current rise or fall. The pinch parameter regimes corresponding to the various categories of equilibrium are derived and the spatial structures of the equilibrium profiles are described in detail.
Self-consistent modification of a fast-tail distribution by resonant fields in nonuniform plasmas
Authors: Morales G. J. , Shoucri Merit M. , Maggs J. E.
Published: July 2002

An analytic study is made of the second-order modifications produced on the fast-tail electron distribution function of a nonuniform plasma subjected to resonant excitation by wave sources. The source models considered can represent excitation by external electromagnetic waves propagating obliquely to the plasma density gradient, mode conversion of electrostatic whistlers, beat of two transparent electromagnetic waves, and direct conversion from ripples in the density profile. The calculation treats the Landau damping provided by fast-tail electrons self-consistently and is applicable to plasmas having a long density scale length L, i.e., (kDL)1/3 ≫1, where kD is the Debye wavenumber of the warm background electrons. A threshold condition is found for the formation of a positive slope in the tail distribution by the various excitation mechanisms.
Heavy ion beam interaction with spherical shell and super-range planar targets
Authors: Piriz Antonio Roberto
Published: July 2002

A simple model for the heavy ion beam driven implosion of uniform spherical shell targets is constructed. The model equation is obtained by averaging the fluid equation of conservation of energy over the thickness of the shell. The energy balance contains the thermal and kinetic energies of the region absorbing the beam energy. The driving power is considered as a constant. The model gives the dependence of the implosion properties on the ion energy and the results are in agreement with published simulation data. The dynamics of a plane slab heated by an intense ion beam with range smaller than the slab thickness is described by a modified version of the model. It yields the temporal behavior of the hydrodynamics efficiency and its dependence on the ratio between the payload and the absorber masses such as is observed in simulation results.
Hamiltonian formulation of inviscid flows with free boundaries
Authors: Abarbanel Henry D. I. , Brown Reggie , Yang Yumin M.
Published: July 2002

The formulation of the Hamiltonian structures for inviscid fluid flows with material free surfaces is presented in both the Lagrangian specification, where the fundamental Poisson brackets are canonical, and in the Eulerian specification, where the dynamics is given in noncanonical form. The noncanonical Eulerian brackets are derived explicitly from the canonical Lagrangian brackets. The Eulerian brackets are, with the exception of a single term at each material free surface separating flows in different phases, identical to those for isentropic flow of a compressible, inviscid fluid. The dynamics of the free surface is located in the Hamiltonian and in the definition of the Eulerian variables of mass density, ρ(x, t), momentum density, M(x,t) [which is ρ times the fluid velocity v(x,t)], and the specific entropy, σ(x,t). The boundary conditions for the Eulerian variables and the evolution equations for the free surfaces come from the Euler equations of the flow. This construction provides a unified treatment of inviscid flows with any number of free surfaces.
Supercritical Reynolds number experiments on a freely rotatable cylinder/splitter plate body
Authors: Cimbala J. M. , Chen K. T.
Published: July 2002

The behavior of a circular cylinder with attached splitter plate, under conditions where the entire cylinder/splitter plate body was free to rotate about the cylinder axis, has been studied experimentally as Reynolds number was increased through the critical value (laminar boundary layer separation replaced by turbulent boundary layer separation farther downstream). As in previous experiments (at lower Reynolds numbers), it was found that the plate did not align itself with the free stream, but instead rotated to some off-axis equilibrium angle, θ. For plates with splitter plate length, L, less than one cylinder diameter, D, θ dropped very quickly to some minimum value in the transitional Reynolds number range, then slowly increased toward some new supercritical value, which in all cases was smaller than that in the subcritical range. For cases with L/D≳1, however, in the transitional Reynolds number range, the splitter plate overshot the centerline and commenced oscillating between extremes on either side. At supercritical Reynolds numbers, for cases with L/D≤2, a new equilibrium angle eventually reestablished itself on one side or the other; but for cases with L/D≥2.5, the cylinder/splitter plate body continued to oscillate between extremes on either side, even at the highest Reynolds numbers tested.
On the role of linear mechanisms in transition to turbulence
Authors: Henningson Dan S. , Reddy Satish C.
Published: July 2002

Recent work has shown that linear mechanisms can lead to substantial transient growth in the energy of small disturbances in incompressible flows even when the Reynolds number is below the critical value predicted by linear stability (eigenvalue) analysis. In this note it is shown that linear growth mechanisms are necessary for transition in flows governed by the incompressible Navier–Stokes equations and that non-normality of the linearized Navier–Stokes operator is a necessary condition for subcritical transition.
Fanno processes in dense gases
Authors: Cramer M. S. , Monaco J. F. , Fabeny B. M.
Published: July 2002

The global behavior of Fanno processes is examined for dense gases. It is shown that three sonic points corresponding to two local maxima and one local minimum in the entropy can occur if the fluid is of the Bethe–Zel’dovich–Thompson type. Both analytical and numerical examples of the nonclassical behavior are provided.
Nonlinear interactions between oblique instability waves on nearly parallel shear flows
Authors: Goldstein M. E.
Published: July 2002

Asymptotic methods are used to describe the nonlinear self-interaction between a pair of oblique instability modes that eventually develops when initially linear, spatially growing instability waves evolve downstream in nominally two-dimensional, unbounded or semibounded, laminar shear flows. The first nonlinear reaction takes place locally within a so-called ‘‘critical layer’’ with the flow outside this layer consisting of a locally parallel mean flow plus a pair of oblique instability waves together with an associated plane wave. The instability wave amplitudes, which are completely determined by nonlinear effects within the critical layer, satisfy a pair of integral differential equations with quadratic to quartic-type nonlinearities. The most important feature of these equations is the oblique mode, self-interaction term that usually leads to a singularity at a finite downstream position. It is shown that this type of interaction is quite ubiquitous and is the dominant nonlinear interaction in many apparently unrelated shear flows—even when the oblique modes do not exhibit the most rapid growth in the initial linear stage.
Kolmogorov inertial range spectra for inhomogeneous turbulence
Authors: Moser Robert D.
Published: July 2002

It is shown that the statistical orthogonality of the Karhunen–Loeve (KL) eigenfunctions with respect to both energy and dissipation makes them a particularly good basis for the definition of an energy spectrum in inhomogeneous fluid flows. An effective wave number is defined to characterize the KL eigenfunctions. The definition preserves the relationship between the dissipation and energy spectra that holds for Fourier spectra. With the spectrum and wave number so defined, the scale-similarity arguments that lead to the existence of a spectral inertial range apply. It is also shown that the existence of a spectral inertial range in the KL eigenspectrum is consistent with Kolmogorov’s scale-similarity formulation for structure functions. An example of the KL spectrum obtained from a numerically simulated plane channel flow is presented.