bluuebunny/crossref_metadata_2025 huggingface dataset:
Quasiexactly solvable problems and the dual (q-)Hahn polynomials
Authors: Krasovsky I. V.
Published: July 2002

A second-order differential (q-difference) eigenvalue equation is contructed whose solutions are generating functions of the dual (q-)Hahn polynomials. The fact is noticed that these generating functions are reduced to the (little q-)Jacobi polynomials, and implications of this for quasiexactly solvable problems are studied. A connection with the Azbel–Hofstadter problem is indicated.
Branch-point structure and the energy level characterization of avoided crossings
Authors: Walkup John R. , Dunn Martin , Watson Deborah K.
Published: July 2002

The appearance of avoided crossings among energy levels as a system parameter is varied is signaled by the presence of square-root branch points in the complex parameter-plane. Even hidden crossings, which are so gradual as to be difficult to resolve experimentally, can be uncovered by the knowledge of the locations of these branch points. As shown in this paper, there are two different analytic structures that feature square-root branch points and give rise to avoided crossings in energy. Either may be present in an actual quantum-mechanical problem. This poses special problems in perturbation theory since the analytic structure of the energy is not readily apparent from the perturbation series, and yet the analytic structure must be known beforehand if the perturbation series is to be summed to high accuracy. Determining which analytic structure is present from the perturbation series is illustrated here with the example of a dimensional perturbation treatment of the diamagnetic hydrogen problem. The branch point trajectories for this system in the complex plane of the perturbation parameter δ (related to the magnetic quantum number and the dimensionality) as the magnetic field strength is varied are also examined. It is shown how the trajectories of the two branch-point pairs as the magnetic field strength varies are a natural consequence of the particular analytic structure the energy manifests in the complex δ-plane. There is no need to invoke any additional analytic structures as a function of the field strength parameter.
A transformation of a Feynman–Kac formula for holomorphic families of type B
Authors: Wittich Olaf
Published: July 2002

A transformation formula for resolvents of families of Schrödinger operators H(ξ)=−12Δ+ξQ, which are assumed to be holomorphic of type B, is proved. It can be used to derive the well-known correspondence between three-dimensional Coulomb problem and four-dimensional harmonic oscillator.
Note on coherent states and adiabatic connections, curvatures
Authors: Fujii Kazuyuki
Published: July 2002

We give a possible generalization to the example in the paper of Zanardi and Rasetti [Phys. Lett. A 264, 94 (1999)]. For this, explicit forms of adiabatic connection, curvature, etc., are given. We also discuss the possibility of another generalization of their model.
Viscosity and ultrasonic attenuation in He4 below 0.6 K
Authors: Um Chung-In , Lee Soo-Young , Yoo Sahng-Kyoon , George Thomas F. , Pandey Lakshmi N. , Adamenko Igor N.
Published: July 2002

Through a treatment of three-phonon processes, the wide-angle scattering rates and the absorption rates of phonons, which characterize viscosity and ultrasonic attenuation, respectively, are calculated for He4 below 0.6 K. These rates are obtained from the collision matrix which is constructed approximately from an integral eigenvalue equation for the collision operator. The sequence of the lowest eigenvalues of the collision matrix as the angular momentum quantum number (l) increases shows a saturated behavior which has not been reported before. The calculated viscosity and ultrasonic attenuation are compared with previous theoretical and experimental results.
The influence of heating of two-level systems on low-temperature nuclear spin–lattice relaxation
Authors: Giorgadze N. P. , Zakharov L. Zh. , Tugushi A. I. , Chotorlishvili L. L.
Published: July 2002

The influence of heating of two-level systems on low-temperature spin–lattice relaxation is studied. Effects of the type of a “phonon bottleneck” are investigated in amorphous substances in which the role of resonant phonons is played by resonant tunnel two-level systems.
Thermomagnetic relaxation in two-phase solid He3–4He mixtures at ultralow temperatures
Authors: Mikhin N. P. , Omelaenko N. F. , Polev A. V. , Rudavskii E. Ya. , Shvarts V. A.
Published: July 2002

NMR investigations of restoration of longitudinal equilibrium magnetization in phase-separated solid He3–4He mixtures are carried out in the temperature range 1–200 mK. It is found that below 100 mK, the results depend on the energy of tipping NMR pulses, while at the lowest temperatures the restoration of magnetization becomes nonmonotonic. The obtained results are explained on the basis of a proposed model in which both magnetic (spin-lattice) and thermal relaxation are assumed to take place between the Zeeman system and the lattice.
Correlated redistribution of optical conductivity spectra of HTSC: contribution of interband excitations to the formation of the metal state of La2−xSrxCuO4 and YBa2Cu3O6+x
Authors: Samovarov V. N.
Published: July 2002

A phenomenological model is proposed for the transformation of interband conductivity caused by electron transitions through the optical (dielectric) gap ℏωg into the intraband conductivity of hole carriers in high-temperature superconductors under chemical doping. The interrelation between the interband and intraband conductivity components is analyzed in terms of the spectral function N(ω)∼∫σ(ω)dω for integral conductivity of the normal phase. Two groups of coexisting charge carries of the p- and d-types with different relations with interband transitions are singled out. The integral conductivity of narrow-band d-carriers is determined by interband excitations with the gap attenuation Γ∝ωg. The integral conductivity of wide-band p-carriers is not connected with interband excitations and is determined by the standard Drude spectrum. The obtained spectral functions are compared with the available data for La2−xSrxCuO4 and YBa2Cu3O6+x in the doping range from the beginning of metallization up to loss of superconductivity. The good agreement with the experimental data leads to the following conclusions: (i) the integral interband conductivity at the doping stage with increasing temperature of superconducting transition is mainly determined by the d-component to which interband excitations are “pumped;” (ii) as soon as one of the planes CuO2 or CuOx goes over to a predominantly p-metal state, a noncorrelated metal with loss of superconductivity is formed.
Taylor vortices in short fluid columns
Authors: Koga J. K. , Koschmieder E. L.
Published: July 2002

A series of experiments has been made investigating Taylor vortex flow in short columns of fluid that are bounded by resting horizontal plates. The outer cylinder was at rest and the radius ratio was 0.885. The fluids were silicone oils of 0.10 and 0.05 cm2/sec viscosity. In all experiments even numbers of vortices have been observed, the number depending on the aspect ratio of the fluid column, the Reynolds number, and the initial conditions. The direction of the flow at the horizontal boundaries was in all cases inward.
A nonlinear theory for describing the propagation of disturbances on a capillary jet
Authors: Torpey Peter A.
Published: July 2002

The problem of the growth of disturbances on a capillary jet has received much attention in the past. However, previous theories have produced only limited correlation with experimental evidence. Traditional perturbation approaches to the problem are not well suited to describing the highly nonlinear behavior of disturbances on a capillary jet, especially near the tip of the jet where it breaks up into isolated drops. On the other hand, numerical solutions necessitate the use of an extremely fine spatial resolution over a large extent to follow disturbances as they progress along the jet and grow in amplitude over several orders of magnitude. In this paper, a new approach to this well-studied problem is described. The new approach is based on a weighted residual technique and takes advantage of the particular strengths of both analytical and numerical methods. The method is shown to correctly predict many of the nonlinear phenomena observed on actual jets and offers some fresh insight into the dynamical processes taking place within the jet.
Convection in rotating binary mixtures. III. Galerkin models
Authors: Bhattacharjee Jayanta K.
Published: July 2002

A few-mode Galerkin truncation is used to set up Lorenz models for convection in rotating binary mixtures. Idealized as well as realistic boundary conditions are treated. An extended model to handle Küppers–Lortz instability is studied. For idealized boundary conditions the nonlinear terms cause the Hopf bifurcation to the traveling wave state to be backward. Finite amplitude traveling waves are expected for negative values of the separation parameter. For Prandtl numbers less than unity, a codimension three-point should be seen. The amplitude equation near the codimension three-point is discussed. Realistic boundary conditions, however, make the possibility of observing the codimension three-point remote, even in 3He–4He mixtures.
Particle distribution functions in suspensions
Authors: Rubinstein Jacob , Keller Joseph B.
Published: July 2002

Equations are derived for the temporal variation of the one- and two-particle position distribution functions in a suspension. The fluid is assumed to be incompressible, viscous, and in slow motion, i.e., to be undergoing Stokes flow. External forces such as gravity are included, but Brownian motion is omitted. The resulting system of equations for the one-particle distribution and for the mean velocity of a particle resemble the Vlasov–Poisson system for the charge density and the electric field in a plasma. The existence and uniqueness of the solution of this system is proved for a nearly uniform distribution of spherical particles. This shows that in this case the equations do not break down because of shock formation or other nonlinear effects.
Small-angle neutron scattering of sheared concentrated dispersions: Microstructure along principal flow axes
Authors: de Kruif C. G. , van der Werff J. C. , Johnson S. J. , May R. P.
Published: July 2002

Using a novel parallel-plate flow cell, the shear-induced distortion of the structure factor S(k) for concentrated hard-sphere dispersions by small-angle neutron scattering is examined. The flow cell is vertically mounted, and the angle of incidence of the neutrons can be varied by rotating the flow cell as a whole. Thus data can be collected in many planes including those containing the principal flow axes. Dispersions containing sterically stabilized silica spheres of 40 nm radius, with volume fractions from 0.03 to 0.45, are studied. The Peclet number is varied between 0 and 1.0, and measured scattering patterns for wave vectors 0<k<0.3 nm−1 are measured. Contour plots for S(k) in part of the shear plane are presented for the first time. Based on the shear-induced distortion of S(k), it is proposed that particle density increases along the compressional and vorticity axes, but decreases along the extensional axis.
Inverse cascades in two-dimensional compressible turbulence. I. Incompressible forcing at low Mach number
Authors: Dahlburg J. P. , Dahlburg R. B. , Gardner J. H. , Picone J. M.
Published: July 2002

A fundamental property of forced, dissipative, two-dimensional incompressible Navier–Stokes (NS) systems is the dominance at long times of the longest wavelengths available to the flow. This dominance, attributed to an inverse cascade of energy with respect to enstrophy [Kraichnan, Phys. Fluids 10, 1417 (1967)], has been observed in spectrally accurate numerical simulations (see Refs. 5–7) of the incompressible NS equations. The numerical investigation of this behavior is extended to the weakly compressible regime by means of the fully compressible Fourier collocation code combox with a solenoidal forcing function that imparts no net momentum and stirs the fluid in a wave-number band in the neighborhood of kf=11. A comparison of spectral results from combox simulations with an average Mach number of 0.22 with those from identically forced incompressible simulations, at Reynolds numbers ≤700, indicates (1) the compressible and incompressible wave-number dependences in both the energy cascading and enstrophy cascading regions are nearly identical; (2) in the compressible calculation, a dual power law is also observed in density and pressure fluctuations; and (3) continued (kf=11) forcing leads to overall continued growth in the longest accessible velocity field wavelength, in both the incompressible and compressible cases.
A numerical study of the effects of spanwise rotation on turbulent channel flow
Authors: Tafti D. K. , Vanka S. P.
Published: July 2002

The effects of spanwise rotation on the large-scale structures in a turbulent channel flow are numerically simulated by integrating the filtered Navier–Stokes equations. A finite-difference technique is used to retain the generality for complex geometries and developing flows to be considered in the future. The computed results are consistent with previous flow visualization data and measurements. It is seen that for the presently considered low Reynolds number, the flow significantly laminarizes on the stable side even for low rotation rates. Cellular spanwise structures are observed to develop as a result of the unstable interaction between mean shear and Coriolis forces. The statistics of these roll cells and the underlying turbulence are analyzed and presented in this paper. It is observed that the roll cells make a significant contribution to total turbulent quantities and also aid in the transport of underlying turbulence.
Nonpropagating soliton and kink soliton in a mildly sloping channel
Authors: Yan Jiaren , Zhou Chuanhui , You Jianqiang
Published: July 2002

The nonlinear equation governing both the nonpropagating soliton and kink soliton in a channel with slowly varying depth of water has been derived using the perturbation method of multiple scales. Both nonpropagating soliton and kink soliton solutions for the special case of a mildly sloping channel have been given. The effects of the surface tension of water on solitons have been taken into account. The results obtained show that the two types of solitons always move slowly toward the shallow end of the channel with uniform accelerations, and the soliton’s average drift velocities as well as accelerations are proportional to the channel slope and slightly reduced by the surface tension.
Plumes in Hele–Shaw cells
Authors: Amar Martine Ben
Published: July 2002

A theoretical treatment of a thermal growing plume in a Hele–Shaw cell is presented. An explanation of why the experiment shows a cap similar to a Saffman–Taylor finger that occupies half the cell is presented. A boundary layer analysis, in two dimensions, reveals a selection mechanism where the thermal boundary layer acts like the curvature effects in ordinary viscous fingering experiments.
Stability theory of an elliptical vortex
Authors: Sela Nathan , Goldhirsch Isaac
Published: July 2002

The process of transition from the laminar to the turbulent flow regime is intimately related to the emergence of both three-dimensional structures and small-scale excitations. It has been proposed that the instabilities of two-dimensional vortices having elliptical streamlines constitute a relevant mechanism that is capable of giving rise to excitations on all scales. The present work is devoted to a detailed linear stability analysis of such vortices (for both the viscous and the inviscid cases). This is conveniently done by transforming the pertinent equations to a set of natural variables in which some symmetries of the problem are evident. A variable related to the pressure is shown to satisfy a Hill equation. The mechanism of instability for a small eccentricity of the vortex is shown to be related to a spectral degeneracy of the circular vortex. The case of large eccentricity is solved by asymptotic methods. One obtains a logarithmic dependence of the rate of growth of the leading instability as a function of the eccentricity. The set of eigenstates is shown to be complete, despite the fact that the pertinent equations are not self-adjoint, and the rates of growth of unstable modes are given by universal functions (in the inviscid limit) of an effective radial wave number that is identified. The degree of localization of an initially localized perturbation is studied and some implications of the results are discussed.
Chaos in Kelvin–Helmholtz instability in magnetic fluids
Authors: Malik S. K. , Singh M.
Published: July 2002

The nonlinear instability of two layers of ferrofluids in relative motion is studied under external driving. With the use of the method of multiple scaling, a generalized derivation of the amplitude evolution is obtained in marginally unstable regions of parameter space. A Melnikov function is formulated for such an instability and it is shown that there exist transverse homoclinic orbits leading to chaos.
Quasiperiodicity and phase locking route to chaos in the 2-D oscillatory flow around a circular cylinder
Authors: Vittori Giovanna , Blondeaux Paolo
Published: July 2002

The two-dimensional oscillatory flow around a circular cylinder is analyzed by means of the numerical approach described in Justesen [J. Fluid Mech. 222, 157 (1991)]. For a fixed value of the ratio between the Stokes viscous thickness and the radius of the cylinder section, when the Reynolds number assumes low values, the flow is periodic and symmetric with respect to an axis aligned with the flow direction and crossing the axis of the cylinder. An increase in the Reynolds number beyond a first critical value causes the flow to bifurcate: the velocity field loses its spatial symmetry even though it retains its time periodicity. When the Reynolds number is larger than a second critical value, a new frequency appears in the flow. This new frequency, which is much smaller than the frequency of the basic flow, increases for increasing values of the Reynolds number till a phase locking takes place. A further increase in the Reynolds number leads the flow to a chaotic status. The ‘‘quasiperiodicity and phase locking’’ route to chaos can be recognized.
Theory of neoclassical resistivity-gradient-driven turbulence
Authors: Kwon O. J. , Diamond P. H. , Hahm T. S.
Published: July 2002

It is shown that rippling instabilities can tap the density gradient expansion free-energy source through the density dependence of the neoclassical resistivity. Linear analyses show that the region where neoclassical rippling modes are significantly excited extends from the edge of the plasma to the region where ν*e ≤1. Since these modes are nondispersive, diamagnetic effects are negligible in comparison to the nonlinear decorrelation rate at saturation. Thus the relevant regime is the ‘‘strong turbulence’’ regime. The turbulent radial diffusivities of the temperature and the density are obtained as eigenvalues of the renormalized eigenmode equations at steady state. The density gradient acts to enhance the level of turbulence, compared to that driven by the temperature gradient alone. The saturated turbulent state is characterized by current decoupling, the breakdown of Boltzmann relation, a radial mode scale of density fluctuations exceeding that of temperature fluctuations, implying that density diffusivity exceeds temperature diffusivity, and that density fluctuation levels exceed temperature fluctuation levels. Magnetic fluctuation levels are negligible.
Parametric instabilities of Langmuir waves in weak/moderate magnetic fields
Authors: Akimoto K.
Published: July 2002

A general dispersion equation, which describes the parametric instabilities of some electrostatic waves in a weak/moderate magnetic field, is derived. The dispersion equation is solved numerically to study the effects of a moderately intense magnetic field on the parametric instabilities of relatively large amplitude Langmuir waves. A Langmuir pump wave can couple with various low-frequency branches such as lower-hybrid, electron-acoustic, ion-cyclotron, and ion-acoustic branches. The transverse modulational instability is most sensitive to a magnetic field. Even for a Langmuir wave with W̄∼0.1, where W̄ is the ratio of the time-averaged wave energy to the electron thermal energy, some portions of the transverse modulational instability in the direction exactly perpendicular to the external magnetic field are quite easily suppressed. However, some oblique instabilities may be enhanced by a magnetic field. In general, a moderate magnetic field suppresses most of the oblique instabilities, and the parametric instabilities become essentially one dimensional.
Fokker–Planck electron diffusion caused by an obliquely propagating electromagnetic wave packet of narrow bandwidth
Authors: Hizanidis Kyriakos
Published: July 2002

The relativistic motion of electrons in an intense electromagnetic wave packet propagating obliquely to a uniform magnetic field is analytically studied on the basis of the Fokker–Planck–Kolmogorov (FPK) approach. The wave packet consists of circularly polarized electron-cyclotron waves. The dynamical system in question is shown to be reducible to one with three degrees of freedom. Within the framework of the Hamiltonian analysis the nonlinear diffusion tensor is derived, and it is shown that this tensor can be separated into zeroth-, first-, and second- order parts with respect to the relative bandwidth. The zeroth order part describes diffusive acceleration along lines of constant unperturbed Hamiltonian. The second order part, which corresponds to the longest time scale, describes diffusion across those lines. A possible transport theory is outlined on the basis of this separation of the time scales.
A model of strong beam–plasma turbulence
Authors: Main William , Benford Gregory
Published: July 2002

Strong beam–plasma interactions occur when beam density nb approaches plasma density, nb/np >0.01. Energy flow from resonant waves to short wavelengths is modeled with existing theory, using instability rates from linear and nonlinear (Zakharov) dispersion relations. Langmuir waves lose energy by wave convection, through observed electromagnetic emission, and to heating by induced return currents acting on anomalous resistivity. Inputs to the model equations are current, voltage, and other parameters of a 600 keV, 5 kA electron beam. The beam propagates in 10 mT helium preionized to 2×1012 cm−3, emitting radiation of peak power 100 kW at an efficiency of 3×10−5. Turbulent electric fields reach 27 kV/cm [Phys. Fluids B 1, 2488 (1989)]. Comparison between experiment and model calculations shows satisfactory agreement.
A nonlocal analysis of electrostatic waves in hot inhomogeneous bounded plasmas
Authors: Sauter O. , Vaclavik J. , Skiff F.
Published: July 2002

A numerical code, seal, solving the full form of a second-order integrodifferential equation that describes electrostatic waves in a slab plasma is presented. No expansion in the smallness of the ion Larmor radius is made. The plasma may have arbitrary density and temperature profiles and is immersed in a nonuniform magnetic field. Only small magnetic field gradients, Maxwellian equilibrium distribution functions, and ky =0 are assumed. First the integral equation is derived in Fourier space using the linearized Vlasov and Poisson equations, and then it is transformed back into real space, which enables us to treat the case of bounded plasmas. The two boundary conditions specified simulate an antenna at one end of the plasma and wave-reflecting walls. Solutions having wavelengths smaller than the ion Larmor radius have been found. Comparison with experiments where ion Bernstein waves are launched in argon and barium plasmas shows very good agreement with the solution of the code seal. A positive-definite formula for the local power absorption is also derived and computed.
Double layers in a plasma with negative ions
Authors: Merlino Robert L. , Loomis Jackson J.
Published: July 2002

The formation of strong double layers in a plasma consisting of positive ions, negative ions, and electrons has been investigated in a triple-plasma device. When a strong double layer is present in a positive ion/electron plasma, the introduction of negative ions results in the formation of a second double layer which is separated from the first double layer by a region of quasineutral plasma.
The dynamics of ion rings in highly conductive plasmas
Authors: Lyster P. M. , Sudan R. N.
Published: July 2002

A numerical study employing a hybrid computer code (particle ions/fluid electrons) is made of the dynamics of translating ion rings in a highly conductive plasma. The translational kinetic energy of such rings is lost through the generation of Alfvén waves. When the initial axial velocity of the ring is greater than the local Alfvén speed in the plasma, a typical slowing down length is zA =(ar/4ζ)v̄4z0/(v2θv2A), where ar is the ring radial width, ζ=‖δB/B0‖, δB is the ring self-magnetic-field strength on axis, B0 is the strength of the axial magnetic field, v̄z0 is the initial translational velocity of the ring, vθ is the average toroidal ring particle velocity, vA=B0/(4πρ)1/2 is the Alfvén velocity, and ρ is the plasma mass density. Also discussed is the merging of an ion ring with a spheromak.
Nonlinear behavior of weakly unstable linear modes in plasmas with aligned equilibrium mass flow
Authors: Peredo M. , Tataronis J. A.
Published: July 2002

The nonlinear evolution of weakly unstable linear magnetohydrodynamic waves in plasma configurations characterized by equilibrium mass flow aligned parallel to the magnetic field is investigated. The analysis is based on field representations expressed as expansions in Fourier harmonics and computation of modifications to the linear theory (first harmonic) arising from the nonlinear coupling between the zeroth and second harmonics. It is found that Landau’s equation governs the nonlinear evolution of the system. A correction to the linearized theory appears at third order in the mode amplitude and is proportional to the linear growth rate. Furthermore, the conditions under which the nonlinearities provide a saturation mechanism to limit the growth of the linear instabilities is explored. Finally, this saturation phenomenon for a specific configuration consisting of a Z pinch with a small axial magnetic field is illustrated.
Implosion symmetry of heavy-ion-driven inertial confinement fusion targets
Authors: Kothe D. B. , Brackbill J. U. , Choi C. K.
Published: July 2002

Mechanisms that induce implosion asymmetries in ion-driven inertial confinement fusion (ICF) targets are identified and investigated by studying the two-dimensional hydrodynamic response of the heavy-ion-driven HIBALL target [Boch, in Heavy Ion Inertial Fusion, AIP Conf. Proc. No. 152, Washington, DC (American Institute of Physics, New York, 1986), p. 23] in planar geometry. The implosion of the multilayered, single-shell target is subjected to two symmetry-reducing mechanisms: (1) spatial beam intensity nonuniformities and (2) target material interface perturbations. In self-consistent numerical calculations, the target implosion symmetry is found to be sensitive to spatial variations in beam energy deposition resulting from interface perturbations in the path of the beam and coherent intensity variations in the beam itself. The asymmetries in beam energy absorption perturb the flow in the target absorption layer. If the resulting fluid perturbations are seeded at the hydrodynamically unstable pusher–fuel interface, they can grow with rates comparable to the Rayleigh–Taylor instability when lateral wavelengths are comparable to the payload shell thickness. Coherent variations in beam intensity as small as 5%–10% at low intensity (1 TW/cm2) and 1% at high intensity (1000 TW/cm2) limit the usable target implosion energy.
First results from the Madison Symmetric Torus reversed field pinch
Authors: Prager S. C. , Almagri A. F. , Assadi S. , Beckstead J. A. , Dexter R. N. , Den Hartog D. J. , Chartas G. , Hokin S. A. , Lovell T. W. , Rempel T. D. , Sarff J. S. , Shen W. , Spragins C. W. , Sprott J. C.
Published: July 2002

The first period of physics operation of the Madison Symmetric Torus (MST) reversed field pinch [Plasma Physics and Controlled Nuclear Fusion Research 1988 (IAEA, Vienna, 1989), Vol 2, p. 757] has produced information on sawtooth oscillations, edge magnetic and electrostatic fluctuations, and equilibrium parameters at large plasma size. Sawtooth oscillations are prevalent at all values of pinch parameter and might constitute discrete dynamo events. Both electrostatic and magnetic fluctuations are of sufficient magnitude to be relevant to transport in the reversed field pinch. In the plasmas studied to date (up to a plasma current of 0.5 MA) the poloidal beta value is about 10% or greater.
Alpha particle destabilization of the toroidicity-induced Alfvén eigenmodes
Authors: Cheng C. Z.
Published: July 2002

The high-frequency, low mode number toroidicity-induced Alfvén eigenmodes (TAE) [Phys. Fluids 29, 3695 (1986)] are shown to be driven unstable by the circulating and/or trapped α particles through the wave–particle resonances. Satisfying the resonance condition requires that the α-particle birth speed vα≥vA/2‖m−nq‖, where vA is the Alfvén speed, m is the poloidal mode number, and n is the toroidal mode number. To destabilize TAE modes, the inverse Landau damping associated with the α-particle pressure gradient free energy must overcome the velocity space Landau damping due to both the α particles and the core electrons and ions. The growth rate was studied analytically with a perturbative formula derived from the quadratic dispersion relation, and numerically with the aid of the nova-k code. Stability criteria in terms of the α-particle beta βα, α-particle pressure parameter (ω*/ωA) (ω* is the α-particle diamagnetic drift frequency), and (vα/vA) parameters will be presented for the Tokamak Fusion Test Reactor (TFTR) [Proceedings of the Thirteenth International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Crystal City, VA, 1990 (International Atomic Energy Agency, Vienna, in press)], Compact Ignition Tokamak (CIT) [Phys. Scr. T16, 89 (1987)], and the International Thermonuclear Experimental Reactor (ITER) [ITER Documentation Series, No. 21 (International Atomic Energy Agency, Vienna, 1991)].

The volume-averaged α-particle beta threshold for TAE instability also depends sensitively on the core electron and ion temperature. Typically the volume-averaged α-particle beta threshold is in the order of 10−4. Typical growth rates of the n=1 TAE mode can be in the order of 10−2ωA , where ωA=vA/qR . Other types of global Alfvén waves are stable in deuterium–tritium (D–T) tokamaks due to toroidal coupling effects.
Ion acoustic parametric decay instability in laser-produced plasma with varying ionic charge
Authors: Mizuno K. , Drake R. P. , Young P. E. , Bahr R. , Seka W. , Estabrook K. G.
Published: July 2002

Studies of the ion acoustic decay instability (IADI) are reported in which the target material of the laser-produced plasma was varied. The IADI was monitored by observing the Stokes peaks of the second-harmonic spectrum. Its threshold was quite low (≊2×1013 W/cm2 ) even in high-Z plasma. The threshold increased only weakly with Z. On the other hand, the instability intensity decreased strongly with Z, which is attributed to the decrease of the growth rate. A simple theory explains these experimental results reasonably well.
Two-dimensional numerical simulation of trapped electron mode turbulent transport in a tokamak
Authors: Kingsbury O. T. , Waltz R. E.
Published: July 2002

Turbulent transport with trapped electrons is simulated with a two-dimensional (2-D) representation. The trapped particles are lumped into hot and cold fluids to treat temperature gradient effects. The ion temperature gradient and dissipative trapped electron modes are simultaneously present. The hot and cold lumped fluid model was found to represent the true kinetic model linearly. The numerically simulated transport compares very well with detailed quasilinear expressions. A plasma particle pinch is found only at extremely low collisionalities and a heat conduction pinch is found at moderate collisionalities, although there is no energy flow pinch seen.
Behavior of magnetic field fluctuations during dynamo activity and its effect on energy confinement in a reversed-field pinch
Authors: Hattori K. , Hirano Y. , Shimada T. , Yagi Y. , Maejima Y. , Hirota I. , Ogawa K.
Published: July 2002

Fluctuations of magnetic fields and related magnetohydrodynamic (MHD) phenomena are investigated in the TPE-1RM15 reversed-field pinch experiment [Plasma Physics and Controlled Fusion Research, 1986 (IAEA, Vienna, 1987), Vol. 2, p. 453]. Mode analysis of fluctuations measured by multichannel coils reveals that nonlinear interactions between m=1 and m=0 modes, such as nonlinear coupling and phase locking, play significant roles during a dynamo event (i.e., the flux genertion process in the sustainment phase), resulting in transition from an unstable state to a stable state. Behaviors of these fluctuations are found to be toroidally asymmetrical due to strong nonlinearity. Study of the current ramping experiment shows that the inverse of global energy confinement time depends on the squared fluctuation level offset linearly, which is consistent with the prediction of the transport model based on the diffusion of stochastic field lines. By examining the dependence of the resistive part of the loop voltage on the fluctuation level, the input power to the electrons and ions are estimated to be about 70% and 30% of the total input power, respectively.
The long-wavelength limit of the ion-temperature gradient mode in tokamak plasmas
Authors: Chen L. , Briguglio S. , Romanelli F.
Published: July 2002

The stability of the ion-temperature gradient (∇Ti) mode in tokamak geometries is examined in the limit of long wavelength and flat density, retaining the nonadiabatic electron response. The existence of three unstable branches is shown. The toroidicity-induced ∇Ti branch tends to be stabilized for increasing wavelength by the finite εTi(εTi = LTi/R) corrections. Meanwhile, the slablike ∇Ti branch remains unstable and is little affected by the electron dynamics. The third branch corresponds to toroidicity-induced ∇Ti eigenmodes propagating, however, in the electron diamagnetic direction, which are destabilized by the nonadiabatic electron dynamics. At shorter wavelengths, the toroidicity-induced ∇Ti branch remains strongly unstable, while the other two branches become stabilized.
Time-dependent phase conjugation and four-wave mixing in plasmas
Authors: Goldman Martin V. , Williams Edward A.
Published: July 2002

Time-dependent four-wave mixing and phase conjugation in plasmas are treated, taking into account resonant longitudinal plasma modes and effects of spatial nonuniformity. A space-time formulation of four-wave processes in the ponderomotive force regime yields linearized equations, which are solved analytically as a combined initial/boundary-value problem in slab and inhomogeneous geometries. The plasma response is incorporated in a ‘‘grating’’ Green’s function, expressed in terms of linear quasilongitudinal susceptibilities. Response times, decay times, and absolute instabilities are treated analytically. Plasma nonuniformity can speed up the response of the conjugate wave and modify resonant absolute instability thresholds. A new class of resonant absolute instabilities occurs when the counterpropagating pump waves have unequal intensities. The thresholds can be rather low for pump waves of modest intensity, provided the resonant grating has a long lifetime. Below these thresholds, regimes of stable amplification of the phase-conjugate wave relative to the incident signal are possible with pumps of unequal intensity.
Raman backscattering in laser wake-field and beat-wave accelerators
Authors: Tripathi V. K. , Liu C. S.
Published: July 2002

An intense short laser pulse propagating through a plasma undergoes stimulated Raman backscattering when oscillatory electron velocity v0≥4c/(2ω0τ0ωpτ0)1/2, where ω0 and τ0 are the frequency and pulse duration of the laser and ωp is the plasma frequency. In a laser wake-field accelerator employing short laser pulses with ωpτ0∼2π, this threshold is exceeded when v0/c≳0.1. The threshold is smaller in a beat-wave accelerator where longer pulses are used.
Geometric optics in a tenuous energetic plasma
Authors: Kirkwood R. K.
Published: July 2002

The theory of geometric optics is formulated taking explicit account of the motion of energetic particles over distances large compared to the wavelength but small compared to the dimension of the plasma. It is shown that spatial variations of the wave number that are consistent with geometric optics cause substantial corrections to the plasma response when energetic particles are present. Solutions obtained for cases in which the Hermitian part of the conductivity is dominated by a small population of energetic particles show that the local wave absorption rate is dependent on the plasma dimension. Numerical calculations of cyclotron absorption by both thermal and nonthermal particles indicate significant corrections in cases similar to present tokamak experiments.
Leakage currents outside an imploding Z pinch
Authors: Terry R. E. , Pereira N. R.
Published: July 2002

Leakage currents outside a pulse-line-driven Z pinch are considered in two circumstances. In the initial stage of the pinch a non-neutral electron flow can arise before magnetic insulation is established. The relative importance of such currents is estimated in terms of diode impedance and pulse-line dimensions. In the later stages of the pinch a neutralized current flow can arise in any tenuous plasma that may be present in the pinch periphery. The effects of the neutral current are estimated through self-similar solutions to a gyrokinetic equation. The collisionless plasma corona can contain an important fraction of the implosion energy.
Theory of electron-beam tracking in reduced-density channels
Authors: Fernsler R. F. , Slinker S. P. , Hubbard R. F.
Published: July 2002

A theory is presented for the guiding of relativistic electron beams by rarefied gaseous channels. The analysis is based on analytic computations of the transverse force felt by a rigid-rod beam propagating off axis from a channel of reduced gas density. The density gradients produce an attractive channel force that can be surprisingly robust, even though it develops from relatively subtle gas chemistry properties. Static numerical calculations support the analytic work. Longitudinal beam coupling and effects that degrade channel guidance are discussed as well.
The effect of an insulating boundary on plasma stability
Authors: Hameiri Eliezer , Mond Michael
Published: July 2002

It is shown that the boundary conditions corresponding to an insulating boundary follow as the ‘‘natural’’ boundary conditions resulting from minimization of the plasma energy without specifying the type of boundary. This property has the implication that the linearized fluid evolution equations are self-adjoint. It also makes possible the derivation of a necessary condition for stability against ‘‘interchange’’ modes, even though the magnetic field lines are not closed.
On electron acceleration by strongly turbulent plasmas
Authors: Gavrilov E. M. , Shvets V. F. , Rubenchik A. M.
Published: July 2002

The process of electron acceleration by collapsing Langmuir cavities is analyzed both theoretically and numerically. The method of successive ‘‘burnout’’ of the cavities is developed and realized in the framework of two-dimensional particle simulation. Both isotropic and anisotropic turbulence are considered. The computer simulation results are found to be in good agreement with developed theoretical ideas. It is shown that all dissipated energy is transferred to the small group of fast electrons. Declining according to a power law the steady-state distribution function of accelerated electrons is formed. The stretching of the tail occurs through the motion of the stationary spectrum boundary to the region of large velocities. The minimum cavity size increases and inertial range decreases in the process of acceleration.
Flow-shear-induced Compton scattering of electron drift instability
Authors: Hahm T. S.
Published: July 2002

Plasma flow-shear effects on nonlinear saturation of electron drift waves are analyzed in the weak turbulence regime. Flow shear can enhance ion Compton scattering of long-wavelength electron drift waves not only by modifying the beat wave–ion resonance condition, but also via the radial dependence of linear susceptibility. A nonlinear dispersion relation is obtained as a solution of the radially nonlocal nonlinear eigenmode equation. At nonlinear saturation, the spectral intensity of the fluctuations scales with flow shear as (∂V0φ/∂r)−2 in addition to the linear dependence on the linear growth rate, and decays according to a power law kθ−1.
A kinetic theory of the extraordinary-mode perturbations in cylindrical relativistic magnetrons
Authors: Uhm Han S.
Published: July 2002

Stability properties of the extraordinary-mode perturbations in a relativistic electron flow generated inside a cylindrical magnetron are investigated within the framework of the linearized Vlasov–Maxwell equations. The stability analysis is carried out under the assumptions that the layer is thin and relatively tenuous, and that the phase velocity of the perturbed waves is very close to the mean drift velocity of the layer. The perturbed distribution function of the extraordinary-mode perturbations is calculated by integrating along the electron orbit. The eigenvalue equation is derived and solved separately in the vacuum and layer regions by properly matching boundary conditions at the inter-regional surface. Solution in the vacuum region includes the resonator and cylindrical curvature effects. A closed algebraic dispersion relation is obtained for the synchronous modes, whose phase velocity is very close to the mean drift velocity of the layer. Analytical investigation of the dispersion relation is carried out for the resonance modes, whose eigenfrequency is very close to the vacuum modes in the magnetron circuit. The necessary and sufficient condition for instability is obtained for the resonance modes. It is shown that typical growth rates of the instability are a few percent of the electron cyclotron frequency.
The physics of megajoule, large-scale, and ultrafast short-scale laser plasmas
Authors: Campbell E. M.
Published: July 2002

Recent advances in laser science and technology have opened new possibilities for the study of high energy density plasma physics. The advances include techniques to control the laser spatial and temporal coherence, and the development of laser architectures and optical materials that have led to the demonstration of compact, short pulse (τ≤10−12 sec) high brightness lasers, capable of irradiating plasmas with intensities ≥1018 W/cm2. Experiments with reduced laser coherence have shown a substantial decrease in laser-driven parametric instabilities and have extended the parameter range where inverse bremsstrahlung absorption is the dominant coupling process. Beam smoothing with short wavelength lasers should result in inverse bremsstrahlung dominated coupling in the irradiance parameter regimes of the millimeter scale-length plasmas envisioned for the megajoule class lasers for ignition and gain in inertial fusion. In addition new regimes of laser–plasma coupling will become experimentally accessible when plasmas are irradiated with I≥1018 W/cm2. Relativistic effects, extreme profile modification, and electrons heated to energies exceeding 1 MeV are several of the phenomena that are expected. Numerous applications in basic and applied plasma physics will result from these new capabilities.
Ponderomotive force effects on temperature-gradient-driven instabilities
Authors: Sundaram A. K. , Hershkowitz N.
Published: July 2002

The modification of temperature-gradient-driven instabilities due to the presence of nonuniform radio-frequency fields near the ion cyclotron frequency is investigated in the linear regime. Employing the fluid theory, it is shown that the induced field line compression caused by ion cyclotron range of frequencies (ICRF) fields makes the net parallel compressibility positive, and thus provides a stabilizing influence on the ion-temperature-gradient-driven mode for an appropriately tailored profile of radio-frequency (rf) pressure. Concomitantly, the radial ponderomotive force generates an additional contribution via coupling between the perturbed fluid motion and the equilibrium ponderomotive force and this effect plays the role of dissipation to enhance or decrease the growth of temperature-gradient-driven modes depending upon the sign of rf pressure gradients. For decreased growth of temperature-gradient-driven instabilities, the plasma density gradients and rf pressure gradients must have opposite signs while enhancement in growth arises when both gradients have the same sign. Finally, the kinetic effects associated with these modes are briefly discussed.
Dielectric energy versus plasma energy, and Hamiltonian action-angle variables for the Vlasov equation
Authors: Morrison P. J. , Pfirsch D.
Published: July 2002

Expressions for the energy content of one-dimensional electrostatic perturbations about homogeneous equilibria are revisited. The well-known dielectric energy, ℰD, is compared with the exact plasma free energy expression, δ2F, that is conserved by the Vlasov–Poisson system [Phys. Rev. A 40, 3898 (1989) and Phys. Fluids B 2, 1105 (1990)]. The former is an expression in terms of the perturbed electric field amplitude, while the latter is determined by a generating function, which describes perturbations of the distribution function that respect the important constraint of dynamical accessibility of the system. Thus the comparison requires solving the Vlasov equation for such a perturbation of the distribution function in terms of the electric field. This is done for neutral modes of oscillation that occur for equilibria with stationary inflection points, and it is seen that for these special modes δ2F=ℰD. In the case of unstable and corresponding damped modes it is seen that δ2F≠ℰD; in fact δ2F≡0. This failure of the dielectric energy expression persists even for arbitrarily small growth and damping rates since ℰD is nonzero in this limit, whereas δ2F remains zero. In the case of general perturbations about stable equilibria, the two expressions are not equivalent; the exact energy density is given by an expression proportional to ω‖E(k,ω)‖2‖ε(k,ω)‖2/εI(k,ω), where E(k,ω) is the Fourier transform in space and time of the perturbed electric field (or equivalently the electric field associated with a single Van Kampen mode) and ε(k,ω) is the dielectric function with ω and k real and independent. The connection between the new exact energy expression and the at-best approximate ℰD is described. The new expression motivates natural definitions of Hamiltonian action variables and signature. A general linear integral transform (or equivalently a coordinate transformation) is introduced that maps the linear version of the noncanonical Hamiltonian structure, which describes the Vlasov equation, to action-angle (diagonal) form.