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The propagation of pressure waves in porous medium containing a gas hydrate is numerically investigated. The study was performed in the framework of the three-phase model of a porous medium (the skeleton, hydrate and fluid). The porous medium is saturated with methane gas and partially filled with methane hydrate. The transmission and reflection of waves at the boundaries between the gas containing and the hydrate containing porous media is studied. It is established that in a partially filled hydrate porous medium an acoustic pulse propagates without distortion, with some attenuation. By increasing hydrate fraction and decreasing gas fraction the acoustic impedance of the porous medium increases. The characteristics of pressure wave propagation in a cylindrical cavity in a porous medium with hydrate-containing layer are studied in the linear approximation. The two-phase model of a porous medium with effective parameters of the skeleton is used for the mathematical description of porous media containing gas hydrate. Skeleton is considered as a homogeneous mixture of solid and hydrate grains. The dispersion relation for the main acoustic mode in a cylindrical cavity for each layer constituting the porous medium is obtained. The reflection and transmission coefficients of waves passing through the boundary of layers inside the cavity are calculated. The influence of rock properties, frequency, and length of layer containing hydrate on the total reflection coefficient from the layer is studied.

In this paper, we deal with the oblique electromagnetic electron cyclotron (EMEC) waves in the Uranus magnetosphere. The expression of the dispersion relation is plotted by using the method of the feature solution. After the kinetic method, the growth rate and the actual frequency of the EMEC wave are studied theoretically in the Uranian system. NASA, Voyager 2, the observed results of the space detectors show that the spin axes of the planets are abnormally oriented and that there are more particles in the high energy tail of the Uranian magnetospheric plasma. Therefore, this paper uses the Kappa distribution instead of the usual Maxwell distribution. The study extends to the tilt propagation of EMEC waves, which has a change in temperature anisotropy and propagation angle with respect to the direction of the magnetic field. These parameters were found to support the growth rate of EMEC waves. However, the response of the actual frequency of these waves is not the same as the rate of growth in all cases. These results apply to the detailed comparison of planetary studies of the space plasma environment and the magnetosphere system.

The opto-fluidics systems can be used for label free refractometric and biosensensing applications. In this work transmission properties of one-dimensional polycarbonate-liquid photonic arrays are studied, where methanol and ethanol were proposed as liquid components. The band structure and the transmission spectrum were calculated using the transference matrix method, in which we consider the dispersion relation for the refractive index n(w) of each material in the visible range. Using lattice parameters of 1 µm, 10 µm, and 4 µm, we obtained forbidden bandgaps in the visible region. When lattice parameters of 1000 µm were considered, we obtained several narrow bandgaps in the visible range.

We analyse the tension between the (indirect) measurements of the total cross section, and show the impact of various assumptions on the extraction of the parameters from the elastic scattering amplitude, with a special attention to the total cross section. In particular, the determination of the phase of the elastic scattering amplitude will play an important role, and we shall study it via dispersion relations. We shall also examine the origin of the dependence on momentum transfer of the slopes of the different parts of the scattering amplitude in different models. We shall also give the results of another similar analysis based on a Regge-trajectory approach for the hadron scattering amplitude., Comment: 5 pages

We derive the spectra of surface states for massive Dirac Hamiltonians with either momentum or energy separation between the left- and right-handed Weyl nodes. Momentum separation between the Weyl nodes corresponds to the explicitly broken time-reversal symmetry and the energy separation - to broken parity. Such Hamiltonians provide the simplest model description of Weyl semimetals. We find that the only effect of the energy separation between the Weyl nodes is to decrease the Fermi velocity in the linear dispersion relation of the surface states of massive Dirac Hamiltonian. In the case of broken time-reversal symmetry, the spectrum of surface states interpolates in a nontrivial way between the Fermi arc-type and the Dirac cone-type dispersion relations. In particular we find that for all values of the mass and the momentum separation between the Weyl nodes the surface states only exist in a strip of finite width in momentum space. We give also some simpler examples of surface states in order to make the...

We discuss the phenomenon of emergent Lorentz invariance in strongly coupled theories that admit a holographic gravity dual. The emergence of Lorentz invariance at low energies is reflected in the two-point functions of local operators and in the dispersion relations of the bound states. The deviations of these observables from the relativistic form at low energies are found to be naturally suppressed.

In this paper, we designed a novel kind of broadband SOG Fresnel lens special for GaInP/GaInAs/Ge multi-junction concentrator solar cells. In the broadband spectrum of 350–1800 nm, every subcell’s spectral response characteristic and the dispersion relation of the material’s refractive index with wavelengths were taken into consideration. Each saw-tooth’s surface profile of Fresnel lens was optimized by finding its design main wavelength. In contrast to conventional Fresnel lens concentrators, this design improves the irradiance uniformity without the complicated theoretical approaches. Finally, the uniformity of illumination intensity and the optical efficiency more than 80% were achieved.

In the last decade, the Angle Resolved Photoemission Spectroscopy (ARPES) has achieved important advances in both energy and angular resolutions, providing a direct measurement of the single-particle dispersion relation and superconducting gap. These dispersion relation data allow a full determination of the self-energy, first and second neighbor parameters in the Hubbard model. This model and its generalizations offer a simple and general way to describe the electronic correlation in solids. In particular, the parameters of correlated hopping interactions, responsible of the d-wave superconductivity in the generalized Hubbard model, are determined from ARPES data and the critical temperature within the mean-field approximation. In this work, we determine the model parameters for Bi2Sr2−xLaxCuO6+δ and study its d-wave superconducting gap as a function of temperature by solving numerically two coupled integral equations. Finally, the calculated electronic specific heat is compared with experimental results.

We present a macroscopic model for electron transport in silicon, in which the state variables are moments of the electron distribution functions. The evolution equations are obtained from the Boltzmann transport equations and are closed by means of the maximum entropy principle (MEP). Analytic approximations are used for the electron and phonon dispersion relations. All the main scattering mechanisms electrons undergo in silicon are taken into account.

In this paper we study time dependent problems, like the propagation of sound waves or the behavior of small local wave disturbances induced by spontaneous internal fluctuations, in a binary mixture undergoing a chemical reaction of type A+A= B+B. The study is developed at the hydrodynamic Euler level, in a chemical regime of fast reactive process in which the chemical reaction is close to its final equilibrium state. The hydrodynamic state of the mixture is described by the balance equations for the mass densities of both constituents A and B, together with the conservation laws for the momentum and total energy of the mixture. The progress of the chemical reaction is specified by an Arrhenius-type reaction rate which defines the net balance between production and consumption of each constituent. Assuming that the considered time dependent problems induce weak macroscopic deviations, the hydrodynamic equations are linearized through a normal mode expansion of the state variables around the equilibrium state. From the dispersion relation of the normal modes, we determine the free and forced phase velocities as well as the attenuation coefficients of the waves. We show that the dispersion and absorption of these waves depend explicitly on the heat of the chemical reaction, the concentrations of the constituents and the activation energy through the exponential factor of Arrhenius law., Fundação para a Ciência e a Tecnologia, Brazilian Research Council (CNPq)

Massive particles are radiated from black holes through the Hawking mechanism together with the more familiar radiation of massless particles. For $E >= m$, the emission rate is identical to the massless case. But $E < m$ particles can also tunnel across the horizon. A study of the dispersion relation and wave packet simulations show that their classical trajectory is similar to that of a boomerang. The tunneling formalism is used to calculate the probability for detecting such $E < m$ particles, for a Schwarzschild black hole of astrophysical size or in an analogue gravity experiment, as a function of the distance from the horizon and the energy of the particle., 4 pages, 2 figures. Proceedings of Spanish Relativity Meeting (ERE2011)

We have carried out molecular dynamics (MD) simulations in order to investigate the onset of negative dispersion of the plasmon mode in the classical one-component plasma (OCP). We find that negative dispersion sets in at a Coulomb coupling strength of Γ∼9.5-10. A good quantitative agreement is obtained with an existing theoretical treatment of the dispersion relation that is based on a memory function approach to the dynamics of the OCP. © 2012 American Institute of Physics.

The $K\pi$ vector form factor, $F_+^{K\pi}$, used to reproduce the Belle spectrum of $\tauKpi$ decays is described by means of a three-times subtracted dispersion relation also incorporating constraints from $K_{l3}$ decays. The slope and curvature of $F_+^{K\pi}$ are fitted to the data yielding $\lambda_+'=(25.49 \pm 0.31) \times 10^{-3}$ and $\lambda_+"= (12.22 \pm 0.14) \times 10^{-4}$. The pole parameters of the $K^*(892)^\pm$ are found to be $m_{K^*(892)^\pm}= 892.0\pm 0.5$ MeV and $\Gamma_{K^*(892)^\pm}= 46.5 \pm1.1$ MeV. The phase-space integrals relevant for $K_{l3}$ analyses and the $P$-wave isospin-1/2 $K\pi$ phase-shift threshold parameters are also calculated., Comment: 3 pages, uses aipproc style. Talk presented by R. Escribano at the IX International Conference on Quark Confinement and Hadron Spectrum (QCHS09), Madrid, Spain, 30.8-3.9.2010

We show how the new precise data on kaon decays together with forward dispersion relations, sum rules and once‐ and twice‐subtracted Roy equations allow for a precise analysis of ππ scattering. The once subtracted Roy equations provide a more stringent consistency check for the parametrizations of the S0‐wave data in the region from 450 to 1100 MeV that allows us to present a preliminary determination of the f0(600) and f0(980) poles from the constrained dispersive data analysis.

During direct numerical simulation of isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations the formation of long wave condensate was observed. Here we study the influence of the condensate presence on the dispersion relation for the gravity waves. Formation of the two side bands, corresponding to the interaction with condensate, was observed. Distortion of the dispersion relation can be a factor influencing the spectra of inverse and direct turbulent cascades.

We give a short overview of our approach, presented in detail in [1], for the ferromagnetic, three‐dimensional, translational‐symmetric Kondo lattice model which allows us to derive both magnon energies and linewidths (lifetimes) and to study the properties of the ferromagnetic phase at finite temperatures. Both anomalous softening and anomalous damping are obtained and discussed.

We present full ab initio calculations of the phonon band structure of thin Si nanowires oriented along the [110] direction. Using these phonon dispersion relations we investigate the structural stability of these wires. We found that all studied wires were stable also when doped with either B or P, if the unit cell was taken sufficiently large along the wire axis. The evolution of the phonon dispersion relations and of the sound velocities with respect to the wire diameters is discussed. Softening is observed for acoustic modes and hardening for optical phonon modes with increasing wire diameters.

We use chirally motivated effective meson-baryon potentials to describe the low energy $\bar{K}N$ data including the characteristics of kaonic hydrogen. Our results are examined in comparison with other approaches based on the unitarity and dispersion relation for the inverse of the T-matrix. We demonstrate that the movements of the poles generated by the model upon varying the model parameters can serve as a tool to get additional insights on the dynamics of the strongly coupled $\pi\Sigma$-$\bar{K}N$ system., Comment: contribution to the Chiral10 workshop, Valencia (Spain), June 21-24, 2010

We address the most critical issue in nano‐devices: the degradation due to lattice heating. We consider different dispersions for the acoustic and optical phonon modes. We find that in small devices, due to the velocity overshoot effect lattice heating has less degrading effect on the device electrical characteristics. We also find that the use of the realistic phonon dispersion relations rather than the simplified ones does not affect the results and conclusions obtained when using linear dispersion for the acoustic modes and constant dispersion for the optical modes.

The optical properties of an organic polycrystalline layer of NTCDA embedded in a microcavity show exciton‐photon coupling between the cavity mode and both the 0–0 and 0–1 transitions. In this work we present a theoretical microscopic model that reproduces the experimental data and explains the creation of an additional third polaritonic dispersion relation. Furthermore, a theoretical insight into the problem of polariton relaxation and photoluminescence in presence of vibronic replicas is given using a general model based on a master equation approach.

Over the recent years, the emergence of accelerator beamlines capable of exchanging the phase space coordinates between two degrees of freedom has opened the path toward the precise control of phase space distribution and in particular to the production of relativistic electron beams with shaped current profiles. After briefly reviewing the technique, we present its application to produce a train of sub‐picosecond microbunches and report on its experimental implementation at the Fermilab’s A0 photoinjector facility.

We construct a perturbative expansion of the scalar sector in the Myers-Pospelov model, up to second order in the Lorentz violating parameter and taking into account its higher-order time derivative character. This expansion allows us to construct an hermitian positive-definite Hamiltonian which provides a correct basis for quantization. Demanding that the modified normal frequencies remain real requires the introduction of an upper bound in the magnitude |k| of the momentum, which is a manifestation of the effective character of the model. The free scalar propagator, including the corresponding modified dispersion relations, is also calculated to the given order, thus providing the starting point to consider radiative corrections when interactions are introduced., Published in AIP Conf.Proc.977:214-223,2008

We investigate the centrifugally driven curvature drift instability to study how field lines twist close to the light cylinder surface of an AGN, through which the free motion of AGN winds can be monitored. By studying the dynamics of the relativistic MHD flow close to the light cylinder surface, we derive and solve analytically the dispersion relation of the instability by applying a single particle approach based on the centrifugal acceleration. Considering the typical values of AGN winds, it is shown that the timescale of the curvature drift instability is far less than the accretion process timescale, indicating that the present instability is very efficient and might strongly influence processes in AGN plasmas.

We briefly discuss the unified theoretical framework that allows explaining a variety of experimental observations with one single "fishbone-like" dispersion relation. We also point out the relationship of MHD and shear Alfvén waves in the kinetic thermal ion frequency gap with microturbulence, Zonal Flows and Geodesic Acoustic Modes, emphasizing its importance in determining long time scale dynamic behaviors in burning plasmas. © 2008 American Institute of Physics.

The self-energies and the spectral densities of longitudinal and transverse gluons at zero temperature in the color-flavor-locked (CFL) phase are calculated. There appears a collective excitation, a light plasmon, at energies smaller than two times the gap parameter and momenta smaller than about eight times the gap. The minimum in the dispersion relation of this mode at some nonzero value of momentum corresponds to the van Hove singularity., 4 pages, 4 figures, Talk given by H. Malekzadeh, to appear in the proceedings of the conference "Quark Confinement and the Hadron Spectrum VII" (QCHS7), Ponta Delgada, 2 - 7 September 2006

Both theory and experiment have suggested that parametric decay instability (PDI) is a possible edge power loss mechanism in ICRF (including HHFW and IBW) heating of tokamak plasmas. In this paper, we consider the extension of previous theoretical models to enable a quantitative evaluation of pump depletion and power loss due to PDI. A set of nonlinear coupled equations for a long‐wavelength “dipole” pump and short‐wavelength daughter modes is derived. The model recovers the standard PDI dispersion relation for fixed pump wave amplitude, and obeys an appropriate nonlinear energy conservation law. When dissipation is present the model provides a description of energy flow from the pump to the daughter modes and the particles. The equations are intended to describe parametric decay and pump depletion in inhomogeneous plasmas. By writing the nonlinear coupling coefficients in terms of a spectral basis, a strategy for implementing the model in full‐wave spectral codes is presented.

The semileptonic decay B->pi is studied starting from a simple quark model and taking into account the effect of the B* resonance. A novel, multiply subtracted, Omn\`es dispersion relation has been implemented to extend the predictions of the quark model to all physical q^2 values. We find |V_{ub}|=0.0034 +/- 0.0003(exp.)+/- 0.0007(theory), in good agreement with experiment., Comment: Three pages, two figures. To appear in the proceedings of Quark Confinament and Hadron Spectrum VII. Azores, September 2006

A helicon source is driven with amplitude modulated RF at modulation frequencies near the ion cyclotron frequency in the VINETA device. In response to the modulation propagating electromagnetic waves are found, whose dispersion differs significantly from linear wave dispersion theory. This indicates that the observed waves are generated by non‐linear wave coupling of the helicon waves with a second strongly damped or evanescent wave. Laser induced fluorescence measurements reveal a local increase of the ion temperature at the minimum of the modulation drive.

Geodesic acoustic mode (GAM) oscillations in tokamak plasmas are known to be sensitive to the value of the safety factor q. Through its linear and nonlinear interactions with ITG turbulence it has recently been shown in direct numerical global simulations that the turbulence driven heat transport is larger when GAM oscilations of large amplitude are present, resulting in an anomalous transport scaling with the inverse plasma current. GAM dispersion relations have been derived for circular, large aspect ratio configurations, and, recently, for helical configurations. Linear simulation results are presented using the global, PIC, finite element codes GYGLES and ORB5 for the GAM frequency, damping rate and Rosenbluth‐Hinton residual zonal flow for a scan in plasma elongation. It is found that CAM frequency slightly decreases, while GAM damping rate and residual zonal flows increase with elongation. Nonlinear ITG simulations using the ORB5 code show that elongation reduces heat transport and that this is related to the plasma current and not q alone.

A dust crystal consisting of charged dust grains of alternating charge sign (…/+/−/+/−/+/…) and mass is considered. Considering the equations of longitudinal motion, a linear dispersion relation is derived from first principles, and then analyzed. Two modes are obtained, including an acoustic mode and an inverse‐dispersive optic‐like one. The nonlinear aspects of longitudinal dust grain motion are also briefly addressed, via a Boussineq and Korteweg‐ de Vries description.

A laser acoustic imaging microscope has been developed that measures acoustic motion with high spatial resolution without scanning. Images are recorded at normal video frame rates and heterodyne principles are used to allow operation at any frequency from Hz to GHz. Fourier transformation of the acoustic amplitude and phase displacement images provides a direct quantitative determination of excited mode wavenumbers at any frequency. Results are presented at frequencies near the first longitudinal thickness mode (∼ 900 MHz) demonstrating simultaneous excitation of lateral modes with nonzero wavenumbers in an electrically driven AlN thin film acoustic resonator. Images combined at several frequencies form a direct visualization of lateral mode dispersion relations for the device under test allowing mode identification and a direct measure of specific lateral mode properties. Discussion and analysis of the results are presented in comparison with plate wave modeling of these devices taking account for material anisotropy and multilayer films.

Direct observation of ICRF (∼80 MHz) waves (k⊥≃0.5 cm−1−10 cm−1) is now possible in Alcator C-Mod using an optical heterodyne technique on the Phase Contrast Imaging (PCI) system, which uses a CO2 laser to observe electron density fluctuations. The PCI observations are vertical chord averages, so the full-wave ICRF code TORIC [1] has been used to simulate the wave fields in these plasmas to aid in interpretation. Mode-converted ion Bernstein waves (IBW) in plasmas composed of H, D and 3He at 6 T have been observed at both high (1 MA) and low (400 kA) current. The fast magnetosonic wave launched from the low-field side has been observed in high density (∼5×1020 m−3) D(H) plasmas with off-axis ICRH at 4.5 T. Comparison between PCI measurements and code results are presented. The measured wave numbers are in good agreement with the local dispersion relations for both types of waves.

We describe low energy physics in the CFL and LOFF phases by means of effective lagrangians. In the CFL case we present also how to derive expressions for the parameters appearing in the lagrangian via weak coupling calculations taking advantage of the dimensional reduction of fermion physics around the Fermi surface. The Goldstone boson of the LOFF phase turns out to be a phonon satisfying an anisotropic dispersion relation., LaTex 10 pages. No figures. Invited talk at the Conference "QCD@work", Martinafranca (Bari), June 16-20, 2001

Regular straight hollow waveguides have phase velocities of propagating electromagnetic waves greater than the free-space speed of light. However, it has been found that, if the waveguide is twisted, the phase velocities of the waveguide modes become slower. By choosing optimum shape of the cross section and pitch angle of a twisted waveguide, a desired phase velocity of the accelerating mode can be obtained for accelerating charged particles. This type of accelerating structure may have advantages over the conventional irisloaded structures. The twisted waveguide structure has been modeled and computer simulated in 3-D electromagnetic solvers to show the slow-wave properties of the accelerating mode.

Vector meson correlators are studied in effective chiral quark models with both local and non-local regulators. A set of sum rules based on dispersion relations is derived, which allows for a comparison of model predictions to data. We show that the two Weinberg sum rules for vector correlators hold in the non-local model., 10 pp., presented at International Workshop on Hadron Physics: Effective Theories of Low-Energy QCD, 10-15 September 1999, Coimbra, Portugal

Most magnetically confined plasma devices cannot take advantage of standard Electron Cyclotron Emission (ECE) diagnostics to measure temperature. They either operate at high density relative to their magnetic field or they do not have sufficient density and temperature to reach the blackbody condition. The standard ECE technique measures the electromagnetic waves emanating from the plasma. Here we propose to measure electron Bernstein waves (EBW) to ascertain the local electron temperature in these plasmas. The optical thickness of EBW is extremely high because it is an electrostatic wave with a large k(subscript i). One can reach the blackbody condition with a plasma density approximately equal to 10(superscript 11) cm(superscript -3) and electron temperature approximately equal to 1 eV. This makes it attractive to most plasma devices. One serious issue with using EBW is the wave accessibility. EBW may be accessible by either direct coupling or mode conversion through an extremely narrow layer (approximately 1-2 mm) in low field devices.

There has recently been a study of the potential uses of multimode dielectric structures for wakefield acceleration [1]. This technique is based on adjusting the wakefield modes of the structure to constructively interfere at certain delays with respect to the drive bunch, thus providing an accelerating gradient enhancement over single mode devices. In this report we examine and attempt to clarify the issues raised by this work in the light of the present state of the art in wakefield acceleration.

Space charge effects on beam dynamics in linear accelerators are discussed. Practical linac beam dynamics calculation methods which include space charge effects are discussed. Also, the status of beam performance experiments including space charge studies are summarized.

The standard definition for an achromat is a transport line having zero values for the spatial dispersion (R16) and the angular dispersion (R26). For a bunched beam with linear space charge this definition of achromaticity does not hold. The linear space charge in the presence of a bend provides coupling between (a) bunch spatial width and bunch length (R15) and (b) bunch angular spread and bunch length (R25). Therefore, achromaticity should be redefined as a line having zero values of the spatial dispersion (R16), the angular dispersion (R26), and matrix elements R15 and R25. These additional conditions (R15 = R25 = 0) can be achieved, for example, with two small RF cavities at appropriate locations in the achromat, to cancel space charge effects. An example of the application of this technique to the Spallation Neutron Source (SNS) high energy beam transport line will be presented.

We review the derivation of moment equations which include the effects of space charge and dispersion in bends first presented in ref. [1]. These equations generalize the familiar envelope equations to include the dispersive effects of bends. We review the application of these equations to the calculation of the change in emittance resulting from a sharp transition from a straight section to a bend section, using an energy conservation constraint. Comparisons of detailed 2D and 3D simulations of intense beams in rings using the WARP code (refs. [2,3]) are made with results obtained from the moment equations. We also compare the analysis carried out in ref. [1], to more recent analyses, refs. [4,5]. We further examine self-consistent distributions of beams in bends and discuss the relevance of these distributions to the moment equation formulation.

Heating and current drive by electron cyclotron waves in high magnetic field tokamaks is commonly done by coupling power from the low-field side to the O-mode. However, for tokamaks with ωpe/ωce>1, such as the spherical tokamak NSTX, the O-mode is cutoff throughout most of the plasma. An alternative method for accessing the cyclotron layer is via the fast X-mode and its mode conversion to an electron-Bernstein wave (EBW)[1]. We show that for a given plasma density and magnetic field profile, an appropriate choice of the frequency allows one to form a triplet (cutoff-resonance-cutoff) X to EBW mode-conversion scenario. This is similar to the low-frequency, ion-ion hybrid resonance scenario for which 100% mode conversion was shown to be possible[2]. The mode-conversion efficiency for DIII-D and NSTX is calculated.

In modeling electron cyclotron (EC) waves for heating (ECH) and current drive (ECCD) applications, the standard approach describes wave propagation using geometric optic ray tracing with cold plasma dispersion and wave absorption using a relativistic warm plasma expression. However, recent vertical O-mode transmission measurements on Tore Supra indicate that wave trajectories near the fundamental resonance frequency can significantly deviate from predictions of cold plasma analysis. The experimental results were attributed to warm plasma refraction effects caused by the anomalous dispersion associated with wave-particle resonance. Here, warm plasma refraction effects on wave propagation and absorption are examined in the context of a slab model in the parameter regime of interest to the upcoming 110 GHz electron cyclotron heating and current drive experiments on DIII-D.

Previous theoretical analysis [1] of mode conversion of fast Alfven waves (FAW) to ion-Bernstein waves (IBW) neglected poloidal variations of the fields and magnetic shear. Full-wave codes show incident FAW fields focused into multiple poloidal modes near the ion-ion hybrid resonance (IHR) [2]. A new mode conversion model has been constructed including poloidal wavenumbers and poloidal magnetic field. The model consists of two coupled equations for the perpendicular components of the FAW electric field. These equations are numerically integrated to find the fraction of FAW power resonantly absorbed at the IHR. When the high-field-side right-hand cutoff is included, nonzero poloidal wavenumbers can change the triplet resonator phase and improve mode conversion at low k∥.

The metastability of a recently proposed candidate for a polymeric structure of nitrogen is confirmed by using linear response theory to calculate the phonon dispersion throughout the Brillouin zone. It is found that the structure is mechanically stable for pressures below at least 360 GPa. Calculations of Raman and infrared‐active phonon frequencies are presented for this metastable phase, and calculations of Raman frequencies for two molecular structures are compared with experimental data.

Rutile (TiO2) samples at 60% of solid density have been shock‐loaded from 0.21 to 6.1 GPa with sample thickness of 4 mm and studied with the PVDF piezoelectric polymer stress‐rate gauge. The technique uses a copper capsule to contain the sample which has PVDF gauge packages in direct contact with the front and rear surfaces. A precise measure is made of the compressive stress wave velocity through the sample, as well as the input and propagated shock stress. The initial density is known from the sample preparation process, and the amount of shock‐compression is calculated from the measurement of shock velocity and input stress. Shock states and re‐shock states are measured. The observed data are consistent with previously published high pressure data. It is observed that rutile has a ‘‘crush strength’’ near 6 GPa. Propagated stress‐pulse rise times vary from 234 to 916 nsec. Propagated stress‐pulse rise times of shock‐compressed HMX, 2Al+Fe2O3, 3Ni+Al, and 5Ti+3Si are presented.

The available momentum space of a FODO lattice is determined by the maximum value of the dispersion function (δx=Dx ∂p/p). In a regular FODO lattice the dispersion function oscillates between its maximum and minimum values, which are always positive. The maximum value of the dispersion function in a FODO cell of a fixed length depends on the cell phase difference. An example of a new lattice, in which the dispersion function is lowered to half its value in the same FODO cell, is presented. The available momentum space in the new lattice is raised to twice that in the FODO lattice by allowing the dispersion function to oscillate between the same positive and negative values. The maxima of the dispersion function in the new lattice have half the value of those within the regular 90° cells.

A systematic review of theoretical results for the longitudinal and transverse impedances obtained by different methods is presented. The paper comprises definitions, general theorems, modal analysis, a diffraction model, and analytical results. Several new results are included. In particular, necessary and sufficient conditions are given for the independence of the impedance from the beam longitudinal direction. The impedances of two basic simple structures—that of a cavity and that of a step—are studied in detail. The transition from the regime of a cavity to the regime of a step is explained, an approximate formula describing this transition is given, and the criterion for determining the applicability of each regime is established. The asymptotic behavior of the impedance for a finite number M of periodically arranged cavities as a function of M is studied. The different behaviors of the impedance for a single cavity and that for an infinite number of cavities are explained as resulting from the interference of the diffracted waves. A criterion for determining the transition in the impedance behavior from small M to large M is presented.

The complex dispersion functions of Eq. (3) in Ref. 1 have recently been computed accurately and reliably over their entire range of parameters, without recourse to the usual ‘‘slightly‐relativistic’’ approximation, which may have difficulty for oblique incidence.2 In the future, the local dispersion properties of ECRF waves will be reevaluated for parameters of interest to ECRF conditions in several existing and proposed fusion experiments, with particular emphasis on the damping and mode‐conversion of both ordinary and extraordinary waves to electrostatic waves near the upper hybrid and cyclotron frequencies.

The limits on the effective growth of the plasma beat wave due to noise in the plasma density and the depletion of the laser driving fields are investigated theoretically.

The triple‐axis neutron scattering technique has been used to measure the temperature dependence of the spin‐wave and critical scattering below Tc(=120 K) in the metallic freromagnet CoS2. The spin‐wave dispersion relations at small propagation vectors (‖q‖?0.3A−1) can be described by h/ω=Dq2−Eq4 with D of about 110 meV−A2 and E/D of 1∠2A2 at 78 K, with a small anisotropy observed in the different symmetry directions of the crystal. At small q, D is found to renormalize as (1−T/Tc)β with β=0.24. Some indication of a triple‐peaked structure in the scattering spectrum was observed immediately below Tc.