Intermediate Frequency Regime Research Articles

Effects of Temperature Anisotropy on Neoclassical Transport in the Plateau and Banana-Plateau Regimes

The neoclassical transport theory in a presence of temperature anisotropy is investigated in the low to the intermediate collision frequency regimes for a large aspect-ratio tokamak plasma. The standard procedure for an isotropic plasma in the plateau regime is extended to an anisotropic plasma, and the neoclassical transport coefficients in this regime are explicitly calculated. By interpolating the results in the plateau regime and the previously obtained ones in the banana regime, the expressions for the neoclassical transport coefficients which are continuously valid from the banana to the plateau regimes are presented.

Dilatational rheology of insoluble polymer monolayers: Poly(vinylacetate)

The dilatational rheology of the poly(vinylacetate) monolayer onto an aqueous subphase with $p\mathrm{H}=2.0$ has been studied between 1 \ifmmode^\circ\else\textdegree\fi{}C and 25 \ifmmode^\circ\else\textdegree\fi{}C. The combination of several techniques, relaxation after a step compression, oscillatory barrier experiments, electrocapillary waves, and surface light scattering (SLS) by thermal capillary waves, has allowed us to explore a broad frequency range. The relaxation experiments show multiexponential decay curves, whose complexity increases with decreasing the temperature. A regularization technique has been used to obtain the relaxation spectra from the relaxation curves and the dilatational viscoelastic parameters have been calculated from the spectra. The oscillatory barrier experiments confirm the results obtained from the step compression experiments. The dilatational viscosity increases very steeply in the frequency range 0.1--0.001 Hz. The shapes of the relaxation spectra follow the qualitative trends predicted a model recently proposed by Noskov [Colloid Polym. Sci. 273, 263 (1995)]. The temperature dependence of the fundamental relaxation time follows a Williams-Landel-Ferry equation above 14 \ifmmode^\circ\else\textdegree\fi{}C. These results correspond to the many-chain dynamics regime. The kilohertz region has been explored by the SLS technique. These results are compatible with the existence of a single Maxwell mode, with a relaxation time that has an Arrhenius-type temperature dependence. In the intermediate-frequency regime (10 Hz to 2 kHz) a further Maxwell process is found. It might correspond to the dynamics of loops and tails out of the surface plane.

Kinetic effects on ideal ballooning stability of the TJ-II heliac device

Kinetic corrections to a previous ideal MHD ballooning stability study of the TJ-II heliac standard configuration are numerically calculated using a criterion derived from the gyrokinetic Maxwell equations for modes with perpendicular wavelengths on the scale of the ion gyroradius in a general magnetic geometry. In this criterion, finite ion gyroradius and trapped particle effects are retained at first order. The existence of temperature gradients and different ion and electron temperatures are accounted for. The relevant kinetic regime for TJ-II is found to be the intermediate frequency regime, with ωbi, ωti < γ < ωbe, ωte across all the relevant region whenever electron cyclotron resonance heating (ECRH) plasmas are considered. Therefore, only trapped electrons are included in the calculations. The threshold poloidal wavenumber mu for diamagnetic stabilization of unstable ballooning modes is obtained, and a reduction of about 30% of the instability region radial width has been found. The trapped electron contribution to the growth rate is shown to be destabilizing for all modes with poloidal wavenumber below this threshold and is evaluated perturbatively, showing that an important part of it is due to those electrons trapped in the ripple of the magnetic field.

Frequency-modulated excitation of a two-level atom

We present a detailed experimental study of the frequency-modulated excitation of a two-level atom, using a microwave field to drive transitions between two Rydberg Stark states of potassium. In the absence of a modulation the interaction is the standard model of the Rabi problem, producing sinusoidal oscillations of the population between the two states. In the presence of a frequency modulation of the interacting field, however, the time evolution of the system is significantly modified, producing square wave oscillations of the population, sinusoidal oscillations at a different frequency, or even sinusoidal oscillations built up in a series of stair steps. The three responses described above are each found in a different regime for the frequency of the modulation with respect to the unmodulated Rabi frequency: the low-, high-, and intermediate-frequency regimes, respectively.

Study of hydrogenated amorphous silicon films prepared at intermediate frequencies

Abstract Hydrogenated amorphous silicon films were prepared in an intermediate-frequency regime, between radio frequency and very high frequency, at 30MHz. The films have optimized deposition rates of about 9 A s and a minimum dihydride contribution of 22%. The films were characterized by the dark conductivity, the photoconductivity, the bandgap, the bonded hydrogen content and the light-induced degradation of the photoconductivity. Optical emission spectroscopy served as the plasma diagnostic tool to compare quantitatively the relative abundance of the different emissive species present in the plasma. The surface was studied through X-ray photoelectron spectroscopy. Light-induced degradation studies of the photoconductivity and short-circuit current density provided some important information about defect creation in the high-substrate-temperature regime. Annealing recovery of the degraded photoconductivity and Fourier transform infrared spectroscopy studies also provided useful information regarding the...

Symmetric diblock copolymers under large amplitude oscillatory shear flow: Dual frequency experiments

Conceptually new experiments are described in which the effects of the superposition of two large amplitude oscillatory shear components on the morphology of a lamellar PS-b-PI diblock copolymer of low molecular weight close to TODT are investigated. First results of such dual frequency experiments are presented for the coupling of two shear components from the lower and intermediate frequency regimes I and II of the shear viscosity leading to parallel and perpendicular orientation behavior, respectively, in single frequency experiments. The employed frequencies were separated by more than two orders of magnitude, rendering possible coupling terms unimportant. Using two-dimensional small-angle x-ray scattering (2D-SAXS) measurements, it is shown that for large rim strain values the perpendicular orientation mechanism completely governs the behavior. In experiments where the applied strain for shear component II leading to perpendicular orientation is significantly reduced with respect to that of component I leading to parallel orientation, a characteristic flip from parallel to perpendicular orientation is observed along the radius of the sample disk. It is further demonstrated that the position of the flipping point along the radius can be altered by varying the amplitude of deformation component II. In these experiments regions of parallel as well as perpendicular orientation exhibiting high order parameters can be achieved. The results are interpreted using concepts for the orientation mechanisms developed in earlier single frequency studies, thereby corroborating the underlying ideas. Furthermore, the results of the dual frequency experiments supply valuable information concerning the competition between different orientation mechanisms not directly obtained from single frequency experiments.

The two-component representation of time-harmonic elastic body waves in the high- and intermediate-frequency regimes

Propagation and diffraction of time-harmonic elastic body waves through homogeneous and isotropic materials is revisited. The two-component representation of body waves is given which is applicable in the high- and intermediate-frequency regimes when the family of rays is (i) regular or (ii) possesses an irregularity due to the presence of a wedge, an acoustic point source located on the boundary, simple caustic, or focal line. Both physical and mathematical description of the phenomena under consideration is offered. The resulting expressions are asymptotic in character and easy to compute. They should prove useful in producing algorithms for describing acoustic fields in homogeneous and isotropic materials with isolated defects and in providing benchmark cases for testing numerical codes designed to solve elastic wave equations in more complicated situations.

Destabilization of singular layer modes in the comparable frequency regime

The nondissipative two-fluid equations for singular modes are employed to investigate the singular layer modes in the toroidal geometry. By matching the solutions in the outer (ideal magnetohydrodynamics (MHD)) and the inner regions a general dispersion relation is obtained, which is able to describe both the interchange and internal kink modes. The results show that the stable modes predicted by the finite-Larmor-radius modified ideal-MHD theory can become unstable due to the parallel electric field effect. The destabilization prevails in the comparable frequency regime (i.e., for a mode frequency comparable to that of the ion acoustic wave propagating along the magnetic field lines) instead of the intermediate frequency regime. Inclusion of the toroidal effect is found to be essential to the destabilization mechanism.

Linear viscoelasticity of concentrated hard-sphere dispersions

The viscoelastic behaviour of model near hard-sphere continuous potential r-36 dispersions have been determined using Brownian dynamics simulations in a hydrodynamics-free approximation. Two methods were used to obtain the real and imaginary components of the complex shear viscosity, eta ' and eta ", respectively: first, calculating a time correlation function under no-shear conditions using a Green-Kubo formula; secondly applying finite-strain amplitude oscillatory shear cycles in the linear response limit to the contents of the BD cell. We find that the normalized stress autocorrelation function can be approximated very well by a two-parameter stretched exponential over the complete volume fraction range. The state dependence of the derived spectrum of relaxation times is determined. As for experimental systems the complex viscosity scales with a 'longest' relaxation time, in dimensionless form, D0 tau 1/a2, where a is the radius of the particle and D0 is the self-diffusion coefficient in the zero-density limit. Also in the intermediate-frequency regime 40<a2 omega /D0<400 we find that both the real and imaginary parts of the complex shear viscosity decay as approximately omega -1/2 in agreement with experiment and theory. The Newtonian viscosities obtained using eta '( omega to 0) agree well with the predictions of the Krieger-Dougherty equations. The product of the Newtonian viscosity and the long-time self-diffusion coefficient increases linearly with volume fraction for most of the fluid range.

Two-fluid equations for singular modes with frequency comparable to the parallel ion acoustic frequency

Braginskii’s two-fluid equations, with collisional effects neglected and electron fluid assumed to be isothermal along the magnetic field lines, are employed to obtain the singular mode equations. While the ordering analysis in the paper indicates that, in the intermediate frequency regime (i.e., that with the frequency of the modes higher than the ion acoustic frequency along the magnetic field lines, but lower than the electron one), the stabilizing finite Larmor radius (FLR) effect on the modes dominates over other collisionless, two-fluid effects, the paper is devoted to the investigation of the comparable frequency regime (i.e., that with the frequency of the modes comparable to the ion acoustic frequency along the field lines). It is found that, in such a regime, the parallel electric field is excited and the plasma behaves nonadiabatically. The singular mode equations consist of two coupled second-order partial differential equations, in which the FLR, the plasma compression, and the parallel electric field effects are present. The results are discussed, and a comparison with the ideal magnetohydrodynamic formalism is given.

Beyond the effective medium: quasi modes in disordered media

For wave propagation in disordered media, the intermediate frequency regime is defined as the frequency range where the wavelength is comparable to the scale of the inhomogeneities. While difficult to treat theoretically, the regime is rich in physical phenomena. The focus of this paper is the transport characteristics of the coherent part of the wave energy in the intermediate frequency range. Through a re-formulation of the well-known coherent potential approximation, a new scheme is developed which is capable of identifying the quasi wave modes as well as yielding their dispersion relations. With no adjustable parameter, this scheme is demonstrated to give an excellent quantitative of the experimental data that showed two branches of the acoustic wave in colloidal suspensions. The new approach is used to predict the quasi modes in a random collection of metallic spheres.

Self-diffusion and viscoelasticity of dense hard-sphere colloids

Brownian dynamics (BD) simulation is used to calculate the viscoelasticity of model near-hard-sphere colloidal liquids using a continuous potential r–n interaction between the model colloidal particles. The exponent n was varied between 6 and 72. The real and reciprocal components of the complex shear viscosity, η′ and η″, were computed via time-correlation functions under no-shear conditions using a Green–Kubo formula. Also, oscillatory shear non-equilibrium BD was employed at finite strain amplitude in the linear-response regime. We find that the normalised stress autocorrelation function can be approximated very well by a two-parameter stretched exponential over the complete volume-fraction range. The parameters used to specify the stretched exponential and also the viscosities and long-time self-diffusion coefficients are quite sensitive to the value of n at a chosen volume fraction. The Newtonian viscosity decreases and the long-time self-diffusion coefficient increases with the softness of the interaction, in agreement with experiment. The value n= 36 gives best agreement with the experimental data, and therefore appears to be a good ‘effective’ interaction which we suggest includes the time-averaged effects of the many-body hydrodynamics to some extent.The state dependence of the derived spectrum of relaxation times is determined. As for experimental systems, the complex, viscosity scales with the dimensionless (‘longest’) relaxation time, Doτ1/a2, where a is the radius of the particle and Do is the self-diffusion coefficient in the zero-density limit. Also in the intermediate frequency regime 20 < a2ω/Do < 200 we find that both the real and imaginary parts of the complex shear viscosity decay as ca. ω–1/2 in agreement with experiment.

Destabilization of singular layer modes in the comparable frequency regime

The nondissipative two-fluid equations for singular modes are employed to investigate the singular layer modes in the toroidal geometry. By matching the solutions in the outer (ideal magnetohydrodynamics (MHD)) and the inner regions a general dispersion relation is obtained, which is able to describe both the interchange and internal kink modes. The results show that the stable modes predicted by the finite-Larmor-radius modified ideal-MHD theory can become unstable due to the parallel electric field effect. The destabilization prevails in the comparable frequency regime (i.e., for a mode frequency comparable to that of the ion acoustic wave propagating along the magnetic field lines) instead of the intermediate frequency regime. Inclusion of the toroidal effect is found to be essential to the destabilization mechanism.

The effects of molecular geometry on the depolarized stimulated gain spectra of simple liquids

Depolarized Rayleigh-wing spectra of simple liquids, including CS2, chlorinated methanes, benzene and benzene derivatives have been recorded using stimulated gain spectroscopy. To adequately interpret these spectra of simple liquids, a dephasing dynamical contribution in an intermediate time scale is needed in addition to a slower Debye reorientation relaxation and a faster broad inhomogeneous oscillator. The curve-fit dynamical characteristic parameters of these simple liquids are tabulated for comparison. The microscopic molecular properties, shape anisotropy, and dominating moment of inertia are found to play an important role in determining the rates of interaction-induced dynamics; smaller shape anisotropy and smaller moment of inertia give rise to faster collision rate in the intermediate frequency regime and faster oscillation in the higher frequency regime, respectively. In the low frequency region, the shear viscosity (a macroscopic property) of the liquid and the general molecular shapes dictate reorientation diffusion; for molecules within a family, the Debye relaxation rate is faster for liquids with smaller viscosity and shape anisotropy. Halogenation of benzene breaks the symmetry of the benzene ring giving two distinct oscillator frequencies. In the case of iodobenzene, three principle molecular axes are clearly distinct; it is necessary to use two Debye relaxation rates and two broad inhomogeneous oscillators to fit its stimulated gain spectrum.

Matching a diffusive and a kinetic approach for escape over a fluctuating barrier.

We study thermally driven escape over a dichotomously fluctuating barrier and present explicit formulas for the mean escape time in three limiting frequency domains. Our analysis is based on the chemically realistic case of large potential barrier, and modest fluctuation amplitude. When the fluctuation frequency is small compared to the time scale for adiabatic adjustment, which includes the low and intermediate frequency regimes, a kinetic approximation reproduces the Fokker-Planck results.

Quantum theory for free energies of electron transfer

We consider the problem of electron transfer between two symmetric redox states for cases in which the interstate coupling can be strong and the coupled harmonic bath can be nonadiabatic. We utilize an adiabatic bath coupled to the charge transfer species as a reference system and treat the solvation effects of nonzero frequency Fourier modes approximately, yielding an analytical theory for the activation free energy in terms of the spectral density of the bath. The theory is exact for both slow and fast bath modes. For small interstate coupling, the theory agrees with the golden rule result. We test the theory’s accuracy at large couplings in the intermediate frequency regime by comparison with Monte Carlo simulation.

Theory of pair breaking by vibrating macroscopic objects in superfluid 3He

An intuitive picture of dissipation through pair breaking by macroscopic, vibrating objects in an isotropic superfluid is presented, which predicts a critical velocity for direct quasi-particle emission of upsilon(c) = upsilon-0/(1 + alpha), where upsilon-0 is the Landau velocity and alpha characterizes the superfluid backflow. A new intermediate frequency regime is identified, in which pulsed experiments should reveal a hierarchy of critical velocities and sinusoidally vibrating objects will exhibit a crossover to diffusive behaviour. A model of flow through a channel with a rough surface is analyzed, which yields for the instantaneous dissipation Q approximately (upsilon - upsilon(c))5 and Q approximately upsilon-2, at low and high velocities, respectively.

Chaotic ionization of highly excited hydrogen atoms: Comparison of classical and quantum theory with experiment

The experimental and theoretical studies of the microwave ionization of highly excited hydrogen atoms provide a unique opportunity to explore two new frontiers of modern physics simultaneously. Since the Coulomb binding fields decrease rapidly with increasing quantum number, these atoms can be easily perturbed by external fields that are comparable or even greater than the atomic fields, which permits a thorough investigation of a variety of interesting, non-perturbative processes involved in the interaction of intense electromagnetic radiation with matter. In addition, since the classical description of the Bohr atom in a strong, oscillating electric field has been shown to exhibit “chaotic” behavior, this physical system serves as an important paradigm for the study of the quantum manifestations and modifications of classical chaos. This review describes a number of surprising phenomena that have emerged from these detailed experimental and theoretical studies of this strongly perturbed quantum system throughout the entire range of the experimentally accessible parameters - from the low-frequency regime of tunnelling ionization, to the high-frequency regime of multiphoton ionization, and to the complex intermediate-frequency regime of “chaotic” ionization. Particular emphasis will be placed on both the striking quantum-classical correspondence in the intermediate-frequency regime where the experimental onset of ionization is well described by the onset of classical chaos, as well as the remarkable quantum suppression of the chaotic ionization in the high-frequency regime because of quantum interference effects closely related to the process of Anderson localization in solid-state physics.

Vibrational relaxation and vibrational cooling in low temperature molecular crystals

The processes of vibrational relaxation (VR) and vibrational cooling (VC) are investigated in low temperature crystals of complex molecules, specifically benzene, naphthalene, anthracene, and durene. In the VR process, a vibration is deexcited, while VC consists of many sequential and parallel VR steps which return the crystal to thermal equilibrium. A theoretical model is developed which relates the VR rate to the excess vibrational energy, the molecular structure, and the crystal structure. Specific relations are derived for the vibrational lifetime T1 in each of three regimes of excess vibrational energy. The regimes are the following: Low frequency regime I where VR occurs by emission of two phonons, intermediate frequency regime II where VR occurs by emission of one phonon and one vibration, and high frequency regime III where VR occurs by evolution into a dense bath of vibrational combinations. The VR rate in each regime depends on a particular multiphonon density of states and a few averaged anharmonic coefficients. The appropriate densities of states are calculated from spectroscopic data, and together with available VR data and new infrared and ps Raman data, the values of the anharmonic coefficients are determined for each material. The relationship between these parameters and the material properties is discussed. We then describe VC in a master equation formalism. The transition rate matrix for naphthalene is found using the empirically determined parameters of the above model, and the time dependent redistribution in each mode is calculated.

Solar wind pickup of ionized Venus exosphere atoms

Previous calculations of electrostatic and electromagnetic growth rates for plasma instabilities have neglected the thermal spread of the distribution function of the planetary ions. We consider the effects of finite temperatures for exospheric ions born in the solar wind. Specifically, growth rates are calculated for electromagnetic instabilities in the low‐frequency case for Alfven waves and the intermediate frequency case for whistlers. Also, electrostatic growth rates are calculated for the intermediate frequency regime. From these growth rates, estimates are derived for the pickup times of the planetary ions. The electromagnetic instabilities are shown to produce the most rapid pickup. In the situation where the angle between the local Venus magnetic field and the plasma flow direction is small, the pickup times for both electromagnetic and electrostatic instabilities become very long. A possible consequence of this effect is to produce regions of enhanced planetary ion density in favorable Venus magnetic field‐solar wind flow geometries.