Quasilinear Effects Research Articles

Spatial clustering of high-redshift Lyman-break galaxies

We present a physically motivated semi-analytic model to understand the clustering of high redshift LBGs. We show that the model parameters constrained by the observed luminosity function, can be used to predict large scale (\theta > 80 arcsec) bias and angular correlation function of galaxies. These predictions are shown to reproduce the observations remarkably well. We then adopt these model parameters to calculate the halo occupation distribution (HOD) using the conditional mass function. The halo model using this HOD is shown to provide a reasonably good fit to the observed clustering of LBGs at both large (\theta>80") and small (\theta < 10") angular scales for z=3-5 and several limiting magnitudes. However, our models underpredict the clustering amplitude at intermediate angular scales, where quasi-linear effects are important. The average mass of halos contributing to the observed clustering is found to be 6.2 x 10^{11} M_\odot and the characteristic mass of a parent halo hosting satellite galaxies is 1.2 \times 10^{12} M_\odot for a limiting absolute magnitude of -20.5 at z=4. For a given threshold luminosity these masses decrease with increasing z and at any given z these are found to increase with increasing value of threshold luminosity. We find that approximately 40 % of the halos above a minimum mass M_{min}, can host detectable central galaxies and about 5-10 % of these halos are likely to also host a detectable satellite. The satellites form typically a dynamical timescale prior to the formation of the parent halo. The small angular scale clustering is due to central-satellite pairs and is quite sensitive to changes in the duration of star formation in a halo. The present data favor star formation in a halo lasting typically for a few dynamical time-scales. Our models also reproduce different known trends between parameters related to star formation.

NONLINEAR EVOLUTION OF BEAM-PLASMA INSTABILITY IN INHOMOGENEOUS MEDIUM

The problem of electron-beam propagation in inhomogeneous solar wind is intimately related to the solar type II and/or type III radio bursts. Many scientists have addressed this issue in the past by means of quasi-linear theory, but in order to fully characterize the nonlinear dynamics, one must employ weak-turbulence theory. Available numerical solutions of the weak-turbulence theory either rely on only one nonlinear process (either decay or scattering), or when both nonlinear terms are included, the inhomogeneity effect is generally ignored. The present paper reports the full solution of weak-turbulence theory that includes both decay and scattering processes, and also incorporating the effects of density gradient. It is found that the quasi-linear effect sufficiently accounts for the primary Langmuir waves, but to properly characterize the back-scattered Langmuir wave, which is important for eventual radiation generation, it is found that both nonlinear decay and scattering processes make comparable contributions. Such a finding may be important in the quantitative analysis of the plasma emission process with application to solar type II and/or type III radio bursts.

Parametric instability and lower hybrid current drive at plasma densities required for thermonuclear reactors

The lower hybrid current drive (LHCD), produced by externally launched lower hybrid (LH) wave, potentially provides the most suitable tool for driving current at large radii of fusion relevant plasmas, as required for the advanced scenarios of operation foreseen in the International Tokamak Experiment Reactor (ITER). In this regard, a critical problem exists due to the circumstance that the LH waves do not penetrate into the plasma cores neither of experiments aimed at heating the plasma ions nor of those aimed at driving current in presence of plasma densities approaching those required for ITER. We present here results of the analysis of parametric instability (PI) of LH waves showing that high growth rates occur for ion-sound quasi-mode-driven PIs, considering the plasma parameters of the plasma periphery of the FTU tokamak (Frascati Tokamak Upgrade). The non-linear PI phenomenon can broaden the launched antenna spectra in frequency and parallel wavenumber (n//), and, consequently, produce via quasi-linear effect a deposition at the very periphery of high-density plasmas. As result, higher electron temperatures at the plasma edge have the effect of diminishing the PI growth rate and, potentially, the broadening of the launched spectrum, thus enabling the penetration of the coupled LH power in the core of high density reactor grade plasmas.

The role of the RF induced electric field in the current drive by EC waves in the presence of magnetic islands

In this paper we discuss the role played by a radiofrequency induced electric field on the current drive efficiency of electron cyclotron (EC) waves when there are locked or rotating magnetic islands in the plasma. The problem is addressed by numerical solution of the Fokker–Planck equation within the framework of the quasilinear theory incorporating realistic features of the geometry of the magnetic islands. The modes 2/1 and 3/2 are analysed. Our main result is the reduction, although not the complete suppression, of the level of the current driven by the waves in the short time scale needed for the induced field to diffuse away from the islands region. Another finding is the suppression of quasilinear effects on the EC current drive efficiency in the case of locked islands for both 2/1 and 3/2 modes.

Short-period VLF emissions as solitary envelope waves in a magnetospheric plasma maser

Space and ground-based experiments have shown evidence of natural short-period VLF emissions in which separate spectral elements are repeated with a periodicity of 2–7 s. Their basic morphological properties are found on the basis of original experimental data. In our opinion, excitation of such emissions is the result of quasi-linear relaxation effects that compensate for natural spectral dispersion. The quasi-linear relaxation of the energetic electron distribution function incrementally changes wave cyclotron instability and hence the VLF emission spectral forms. Some properties of the quasi-linear interaction of whistler waves with magnetospheric radiation belt electrons are studied. It is shown that quasi-linear relaxation can increase the cyclotron instability at the leading edge of an electromagnetic pulse. This effective saturation of absorption facilitates the division of VLF hiss-like emission into separate electromagnetic pulses without spectral modification from one pulse to the next. Some features and manifestations of this effective saturation of absorption are discussed. The results are important for a better understanding of temporal and spatial structures of VLF whistler-mode emissions and energetic electron fluxes.

Multi-scale transport simulation of toroidal momentum source profile effect on internal transport barrier collapse

The mechanism of internal transport barrier (ITB) collapse in the reversed magnetic shear configuration is investigated using a global ion temperature gradient (ITG) driven drift wave turbulence code. A heating source and a toroidal momentum source are introduced to follow the self-consistent evolution of the ion temperature and flow profiles. A scenario of transport barrier collapse driven by a meso-scale mode excited in the barrier region is suggested. The importance of the quasi-linear effect due to profile modification as well as three-wave coupling is clearly shown by means of energy transfer analysis. The effect of the toroidal flow shear (TFS) profile on the dynamics of ITB evolution is investigated. It is found that the decorrelation between meso-scale modes and ITG driven modes due to the TFS can prevent global relaxation.

Three-point correlations inf(R)models of gravity

Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We calculate quasilinear effects in the growth of structure in f(R) models of gravity using perturbation theory. We find significant deviations in the bispectrum that depend on cosmic time, length scale and triangle shape. However the deviations in the reduced bispectrum Q for f(R) models are at the percent level, much smaller than the deviations in the bispectrum itself. This implies that three-point correlations can be predicted to a good approximation simply by using the modified linear growth factor in the standard gravity formalism. Our results suggest that gravitational clustering in the weakly nonlinear regime is not fundamentally altered, at least for a class of gravity theories that are well described in the Newtonian regime by the parameters G{sub eff} and {phi}/{psi}. This approximate universality was also seen in the N-body simulation measurements of the power spectrum by Stabenau and Jain (2006), and in other recent studies based on simulations. Thus predictions for such modified gravity models in the regime relevant to large-scale structure observations may be less daunting than expected on first principles. We discuss the many caveats that apply tomore » such predictions.« less

Effect of the curvature and the β parameter on the nonlinear dynamics of a drift tearing magnetic island

We present numerical simulation studies of 2D reduced MHD equations investigating the impact of the electronic β parameter and of curvature effects on the nonlinear evolution of drift tearing islands. We observe a bifurcation phenomenon that leads to an amplification of the pressure energy, the generation of E × B poloidal flow and a nonlinear diamagnetic drift that affects the rotation of the magnetic island. These dynamical modifications arise due to quasilinear effects that generate a zonal flow at the onset point of the bifurcation. Our simulations show that the transition point is influenced by the β parameter such that the pressure gradient through a curvature effect strongly stabilizes the transition. Regarding the modified rotation of the island, a model for the frequency is derived in order to study its origin and the effect of the β parameter. It appears that after the transition, an E × B poloidal flow as well as a nonlinear diamagnetic drift are generated due to an amplification of the stresses by pressure effects.

Observational tests of modified gravity

Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the Universe. Modified gravity theories have richer observational consequences for large-scale structures than conventional dark energy models, in that different observables are not described by a single growth factor even in the linear regime. We examine the relationships between perturbations in the metric potentials, density and velocity fields, and discuss strategies for measuring them using gravitational lensing, galaxy cluster abundances, galaxy clustering/dynamics, and the integrated Sachs-Wolfe effect. We show how a broad class of gravity theories can be tested by combining these probes. A robust way to interpret observations is by constraining two key functions: the ratio of the two metric potentials, and the ratio of the gravitational constant in the Poisson equation to Newton's constant. We also discuss quasilinear effects that carry signatures of gravity, such as through induced three-point correlations. Clustering of dark energy can mimic features of modified gravity theories and thus confuse the search for distinct signatures of such theories. It can produce pressure perturbations and anisotropic stresses, which break the equality between the two metric potentials even in general relativity. With these two extra degrees of freedom, can a clustered dark energy model mimic modified gravity models in all observational tests? We show with specific examples that observational constraints on both the metric potentials and density perturbations can in principle distinguish modifications of gravity from dark energy models. We compare our result with other recent studies that have slightly different assumptions (and apparently contradictory conclusions).

MACCEPA, the mechanically adjustable compliance and controllable equilibrium position actuator: Design and implementation in a biped robot

In this paper a rotational actuator with a novel adaptable compliance (inverse of stiffness) is presented. First, a number of comparable designs are given with their possible drawbacks. The MACCEPA concept and design is then described in detail. The equation to calculate the generated torque is derived. Depending on the design parameters, it is shown that the torque is a quasi linear function with respect to the angle between the equilibrium position and the actual position. Also, the change of the pre-tension has a quasi linear effect on the torque. Another advantage is that the actuator can be built with standard components, e.g. electrical servo motors. Experiments show independent control of the equilibrium position and compliance. The use of the MACCEPA in the Controlled Passive Walking biped Veronica is described. Controlled Passive Walking is an approach that combines the advantages of actively controlled robots and passive walkers. By adapting the compliance of the joints, natural motions can be chosen in order to obtain a controllable and energy efficient walking motion. To test the concept, the biped Veronica is built, actuated by six MACCEPAs.

Nonlinear analysis and simulations of measured freak wave time series

The analysis of surface waves time series is performed to understand the nature of freak waves. Contributions of quasi-linear dispersive focusing effects and nonlinear self-modulation (Benjamin–Feir) effects are estimated with the help of kinematical description, nonlinear spectral analysis and numerical simulations. The nonlinear dynamics of an envelope soliton over a background wave is investigated and a possible extreme wave appearance is predicted.

Viscoelasticity of Esophageal Tissue and Application of a QLV Model

The time-dependent mechanical properties of the porcine esophagus were investigated experimentally and theoretically. It was hypothesized that the viscoelasticity was quasilinear, i.e., the time and strain effects were independent. In order to verify the separability of time and strain effects, the stress-relaxation test was conducted at various strains and the data were fitted with the Fung's quasilinear viscoelastic (QLV) model. By using the material parameters obtained from the stress relaxation test, the cyclic peak stress and hysteresis were predicted. Results showed that the stress relaxed by 20-30% of the peak stress within the first 10 s and stabilized at approximately 50% at the time of 300 s. The relative stress relaxation R(2) (i.e., the difference of stress at a particular time to the final equilibrium stress normalized by the total difference of the peak and final stress) was not different significantly for various strains. It was also found that, by using the stress-time data during both the ramp and relaxation phases, the correlation between parameters was substantially reduced. The model could also predict the cyclic peak stress and hysteresis except for the underestimate of valley stress. We conclude that the QLV model could be used as the material characterization of the esophageal tissue.

Heating and current drive by electron cyclotron waves

The physics model of electron cyclotron heating (ECH) and current drive (ECCD) is becoming well validated through systematic comparisons of theory and experiment. This work has shown that ECH and ECCD can be highly localized and robustly controlled in toroidal plasma confinement systems, leading to applications including stabilization of magnetohydrodynamic instabilities like neoclassical tearing modes, control and sustainment of desired profiles of current density and plasma pressure, and studies of localized transport in laboratory plasmas. The experimental work was supported by a broad base of theory based on first principles which is now well encapsulated in linear ray tracing codes describing wave propagation, absorption, and current drive and in fully relativistic quasilinear Fokker–Planck codes describing in detail the response of the electrons to the energy transferred from the wave. The subtle balance between wave-induced diffusion and Coulomb relaxation in velocity space provides an understanding of the effects of trapping of current-carrying electrons in the magnetic well. Strong quasilinear effects and radial transport of electrons, which may broaden the driven current profile, have also been observed under some conditions and appear to be consistent with theory, but in large devices these are usually insignificant. The agreement of theory and experiment, the wide range of established applications, and the technical advantages of ECH support the application of ECH in next-step tokamaks and stellarators.

Mathematical analysis of the quasilinear effects in a hyperbolic model blood flow through compliant axi‐symmetric vessels

AbstractIn this paper, we present a mathematical analysis of the quasilinear effects arising in a hyperbolic system of partial differential equations modelling blood flow through large compliant vessels. The equations are derived using asymptotic reduction of the incompressible Navier–Stokes equations in narrow, long channels.To guarantee strict hyperbolicity we first derive the estimates on the initial and boundary data which imply strict hyperbolicity in the region of smooth flow. We then prove a general theorem which provides conditions under which an initial–boundary value problem for a quasilinear hyperbolic system admits a smooth solution. Using this result we show that pulsatile flow boundary data always give rise to shock formation (high gradients in the velocity and inner vessel radius). We estimate the time and the location of the first shock formation and show that in a healthy individual, shocks form well outside the physiologically interesting region (2.8m downstream from the inlet boundary). In the end we present a study of the influence of vessel tapering on shock formation. We obtain a surprising result: vessel tapering postpones shock formation. We provide an explanation for why this is the case. Copyright © 2003 John Wiley &amp; Sons, Ltd.

On cyclotron emission from toroidal plasmas near the ECR heating frequency

High power electron cyclotron plasma heating in toroidal traps results in the generation of non-Maxwellian electron distribution functions. Electron cyclotron emission (ECE) spectra originating from such distributions in a close vicinity of the heating frequency are investigated analytically based on a simplified kinetic approach. An increase of the ECE level due to the quasi-linear degradation of re-absorption near the heating frequency is shown to be rather sensitive to the non-thermal distortions in the bulk electron distribution function. This effect is of peculiar interest for the diagnostics of quasi-linear effects in the case of low-field-side launch of the heating rf beam when absorbed electron cyclotron resonance (ECR) power is mainly deposited to the low-energetic electron fraction.

Comparison of high-field-side and low-field-side launch ECCD in the W7-AS stellarator

The electron cyclotron current drive (ECCD) with extraordinary mode at the second cyclotron harmonic launched from the high-field-side (HFS) is investigated in W7-AS stellarator. Trapped particle effects and quasi-linear effects are taken into account in linear ray-tracing and quasi-linear bounce-averaged Fokker–Planck computations of the driven current. The results for both low-field-side (LFS) and HFS injection in W7-AS are compared with the experimental results. A slightly lower current drive efficiency is obtained, both theoretically and experimentally, in the case of HFS injection, confirming the LFS launch as the preferred mode of operation for ECCD.

ECH physics and new operational regimes on TCV

The physics of tokamak plasmas, in which electrons are heated by electron cyclotron heating (ECH) and whose current is driven by electron cyclotron current drive (ECCD), is investigated in this paper together with applications on tokamak à configuration variable (TCV) using modifications of the pressure and current profiles to improve the operational regimes. In order to explain the experimentally determined current drive efficiency and hard x-ray and electron cyclotron emission measurements, it is shown that quasi-linear effects and radial transport of the suprathermal electrons are necessary. Plasmas with fully non-inductively driven currents were obtained with 0.9 MW of off-axis ECCD and 0.45 MW of on-axis counter ECCD. The combination of the driven current and the bootstrap current, accounting for 50% of the total current and peaking off-axis, yields a reversed safety factor profile and a wide and stable electron internal transport barrier. This barrier leads to an enhancement in the energy confinement by a factor of 4.5. ECH is also used to broaden the current profile of high elongation, low normalized-current plasmas whose vertical position would otherwise be uncontrollable on TCV, but whose MHD stability properties should allow high β values. An elongation of 2.47 at a normalized-current of 1.05 MA mT−1 is obtained with off-axis ECH absorbed at an optimized normalized radius between 0.55 and 0.7. Finally, third harmonic ECH is tested in various scenarios, all using vertical beam launching. In particular, high density Ohmic target and preheating with second harmonic ECH are presented. The fraction of third harmonic power absorbed reaches 65% and 85%, respectively.

Modeling of Coulomb collisions in a kinetic description of the electron cyclotron resonance plasma heating

The electron distribution function is modeled numerically with allowance for Coulomb collisions and quasilinear effects under cyclotron resonance conditions by solving a two-dimensional kinetic equation containing the quasilinear diffusion operator and the Coulomb collision operator in the Landau form. Two simplified model collision integrals that make it possible to describe electron heating by microwave radiation are considered. The first model collision operator is obtained by introducing the parametric time dependence of the temperature of the background Maxwellian electrons into the linear collision integral. It is shown that the heating of the bulk electrons can be described in a noncontradictory way if the temperature dynamics of the background electrons is calculated from the equation of energy balance, which is governed by the amount of the microwave power absorbed by the resonant electrons with the distribution function modified due to quasilinear effects. This conclusion is confirmed in a more rigorous fashion by comparing the solutions obtained using the first model Coulomb collision integral with those obtained using the second model integral, namely, the nonlinear operator derived by averaging the distribution function of the scattering electrons over pitch angles. The time-dependent linear collision integral is used to obtain analytic solutions describing quasi-steady electron heating with allowance for the quasilinear degradation of microwave power absorption.

Prediction of turbulence-generated secondary mean flow in a square duct

Near-wall second-moment closures have revealed a tendency to severely underpredict the strength of the turbulence-generated secondary flow in noncircular ducts. The aim of this study has been to elucidate the reasons for this failure that seems to be present at both high and low Reynolds numbers. Fully developed three-componential turbulent flow inside a straight square duct has been computed with the quasi-linear SSG second-moment closure and near-wall effects were modeled by elliptic relaxation.

Ion‐acoustic resistivity in plasmas with similar ion and electron temperatures

Analytical estimates of resistivity due to electrostatic current‐driven ion‐acoustic waves are compared with Vlasov simulation results. Particular attention is given to the case of similar ion and electron temperatures that is appropriate to the magnetopause and low‐latitude boundary layer (LLBL). It is shown that Vlasov simulation runs of growing ion‐acoustic waves with Te = 2Ti give values of resistivity which are at least three orders of magnitude higher than an existing analytical estimate [Labelle and Treumann, Sp. Sci. Rev., 47, 1988] and exhibit a different dependence on the wave energy density. A particle‐in‐cell code was also run with the same temperature ratio and gave similar resistivity values that back up the Vlasov simulation results. The discrepancy between simulation and analytical estimate arises because the derivation of the analytical estimate assumes that the quasilinear effects of the instability are weak. The simulation results show that this is not the case, since plateau formation is clearly seen in the electron distribution function. These simulation results show that the ion‐acoustic instability may be more important in the magnetopause and LLBL than previously thought.