Quasi-linear Regime Research Articles

Gaussian covariance matrices for anisotropic galaxy clustering measurements

Measurements of the redshift-space galaxy clustering have been a prolific source of cosmological information in recent years. Accurate covariance estimates are an essential step for the validation of galaxy clustering models of the redshift-space two-point statistics. Usually, only a limited set of accurate N-body simulations is available. Thus, assessing the data covariance is not possible or only leads to a noisy estimate. Further, relying on simulated realisations of the survey data means that tests of the cosmology dependence of the covariance are expensive. With these points in mind, this work presents a simple theoretical model for the linear covariance of anisotropic galaxy clustering observations with synthetic catalogues. Considering the Legendre moments (`multipoles') of the two-point statistics and projections into wide bins of the line-of-sight parameter (`clustering wedges'), we describe the modelling of the covariance for these anisotropic clustering measurements for galaxy samples with a trivial geometry in the case of a Gaussian approximation of the clustering likelihood. As main result of this paper, we give the explicit formulae for Fourier and configuration space covariance matrices. To validate our model, we create synthetic HOD galaxy catalogues by populating the haloes of an ensemble of large-volume N-body simulations. Using linear and non-linear input power spectra, we find very good agreement between the model predictions and the measurements on the synthetic catalogues in the quasi-linear regime.

Leaking of trajectories from the phase space of discontinuous dynamics

The escape of particles from the phase space produced by a two-dimensional, nonlinear and area-preserving, discontinuous map is investigated by using both numerical simulations and the explicit solution of the corresponding diffusion equation. The mapping, given in action-angle variables, is parameterized by K, which controls a transition from integrability to non-integrability. We focus on the two dynamical regimes of the map: slow diffusion () and quasilinear diffusion () regimes, separated by the critical parameter value Kc = 1. When a hole is introduced in the action axis, we find the histogram of escape times and the survival probability of particles to be scaling invariant in both the slow and the quasilinear diffusion regimes, with scaling laws proportional to the corresponding diffusion coefficients, namely, proportional to and K2, respectively. Our numerical simulations agree remarkably well with the analytical results obtained from the explicit solution of the diffusion equation, hence giving robustness to the escape formalism.

Simultaneous evaluation of acoustic nonlinearity parameter and attenuation coefficients using the finite amplitude method

A novel method to determine acoustic parameters involved in measuring the nonlinearity parameter of fluids or solids is proposed. The approach is based on the measurement of fundamental and second harmonic pressures with a calibrated receiver, and on a nonlinear least squares data-fitting to multi-Gaussian beam (MGB) equations which explicitly define the attenuation and diffraction effects in the quasilinear regime. Results obtained in water validate the proposed method. The choice of suitable source pressure is discussed with regard to the quasilinear approximation involved. The attenuation coefficients are also acquired in nonlinear regime and their relations are discussed.

DYNAMICAL FIELD LINE CONNECTIVITY IN MAGNETIC TURBULENCE

Point-to-point magnetic connectivity has a stochastic character whenever magnetic fluctuations cause a field line random walk, but this can also change due to dynamical activity. Comparing the instantaneous magnetic connectivity from the same point at two different times, we provide a nonperturbative analytic theory for the ensemble average perpendicular displacement of the magnetic field line, given the power spectrum of magnetic fluctuations. For simplicity, the theory is developed in the context of transverse turbulence, and is numerically evaluated for the noisy reduced MHD model. Our formalism accounts for the dynamical decorrelation of magnetic fluctuations due to wave propagation, local nonlinear distortion, random sweeping, and convection by a bulk wind flow relative to the observer. The diffusion coefficient DX of the time-differenced displacement becomes twice the usual field line diffusion coefficient Dx at large time displacement t or large distance z along the mean field (corresponding to a pair of uncorrelated random walks), though for a low Kubo number (in the quasilinear regime) it can oscillate at intermediate values of t and z. At high Kubo number the dynamical decorrelation decays mainly from the nonlinear term and DX tends monotonically toward 2Dx with increasing t and z. The formalism and results presented here are relevant to a variety of astrophysical processes, such as electron transport and heating patterns in coronal loops and the solar transition region, changing magnetic connection to particle sources near the Sun or at a planetary bow shock, and thickening of coronal hole boundaries.

Arclength Continuation Methods for the Investigation of Non‐linear Oscillating Systems with the Concept of Non‐linear Normal Modes

AbstractNon‐linear normal modes (NNMs) can be considered as a non‐linear analogon to the description of linear systems with linear normal modes (LNMs). The definition of NNMs can be found in [1]. Small systems with a low number of degrees of freedom and non‐linear couplings (cubic springs) are investigated here. With increasing energy in the system the progressive non‐linearity leads to a hardening effect. One typical dynamical property of non‐linear systems is the frequency‐energy dependency of the resulting oscillations. A good graphic illustration is to plot such a dependency in a so called frequency‐energy plot (FEP). A NNM branch can be calculated by a numerical continuation method with starting at low energy level in a quasi linear regime and increasing the energy and reducing the period of the oscillation iteratively. Thereby a branch is a family of NNM oscillations with qualitatively equal motion properties [2]. In non‐linear systems internal resonances and other phenomena can occur. Several tongues can bifurcate from a NNM branch. Therefore ordinary continuation methods may fail at such bifurcation points. Here a predictor‐corrector‐method is used and different corrector algorithms are discussed for the branch continuation. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

SIMULATIONS OF ION ACCELERATION AT NON-RELATIVISTIC SHOCKS. III. PARTICLE DIFFUSION

We use large hybrid (kinetic protons-fluid electrons) simulations to investigate the transport of energetic particles in self-consistent electromagnetic configurations of collisionless shocks. In previous papers of this series, we showed that ion acceleration may be very efficient (up to $10-20\%$ in energy), and outlined how the streaming of energetic particles amplifies the upstream magnetic field. Here, we measure particle diffusion around shocks with different strengths, finding that the mean free path for pitch-angle scattering of energetic ions is comparable with their gyroradii calculated in the self-generated turbulence. For moderately-strong shocks, magnetic field amplification proceeds in the quasi-linear regime, and particles diffuse according to the self-generated diffusion coefficient, i.e., the scattering rate depends only on the amount of energy in modes with wavelengths comparable with the particle gyroradius. For very strong shocks, instead, the magnetic field is amplified up to non-linear levels, with most of the energy in modes with wavelengths comparable to the gyroradii of highest-energy ions, and energetic particles experience Bohm-like diffusion in the amplified field. We also show how enhanced diffusion facilitates the return of energetic particles to the shock, thereby determining the maximum energy that can be achieved in a given time via diffusive shock acceleration. The parametrization of the diffusion coefficient that we derive can be used to introduce self-consistent microphysics into large-scale models of cosmic ray acceleration in astrophysical sources, such as supernova remnants and clusters of galaxies.

Case studies in space charge and plasma acceleration of charged beams

Plasma acceleration with electron or proton driver beams is a challenging opportunity for high-energy physics. An energy doubling experiment with electron drivers was successfully performed at SLAC and a key experiment AWAKE with proton drivers is on schedule at CERN. Simulations play an important role in choosing the best experimental conditions and in interpreting the results. The Vlasov equation is the theoretical tool to describe the interaction of a driver particle beam or a driver laser pulse with a plasma. Collective effects, such as tune shift and mismatch instabilities, appear in high intensity standard accelerators and are described by the Poisson–Vlasov equation. In the paper, we review the Vlasov equation in the electrostatic and fully electromagnetic cases. The general framework of variational principles is used to derive the equation, the local form of the balance equations and related conservation laws. In the electrostatic case, we remind the analytic Kapchinskij–Vladimirskij (K–V) model and we propose an extension of the adiabatic theory for Hamiltonian systems, which ensures stability for perturbation of size ϵ on times of order 1/ϵ. The variational framework is used to derive the Maxwell–Vlasov equations and related conservation laws and to briefly sketch the particle-in-cell (PIC) approximation schemes. Finally, the proton-driven acceleration is examined in the linear and quasi-linear regime. A PIC simulation with the code ALaDyn developed at Bologna University is presented to illustrate the longitudinal and transverse fields evolution which allow a witness electron bunch to be accelerated with a gradient of a few GeV/m. We also present some remarks on future perspectives.

DIFFUSION AND STOCHASTIC ISLAND GENERATION IN THE MAGNETIC FIELD LINE RANDOM WALK

The cross-field diffusion of field lines in stochastic magnetic fields described by the 2D+slab model is studied using a semi-analytic statistical approach, the decorrelation trajectory method. We show that field line trapping and the associated stochastic magnetic islands strongly influence the diffusion coefficients, leading to dependences on the parameters that are different from the quasilinear and Bohm regimes. A strong amplification of the diffusion is produced by a small slab field in the presence of trapping. The diffusion regimes are determined and the corresponding physical processes are identified.

Galaxy and Mass Assembly (GAMA): galaxy pairwise velocity dispersion

AbstractWe describe preliminary measurements of the pairwise velocity dispersion (PVD) of galaxies in the Galaxy and Mass Assembly (GAMA) survey as a function of projected separation and galaxy luminosity. Due to the faint magnitude limit (r < 19.8) and highly-complete spectroscopic sampling of the GAMA survey, we are able to measure the PVD to smaller scales and for lower-luminosity galaxies than previous SDSS-based work. We see no strong scale-dependence at most luminosities in the quasi-linear regime. We observe an apparent drop in PVD towards very small scales (below ≈ 0.1h−1 Mpc), but this could in part be due to a restriction of the streaming model employed. At intermediate scales, the PVD is highest (~ 500 km/s) at intermediate luminosities, dropping at both fainter and brighter luminosities.

The Lyα forest and the Cosmic Web

AbstractThe accurate description of the properties of the Lyman-α forest is a spectacular success of the Cold Dark Matter theory of cosmological structure formation. After a brief review of early models, it is shown how numerical simulations have demonstrated the Lyman-α forest emerges from the cosmic web in the quasi-linear regime of overdensity. The quasi-linear nature of the structures allows accurate modeling, providing constraints on cosmological models over a unique range of scales and enabling the Lyman-α forest to serve as a bridge to the more complex problem of galaxy formation.

Super-sample covariance in simulations

Using separate universe simulations, we accurately quantify super-sample covariance (SSC), the typically dominant sampling error for matter power spectrum estimators in a finite volume, which arises from the presence of super survey modes. By quantifying the power spectrum response to a background mode, this approach automatically captures the separate effects of beat coupling in the quasilinear regime, halo sample variance in the nonlinear regime and a new dilation effect which changes scales in the power spectrum coherently across the survey volume, including the baryon acoustic oscillation scale. It models these effects at typically the few percent level or better with a handful of small volume simulations for any survey geometry compared with directly using many thousands of survey volumes in a suite of large volume simulations. The stochasticity of the response is sufficiently small that in the quasilinear regime, SSC can be alternately included by fitting the mean density in the volume with these fixed templates in parameter estimation. We also test the halo model prescription and find agreement typically at better than the 10% level for the response.

The quasilinear large-amplitude viscoelastic regime and its significance in the rheological characterization of soft matter

We present a novel approach for using large-amplitude oscillatory shear flow experiments (LAOS) to determine—in a simple, direct, and robust manner—the mechanical behavior of materials that possess a microstructure and may exhibit solidlike, liquidlike, viscoelastic, viscoplastic, and/or thixotropic behavior. As the stress amplitude and frequency are independently varied, two classes of motion are observed: (i) structure-changing motions, characterized by a nonsinusoidal response, when the stress amplitude is large enough to cause microstructural changes and the frequency is of the order of the reciprocal of the time scale of microstructural changes; and (ii) constant-structure motions, characterized by a sinusoidal response, when either the stress amplitude is not large enough to cause microstructural changes or the stress amplitude is large enough to cause microstructural changes but the frequency is much larger than the reciprocal of the time scale of microstructural changes. For a commercial hair gel, we confirm experimentally the existence of these two classes of motions, which was theoretically predicted by de Souza Mendes and Thompson [Rheol. Acta 52(7), 673–694 (2013)]. In contrast to the presently available LAOS analyses, which focus on the structure-changing motions, our methodology—quasilinear LAOS or QL-LAOS—relies for the most part on data obtained from constant-structure motions. This fact simplifies dramatically the experiments and the analysis and provides material functions the physical meanings of which are quite evident.

Laser plasma acceleration of electrons with multi-PW laser beams in the frame of CILEX

Laser plasma acceleration of electrons has progressed along with advances in laser technology. It is thus expected that the development in the near-future of multi-PW-class laser and facilities will enable a vast range of scientific opportunities for laser plasma acceleration research. On one hand, high peak powers can be used to explore the extremely high intensity regime of laser wakefield acceleration, producing for example large amounts of electrons in the GeV range or generating high energy photons. On the other hand, the available laser energy can be used in the quasi-linear regime to create accelerating fields in large volumes of plasma and study controlled acceleration in a plasma stage of externally injected relativistic particles, either electrons or positrons. In the frame of the Centre Interdisciplinaire de la Lumière EXtrême (CILEX), the Apollon-10P laser will deliver two beams at the 1PW and 10PW levels, in ultra-short (>15fs) pulses, to a target area dedicated to electron acceleration studies, such as the exploration of the non-linear regimes predicted theoretically, or multi-stage laser plasma acceleration.

The role of the Kubo number in two-component turbulence

We explore the random walk of magnetic field lines in two-component turbulence by using computer simulations. It is often assumed that the two-component model provides a good approximation for solar wind turbulence. We explore the dependence of the field line diffusion coefficient on the Kubo number which is a fundamental and characteristic quantity in the theory of turbulence. We show that there are two transport regimes. One is the well-known quasilinear regime in which the diffusion coefficient is proportional to the Kubo number squared, and the second one is a nonlinear regime in which the diffusion coefficient is directly proportional to the Kubo number. The so-called percolative transport regime which is often discussed in the literature cannot be found. The numerical results obtained in the present paper confirm analytical theories for random walking field lines developed in the past.

Numerical modeling of multi-GeV laser wakefield electron acceleration inside a dielectric capillary tube

Numerical modeling of laser wakefield electron acceleration inside a gas filled dielectric capillary tube is presented. Guiding of a short pulse laser inside a dielectric capillary tube over a long distance (∼1 m) and acceleration of an externally injected electron bunch to ultra-relativistic energies (∼5-10 GeV) are demonstrated in the quasi-linear regime of laser wakefield acceleration. Two dimensional axisymmetric simulations were performed with the code WAKE-EP (Extended Performances), which allows computationally efficient simulations of such long scale plasma. The code is an upgrade of the quasi-static particle code, WAKE [P. Mora and T. M. Antonsen, Jr., Phys. Plasmas 4, 217 (1997)], to simulate the acceleration of an externally injected electron bunch (including beam loading effect) and propagation of the laser beam inside a dielectric capillary. The influence of the transverse electric field of the plasma wake on the radial loss of the accelerated electrons to the dielectric wall is investigated. The stable acceleration of electrons to multi-GeV energy with a non-resonant laser pulse with a large spot-size is demonstrated.

Nonlinear stochastic biasing of halos: Analysis of cosmologicalN-body simulations and perturbation theories

It is crucial to understand and model a behavior of galaxy biasing for future ambitious galaxy redshift surveys. Using 40 large cosmological N-body simulations for a standard LambdaCDM cosmology, we study the cross-correlation coefficient between matter and the halo density field, which is an indicator of the stochasticity of bias, over a wide redshift range 0\le z \le 3. The cross-correlation coefficient is important to extract information on the matter density field, e.g., by combining galaxy clustering and galaxy-galaxy lensing measurements. We compare the simulation results with integrated perturbation theory (iPT) proposed by one of the present authors and standard perturbation theory (SPT) combined with a phenomenological model of local bias. The cross-correlation coefficient derived from the iPT agrees with N-body simulation results down to r~15 (10) h^{-1}Mpc within 0.5 (1.0) % for all redshifts and halo masses we consider. The SPT with local bias does not explain complicated behaviors on quasilinear scales at low redshifts, while roughly reproduces the general behavior of the cross-correlation coefficient on fully nonlinear scales. The iPT is powerful to predict the cross-correlation coefficient down to quasilinear regimes with a high precision.

Kinetic theory of weak turbulence in plasmas

From the nonlinear Vlasov equation, a nonlinear turbulence scattering term is found to describe stochastic dissipation on a time scale longer than the turbulence correlation time. The evolution of the plasma distribution is determined by the well-understood unperturbed motion of charged particles, with the effects of the fluctuating part of fields described by the turbulence scattering term. In the present framework, one can identify various important physics, from the linear and quasilinear regimes to the nonlinear regime, in particular, the connections between the widely used Kadomtsev-Pogutse equation [B. B. Kadomtsev and O. P. Pogutse, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1970), pp. 368-387] and the Frieman-Chen equation [Frieman and Chen, Phys. Fluids 25, 502 (1982)]. The nonlinear scattering term indicates the Onsager symmetry relation of turbulent transport and a nonlinear frequency or k spectrum shift of a resonantly excited wave.

Nonclassical Transport and Particle-Field Coupling: from Laboratory Plasmas to the Solar Wind

Understanding transport of thermal and suprathermal particles is a fundamental issue in laboratory, solar-terrestrial, and astrophysical plasmas. For laboratory fusion experiments, confinement of particles and energy is essential for sustaining the plasma long enough to reach burning conditions. For solar wind and magnetospheric plasmas, transport properties determine the spatial and temporal distribution of energetic particles, which can be harmful for spacecraft functioning, as well as the entry of solar wind plasma into the magnetosphere. For astrophysical plasmas, transport properties determine the efficiency of particle acceleration processes and affect observable radiative signatures. In all cases, transport depends on the interaction of thermal and suprathermal particles with the electric and magnetic fluctuations in the plasma. Understanding transport therefore requires us to understand these interactions, which encompass a wide range of scales, from magnetohydrodynamic to kinetic scales, with larger scale structures also having a role. The wealth of transport studies during recent decades has shown the existence of a variety of regimes that differ from the classical quasilinear regime. In this paper we give an overview of nonclassical plasma transport regimes, discussing theoretical approaches to superdiffusive and subdiffusive transport, wave–particle interactions at microscopic kinetic scales, the influence of coherent structures and of avalanching transport, and the results of numerical simulations and experimental data analyses. Applications to laboratory plasmas and space plasmas are discussed.

C-axis resistivity, pseudogap, superconductivity, and Widom line in doped Mott insulators

Layered doped Mott insulators, such as the cuprates, show unusual temperature dependence of the resistivity. Intriguingly, the resistivity perpendicular to the CuO$_2$ planes, $\rho_c(T)$, shows both metallic ($d\rho_c/dT > 0$) and semi-conducting ($d\rho_c/dT<0$) behavior. We shed light on this puzzle by calculating $\rho_c$ for the two-dimensional Hubbard model within plaquette cellular dynamical mean-field theory and strong-coupling continuous-time quantum Monte Carlo as the impurity solver. The temperature, $T$, and doping, $\delta$, dependencies of $\rho_c$ are controlled by the first-order transition between pseudogap and correlated metal phases from which superconductivity can emerge. On the large doping side of the transition $\rho_c(T)$ is metallic, while on the low-doping side $\rho_c(T)$ changes from metallic to semi-conducting behavior with decreasing $T$. As a function of doping, the jump in $\rho_c$ across the first-order transition evolves into a sharp crossover at higher temperatures. This crossover coincides with the pseudogap temperature $T^*$ in the single-particle density of states, the spin susceptibility and other observables. Such coincidence in crossovers is expected along the continuation of the first-order transition into the super-critical regime, called the Widom line. This implies that not only the dynamic and the thermodynamic properties but also the DC transport in the normal state are governed by the hidden first-order transition. $\rho_c(T)$ has a high-temperature quasi-linear regime where it can exceed the Mott-Ioffe-Regel limit and when it has a minimum it is nearly parallel to the Widom line.

Theory of magnetic field line random walk in noisy reduced magnetohydrodynamic turbulence

When a magnetic field consists of a mean part and fluctuations, the stochastic wandering of its field lines is often treated as a diffusive process. Under suitable conditions, a stable value is found for the mean square transverse displacement per unit parallel displacement relative to the mean field. Here, we compute the associated field line diffusion coefficient for a highly anisotropic “noisy” reduced magnetohydrodynamic model of the magnetic field, which is useful in describing low frequency turbulence in the presence of a strong applied DC mean magnetic field, as may be found, for example, in the solar corona, or in certain laboratory devices. Our approach is nonperturbative, based on Corrsin's independence hypothesis, and makes use of recent advances in understanding factors that control decorrelation over a range of parameters described by the Kubo number. Both Bohm and quasilinear regimes are identified.