Phase-space Perturbation Research Articles

Phase-space tomography in magnetically confined plasmas

In this paper, a tomography approach aiming at reconstructing a phase-space structure is proposed. For the phase-space resolved diagnostic system, a signal must be decomposed in real-space, velocity-space, and time; therefore, it is challenging to obtain a sufficiently high signal intensity in a single detector bin. To overcome this difficulty, three different sets of data having different integration directions in real-space, velocity-space, and time are simultaneously used, and a reconstruction of the original structure in the phase-space is attempted by a tomographic manner. The proposed method is demonstrated using a synthetic dataset in the actual diagnostic setup in the Large Helical Device. Time evolution of a phase-space perturbation induced by the Landau damping, which is caused by energetic particle-driven magnetohydrodynamic bursts, is successfully reconstructed by this method. Robustness against realistic diagnostic noise is also presented.

Sensitivity estimation for dark matter subhalos in synthetic Gaia DR2 using deep learning

The abundance of dark matter subhalos orbiting a host galaxy is a generic prediction of the cosmological framework, and is a promising way to constrain the nature of dark matter. In this paper, we investigate the use of machine learning-based tools to quantify the magnitude of phase-space perturbations caused by the passage of dark matter subhalos. A simple binary classifier and an anomaly detection model are proposed to estimate if stars or star particles close to dark matter subhalos are statistically detectable in simulations. The simulated datasets are three Milky Way-like galaxies and nine synthetic Gaia DR2 surveys derived from these. Firstly, we find that the anomaly detection algorithm, trained on a simulated galaxy with full 6D kinematic observables and applied on another galaxy, is nontrivially sensitive to the dark matter subhalo population. On the other hand, the classification-based approach is not sufficiently sensitive due to the extremely low statistics of signal stars for supervised training. Finally, the sensitivity of both algorithms in the Gaia-like surveys is negligible. The enormous size of the Gaia dataset motivates the further development of scalable and accurate data analysis methods that could be used to select potential regions of interest for dark matter searches to ultimately constrain the Milky Way’s subhalo mass function, as well as simulations where to study the sensitivity of such methods under different signal hypotheses.

Self-interacting dark matter in cosmology: accurate numerical implementation and observational constraints

This paper presents a systematic and accurate treatment of the evolution of cosmological perturbations in self-interacting dark matter models, for particles which decoupled from the primordial plasma while relativistic. We provide a numerical implementation of the Boltzmann hierarchies developed in a previous paper [JCAP, 09 (2020) 041] in a publicly available Boltzmann code and show how it can be applied to realistic DM candidates such as sterile neutrinos either under resonant or non-resonant production mechanisms, and for different field mediators. At difference with traditional fluid approximations — also known as a c eff-c vis parametrizations — our approach follows the evolution of phase-space perturbations under elastic DM interactions for a wide range of interaction models, including the effects of late kinetic decoupling. Finally, we analyze the imprints left by different self interacting models on linear structure formation, which can be constrained using Lyman-α forest and satellite counts. We find new lower bounds on the particle mass that are less restrictive than previous constraints.

Higher-order Hamilton–Jacobi perturbation theory for anisotropic heterogeneous media: transformation between Cartesian and ray-centred coordinates

SUMMARY Within the field of seismic modelling in anisotropic media, dynamic ray tracing is a powerful technique for computation of amplitude and phase properties of the high-frequency Green’s function. Dynamic ray tracing is based on solving a system of Hamilton–Jacobi perturbation equations, which may be expressed in different 3-D coordinate systems. We consider two particular coordinate systems; a Cartesian coordinate system with a fixed origin and a curvilinear ray-centred coordinate system associated with a reference ray. For each system we form the corresponding 6-D phase spaces, which encapsulate six degrees of freedom in the variation of position and momentum. The formulation of (conventional) dynamic ray tracing in ray-centred coordinates is based on specific knowledge of the first-order transformation between Cartesian and ray-centred phase-space perturbations. Such transformation can also be used for defining initial conditions for dynamic ray tracing in Cartesian coordinates and for obtaining the coefficients involved in two-point traveltime extrapolation. As a step towards extending dynamic ray tracing in ray-centred coordinates to higher orders we establish detailed information about the higher-order properties of the transformation between the Cartesian and ray-centred phase-space perturbations. By numerical examples, we (1) visualize the validity limits of the ray-centred coordinate system, (2) demonstrate the transformation of higher-order derivatives of traveltime from Cartesian to ray-centred coordinates and (3) address the stability of function value and derivatives of volumetric parameters in a higher-order representation of the subsurface model.

Implications of a Time-varying Galactic Potential for Determinations of the Dynamical Surface Density

Recent studies have shown that the passage of a massive satellite through the disk of a spiral galaxy can induce vertical wobbles in the disk and produce features such as in-plane rings and phase-space spirals. Here we analyze a high-resolution N-body simulation of a live stellar disk perturbed by the recent passage of a massive dwarf galaxy that induces such perturbations. We study the implications of the phase-space structures for the estimate of the matter density through traditional Jeans modelling. The dwarf satellite excites rapid time-variations in the potential, leading to a significant bias of the local matter surface density determined through such a method. In particular, while the Jeans modelling gives reasonable estimates in the most overdense regions of the disk, we show that it tends to overestimate the dynamical surface density in underdense regions. In these regions, the phase-space spiral is indeed more marked in the surface of section of height vs. vertical velocity. This prediction can be verified with future Gaia data releases. Our finding is highly relevant for future attempts at determining the dynamical surface density of the outer Milky Way disk as a function of radius. The outer disk of the Milky Way is indeed heavily perturbed, and \textit{Gaia} DR2 data have clearly shown that such phase-space perturbations are even present locally. While our results show that traditional Jeans modelling should give reliable results in overdense regions of the disk, the important biases in underdense regions call for the development of non-equilibrium methods to estimate the dynamical matter density locally and in the outer disk.

Three dimensional analysis of longitudinal plasma oscillations in a thermal relativistic electron beam: Application to an initial value problem

In this paper, we study the initial value problem of longitudinal plasma oscillations in a relativistic electron beam. Our analysis is based on the formalism developed in Marinelli et al. [Phys. Plasmas 18, 103105 (2011)]. We study the evolution of an arbitrary six-dimensional phase-space perturbation under the effect of longitudinal space-charge forces, with the inclusion of three-dimensional effects due to the finite size of the beam, transverse betatron motion, and longitudinal thermal motion induced by both energy-spread and transverse emittance. We expand the phase-space perturbation in a series of eigenmodes of a Schrödinger-like equation, corresponding to a set of propagating space-charge waves. We develop a general formalism, which we use to find explicit expressions for the evolution of an initial perturbation coupled to the fundamental plasma eigenmode. This work has important applications in the theory of space-charge instabilities in high brightness electron beams and control of shot-noise in seeded free-electron lasers. We discuss the application of the present theory to a specific experimental scenario corresponding to a shot-noise suppression scheme at optical wavelengths.

Self-organized relaxation in a collisionless gravitating system

We propose the self-organized relaxation process which drives a collisionless self-gravitating system to the equilibrium state satisfying local virial (LV) relation. During the violent relaxation process, particles can move widely within the time interval as short as a few free-fall times, because of the effective potential oscillations. Since such particle movement causes further potential oscillations, it is expected that the system approaches the critical state where such particle activities, which we call gravitational fugacity, is independent of the local position as much as possible. Here we demonstrate that gravitational fugacity can be described as the functional of the LV ratio, which means that the LV ratio is a key ingredient estimating the particle activities against gravitational potential. We also demonstrate that the LV relation is attained if the LV ratio exceeds the critical value b=1 everywhere in the bound region during the violent relaxation process. The local region which does not meet this criterion can be trapped into the presaturated state. However, small phase-space perturbation can bring the inactive part into the LV critical state.

Lyapunov hydrodynamics in the dilute limit

We study the hydrodynamic Lyapunov exponents of the hard-disk fluid in the dilute limit. These exponents appear in discrete groups and their values depend on the system size. In a previous paper [Phys. Rev. E 64 (2001) 051103], we presented a theory for these exponents, explaining them as the growth rate of collective, organized perturbations in phase space. That theory successfully described the basic features of the hydrodynamic exponents, but it had some difficulties. Many of these difficulties can be removed by considering the dilute limit.

Perturbed phase-space dynamics of hard-disk fluids

The Lyapunov spectrum describes the exponential growth, or decay, of infinitesimal phase-space perturbations. The perturbation associated with the maximum Lyapunov exponent is strongly localized in space, and only a small fraction of all particles contributes to the perturbation growth at any instant of time. This fraction converges to zero in the thermodynamic large-particle-number limit. For hard-disk and hard-sphere systems the perturbations belonging to the smallest of the non-vanishing exponents are coherently spread out and form orthogonal periodic structures in space, the “Lyapunov modes”. There are two types of mode polarizations, transverse and longitudinal. The transverse modes do not propagate, but the longitudinal modes do, with a speed about one third of the sound speed. We characterize the symmetry and the degeneracy of the modes. In the thermodynamic limit the Lyapunov spectrum has a diverging slope near the intersection with the abscissa. No positive lower bound exists for the positive exponents. The mode amplitude scales with the inverse square root of the particle number as expected from the normalization of the perturbation vectors.

Origin of the hydrodynamic Lyapunov modes.

Recent studies of the Lyapunov spectrum of the hard sphere fluid reveal that there are "hydrodynamic" Lyapunov exponents corresponding to collective perturbations in phase space. We show that these collective perturbations are due to the conservation of certain quantities during collisions. These new conservation laws generate new hydrodynamic fields, just as the conservation of mass, momentum, and energy generate the density, velocity, and temperature fields. We then construct a detailed theory of the new hydrodynamic fields using a kinetic theory approach. This theory predicts several properties of the modes, but not all of them. This suggests that the underlying idea is correct, but a detailed theory must be elaborated in another way. The hydrodynamic exponents are not related in a simple way to the transport coefficients.

Kolmogorov-Sinai entropy and Lyapunov spectra of a hard-sphere gas

The mixing behavior of a hard-sphere gas has its origin in the exponential growth of small perturbations in phase space. This instability is characterized by the so-called Lyapunov exponents. In this work, we compute full spectra of Lyapunov exponents for the hard-sphere gas for a wide range of densities ϱ and particle numbers by using a recently developed algorithm. In the dilute-gas regime, the maximum Lyapunov exponent is found to obey the Krylov relation λ ∝ ϱ ln ϱ, a formula exactly derived for the low-density Lorentz gas by Dorfman and van Beijeren. We study the system-size dependence and the effect of the fluid-solid-phase transition on the spectra. In the second part of this work we describe and test a direct simulation Monte Carlo method (DSMC) for the computation of Lyapunov spectra and present results for dilute hard-sphere gases. Excellent agreement is obtained with the results of the deterministic simulations. This suggests that the Lyapunov instability of a hard sphere gas may be analyzed within the framework of kinetic theory.

A connected-graph expansion of the anharmonic-oscillator propagator

Two series representations of the propagator associated with the quantum anharmonic-oscillator are developed. A closed form for the Dyson series expansion of the propagator is obtained by using a phase-space perturbation technique. For Abelian interactions the Dyson series can be rearranged into an exponentiated connected-graph series. This representation is structurally similar to the cluster expansions of propagators associated with perturbations of the kinetic-energy Hamiltonian. The connected-graph series is particularly useful for the development of semiclassical expansions such as the WKB expansion. The analytic structure in the physical parameters such as mass, time and Planck's constant is readily extracted from the connected-graph series because of the explicit closed-form formula for the series.

Collisionless Wave-Particle Interactions Perpendicular to the Magnetic Field

The collisionless interaction between particles undergoing $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ifmmode\times\else\texttimes\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}$ drift and Kelvin-Helmholtz instabilities propagating across a strong magnetic field is investigated using a test-wave technique. Orbit perturbations in phase space are observed with increasing instability amplitude. We also present the first direct measurements of finite---Larmor-radius effects.