621 research outputs found
Turbulence without pressure
We develop exact field theoretic methods to treat turbulence when the effect
of pressure is negligible. We find explicit forms of certain probability
distributions, demonstrate that the breakdown of Galilean invariance is
responsible for intermittency and establish the operator product expansion. We
also indicate how the effects of pressure can be turned on perturbatively.Comment: 12 page
Unique Fock quantization of scalar cosmological perturbations
We investigate the ambiguities in the Fock quantization of the scalar
perturbations of a Friedmann-Lema\^{i}tre-Robertson-Walker model with a massive
scalar field as matter content. We consider the case of compact spatial
sections (thus avoiding infrared divergences), with the topology of a
three-sphere. After expanding the perturbations in series of eigenfunctions of
the Laplace-Beltrami operator, the Hamiltonian of the system is written up to
quadratic order in them. We fix the gauge of the local degrees of freedom in
two different ways, reaching in both cases the same qualitative results. A
canonical transformation, which includes the scaling of the matter field
perturbations by the scale factor of the geometry, is performed in order to
arrive at a convenient formulation of the system. We then study the
quantization of these perturbations in the classical background determined by
the homogeneous variables. Based on previous work, we introduce a Fock
representation for the perturbations in which: (a) the complex structure is
invariant under the isometries of the spatial sections and (b) the field
dynamics is implemented as a unitary operator. These two properties select not
only a unique unitary equivalence class of representations, but also a
preferred field description, picking up a canonical pair of field variables
among all those that can be obtained by means of a time-dependent scaling of
the matter field (completed into a linear canonical transformation). Finally,
we present an equivalent quantization constructed in terms of gauge-invariant
quantities. We prove that this quantization can be attained by a mode-by-mode
time-dependent linear canonical transformation which admits a unitary
implementation, so that it is also uniquely determined.Comment: 19 pages, minor impovementes included, typos correcte
Anticorrelation between Ion Acceleration and Nonlinear Coherent Structures from Laser-Underdense Plasma Interaction
In laser-plasma experiments, we observed that ion acceleration from the
Coulomb explosion of the plasma channel bored by the laser, is prevented when
multiple plasma instabilities such as filamentation and hosing, and nonlinear
coherent structures (vortices/post-solitons) appear in the wake of an
ultrashort laser pulse. The tailoring of the longitudinal plasma density ramp
allows us to control the onset of these insabilities. We deduced that the laser
pulse is depleted into these structures in our conditions, when a plasma at
about 10% of the critical density exhibits a gradient on the order of 250
{\mu}m (gaussian fit), thus hindering the acceleration. A promising
experimental setup with a long pulse is demonstrated enabling the excitation of
an isolated coherent structure for polarimetric measurements and, in further
perspectives, parametric studies of ion plasma acceleration efficiency.Comment: 4 pages, 5 figure
Early out-of-equilibrium beam-plasma evolution
We solve analytically the out-of-equilibrium initial stage that follows the
injection of a radially finite electron beam into a plasma at rest and test it
against particle-in-cell simulations. For initial large beam edge gradients and
not too large beam radius, compared to the electron skin depth, the electron
beam is shown to evolve into a ring structure. For low enough transverse
temperatures, the filamentation instability eventually proceeds and saturates
when transverse isotropy is reached. The analysis accounts for the variety of
very recent experimental beam transverse observations.Comment: to appear in Phys. Rev. Letter
Laser-plasma interactions with a Fourier-Bessel Particle-in-Cell method
A new spectral particle-in-cell (PIC) method for plasma modeling is presented
and discussed. In the proposed scheme, the Fourier-Bessel transform is used to
translate the Maxwell equations to the quasi-cylindrical spectral domain. In
this domain, the equations are solved analytically in time, and the spatial
derivatives are approximated with high accuracy. In contrast to the
finite-difference time domain (FDTD) methods that are commonly used in PIC, the
developed method does not produce numerical dispersion, and does not involve
grid staggering for the electric and magnetic fields. These features are
especially valuable in modeling the wakefield acceleration of particles in
plasmas. The proposed algorithm is implemented in the code PLARES-PIC, and the
test simulations of laser plasma interactions are compared to the ones done
with the quasi-cylindrical FDTD PIC code CALDER-CIRC.Comment: submitted to Phys. Plasma
Correlated two-particle scattering on finite cavities
The correlated two-particle problem is solved analytically in the presence of
a finite cavity. The method is demonstrated here in terms of exactly solvable
models for both the cavity as well as the two-particle correlation where the
two-particle potential is chosen in separable form. The two-particle phase
shift is calculated and compared to the single-particle one. The two-particle
bound state behavior is discussed and the influence of the cavity on the
binding properties is calculated.Comment: Derivation shortened and corrected, 14 pages 10 figure
Computationally efficient methods for modelling laser wakefield acceleration in the blowout regime
Electron self-injection and acceleration until dephasing in the blowout
regime is studied for a set of initial conditions typical of recent experiments
with 100 terawatt-class lasers. Two different approaches to computationally
efficient, fully explicit, three-dimensional particle-in-cell modelling are
examined. First, the Cartesian code VORPAL using a perfect-dispersion
electromagnetic solver precisely describes the laser pulse and bubble dynamics,
taking advantage of coarser resolution in the propagation direction, with a
proportionally larger time step. Using third-order splines for macroparticles
helps suppress the sampling noise while keeping the usage of computational
resources modest. The second way to reduce the simulation load is using
reduced-geometry codes. In our case, the quasi-cylindrical code CALDER-CIRC
uses decomposition of fields and currents into a set of poloidal modes, while
the macroparticles move in the Cartesian 3D space. Cylindrical symmetry of the
interaction allows using just two modes, reducing the computational load to
roughly that of a planar Cartesian simulation while preserving the 3D nature of
the interaction. This significant economy of resources allows using fine
resolution in the direction of propagation and a small time step, making
numerical dispersion vanishingly small, together with a large number of
particles per cell, enabling good particle statistics. Quantitative agreement
of the two simulations indicates that they are free of numerical artefacts.
Both approaches thus retrieve physically correct evolution of the plasma
bubble, recovering the intrinsic connection of electron self-injection to the
nonlinear optical evolution of the driver
Normal modes for metric fluctuations in a class of higher-dimensional backgrounds
We discuss a gauge invariant approach to the theory of cosmological
perturbations in a higher-dimensonal background. We find the normal modes which
diagonalize the perturbed action, for a scalar field minimally coupled to
gravity, in a higher-dimensional manifold M of the Bianchi-type I, under the
assumption that the translations along an isotropic spatial subsection of M are
isometries of the full, perturbed background. We show that, in the absence of
scalar field potential, the canonical variables for scalar and tensor metric
perturbations satisfy exactly the same evolution equation, and we discuss the
possible dependence of the spectrum on the number of internal dimensions.Comment: 19 pages, LATEX, an explicit example is added to discuss the possible
dependence of the perturbation spectrum on the number of internal dimensions.
To apper in Class. Quantum Gra
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