757 research outputs found
Propagation of charged particle waves in a uniform magnetic field
This paper considers the probability density and current distributions
generated by a point-like, isotropic source of monoenergetic charges embedded
into a uniform magnetic field environment. Electron sources of this kind have
been realized in recent photodetachment microscopy experiments. Unlike the
total photocurrent cross section, which is largely understood, the spatial
profiles of charge and current emitted by the source display an unexpected
hierarchy of complex patterns, even though the distributions, apart from
scaling, depend only on a single physical parameter. We examine the electron
dynamics both by solving the quantum problem, i. e., finding the energy Green
function, and from a semiclassical perspective based on the simple cyclotron
orbits followed by the electron. Simulations suggest that the semiclassical
method, which involves here interference between an infinite set of paths,
faithfully reproduces the features observed in the quantum solution, even in
extreme circumstances, and lends itself to an interpretation of some (though
not all) of the rich structure exhibited in this simple problem.Comment: 39 pages, 16 figure
Caustic structures in the spectrum of x-ray Compton scattering off electrons driven by a short intense laser pulse
We study the Compton scattering of x-rays off electrons that are driven by a
relativistically intense short optical laser pulse. The frequency spectrum of
the laser-assisted Compton radiation shows a broad plateau in the vicinity of
the laser-free Compton line due to a nonlinear mixing between x-ray and laser
photons. Special emphasis is placed on how the shape of the short assisting
laser pulse affects the spectrum of the scattered x-rays. In particular, we
observe sharp peak structures in the plateau region, whose number and locations
are highly sensitive to the laser pulse shape. These structures are interpreted
as spectral caustics by using a semiclassical analysis of the laser-assisted
QED matrix element
Caustics, cold flows, and annual modulation
We discuss the formation of dark matter caustics, and their possible
detection by future dark matter experiments. The annual modulation expected in
the recoil rate measured by a dark matter detector is discussed. We consider
the example of dark matter particles with a Maxwell-Boltzmann velocity
distribution modified by a cold stream due to a nearby caustic. It is shown
that the effect of the caustic flow is potentially detectable, even when the
density enhancement due to the caustic is small. This makes the annual
modulation effect an excellent probe of inner caustics. We also show that the
phase of the annual modulation at low recoil energies does not constrain the
particle mass unless the velocity distribution of particles in the solar
neighborhood is known.Comment: Minor corrections made, replaced to reflect the published versio
Solar Wakes of Dark Matter Flows
We analyze the effect of the Sun's gravitational field on a flow of cold dark
matter (CDM) through the solar system in the limit where the velocity
dispersion of the flow vanishes. The exact density and velocity distributions
are derived in the case where the Sun is a point mass. The results are extended
to the more realistic case where the Sun has a finite size spherically
symmetric mass distribution. We find that regions of infinite density, called
caustics, appear. One such region is a line caustic on the axis of symmetry,
downstream from the Sun, where the flow trajectories cross. Another is a
cone-shaped caustic surface near the trajectories of maximum scattering angle.
The trajectories forming the conical caustic pass through the Sun's interior
and probe the solar mass distribution, raising the possibility that the solar
mass distribution may some day be measured by a dark matter detector on Earth.
We generalize our results to the case of flows with continuous velocity
distributions, such as that predicted by the isothermal model of the Milky Way
halo.Comment: 30 pages, 8 figure
Refraction of a Gaussian Seaway
Refraction of a Longuet-Higgins Gaussian sea by random ocean currents creates
persistent local variations in average energy and wave action. These variations
take the form of lumps or streaks, and they explicitly survive dispersion over
wavelength and incoming wave propagation direction. Thus, the uniform sampling
assumed in the venerable Longuet-Higgins theory does not apply following
refraction by random currents. Proper handling of the non-uniform sampling
results in greatly increased probability of freak wave formation. The present
theory represents a synthesis of Longuet-Higgins Gaussian seas and the
refraction model of White and Fornberg, which considered the effect of currents
on a plane wave incident seaway. Using the linearized equations for deep ocean
waves, we obtain quantitative predictions for the increased probability of
freak wave formation when the refractive effects are taken into account. The
crest height or wave height distribution depends primarily on the ``freak
index", gamma, which measures the strength of refraction relative to the
angular spread of the incoming sea. Dramatic effects are obtained in the tail
of this distribution even for the modest values of the freak index that are
expected to occur commonly in nature. Extensive comparisons are made between
the analytical description and numerical simulations.Comment: 18 pages, 10 figure
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