1,484 research outputs found
A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula
Continuing our development of a mathematical theory of stochastic
microlensing, we study the random shear and expected number of random lensed
images of different types. In particular, we characterize the first three
leading terms in the asymptotic expression of the joint probability density
function (p.d.f.) of the random shear tensor at a general point in the lens
plane due to point masses in the limit of an infinite number of stars. Up to
this order, the p.d.f. depends on the magnitude of the shear tensor, the
optical depth, and the mean number of stars through a combination of radial
position and the stars' masses. As a consequence, the p.d.f.s of the shear
components are seen to converge, in the limit of an infinite number of stars,
to shifted Cauchy distributions, which shows that the shear components have
heavy tails in that limit. The asymptotic p.d.f. of the shear magnitude in the
limit of an infinite number of stars is also presented. Extending to general
random distributions of the lenses, we employ the Kac-Rice formula and Morse
theory to deduce general formulas for the expected total number of images and
the expected number of saddle images. We further generalize these results by
considering random sources defined on a countable compact covering of the light
source plane. This is done to introduce the notion of {\it global} expected
number of positive parity images due to a general lensing map. Applying the
result to microlensing, we calculate the asymptotic global expected number of
minimum images in the limit of an infinite number of stars, where the stars are
uniformly distributed. This global expectation is bounded, while the global
expected number of images and the global expected number of saddle images
diverge as the order of the number of stars.Comment: To appear in JM
The BetaCage, an ultra-sensitive screener for surface contamination
Material screening for identifying low-energy electron emitters and
alpha-decaying isotopes is now a prerequisite for rare-event searches (e.g.,
dark-matter direct detection and neutrinoless double-beta decay) for which
surface radiocontamination has become an increasingly important background. The
BetaCage, a gaseous neon time-projection chamber, is a proposed ultra-sensitive
(and nondestructive) screener for alpha- and beta-emitting surface contaminants
to which existing screening facilities are insufficiently sensitive.
Sensitivity goals are 0.1 betas per keV-m-day and 0.1 alphas per m-day,
with the former limited by Compton scattering of photons in the screening
samples and (thanks to tracking) the latter expected to be signal-limited;
radioassays and simulations indicate backgrounds from detector materials and
radon daughters should be subdominant. We report on details of the background
simulations and detector design that provide the discrimination, shielding, and
radiopurity necessary to reach our sensitivity goals for a chamber with a
9595 cm sample area positioned below a 40 cm drift region and
monitored by crisscrossed anode and cathode planes consisting of 151 wires
each.Comment: 5 pages, 3 figures, Proceedings of Low Radioactivity Techniques (LRT)
2013, Gran Sasso, Italy, April 10-12, 201
Observations and predictions at CesrTA, and outlook for ILC
In this paper, we will describe some of the recent experimental measurements
[1, 2, 3] performed at CESRTA [4], and the supporting simulations, which probe
the interaction of the electron cloud with the stored beam. These experiments
have been done over a wide range of beam energies, emittances, bunch currents,
and fill patterns, to gather sufficient information to be able to fully
characterize the beam-electron-cloud interaction and validate the simulation
programs. The range of beam conditions is chosen to be as close as possible to
those of the ILC damping ring, so that the validated simulation programs can be
used to predict the performance of these rings with regard to electroncloud-
related phenomena. Using the new simulation code Synrad3D to simulate the
synchrotron radiation environment, a vacuum chamber design has been developed
for the ILC damping ring which achieves the required level of photoelectron
suppression. To determine the expected electron cloud density in the ring, EC
buildup simulations have been done based on the simulated radiation environment
and on the expected performance of the ILC damping ring chamber mitigation
prescriptions. The expected density has been compared with analytical estimates
of the instability threshold, to verify that the ILC damping ring vacuum
chamber design is adequate to suppress the electron cloud single-bunch
head-tail instability.Comment: 11 pages, contribution to the Joint INFN-CERN-EuCARD-AccNet Workshop
on Electron-Cloud Effects: ECLOUD'12; 5-9 Jun 2012, La Biodola, Isola d'Elba,
Ital
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