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$^2$-day and 0.1 alphas per m$^2$-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 95$\times$95 cm$^2$ 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