Gravitational microlensing

The formulation of the Theory of General Relativity and the observational evidence for the expansion of the universe provided the basis for much of the work carried out in the field of cosmology over the past hundred years. Huge volumes of research have been conducted to find reliable values for cosmological parameters and to describe the amount and nature of the matter in the universe. Chapter 1 of this thesis attempts to summarise current theoretical and observational thinking on these matters and, in particular, examines the wide-ranging application of gravitational lensing to the search for so-called dark matter. The use of gravitational microlensing to investigate a cosmological population of compact objects, their effects on the long term variability of the apparent luminosity of quasars and on the results of the on-going observations of high redshift supernovae is discussed. Such investigation forms the basis for this thesis.The main tool for this investigation is a computer model which simulates the gravitational lensing effect of a population of compact object over a period of time. Chapter 2 sets out the theoretical background for this simulation. In particular, the methods used to set the physical parameters of the simulation, such as its volume, the redshifts of the lenses and their masses, are outlined.Chapter 3 presents the implementation of the computer model. Modelling techniques used by other researchers are discussed, as are alternative approaches considered for the implementation of this model. In order to simulate the evolving distribution of the lensing objects over time, the simulation was designed to run on high performance parallel supercomputers. The method by which the simulation was designed to take advantage of this type of computing platform is also discussed.In order to examine the effects of a cosmological distribution of compact objects on high redshift sources properly, it is necessary to have observational data. For this thesis, the observational data consists of a set of lightcurves from high redshift quasars observed over a 25 year period. This data set is outlined in Chapter 4. The results from the computer simulation are then presented, including both example light curves and power spectra for a variety of cosmological models, source sizes, source redshifts and lens masses. This observational data is compared with the simulation data and is found to have comparable levels of power for a number of simulation models.Chapter 5 examines the effect of a cosmological population of compact objects on the ongoing high redshift supernovae searches. The effects of such objects are modelled for a number of cosmological models for the range of redshifts proposed for the SNAP and VISTA searches. It is found that the proposed number counts for supernovae detection in each redshift bin are sufficient to differentiate between the different cosmological models

The Double Quasar Q2138-431: Lensing by a Dark Galaxy?

We report the discovery of a new gravitational lens candidate Q2138-431AB, comprising two quasar images at a redshift of 1.641 separated by 4.5 arcsecs. The spectra of the two images are very similar, and the redshifts agree to better than 115 km.sec$^{-1}$. The two images have magnitudes $B_J = 19.8$ and $B_J = 21.0$, and in spite of a deep search and image subtraction procedure, no lensing galaxy has been found with $R < 23.8$. Modelling of the system configuration implies that the mass-to-light ratio of any lensing galaxy is likely to be around $1000 M_{\odot}/L_{\odot}$, with an absolute lower limit of $200 M_{\odot}/L_{\odot}$ for an Einstein-de Sitter universe. We conclude that the most likely explanation of the observations is gravitational lensing by a dark galaxy, although it is possible we are seeing a binary quasar.Comment: 17 pages (Latex), 8 postscript figures included, accepted by MNRA

Analysis and correction of vertical dispersion in RHIC

In the context of preserving the polarization of proton beams, the source of vertical dispersion in RHIC is analyzed. Contributions to dispersion from non-coupling sources and coupling sources are compared. Based on the analysis of sources for dispersion, the right actuator for correcting dispersion is determined and a corresponding algorithm is developed

Reconfiguring Independent Sets in Claw-Free Graphs

We present a polynomial-time algorithm that, given two independent sets in a claw-free graph $G$, decides whether one can be transformed into the other by a sequence of elementary steps. Each elementary step is to remove a vertex $v$ from the current independent set $S$ and to add a new vertex $w$ (not in $S$) such that the result is again an independent set. We also consider the more restricted model where $v$ and $w$ have to be adjacent

Expected polarization in the present PEP-2 design

In the present design of PEP-2, operation with polarized beams is not anticipated. The amount of polarization that the existing design does support is however of interest. Calculations are presented for the expected polarization for both the High Energy (HER) and the Low Energy (LER) Rings of PEP-2 arising from the Sokolov-Ternov build-up. In both rings, the authors find that with the detector solenoid turned on, the equilibrium polarization is less than 1% at the design operating energies. Furthermore, if a polarized beam were injected, it would depolarize in a short time. To improve the polarization, they consider spin matching; i.e., implementing a set of spin transparency conditions on the lattice design. While to demand complete spin transparency around the entire machine is impractical, six conditions are derived to make the lattice partially spin transparent. Among these six conditions, perhaps only two are dominant for PEP-2. It remains to be seen whether these six (or two) conditions can be implemented into the lattice design in practice, and if implemented, whether they are sufficient to increase the polarization to useful levels. The authors have not studied spin rotator schemes to provide longitudinal polarization at the interaction point or their effect on the beam polarization. Similar calculations are presented for the Beijing Tau-Charm Factory (BTCF) design, including a possible spin rotator scheme. It is found that when this spin rotator is turned on without spin matching, the polarization level is low

An orbit fit program for localizing errors in RHIC

Many errors in an accelerator are evidenced as transverse kicks to the beam which distort the beam trajectory. Therefore, the information of the errors are imprinted in the distorted orbits, which are different from what would be predicted by the optics model. In this note, we introduce an algorithm for fitting the orbit based on an on-line optics model. By comparing the measured and fitted orbits, we first present results validating the algorithm. We then apply the algorithm and localize the location of the elusive source of vertical diurnal variations observed in RHIC. The difference of two trajectories (linear accelerator) or closed orbits (storage ring) should match exactly a betatron oscillation, which is predictable by the optics model, in an ideal machine. However, in the presence of errors, the measured trajectory deviates from prediction since the model is imperfect. Comparison of measurement to model can be used to detect such errors. To do so the initial conditions (phase space parameters at any point) must be determined which can be done by comparing the difference orbit to prediction using only a few beam position monitors (BPMs). The fitted orbit can be propagated along the beam line based on the optics model. Measurement and model will agree up to the point of an error. The error source can be better localized by additionally fitting the difference orbit using downstream BPMs and back-propagating the solution. If one dominating error source exist in the machine, the fitted orbit will deviate from the difference orbit at the same point

MULTIPLE HIGH CURRENT BUNCHES IN PEP-II

Operation with colliding beams at PEP-II has progressed remarkably well with over half the design specific luminosity and 5:2 10 32 cm,2s,1 in multiple bunches demonstrated during the last commissioning period before installation of the BABAR detector. Further luminosity increases are anticipated as the vertical beam size is reduced and beam currents are raised towards design values. At high currents interesting multibunch dynamics, which depend strongly on current distribution, have been observed during single-beam commissioning studies. Transverse beam instabilities nominally controlled using bunch-by-bunch feedback were observed to be significantly suppressed, in the absence of feedback, with beams in collision.

The Analyzing Power for p-p Scattering at 180 MeV

This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440