Geometrical inverse preconditioning for symmetric positive definite matrices

We focus on inverse preconditioners based on minimizing $F(X) = 1-\cos(XA,I)$, where $XA$ is the preconditioned matrix and $A$ is symmetric and positive definite. We present and analyze gradient-type methods to minimize $F(X)$ on a suitable compact set. For that we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of $F(X)$ on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included

Considerations on the Diffraction Limitations to the Spatial Resolution of Optical Transition Radiation

The interest in using optical transition radiation (OTR) in high energy (multiGeV) beam diagnostics has motivated theoretical and experimental investigations on the limitations brought by diffraction on the attainable resolution. This paper presents calculations of the diffraction effects in an optical set-up using OTR. The OTR diffraction pattern in a telescopic system is calculated taking into account the radial polarization of OTR. The obtained diffraction pattern is compared to the patterns obtained by other authors and the effects of different parameters on the shape and on the size of the OTR diffraction pattern are studied. The major role played by the radial polarization on the shape of the diffraction pattern is outlined. An alternative method to calculate the OTR diffraction pattern is also sketchedComment: Submitted to Particle Accelerator

Generation of circularly polarized photons for a linear collider polarized positron source

Various methods of obtaining longitudinally polarized positrons for future linear colliders are reviewed. Special attention is paid to the schemes using circularly polarized high-energy photons for positron production. Most effectively such photons are obtained from electrons passing through a helical undulator or colliding with a circularly polarized laser wave. Spectrum and polarization of radiation emitted during helical motion of electrons are considered in detail. A new simple presentation of known formulas is used to account for the influence of the wave intensity, of the electron-beam angular divergence, of the collimation of radiation, and of the lateral and temporal profiles of the laser bunch on the radiation properties.Comment: 16 pages, 6 figure