Perturbation Analysis of Orthogonal Matching Pursuit

Orthogonal Matching Pursuit (OMP) is a canonical greedy pursuit algorithm for sparse approximation. Previous studies of OMP have mainly considered the exact recovery of a sparse signal $\bm x$ through $\bm \Phi$ and $\bm y=\bm \Phi \bm x$, where $\bm \Phi$ is a matrix with more columns than rows. In this paper, based on Restricted Isometry Property (RIP), the performance of OMP is analyzed under general perturbations, which means both $\bm y$ and $\bm \Phi$ are perturbed. Though exact recovery of an almost sparse signal $\bm x$ is no longer feasible, the main contribution reveals that the exact recovery of the locations of $k$ largest magnitude entries of $\bm x$ can be guaranteed under reasonable conditions. The error between $\bm x$ and solution of OMP is also estimated. It is also demonstrated that the sufficient condition is rather tight by constructing an example. When $\bm x$ is strong-decaying, it is proved that the sufficient conditions can be relaxed, and the locations can even be recovered in the order of the entries' magnitude.Comment: 29 page

Statistical Analysis of Crossed Undulator for Polarization Control in a SASE FEL

There is a growing interest in producing intense, coherent x-ray radiation with an adjustable and arbitrary polarization state. In this paper, we study the crossed undulator scheme (K.-J. Kim, Nucl. Instrum. Methods A {\bf 445}, 329 (2000)) for rapid polarization control in a self-amplified spontaneous emission (SASE) free electron laser (FEL). Because a SASE source is a temporally chaotic light, we perform a statistical analysis on the state of polarization using FEL theory and simulations. We show that by adding a small phase shifter and a short (about 1.3 times the FEL power gain length), $90^\circ$ rotated planar undulator after the main SASE planar undulator, one can obtain circularly polarized light -- with over 80% polarization -- near the FEL saturation.Comment: 14 pages, 4 figure

SASE FEL Polarization Control Using Crossed Undulator

There is a growing interest in producing intense, coherent x-ray radiation with an adjustable and arbitrary polarization state. In this paper, we study the crossed undulator scheme for rapid polarization control in a self-amplified spontaneous emission (SASE) free electron laser (FEL). Because a SASE source is a temporally chaotic light, we perform a statistical analysis on the state of polarization using FEL theory and simulations. We show that by adding a small phase shifter and a short (about 1.3 times the FEL power gain length), 90{sup o} rotated planar undulator after the main SASE planar undulator, one can obtain circularly polarized light--with over 80% polarization--near the FEL saturation

Analysis of Slice Transverse Emittance Evolution in a Photocathode RF Gun

This report is an analysis of slice transverse emittance evolution in a photocathode RF gu

Nonlinearly Shaped Pulses in Photoinjectors and Free-Electron Lasers

Photoinjectors and Free Electron Lasers (FEL) are amongst the most advanced systems in accelerator physics and have consistently pushed the boundaries of emittance and x-ray peak power. In this paper, laser shaping at the cathode is proposed to further lower the emittance and reduce electron beam tails, which would result in brighter x-ray production. Using dispersion controlled nonlinear shaping (DCNS), laser pulses and beam dynamics were simulated in LCLS-II. The photoinjector emittance was optimized and the resulting e-beam profiles were then simulated and optimized in the linac. Finally, the expected FEL performance is estimated and compared to the current technology: Gaussian laser pulses on the cathode. The e-beams produced by DCNS pulses show a potential for 35% increase in x-ray power per pulse during SASE when compared to the standard Gaussian laser pulses