p-adic Strings and their Applications

The theory of p-adic strings is reviewed along with some of their applications, foremost among them to the tachyon condensation problem in string theory. Some open problems are discussed, in particular that of the superstring in 10 dimensions as the end-stage of the 26-dimensional closed bosonic string's tachyon condensation.Comment: 12 pages, Based on a talk at the 2nd International Conference on p-adic Mathematical Physics, 15 - 21 September 2005, Belgrade, Serbia and Montenegr

Dirac Monopoles and Witten's Monopole Equations

A simple solution of Witten's monopole equations is given.Comment: 3 pages. Late

Discrete Scale Invariance and the "Second Black Monday"

Evidence is offered for log-periodic (in time) fluctuations in the S&P 500 stock index during the three years prior to the October 27, 1997 "correction". These fluctuations were expected on the basis of a discretely scale invariant rupture phenomenology of stock market crashes proposed earlier.Comment: LaTeX file, 4 pages, 2 figure

An X-Ray Regenerative Amplifier Free-Electron Laser Using Diamond Pinhole MIrrors

Free-electron lasers (FELs) have been built ranging in wavelength from long-wavelength oscillators using partial wave guiding through ultraviolet through hard x-ray FELs that are either seeded or start from noise (SASE). Operation in the x-ray spectrum has relied on single-pass SASE due either to the lack of seed lasers or difficulties in the design of x-ray mirrors. However, recent developments in the production of diamond crystal Bragg reflectors point the way to the design of regenerative amplifiers (RAFELs) which are, essentially, low-Q x-ray free-electron laser oscillators (XFELOs) that out-couple a large fraction of the optical power on each pass. A RAFEL using a six-mirror resonator providing out-coupling of 90% or more through a pinhole in the first downstream mirror is proposed and analyzed using the MINERVA simulation code for the undulator interaction and the Optics Propagation Code (OPC) for the resonator. MINERVA/OPC has been used in the past to simulate infrared FEL oscillators. For the present purpose, OPC has been modified to treat Bragg reflection from diamond crystal mirrors. The six-mirror resonator design has been analyzed within the context of the LCLS-II beamline under construction at the Stanford Linear Accelerator Center and using the HXR undulator which is also to be installed on the LCLS-II beamline. Simulations have been run to optimize and characterize the properties of the RAFEL, and indicate that substantial powers are possible at the fundamental (3.05 keV) and third harmonic (9.15 keV).Comment: 9 pages, 14 figure