Multi-objective Optimizations of a Novel Cryo-cooled DC Gun Based Ultra Fast Electron Diffraction Beamline

We present the results of multi-objective genetic algorithm optimizations of a potential single shot ultra fast electron diffraction beamline utilizing a 225 kV dc gun with a novel cryocooled photocathode system and buncher cavity. Optimizations of the transverse projected emittance as a function of bunch charge are presented and discussed in terms of the scaling laws derived in the charge saturation limit. Additionally, optimization of the transverse coherence length as a function of final rms bunch length at sample location have been performed for three different sample radii: 50, 100, 200 microns, for two final bunch charges: 100k and 1000k electrons. Analysis of the solutions is discussed, as are the effects of disorder induced heating. In particular, a coherence length per rms spot size of 0.27 nm/micron was obtained for a final bunch charge of 100k electrons and final rms bunch length of approximately 100 fs. For a final charge of 1000k electrons the cryogun produces a coherence length per rms spot size of 0.1 nm/micron for an rms bunch length of 100-200 fs and final spot size of 50 micron. These results demonstrate the viability of using genetic algorithms in the design and operation of ultrafast electron diffraction beamlines

Einstein equations in the null quasi-spherical gauge III: numerical algorithms

We describe numerical techniques used in the construction of our 4th order evolution for the full Einstein equations, and assess the accuracy of representative solutions. The code is based on a null gauge with a quasi-spherical radial coordinate, and simulates the interaction of a single black hole with gravitational radiation. Techniques used include spherical harmonic representations, convolution spline interpolation and filtering, and an RK4 "method of lines" evolution. For sample initial data of "intermediate" size (gravitational field with 19% of the black hole mass), the code is accurate to 1 part in 10^5, until null time z=55 when the coordinate condition breaks down.Comment: Latex, 38 pages, 29 figures (360Kb compressed

On the Bartnik extension problem for the static vacuum Einstein equations

We develop a framework for understanding the existence of asymptotically flat solutions to the static vacuum Einstein equations with prescribed boundary data consisting of the induced metric and mean curvature on a 2-sphere. A partial existence result is obtained, giving a partial resolution of a conjecture of Bartnik on such static vacuum extensions. The existence and uniqueness of such extensions is closely related to Bartnik's definition of quasi-local mass.Comment: 33 pages, 1 figure. Minor revision of v2. Final version, to appear in Class. Quantum Gravit

Einstein equations in the null quasi-spherical gauge

The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we describe the structure of timelike boundary conditions; the matching problem across null hypersurfaces; and the propagation of gravitational shocks.Comment: 12 pages, LaTeX (revtex, amssymb), revision 18 pages, contains expanded discussion and explanations, updated references, to appear in CQ