Numerous computer codes calculate beam dynamics of particles traversing an accelerating gap. In order to carry out these calculations the electric field of a gap must be determined. The electric field is obtained from derivatives of the scalar potential which solves Laplace`s equation and satisfies the appropriate boundary conditions. An integral approach for the solution of Laplace`s equation is used in this work since the objective is to determine the potential and fields without solving on a traditional spatial grid. The motivation is to quickly obtain forces for particle transport, and eliminate the need to keep track of a large number of grid point fields. The problem then becomes one of how to evaluate the appropriate integral. In this work the integral solution has been converted to a finite sum of easily computed functions. Representing the integral solution in this manner provides a readily calculable formulation and avoids a number of difficulties inherent in dealing with an integral that can be weakly convergent in some regimes, and is, in general, highly oscillatory.

I discuss non-trivial effects in the soft SUSY breaking terms which appear when one integrates out heavy fields. The effects exist only when the SUSY breaking terms are non-universal. They may spoil (1) the hierarchy between the weak and high-energy scales, or (2) degeneracy among the squark masses even in the presense of a horizontal symmetry. I argue, in the end, that such new effects may be useful in probing physics at high-energy scales from TeV-scale experiments.

The Nd-doped phosphate laser glass described herein can withstand 2.3 times greater thermal loading without fracture, compared to APG-1 (commercially-available average-power glass from Schott Glass Technologies). The enhanced thermal loading capability is established on the basis of the intrinsic thermomechanical properties (expansion, conduction, fracture toughness, and Young`s modulus), and by direct thermally-induced fracture experiments using Ar-ion laser heating of the samples. This Nd-doped phosphate glass (referred to as APG-t) is found to be characterized by a 29% lower gain cross section and a 25% longer low-concentration emission lifetime.