A full-order, almost-deterministic optical matching algorithm

TL;DR: In this paper, an algorithm was developed for beam envelope matching with fixed geometry, taking into account the full order behavior of the quadrupoles and their compounded effects, which resulted in two algebraic systems that are independent but can be solved in tandem.

Abstract: An algorithm was developed for beam envelope matching with fixed geometry, taking into account the full order behavior of the quadrupoles and their compounded effects. In the present approach an algorithm was employed to systematically reduce the overall dimensionality of the problem. This resulted in two algebraic systems that are independent but can be solved in tandem. At the numerical level these 2 reduced systems are input to an equation solver in Mathematica 4.0 based on Grobner-basis techniques, capable of providing global solutions to such algebraic systems. This has resulted in a robust and effective algorithm for on-line optical beam envelope matching. The global nature of the algorithm also may point to possible deficiencies in the optical system configuration. An on-line high precision transfer matrix measurement program was developed in conjunction to provide input to this algorithm. Preliminary on-line testing on the CEBAF accelerator has positively demonstrated the effectiveness of this method.