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. The algebraic complexity of the system has hitherto defied attempts to obtain global so lutions in any deterministic manner. In the present approach an algorithm to systematically reduce the overall system of equations has resulted in a system of two 8th order equations in only two variables in the thin lens approximation, and a system of tw o 12th order equations in two variables in the semi-thin lens approximation. The former displays a high degree of robustness in providing true global solutions, while the latter can be deterministically iterated to approach the exact thick lens solution t o very high accuracy, and can be applied to configurations with arbitrary non-dispersive intervening optics. 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 pr oviding global solutions to such algebraic systems. The combined application of these 2 systems of equations has resulted in a very robust and effective algorithm for on-line optical beam envelope matching. The global nature of the algorithm also may poin t to possible deficiencies in the optical system configuration when no solution in real numbers exists. This affords a higher degree of insight and confidence than is possible with local-root-searching algorithms. 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 at the Thomas Jefferson National Accelerator Facility has positively demonstrated the effectiveness of this method. Direction for further enhancement of the algorithm will also be discussed.

This work was supported by U.S. DOE under contract DE-AC05-84ER40150.

Author: Yu-Chiu Chao

Abstract submitted to PAC 2001, Chicago, IL, June 18-24, 2001

Updated March 28, 2001

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