A Full-Order, Almost Deterministic Optical Matching Algorithm

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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 solutions 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 two 12th order equations in two variables in the semi-thin lens approximation. The former displays a high degree of robustness ... continued below

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40 Kilobytes pages

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Chao, Yu-Chiu June 1, 2001.

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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 solutions 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 two 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 to 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 providing 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 point 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.

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40 Kilobytes pages

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  • PAC 2001, Chicago, IL (US), 06/18/2001--06/22/2001

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  • Report No.: JLAB-ACC-01-08
  • Report No.: DOE/ER/40150-1860
  • Grant Number: AC05-84ER40150
  • Office of Scientific & Technical Information Report Number: 783607
  • Archival Resource Key: ark:/67531/metadc716614

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • June 1, 2001

Added to The UNT Digital Library

  • Sept. 29, 2015, 5:31 a.m.

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  • Feb. 5, 2016, 8:09 p.m.

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Chao, Yu-Chiu. A Full-Order, Almost Deterministic Optical Matching Algorithm, article, June 1, 2001; Newport News, Virginia. (digital.library.unt.edu/ark:/67531/metadc716614/: accessed October 19, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.