Open AccessImpedance studies: Part 1, A composition rule
Author(s) -
Weiren Chou,
Yang Jin
Publication year - 1988
Publication title -
osti oai (u.s. department of energy office of scientific and technical information)
Language(s) - English
Resource type - Reports
DOI - 10.2172/93502
Subject(s) - composition (language) , computation , variety (cybernetics) , beam (structure) , slide rule , electrical impedance , analogy , sequence (biology) , extension (predicate logic) , set (abstract data type) , instability , computer science , simple (philosophy) , mathematics , pure mathematics , algorithm , physics , mathematical analysis , mechanics , artificial intelligence , chemistry , programming language , optics , quantum mechanics , philosophy , linguistics , biochemistry , epistemology
The impedances and the loss factors experienced by a particle beam that circulates in the APS storage ring play an essential role in the studies of the beam instability problem. Due to a large variety of structures in the ring, the computation of these parameters amounts to enormous work. During the last months, this was tackled numerically by invoking the MAFIA family, a set of codes developed mainly at DESY. The results are to be reported in several LS notes. This note is the first part and will discuss a composition rule that we observed in our calculations. The composition rule can be stated as follows. For a complicated structure, one may decompose it into simple components and compose these components to form new structures. Under certain conditions, the old and the new structures will give the same loss factors. This rule is in analogy to and an extension of the law of addition of resistances in sequence in the conventional circuit theory. We will discuss two examples to illustrate this rule
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