Abstract
We present detailed calculations of RMS-envelope matching over a broad range of beam intensities for the University of Maryland Electron Ring (UMER). Containment of beams from zero current to extreme space charge, all without changing the strength of external focusing in the periodic lattice, is possible thanks to the high density of quadrupoles in UMER. In turn, the small-aspect ratio of the UMER magnets results in gradient or field profiles that are ``all edges,'' thus requiring special treatment when constructing accurate hard-edge models. Further, the results of matching calculations, for both symmetric and asymmetric FODO (alternating gradient) schemes, are compared with calculations from simple general expressions valid in the uniform-focusing approximation of the periodic lattice. Finally, some aspects of the source-to-FODO matching calculation/optimization problem are discussed, together with sensitivity studies of the matching solutions under realistic conditions. The examples from the UMER project, which include experimental results, emphasize the practical aspects of beam envelope matching.
Highlights
Envelope matching, or betatron-function matching, of a beam into a periodic focusing lattice is a problem that must be solved early in the development of many particle accelerators
We present results of RMS envelope matching of spacecharge dominated as well as emittance-dominated beams, using the same matching geometry and without changing the strength of external focusing in the periodic lattice
We show that containment of beams over such a broad range of intensities is possible thanks to the high density of quadrupoles in University of Maryland Electron Ring (UMER), a feature not to be found in any other circular machine. (Previous work, published by some of us, related to matching of a space-charge dominated electron beam in a prototype experiment [11].) Further, we revisit the basic characterization of the short UMER magnets and show how proper modeling is important for envelope matching in special cases
Summary
Betatron-function matching, of a beam into a periodic focusing lattice is a problem that must be solved early in the development of many particle accelerators. A more general account of beam transport including space charge, lens modeling, and envelope matching appears in a recent paper by Lund and. We bring together all key aspects of envelope matching within a linear model that includes space charge and apply them to the University of Maryland Electron Ring (UMER) [10]. We present results of RMS envelope matching of spacecharge dominated as well as emittance-dominated beams, using the same matching geometry and without changing the strength of external focusing in the periodic lattice. (Previous work, published by some of us, related to matching of a space-charge dominated electron beam in a prototype experiment [11].) Further, we revisit the basic characterization of the short UMER magnets and show how proper modeling is important for envelope matching in special cases.
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