Preliminaries toward studying resonant extraction from the Debuncher

Abstract

A recent proposal to detect {mu} {yields} e direct conversion at Fermilab asks for slow extraction of protons from the antiproton source, specifically from the Debuncher. [1] A third-integer resonance originally was considered for this, partly because of the Debuncher's three-fold symmetry and partly because its operational horizontal tune, {nu}{sub x} {approx} 9.765, is already within 0.1 of {nu}{sub x} = 29/3. Using a half integer resonance, {nu}{sub x} = 19/2, though not part of the original proposal, has been suggested more recently because (a) Fermilab has had a good deal of experience with half-integer extraction from the Tevatron, the Main Injector and the erstwhile Main Ring, and (b) for reasons we shall examine later, it depopulates the entire bunch without an abort at the end. This memo presents considerations preliminary to studying both possibilities. It is meant only as a starting point for investigations to be carried out in the future. The working constraints and assumptions have oscillated between two extremes: (1) making minimal changes in the antiproton source to minimize cost and (2) building another machine in the same tunnel. In this memo we adopt an attitude aligned more toward the first. The assumed parameters are listed in Table 1. A few are not (easily) subject to change, such as those related to the beam's momentum and revolution frequency and the acceptance of the debuncher. Two resonance exemplars are presented in the next section, with an explanation of the analytic and semi-analytic calculations that can be done for each. Section 3 contains preliminary numerical work that was done to validate the exemplars within the context of extraction from the Debuncher. A final section contains a summary. Following the bibliography, appendices contain (a) a qualitative, conceptual discussion of extraction for the novice, (b) a telegraphic review of the perturbative incantations used to filter the exemplars as principal resonances of quadrupole, sextupole and octupole distributions, (c) a brief discussion of linearly independent control circuits, and (d) two files describing the antiproton source's rings in MAD v.8 format, not readily available elsewhere. All figures are located at the end. We emphasize again, the work reported here barely begins the effort that will be required to design, validate and perform resonant extraction from the Debuncher. Our goal was to compile these preliminary notes in one place for easy future reference, preferably by a young, intelligent, motivated and energetic graduate student.