skip to main content

Title: Analysis and approximations for crossing two nearby spin resonances

Solutions to the T-BMT spin equation have to date been confined to the single resonance crossing. However, in reality most cases of interest concern the overlapping of several resonances. To date there has been several serious studies of this problem; however, a good analytical solution or even approximation has eluded the community. We show that the T-BMT equation can be transformed into a Hill’s like equation. In this representation it can be shown that, while the single resonance crossing represents the solution to the Parabolic Cylinder equation, the overlapping case becomes a parametric type of resonance. We present possible approximations for both the non-accelerating case and accelerating case.
Authors:
 [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States). Collider-Accelerator Dept.
Publication Date:
OSTI Identifier:
1119566
Report Number(s):
BNL--103710-2014-IR; BNL--C-A/AP/497
R&D Project: KBCH139; 18031; KB0202011; TRN: US1500091
DOE Contract Number:
AC02-98CH10886
Resource Type:
Technical Report
Research Org:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; BEAM DYNAMICS; APPROXIMATIONS; SPIN; ANALYTICAL SOLUTION; EQUATIONS; RESONANCE; ACCELERATION T-BMT spin equation