Analysis and approximations for crossing two nearby spin resonances

Ranjbar, V. H.¹ 

[1] Brookhaven National Lab. (BNL), Upton, NY (United States). Collider-Accelerator Dept.

关键词: BEAM DYNAMICS;    APPROXIMATIONS;    SPIN;    ANALYTICAL SOLUTION;    EQUATIONS;    RESONANCE;    ACCELERATION T-BMT spin equation;   

DOI  :  10.2172/1119566
RP-ID  :  BNL--103710-2014-IR
RP-ID  :  BNL--C-A/AP/497
PID  :  OSTI ID: 1119566
Others  :  R&D Project: KBCH139
Others  :  18031
Others  :  Other: KB0202011
Others  :  TRN: US1500091

学科分类：核物理和高能物理

美国|英语

来源: SciTech Connect

【 摘 要 】

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.