Envelope Modes of Beams with Angular Momentum.

Barnard, J. J. ; Losic, B.

Technical Information Center Oak Ridge Tennessee

关键词: Particle beams;    Angular momentum;    Gradients;    Eigenmodes;    Quadrupoles;   

RP-ID  :  DE200515013246

学科分类：工程和技术（综合）

美国|英语

来源: National Technical Reports Library

【 摘 要 】

For a particle beam propagating in an alternating gradient focusing system, envelope equations are often employed to describe the evolution of the beam radii in the two directions transverse to the direction of propagation, and aligned with the principle axes of the alternating gradient system. When the beams have zero net angular momentum and when the alternating gradient focusing is approximated by a continuous focusing system, there are two normal modes to the envelope equations: the 'breathing' mode and a 'quadrupole' mode. In the former, the two radii oscillate in phase, and in the latter the radii oscillate 180 degrees out of phase. In this paper, we extend the analysis to include beams that have a finite angular momentum. We perturb the moment equations of ref. (1), wherein it was assumed that space charge is a distributed in a uniform density ellipse. Two additional modes are obtained. The breathing mode remains, but the quadrupole mode is split into two modes, and a new low frequency mode appears. We calculate the frequencies and eigenmodes of these four modes as a function of tune depression and a dimensionless net angular momentum.