BNL, Upton, Long Island, New York
Hiroshima University, Higashi-Hiroshima
LBNL, Berkeley, California
HU/AdSM, Higashi-Hiroshima
Recent theoretical investigations of beam crystallization mainly use computer modeling based on the method of molecular dynamics (MD) and analytical study based on phonon theory [1]. Topics of investigation include crystal stability in various accelerator lattices under different beam conditions, colliding crystalline beams [2], and crystalline beam formation in shear-free ring lattices with both magnets and electrodes [3]. In this paper, we review the above mentioned theoretical studies and, in particular, discuss the development of the phonon theory in a time-dependent Hamiltonian system representing a storage ring of AG focusing. Analytical study of crystalline beam stability in an AG-focusing ring was previously limited to the smooth approximation. In a typical ring, analytical results obtained under such approximation largely agrees with the results obtained with the molecular dynamics (MD) simulation method. However, as we explore ring lattices appropriate for beam crystallization at high energies (Lorentz factor gamma much higher than the betatron tunes) [2,4], this approximation fails. Here, we present a newly developed formalism to exactly predict the stability of a 1-dimensional crystalline beam in an AG focusing ring lattice.
[1] X.-P. Li, et al, PR ST-AB, 9, 034201 (2006). [2] J. Wei, A. M. Sessler, EPAC, 862 (1998)[3] M. Ikegami, et al, PR ST-AB 7, 120101 (2004).[4] J. Wei, H. Okamoto, et al, EPAC 2006.
