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.
BNL, Upton, Long Island, New York
IHEP Beijing, Beijing
During the EPAC 2006 we reported the lattice design for rapid-cycling synchrotrons used to accelerate high-intensity proton beams to energy of tens of GeV for secondary beam production. After primary beam collision with a target, the secondary beam can be collected, cooled, accelerated or decelerated by ancillary synchrotrons for various applications. For the main synchrotron, the lattice has:
- flexible momentum compaction to avoid transition and to facilitate RF gymnastics
- long straight sections for low-loss injection, extraction, and high-efficiency collimation
- dispersion-free straights to avoid longitudinal-transverse coupling, and
- momentum cleaning at locations of large dispersion with missing dipoles.