Hiroshima University, Higashi-Hiroshima
HU/AdSM, Higashi-Hiroshima
LBNL, Berkeley, California
Liouville's theorem implies that the six-dimensional phase-space volume occupied by a charged-particle beam is an approximate invariant unless the beam is subjected to dissipative interactions (such as in cooling). Symplectic conditions, in a Hamiltonian system (once again, no dissipation), put constraints upon emittance transfer between the various degrees of freedom. [1] We can, however, even in non-dissipative Hamiltonian systems arrange for partial emittance transfers. This process results in phase space correlations and change in the emittance projections on to various phase planes; namely, the projected emittances in three degrees of freedom are controllable while the direction and amount of a possible emittance flow are not very flexible because of the symplectic nature of Hamiltonian system. In some applications, it is clearly advantageous to optimize the ratios of projected emittances despite the effect of correlations. Since the three emittances are not always equally important, we may consider reducing the emittance of one direction at the sacrifice of the other emittance(s). As a possible scheme to achieve such emittance control, we study a compact storage ring operating near resonance. The basic features of linear and nonlinear emittance flow are briefly discussed with numerical examples. A general discussion touching on some of these matters has been previously presented. [2]
[1] E. D. Courant, Perspectives in Modern Physics, edit R. E. Marshak (1966).[2] H. Okamoto, K. Kaneta and A. M. Sessler, to be published in J. Phys. Soc. Jpn.
