Phase space control and consequences for cooling by using a laser-undulator beat wave

We present a general method to control the phase space structure of charged particle beams by both Hamiltonian and non-Hamiltonian manipulations by employing multiple optical pulses. In particular. we focus on beam cooling as an example of the method. In order to rapidly cool a bunched beam of charged particles, one needs to introduce non-Hamiltonian manipulation of the internal structure of the phase space of the bunch. A spatially dependent force, which cancels the velocity moment fluctuations arising from the irregularity and granularity of the phase space, is shown to be effective in cooling the bunch. We introduce a method of cooling by creating a ponderomotive force due to a beat between a laser and an undulator that are appropriately adjusted turn by turn through feedback. If a high enough resolution feedback system fan be achieved, this results in a rapid reduction of the longitudinal emittance of the bunch with a corresponding increase in the phase space of the scattered laser light. In this process we find that when the structure of the laser input is matched well with that of the beam, a large amount of entropy transfer without much energy transfer takes place (''entropy resonance''), while when it is ill matched, no such entropy resonance takes place. We measure the correlation dimension and higher entropy of the scattered laser light. It is found that bath quantities are useful for determining the amount of cooling. By combining an appropriately timed Hamiltonian longitudinal beam stretching with the present cooling procedure, we can continue the cooling. Numerical simulation is carried out to demonstrate this method.