Radio-frequency beam conditioner for fast-wave free-electron generators of coherent radiation

Transverse to Longitudinal Emittance Exchange

“…[7]. Cylindrical cavities operating in the TM 210 mode (thus with a quadratic dependence of the longitudinal electric field on the distance from the axis) to couple the longitudinal and transverse motion to enhance laser cooling of ions in a storage ring [8], or to establish a correlation between betatron amplitude and momentum deviation to condition an FEL electron beam [9], have also been proposed. For the system under consideration we use a rectangular cavity having a longitudinal electric field which varies linearly with transverse distance, x, from the axis, as shown in Fig.…”

“…Therefore, the emittance exchanger for a thick-lens works almost exactly like the thin-lens as long as α z (i.e., the incoming energy chirp) is given by (46) (i.e., α z ≈ 9.4 in this case). From (9), this means an initial correlated energy spread of 0.03%.…”

Physically transparent formulation of a free-electron laser in the linear gain regime

“…[5] A graph of 1m Il for a Gaussian beam with a "conditioned" energy distribution, Fig. 4a, when compared with the corresponding graphs for a beam without conditioning, Fig.…”

Electromagnetic instability of the ion-focused regime

“…Neglect of this "jitter" is appropriate In the limit q x. qy«1. In addition, it is assumed that the phase of the transverse motion measured with respect to the phase of the radiation field and averaged over the betatron period, (19) is slowly varying on the scalekp-l. This condition requires that the "detuning" parameter…”