Envelope analysis of intense relativistic quasilaminar beams in rf photoinjectors:mA theory of emittance compensation

Abstract

In this paper we provide an analytical description for the transverse dynamics of relativistic, space-chargedominated beams undergoing strong acceleration, such as those typically produced by rf photoinjectors. These beams are chiefly characterized by a fast transition, due to strong acceleration, from the nonrelativistic to the relativistic regime in which the initially strong collective plasma effects are greatly diminished. However, plasma oscillations in the transverse plane are still effective in significantly perturbing the evolution of the transverse phase space distribution, introducing distortions and longitudinal-transverse correlations that cause an increase in the rms transverse emittance of the beam as a whole. The beam envelope evolution is dominated by such effects and not by the thermal emittance, and so the beam flow can be considered quasilaminar. The model adopted is based on the rms envelope equation, for which we find an exact particular analytical solution taking into account the effects of linear space-charge forces, external focusing due to applied as well as ponderomotive RF forces, acceleration, and adiabatic damping, in the limit that the weak nonlaminarity due to the thermal emittance may be neglected. This solution represents a special mode for beam propagation that assures a secularly diminishing normalized rms emittance and it represents the fundamental operating condition of a space-charge-compensated RF photoinjector. The conditions for obtaining emittance compensation in a long, integrated photoinjector, in which the gun and linac sections are joined, as well as in the case of a short gun followed by a drift and a booster linac, are examined. ͓S1063-651X͑97͒10706-1͔

Gain length fitting formula for free-electron lasers with strong space-charge effects

“…Figure 5 shows the qualitative consistency between the analytic contour from (14) and data points obtained through GENESIS simulations for the specific case of ¼ 0. Figure 6 shows the relative difference between the analytic and simulated fits, given by F ¼ 1 À k i F = k i .…”

“…The FEL simulation code GENESIS 1.3 [18] was used to evaluate the accuracy of the fitting formula in (14). Nearly 14 000 time-independent simulations were performed using a large range of rms transverse electron beam sizes order to sample a significant portion of the scaled parameter space where the analytical model is applicable (see Table I).…”

“…We note in this regard that the e-beam used in such FELs will operate in a space-charge dominated, rather than emittance dominated, mode, and thus the dominance of space charge over emittance effects in the longitudinal FEL dynamics should not be surprising. Similarly, the investigation of longitudinal space-charge waves in high-brightness beams is still currently of great theoretical interest [12,13], following past emphases on understanding transverse beam-plasma oscillations [14]. With all this in mind, we note that there is currently no handy formulation for quickly predicting important FEL characteristics when space charge has significant influence, despite the fact that there has been strong historical interest and recent experimental investigations into FELs that operate under these conditions.…”

Photoinjector design for the LCLs

“…Using the semi-analytic code HOMDYN [9], a wide range of injector parameters was investigated earlier under the constraints imposed by the invariant-envelope [10] matching condition: injection into the matched accelerating gradient of the booster at a laminar waist. As a result, it was found that by adjusting the gun solenoid strength so that the waist also occurs when the emittance has its relative maximum, the second emittance maximum can be shifted to higher energy with a lower final emittance value than previously achieved [2,11].…”

Universal envelope equation and emittance evolution of high-brightness beam in linac

“…This critical process is governed by the nonlinear envelope equation addressed shortly. The first beam-envelope theory of emittance compensation is based on perturbative treatment of space-charge-dominated beam evolution in constant focusing channels nearby a special quasiequilibrium solution, known as the invariant envelope [3,4]. For spacecharge-dominated beams, the invariant envelope is analogous to Brillouin flow for nonaccelerating beams, where focusing and defocusing forces are balanced to produce a stable beam.…”