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

In this paper we provide an analytical description for the transverse dynamics of relativistic, space-charge dominated 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 booster linac, are examined.