Space charge dynamics of bright electron beams

The longitudinal dynamics and its coupling with the transverse dynamics of bunched beams with strong space charge are analyzed. We introduce a self-consistent Vlasov description for the longitudinal phase space similar to the familiar description for the transverse phase space using a Kapchinskij-Vladimirskij distribution. A longitudinal beam envelope equation is derived. An exact solution is then obtained when coupling to the transverse dynamics is ignored. This longitudinal envelope equation is coupled to the transverse envelope equation to form a set of coupled dynamical equations, which is then solved numerically. This analysis is prompted by the surprising results of recent experiments which showed that by driving an intense laser pulse into matter, which in turn creates a plasma, short bright relativistic electron bunches are produced, surprisingly narrowly focused. We find that because the space charge forces weaken with increasing transverse and longitudinal phase space, both the transverse and longitudinal emittance blowouts anticipated of bright compact bunches are mitigated by this coupling. It should be possible to capture these bunches into an rf cavity to accelerate to higher energies.