Abstract
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.
Highlights
The past several years have witnessed an increasing array of experiments in which very short and bright bunches of electrons have been accelerated to relativistic energies in the MeV range in plasma and driven out of the plasma by intense short laser pulses [1,2,3,4,5]
Though details vary from experiment to experiment, the general features of these laser-driven beams are the very short bunch length (100’s of femtoseconds) and the relatively large energy spread of the electron beam
The short bunch length is due to the short pulse length of the laser and, within reason a variable parameter of the experiment
Summary
The past several years have witnessed an increasing array of experiments in which very short and bright bunches of electrons have been accelerated to relativistic energies in the MeV range in plasma and driven out of the plasma by intense short laser pulses [1,2,3,4,5]. This is because in these experiments (a) the longitudinal bunch length is much shorter than that of the conventional beams; (b) the longitudinal energy spread is much larger than that of the conventional ones These two characteristics of laser-driven sources make the bunch length change rapidly as soon as the beam emerges out of the plasma wave, in particular, at low relativistic energies (a few MeV) when the space charge forces should be largest. The increase in transverse beam spread can mitigate the longitudinal bunch lengthening, as it too reduces the space charge effects It is, crucial to incorporate the coupling between the longitudinal and transverse dynamics in order to evaluate the property of the laser-driven bunches and to control and utilize this potentially important new technology in high energy accelerators. P=P.) We consider z and to be small, so that all equations of motion can be linearized in these variables
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