Space charge dynamics of bright electron beams

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 KapchinskijVladimirskij 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.

Controlled Electron Injection into Plasma Accelerators and SpaceCharge Estimates

“…The derivation of the force is tedious and is shown in Appendix K for the specific configuration discussed by A. Chao et al [71], that is a cylindrical beam with a uniform transverse and quadratic longitudinal density profile. Other configurations are also discussed such as hollow beams, linear longitudinal density profile, etc.…”

“…The shell approach has been compared to several other methods such as the direct integration of the coupled envelope equations [35,68,71], a modified Poisson solver and a 3-D point to point interaction code [72]. Each of these methods have their own set of approximations which we are going to review next.…”

Properties of Trapped Electron Bunches in a Plasma Wakefield Accelerator

“…Conventional RF sources can generate electron bunches with longitudinal emittance of order MeV·ps [16] (300 MeV·µm/c). To be useful as a particle source, the , 20/k p ≈ 200 µm.…”

“…However, the movement of r only becomes an issue once the radial velocity becomes comparable to c. Thus, to find the condition that causes the sheath electrons to move relativistically, r can be treated as a constant, 2/k p . The radial momentum transferred from the drive bunch to the sheath electrons 16) where N d is the total number of drive bunch electrons and r e is the classical electron radius. For v r to approach c, ∆p r must at least be mc.…”

“…At present, thermionic and photoemission based electron sources are widely used [25]; however, plasma based electron sources are an active topic of research due to their potential to produce high current and low emittance electron bunches [67,23,17,3,40,44,49,16]. Recently it was shown that PWFAs, operated in the nonlinear bubble regime, can trap electrons that are released by ionization inside the plasma wake [58] and accelerate them to high energies.…”