Abstract
In plasma wakefield acceleration, the witness beam's emittance needs to be preserved when it propagates through a plasma stage. The plasma includes density ramps at both the entrance and the exit. Using the Wentzel-Kramers-Brillouin solution of a single particle's motion, analytical expressions for the evolution of the beam emittance and the Twiss parameters in an arbitrary adiabatic plasma profile are provided neglecting the acceleration of the beam inside the plasma. It is shown that the beam emittance can be preserved under the matching condition even when the beam has an initial energy spread. It is also shown that the emittance growth for an unmatched beam is minimized when it is focused to the same vacuum plane for a matched beam. The emittance evolution from 3D QuickPIC simulation results agree well with the theoretical results. In the some of the proposed experiments on nearly completed FACET II facility, the matching condition may not be perfectly satisfied and the wake may not be perfectly symmetric. It is shown that for a given set of beam parameters that are consistent with FACET II capabilities, even when the assumptions of the theory are not satisfied, the emittance growth can still be minimized by choosing the optimal focal plane. Last, another issue that may cause emittance growth in realistic plasmas is also examined. When using a lithium plasma source in FACET II experiments a helium buffer gas is used. The plasma is formed from field ionization which can lead to a nonlinear focusing force when there are nonuniform helium ions due to its high ionization potential. For an initial beam emittance of $20\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$, the helium ionization is found to be small and the witness beam's emittance can be preserved.
Highlights
During the past two decades of research, a number of impressive advances have been made in the beam-driven plasma wakefield acceleration (PWFA) concept
We note that even though the plasma and the beam parameters used in these simulations do not satisfy the assumptions we made in the previous sections, (21) still appears to predict the optimal focal position of the witness beam very well, the initial matched Twiss parameters αmi, βmi are calculated in a different way
We have used theory and QuickPIC simulations to examine the evolution of the emittance and the Twiss parameters of particle beams in plasmas whose density is changing adiabatically
Summary
During the past two decades of research, a number of impressive advances have been made in the beam-driven plasma wakefield acceleration (PWFA) concept. We first derive an analytical expression for the beam’s emittance evolution in an arbitrary adiabatic plasma profile, assuming the beam has no longitudinal acceleration. This analytical expression can be used to predict the emittance growth when the beam has an energy spread and is not initially matched. S 1⁄4 dφfφðφÞ sin 2φ; pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi and εi 1⁄4 hx2i ihx0i2i − hxix0ii, βi 1⁄4 hxi2i=εi, γi 1⁄4 hx0i2i=εi, αi 1⁄4 −hxix0ii=εi are the beam’s initial geometric emittance and Twiss parameters, γm 1⁄4 ð1 þ α2mÞ=βm, and fφðφÞ is the distribution function for the beam particles’ phase advance. When the relative energy spread of the beam is very small (i.e., for every particle jΔγj 1⁄4 jγ − γj ≪ γ), the particle’s phase advance in the plasma φ will become φðγÞ 1⁄4
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