Emittance preservation in a plasma wakefield accelerator
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Emittance preservation in a plasma wakefield accelerator


Plasma-based acceleration (PBA) is being considered as the basis for a future linear collider,where electrons and positron bunches must collide with extremely small spot sizes. In order to be focused to such spot sizes the beams must have extremely small emittances. Thus one challenge to a PBA collider is preserving the emittance of the accelerated beams.

In this dissertation, the evolution and preservation of the witness beam emittance in aplasma-based accelerator in the nonlinear blowout regime is investigated using theory and particle-in-cell simulations. It it found that the use of plasma density ramps as matching sections are beneficial for emittance emittance growth mitigation and preservation even when the witness beam is focused so tightly within the plasma that its space charge force pulls ions inwards within the beam.

In order to study the evolution of a beam in the wakefield, details of the motion ofa single beam particle in the accelerating and focusing fields of a nonlinear wakefield are presented. The exact solution to the transverse equation of motion of a single beam particle under the assumption of adiabatic acceleration is derived. Approximate and thus simpler solutions are provided under the assumptions that plasma density also changes adiabatically. Some important concepts, including the beam’s envelope equation, geometric emittance, normalized emittance, single and beam C-S parameters, transport matrices, and matching are reviewed and elaborated upon. Emittance evolution and the importance of matching are discussed in the context of a uniform plasma.

Using the approximate solution (WKB solution) of a single particle’s motion, analyticalexpressions for the evolution of the beam emittance and the C-S 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 when the beams C-S parameters are matched to the entrance of the density profile 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 as for a matched beam. The emittance evolution without ion motion is studied using 3D particle-in-cell QuickPIC simulation and the results agree well with the theoretical predictions.

In some of the proposed experiments for the recently commissioned 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, the emittance growth can still be minimized by choosing the optimal focal plane even when the assumptions of the theory are not satisfied. Additional considerations for FACET II experiments were investigated. The plasma source is a lithium plasma confined by a helium buffer gas. The plasma is formed from field ionization which can lead to a nonlinear focusing force inside the helium buffer gas due to its high ionization potential leading to a nonuniform transverse profile for the plasma. It is found in simulations that for an initial beam emittance of 20 μm, the helium ionization is found to be small and the witness beam’s emittance can still be preserved.

Emittance evolution for beam and plasma parameters relevant to a single stage of amulti-staged plasma-based linear collider (LC) is investigated. In some plasma-based LC designs the transverse space charge forces for extreme accelerating beam parameters are expected to pull background ions into the beam which can lead to longitudinally varying nonlinear focusing forces and result in emittance growth of the beam. To mitigate this, the use of an adiabatic plasma density ramp as a matching section is proposed and examined using theory and PIC simulations. The witness beam is matched to the low density plasma entrance, where the beam initially has a large matched spot size so the ion motion effects are relatively small. As the beam propagates in the plasma density upramp (downramp), it is adiabatically focused (defocused) and its phase space distribution evolves slowly towards an equilibrium distribution including the effects of the adiabatically changing ion motion. Simulation results from QPAD, a new quasi-3D, quasi-static PIC code, show that within a single acceleration stage, this concept can limit the projected emittance growth to only ∼2% for a 25 GeV, 100 nm emittance witness beam and ∼20% for a 100 GeV, 100 nm emittance witness beam. The trade-off between the adiabaticity of the plasma density ramp and the initial ion motion at the entrance for a given length of the plasma density ramp is also discussed.

Additional issues for building a plasma based linear collider are discussed. Preliminaryparticle-in-cell simulation results which examine and illustrate problems like staging, shaped witness beam (for improved beam loading), emittance growth and hosing of a witness beam with an initial offset, ion motion triggered by the driver, and asymmetric witness beams are presented. The implications of these issues on a plasma based linear collider are discussed. Simulation results for witness beams with initial energy of 500 GeV such as would exist in a final stage of a PBA linear collider or an afterburner are presented.

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