Chromatic Dynamics of an Electron Beam in a Plasma Based Accelerator

TL;DR

This paper develops a theoretical model to analyze the chromatic dynamics of electron beams in plasma accelerators, accounting for various effects and providing design insights for beam quality control.

Contribution

It introduces a comprehensive analytical model for electron beam dynamics in plasma accelerators, including effects like energy change, mismatches, and density ramps, with practical scaling laws.

Findings

Derived analytic saturation lengths for emittance.

Showed how beam centroid oscillations vary with beam loading.

Provided scaling laws for plasma injector design.

Abstract

We present a theoretical investigation of the chromatic dynamics of the witness beam within a plasma based accelerator. We derive the single particle motion of an electron in an ion column within a nonlinear, blowout wake including adiabatic dampening and adiabatic variations in plasma density. Using this, we calculate the evolution of the beam moments and emittance for an electron beam. Our model can handle near arbitrary longitudinal phase space distributions. We include the effects of energy change in the beam, imperfect wake loading, initial transverse offsets of the beam, and mismatch between the beam and plasma. We use our model to derive analytic saturation lengths for the projected, longitudinal slice, and energy slice emittance under different beam loading conditions. Further, we show that the centroid oscillations and spot sizes vary between the slices and the variation depends strongly on the beam loading. Next, we show how a beam evolves in a full plasma source with density ramps and show that the integral of the plasma density along the ramp determines the impact on the beam. Finally, we derive several simple scaling laws that show how to design a plasma based injector to produce a target beam energy and energy spread.