Abstract
An electron beam experiences chromatic emittance growth in a plasma-based accelerator if it is not matched to the focusing force in the plasma wake. A ramped plasma density profile at the entrance and exit of the plasma source can control the focusing of the beam into and out of the plasma accelerator, limiting emittance growth. Here, we present a comprehensive, analytic theory to describe the transverse beam dynamics and emittance growth in a nearly arbitrary plasma ramp profile. For a given incoming beam, this theory can be used to determine the length of the ramp required to correctly focus the electron beam, the optimal location of the beam's vacuum focus, and the chromatic emittance growth in the ramp. In addition, the theory can be used to determine the effect that errors in the beam focusing and plasma profile have on the emittance of the beam. We illustrate two example ramps to demonstrate the theory: one that provides very fast focusing for beam matching, and one that is robust to errors in the plasma density profile.
Highlights
Modern, high energy particle accelerators powered by radio frequency klystrons are becoming increasingly large and expensive
A second electron beam placed within the wake—the witness beam—is accelerated by the electric field, gaining significant energy in a short distance
Recent experiments have shown that an electron beam driven plasma wakefield accelerator (PWFA) can produce accelerating gradients in excess of 10 GeV=m with high efficiency and low energy spread [1,2,3]
Summary
High energy particle accelerators powered by radio frequency (rf) klystrons are becoming increasingly large and expensive. In a plasma-based accelerator, a laser or particle beam drives an electron density wave in the plasma, called a wake, producing a strong, longitudinal electric field. Energy spread in the electron beam drives emittance growth when the beam’s divergence is not matched to the focusing strength of the plasma. A similar ramp placed at the exit of the accelerating region gradually increases the size of the beam, controlling its divergence as it exits the plasma. We demonstrate how the theory can be used to design an entrance ramp for a plasma based accelerator and predict the emittance evolution for a beam with incoming chromatic effects. We show that rapid focusing occurs for a highly mismatched beam entering a uniform density plasma, producing a very short ramp that can match the beam into the accelerating section
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