Modeling of three-dimensional betatron oscillation and radiation reaction in plasma accelerators

TL;DR

This paper extends the model of betatron oscillations in plasma accelerators to three dimensions, analyzing long-term dynamics including radiation reaction effects and phenomena like phase drift and polarization change.

Contribution

It introduces a comprehensive three-dimensional model of betatron oscillations with long-term equations considering radiation reaction effects, advancing understanding of plasma accelerator physics.

Findings

Identification of longitudinal phase drift and betatron phase shift.

Demonstration of betatron polarization change.

Comparison of extended model with original equations via numerical methods.

Abstract

Betatron oscillation is a commonly known phenomenon in laser or beam driven plasma wakefield accelerators. In the conventional model, the plasma wake provides a linear focusing force to a relativistic electron, and the electron oscillates in one transverse direction with the betatron frequency proportional to $1/\sqrt{\gamma}$, where $\gamma$ is the Lorentz factor of the electron. In this work, we extend this model to three-dimensional by considering the oscillation in two transverse and one longitudinal directions. The long-term equations, with motion in the betatron time scale averaged out, are obtained and compared with the original equations by numerical methods. In addition to the longitudinal and transverse damping due to radiation reaction which has been found before, we show phenomena including the longitudinal phase drift, betatron phase shift and betatron polarization change based on our long-term equations. This work can be highly valuable for future plasma based high-energy accelerators and colliders.