Transverse envelope dynamics of beam slices in a uniform charged ellipsoidal model of the plasma bubble regime

TL;DR

The paper addresses transverse envelope dynamics in plasma bubble wakefields by modeling the nonlinear blowout as an ellipsoidal ion cavity with linear fields. It develops a multi-slice rms envelope framework for a driver-witness beam pair, deriving analytic matching conditions and performing numerical simulations with $N=150$ slices, later validated against PIC results. The authors show that matched beams quickly settle into stable envelope sizes with minimal emittance growth, while mismatched beams undergo initial envelopes oscillations before relaxing; energy spread evolves with the slice dynamics. The work provides a practical, physics-based tool for designing beam transport and acceleration in the bubble regime, including asymmetric driver/witness configurations, and offers a computationally efficient alternative to full PIC simulations.

Abstract

We consider a pair of driver/witness electron bunches propagating in an ionized gas background a configuration similar to the one produced in a capillary discharge where a plasma oscillation has been excited by a driving pulse. We assume as in the plasma nonlinear regime that the plasma electrons behind the driver are completely expelled and an ellipsoidal cavity filled with ions only is formed. The fields are linear in both longitudinal and transverse directions, at least in the region of interest for particle acceleration, as the one produced by a uniform ion distribution within a uniformly charged ellipsoidal volume. The fields produced by the ions and experienced by a witness electron beam are purely electrostatic, being the ions at rest in the laboratory frame on the time scale of interest and it can be represented with the field distribution produced by a 3D charged ellipsoidal. The energy spread and emittance degradation has been studied by slicing the bunch in an array of cylinders and solving envelope equations for each bunch slice. The properties of transverse envelope and emittance oscillations and energy spread degradation have been analyzed together with the related matching conditions for optimal transport and acceleration.

Figures (7)

• Figure 1: Schematic representation of the longitudinal wake field (black line) and ion distribution (red area) behind a driving laser or particle beam Joshi2006.
• Figure 2: The matched beam envelope [represented by the equilibrium solution of \ref{['solution-d']} and \ref{['solution-w']}]. The physical parameters of the driving beam (Left) and witness beam (Right) are displayed in Table \ref{['tab1']}.
• Figure 3: The evolution of transverse spot size and emittance in the case of driving beam: (i) numerical results (left side) and (ii) PIC simulation results (right side).
• Figure 4: The evolution of transverse spot size and emittance in the case of trailing beam: (i) numerical results (left side) and (ii) PIC simulation results (right side).
• Figure 5: The energy and energy spread in the case of both driver and trailing beams: (i) numerical results (left side) and (ii) PIC simulation results (right side).