# The filamented electron bunch of the bubble regime

## TL;DR

This paper develops a theoretical model for the internal structure of electron bunches in the bubble regime, revealing filamented and shell-like arrangements that depend on initial conditions and particle number.

## Contribution

It introduces a new energy minimization approach to predict the filamented and shell structures of electron bunches in the bubble regime.

## Key findings

- Filamented electron structures form in the bubble regime.
- High particle numbers lead to hexagonal close-packing arrangements.
- 2D structures agree with the equilibrium slice model.

## Abstract

We present a theory for describing the inner structure of the electron bunch in the bubble regime starting from a random distribution of electrons inside the bubble and subsequently minimizing the system's energy. Consequently, we find a filament-like structure in the direction of propagation that is surrounded by various shells consisting of further electrons. If we specify a 2D initial structure, we observe a hexagonal structure for a high number of particles, corresponding to the close-packing of spheres in two dimensions. The two-dimensional structures are in agreement with the equilibrium slice model (ESM).