Electron Filament Structures of Injected Electrons in LWFA

We observe the formation of thread-like elongated electron structures, referred to as electron filaments, during the self-injection in the bubble regime of laser wakefield acceleration (LWFA) using 2-D particle in cell (PIC) simulations, for no plasma density upramp preceding the laser pulse. At relatively low plasma densities, around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {\mathrm {e18~\text {c}\text {m} }}^{-3}$ </tex-math></inline-formula>, the self-injected electrons continue to move on separate trajectories inside the bubble creating well-defined electron filaments when a large bubble closes its rear edges from behind, making an angle larger than 180° measured from the interior of the bubble. At higher plasma densities, above 2.5 × 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup>, the bubble closes at its rear with the edges making a smaller angle than 180°, resulting in a different injection dynamics. We examine these trajectories using Hamiltonian mechanics and how they impact the betatron oscillations in these cases. The results indicate that higher plasma densities result in smaller betatron oscillation amplitudes and larger wiggler strength parameter due to the stronger accelerating fields in the bubble, which accelerate the electrons to higher energies, giving higher Lorentz factors. We also show that by introducing a linear density upramp at the beam entrance, the bubble’s geometry is modified, thereby influencing the betatron oscillations and potentially tuning the acceleration process.