  The quality of electron beams produced from plasma-based accelerators, i.e.,
normalized brightness and energy spread, has made transformative progress in
the past several decades in both simulation and experiment. Recently,
full-scale particle-in-cell (PIC) simulations have shown that electron beams
with unprecedented brightness
($10^{20}\sim10^{21}~\mathrm{A}/\mathrm{m}^2/\mathrm{rad}^2$) and $0.1\sim 1$
MeV energy spread can be produced through controlled injection in a slowly
expanding bubble that arises when a particle beam or laser pulse propagates in
density gradient, or when a particle beam self-focuses in uniform plasma or has
a superluminal flying focus. However, in previous simulations of work on
self-injection triggered by an evolving laser driver in a uniform plasma, the
resulting beams did not exhibit comparable brightnesses and energy spreads.
Here, we demonstrate through the use of large-scale high-fidelity PIC
simulations that a slowly expanding bubble driven by a laser pulse in a uniform
plasma can indeed produce self-injected electron beams with similar
brightnesses and energy spreads as for an evolving bubble driven by an electron
beam driver. We consider laser spot sizes roughly equal to the matched spot
sizes in a uniform plasma and find that the evolution of the bubble occurs
naturally through the evolution of the laser. The effects of the electron beam
quality on the choice of physical as well as numerical parameters, e.g. grid
sizes and field solvers used in the PIC simulations are presented. It is found
that this original and simplest injection scheme can produce electron beams
with beam quality exceeding that of the more recent concepts.
