  Many current laser wakefield acceleration (LWFA) experiments are carried out
in a regime where the laser pulse length is on the order of or longer than the
wake wavelength and where ionization injection is employed to inject electrons
into the wake. In these experiments, the trapped electrons will co-propagate
with the longitudinal wakefield and the transverse laser field. In this
scenario, the electrons can gain a significant amount of energy from both the
direct laser acceleration (DLA) mechanism as well as the usual LWFA mechanism.
Particle-in-cell (PIC) codes are frequently used to discern the relative
contribution of these two mechanisms. However, if the longitudinal resolution
used in the PIC simulations is inadequate, it can produce numerical heating
that can overestimate the transverse motion, which is important in determining
the energy gain due to DLA. We have therefore carried out a systematic study of
this LWFA regime by varying the longitudinal resolution of PIC simulations from
the standard, best-practice resolution of 30 points per laser wavelength to
four times that value and then examining the energy gain characteristics of
both the highest-energy electrons and the bulk electrons. By calculating the
contribution of DLA to the final energies of the electrons produced from the
LWFA, we find that although the transverse momentum and oscillation radii are
over-estimated in the lower-resolution simulations, this over-estimation does
not lead to artificial energy gain by DLA. Rather, the DLA contribution to the
highest-energy electrons is larger in the higher-resolution cases because the
DLA resonance is better maintained. Thus, even at the highest longitudinal
resolutions, DLA contributes a significant portion of the energy gained by the
highest-energy electrons and also contributes to accelerating the bulk of the
charge in the electron beam produced by the LWFA.
