Modeling of laser wakefield acceleration at CO₂ laser wavelengths

The upgraded Accelerator Test Facility (ATF) CO₂ laser located at Brookhaven National Laboratory offers a unique opportunity to investigate laser wakefield acceleration (LWFA) with a 10.6-μm laser, a wavelength where little experimental work exists. While long laser wavelengths have certain advantages over short wavelengths, our modeling analysis has uncovered another important effect. The upgraded ATF CO₂ laser will have a pulse length as short as 2 ps. At a nominal plasma density of ∼10¹⁶  cm^-3, this pulse length would normally be considered too long for resonant LWFA, but too short for self-modulated LWFA. However, our model simulations indicate that a well-formed wakefield is nevertheless generated with electric field gradients of E_z≳2  GV/m assuming 2.5 TW laser peak power. The model indicates pulse steepening is occurring due to various nonlinear effects. It is possible that this intermediate laser pulse length mode of operation may permit the creation of well-formed, regular-shaped wakefields, which would be needed for staging the LWFA process. Discussed in this paper are the model, its predictions for an LWFA experiment at the ATF, and the pulse steepening effect.