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A new approach to laser-wakefield acceleration (LWFA) has been analyzed. A seed electron beam bunch precedes the laser pulse into the plasma. This seed bunch initiates formation of plasma waves via a plasma wakefield acceleration mechanism. The amplitude of the plasma waves is subsequently amplified by the laser pulse via a self-modulated LWFA (SM-LWFA) process. This method enables the generation of strong wakefields even when the laser pulse by itself has characteristics that are insufficient for driving resonant LWFA or SM-LWFA. Another advantage is the wakefield formation begins at the seed bunch and does not start from noise as typically occurs in SM-LWFA. This feature may be helpful when the phase of the wakefield must be accurately controlled, for example, when staging multiple LWFA devices in series.

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.