Flying-focus wakefields, which can propagate with a tunable velocity along the optical axis, are promising solutions to electron dephasing in laser-wakefield accelerators. This is accomplished by a combination of spatio-temporal couplings and focusing with an axiparabola, a specialized optical element which produces a quasi-Bessel beam. If implemented, dephasingless acceleration would allow for a hitherto unachievable mixture of high acceleration gradients and long acceleration lengths. Here, we conduct an in-depth study of the structure and behavior of such a flying-focus wakefield, through a combination of direct imaging and simulations. We show the stability of the wakefield structures, explore how the wakefield evolves with changes of density, study the effects of ionization on the wakefield structure with a variety of gases, and analyze the importance of the focusing position. These insights shed light onto this novel wakefield regime and bring understanding that is important to the realization of dephasingless acceleration.
Liberman et al. (2026) studied this question.