Effects of Chromatic Aberration in a Dephasingless Laser Wakefield Accelerator

In laser wakefield accelerators, the ponderomotive force of an intense laser pulse propagating through a plasma excites a large-amplitude plasma wakefield that can trap and accelerate electrons. To overcome dephasing and prevent the electrons from outrunning the wakefield, spatiotemporal pulse shaping can be used to propagate the laser intensity at the speed of light in the plasma over long distances without the need for guiding structures. An axiparabola enables spatiotemporal control by focusing light rays at different near-field radial locations to different far-field axial locations, while maintaining a small spot size over distances greater than a Rayleigh range. To control the time at which each radius comes to its corresponding focus, a radial group delay is introduced to the shape of the pulse. Two methods to achieve this are compared: (1) a reflective, radially stepped echelon optic and (2) two specially shaped glasses. Both techniques inherently introduce k-vector spread and thereby far-field pulse broadening. The physical origins and implications of these chromatic aberrations are compared and discussed using scalar diffraction theory and ray-trace modeling.