  This paper presents the first experimental realization of a scheme that
allows for the tuning of the axial energy deposition velocity of a focal spot
with relativistic intensity. By combining a tunable pulse-front curvature with
the axial energy deposition characteristics of the axiparabola, an aspheric
optical element, this system allows for controlling the dynamics of
laser-wakefield accelerators. We demonstrate the ability to modify the axial
energy deposition velocity of 100 TW laser pulses to be superluminal or
subluminal. The experimental results are supported by theoretical calculations
and simulations, strengthening the case for the axiparabola as a pertinent
strategy to achieve dephasingless acceleration.
