  Laser wakefield accelerators (LWFAs) have electric fields that are orders of
magnitude larger than those of conventional accelerators, promising an
attractive, small-scale alternative for next-generation light sources and
lepton colliders. The maximum energy gain in a single-stage LWFA is limited by
dephasing, which occurs when the trapped particles outrun the accelerating
phase of the wakefield. Here, we demonstrate that a single space-time
structured laser pulse can be used for ionization injection and electron
acceleration over many dephasing lengths in the bubble regime. Simulations of a
dephasingless laser wakefield accelerator driven by a 6.2-J laser pulse show 25
pC of injected charge accelerated over 20 dephasing lengths (1.3 cm) to a
maximum energy of 2.1 GeV. The space-time structured laser pulse features an
ultrashort, programmable-trajectory focus. Accelerating the focus, reducing the
focused spot-size variation, and mitigating unwanted self-focusing stabilize
the electron acceleration, which improves beam quality and leads to projected
energy gains of 125 GeV in a single, sub-meter stage driven by a 500-J pulse.
