  Laser-triggered ionization injection is a promising way of generating
controllable high-quality electrons in plasma-based acceleration. We show that
ionization injection of electrons into a fully nonlinear plasma wave wake using
a laser pulse comprising of one or more Laguerre-Gaussian modes with
combinations of spin and orbital angular momentum can generate exotic
three-dimensional (3D) spatial distributions of high-quality relativistic
electrons. The phase dependent residual momenta and initial positions of the
ionized electrons are encoded into their final phase space distributions,
leading to complex spatiotemporal structures. The structures are formed as a
result of the transverse (betatron) and longitudinal (phase slippage and energy
gain) dynamics of the electrons in the wake immediately after the electrons are
injected. Theoretical analysis and 3D simulations verify this mapping process
leads to the generation of these complex topological beams. These beams may
trigger novel beam-plasma interactions as well as produce coherent radiation
with orbital angular momentum when sent through a resonant undulator.
