Coherent control of a system involves steering an interaction to a final
coherent state by controlling the phase of an applied field. Plasmas support
coherent wave structures that can be generated by intense laser fields. Here,
we demonstrate the coherent control of plasma dynamics in a laser wakefield
electron acceleration experiment. A genetic algorithm is implemented using a
deformable mirror with the electron beam signal as feedback, which allows a
heuristic search for the optimal wavefront under laser-plasma conditions that
is not known a priori. We are able to improve both the electron beam charge and
angular distribution by an order of magnitude. These improvements do not simply
correlate with having the `best' focal spot, since the highest quality vacuum
focal spot produces a greatly inferior electron beam, but instead correspond to
the particular laser phase that steers the plasma wave to a final state with
optimal accelerating fields
