  A theory that describes how to load negative charge into a nonlinear,
three-dimensional plasma wakefield is presented. In this regime, a laser or an
electron beam blows out the plasma electrons and creates a nearly spherical ion
channel, which is modified by the presence of the beam load. Analytical
solutions for the fields and the shape of the ion channel are derived. It is
shown that very high beam-loading efficiency can be achieved, while the energy
spread of the bunch is conserved. The theoretical results are verified with the
Particle-In-Cell code OSIRIS.
