Beams consisting of charged particles which are all directed towards a given virtual focus will generally not reach this focus but, due to their mutual repulsion, they will pass through a waist and then become divergent. Ray tracing shows that either positive or negative spherical aberration is introduced in a beam passing through a waist. This aberration is caused by the interaction of the electrons; its sign depends on voltage, current, and on the angle of initial convergence of the beam. For sufficiently high voltages or low currents, waist formation no longer occurs, but the electron rays cross the axis of the beam. With decreasing current density, the transition from waist to crossover is found to occur first for the inner rays of the beam while the outer rays still form a waist. All experimental results are found to be in approximate agreement with theoretical predictions.