Particle accelerator and method of reducing beam divergence in the particle accelerator

An oscillating field particle accelerator and a method of reducing beam divergence in the particle accelerator are provided. The particle accelerator includes an intermediate electrode disposed within the particle accelerator between a source of charged particles and a second electrode of the particle accelerator. The charged particles are exposed to a first electric field extending between the source and the intermediate electrode prior to being exposed to a second electric field extending between the intermediate electrode and the second electrode. The magnitude of the first electric field is less than the peak magnitude of the second electric field, and may be less than or equal to a minimum magnitude of the second electric field occurring during a phase acceptance time period associated with a phase acceptance of the particle accelerator. The accelerated charged particles emerge from the second electrode as a non-diverging or reduced divergence particle beam.