An example particle accelerator includes the following: a resonant cavity in which particles are accelerated, where the resonant cavity has a background magnetic field having a first shape; and an extraction channel for receiving particles output from the resonant cavity. The extraction channel comprises a series of focusing regions to focus a beam of received particles. At least one of the focusing regions is a focusing element configured to alter a shape of the background magnetic field to a second shape that is substantially opposite to the first shape in the presence of a magnetic field gradient resulting from reduction of the background magnetic field from the resonant cavity to the extraction channel.