Focusing a particle beam using magnetic field flutter

A particle accelerator comprising:

• a voltage source to sweep a radio frequency (RF) voltage in a cavity to accelerate particles from a plasma column, the cavity having a magnetic field causing particles accelerated from the plasma column to move orbitally within the cavity, the magnetic field having flux that bows at edges of the cavity;
• a regenerator to provide a magnetic field bump within the cavity to thereby change successive orbits of the particles accelerated from the plasma column so that, eventually, particles output to an extraction point, the regenerator being located at a radius in the cavity relative to the plasma column;
• and
• ferromagnetic arrangements located in the cavity proximate to the radius, each ferromagnetic arrangement providing a magnetic field bump, wherein at least two ferromagnetic arrangements are on radially adjacent sides of the regenerator, are separated from the regenerator by a space, and are configured to at least partly restore vertical focusing of particles in orbit disrupted by the regenerator.