Focusing a particle beam

A particle accelerator comprising:

• a coil to provide a magnetic field to a resonant cavity such that the resonant cavity has a background magnetic field having a first shape, the background magnetic field being at least 6 Tesla;
• a particle source to provide a plasma column to the resonant cavity;
• a voltage source to provide a radio frequency (RF) voltage to the resonant cavity to accelerate particles from the plasma column, the magnetic field causing particles accelerated from the plasma column to move orbitally within the resonant cavity;
• and
• an enclosure containing an extraction channel for receiving the particles output from the resonant cavity, the extraction channel comprising a series of focusing regions to focus a beam of received particles, wherein 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,
• wherein the focusing element comprises ferromagnetic quadrupoles, each ferromagnetic quadrupole having a cross-sectional shape of a substantially right-angled trapezoid having a canted surface, the ferromagnetic quadrupoles being oppositely arranged one above the other such that canted surfaces of the ferromagnetic quadrupoles at least partially face each other.