Each cavity can be thought of as two large washer-shaped disks connected by an outer cylindrical tube.
A voltage pulse applied between the two disks causes an increasing magnetic field which inductively couples power into the charged particle beam.
[1] The linear induction accelerator was invented by Christofilos in the 1960s.
[2] Linear induction accelerators are capable of accelerating very high beam currents (>1000 A) in a single short pulse.
They have been used to generate X-rays for flash radiography (e.g. DARHT at LANL), and have been considered as particle injectors for magnetic confinement fusion and as drivers for free electron lasers.