A linear accelerator comprises a series of accelerating cavities, adjacent pairs of which are coupled via coupling cavities, in which at least one coupling cavity comprises a rotationally asymmetric element that is rotateable thereby to vary the coupling offered by that cavity. A control means for the accelerator is also provided, adapted to control operation of the accelerator and rotation of the asymmetric element, arranged to operate the accelerator in a pulsed manner and to rotate the asymmetric element between pulses to control the energy of successive pulses. A beneficial way of doing so is to rotate the asymmetric element continuously during operation of the linear accelerator. Then, the control means need only adjust the phase of successive pulses so that during the brief period of the pulse, the asymmetric element is "seen" to be at the required position. The asymmetric element can disposed within an evacuated part of the accelerator and rotated by way of an electromagnetic interaction with parts outside the evacuated part. No parts associated with the drive need therefore pass through the vacuum seal. This could be achieved by providing at least one magnetically polarized member on the asymmetric element and at least one electrical coil outside the evacuated part.