Passage through LINACs of electron bunches in their acceleration phase is co-ordinated with passage through the LINACs of electron bunches in their deceleration phase. Each successive pair of electron bunches are spaced in time by a respective bunch spacing, in accordance with a repeating electron bunch sequence. The electron source provides clearing gaps in the electron bunch sequence to allow clearing of ions at the undulator. The electron source provides the clearing gaps in accordance with a clearing gap sequence such that, for each of the plurality of energy recovery LINACS, and for substantially all of the clearing gaps:- for each passage of the clearing gap through the LINAC in an acceleration phase or deceleration phase the clearing gap is co-ordinated with a further one of the clearing gaps passing through the LINAC in a deceleration phase or acceleration phase thereby to maintain energy recovery operation of the LINAC.