Axions are hypothetical, very weakly interacting low-mass particles that remain popular candidates for dark matter. Most of the effort in the search for axions has focussed on astrophysical sources, although the evolution of high-power laser facilities has generated significant interest in ‘light shining through wall’ experiments where axions are produced in the laboratory. With this in mind, a lower bound on the average number flux of axions produced by a laser wakefield accelerator is calculated from the perspective of quantum theory. The new result is better behaved for very low mass axions than the estimate of the average number flux obtained previously using entirely classical considerations. In particular, it converges in the limit as the axion mass tends to zero. Further calculations suggest that the number flux of axions should be tolerable at practical laboratory-scale distances from the source, accounting for dispersion.