Abstract : The original version of this Article contained an error in the last sentence of the first paragraph of the Introduction and incorrectly read `A proper electron beam control is one of the main challenges towards the Graal of developing a compact alternative of X-ray free-electron lasers by coupling LWFA gigaelectron-volts per centimetre acceleration gradient with undulators in the amplification regime in equation 11, nx(n-β) x β: n the two times and beta the two times should be bold since they are vectorsin Eq. 12, β should be bold as well.' The correct version is `A proper electron beam control is one of the main challenges towards the Graal of developing a compact alternative of X-ray free-electron lasers by coupling LWFA gigaelectron-volts per centimetre acceleration gradient with undulators in the amplification regime.'This has been corrected in both the PDF and HTML versions of the Article.