On electron betatron motion and electron injection in laser wakefield accelerators

We performed laser wakefield electron acceleration experiments using laser powers up to 100TW in the 'bubble' regime. The measured angularly resolved energy spectra of the electron beam showed evidence of betatron oscillations during the acceleration process. Through diagnosis of these oscillations, electron injection into the wakefield could be controlled through adjustment of the shape of the laser focal spot or through changes in the plasma density. Several different acceleration regimes could be accessed including (i) injection of a single electron bunch into the wakefield 'bubble' (ii) multiple injection of several electron bunches and/or (iii) production of a transverse break up of the electron beam within the 'bubble' due to an asymmetry of the wakefield. We apply analytical formulae for electron motion in a wakefield to understand the experimental data.