Direct laser acceleration in varying plasma density profiles

Direct laser acceleration has proven to be an efficient source of high-charge electron bunches and high brilliance x-rays. However, an analytical description of the acceleration in the interaction with varying plasma density targets is still missing. Here, we provide an analytical estimate of the maximum energies that electrons can achieve in such a case. We demonstrate that the maximum energy depends on the local electron properties at the moment when the electron fulfills the resonant condition at the beginning of the acceleration. This knowledge enables density shaping for various purposes. One application is to decrease the required acceleration distance needed to achieve the maximum electron energy. Another use for density tailoring is to achieve acceleration beyond the radiation reaction limit. We derive the energy scaling law that is valid for arbitrary density profile that varies slowly compared with the betatron period. Our results can be applied to electron heating in exponential preplasma of thin foils, ablating plasma plumes, or gas jets with long-scale ramp-up.