Control of laser-wakefield acceleration by the plasma-density profile

We show that both the maximum energy gain and the accelerated beam quality can be efficiently controlled by the plasma-density profile. Choosing a proper density gradient one can uplift the dephasing limitation and keep the phase synchronism between the bunch of relativistic particles and the plasma wave over extended distances. Putting electrons into the nth wake period behind the driving laser pulse, the maximum energy gain is increased by the factor, which is proportional to n, over that in the case of uniform plasma. Layered plasma is suggested to keep the resonant condition for laser-wakefield excitation. The acceleration is limited then by laser depletion rather than by dephasing. Further, we show that the natural energy spread of the particle bunch acquired at the acceleration stage can be effectively removed by a matched deceleration stage, where a larger plasma density is used.