Control of laser wake field acceleration by 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. When a periodic wake field is exploited, the phase synchronism between the bunch of relativistic particles and the plasma wave can be maintained over extended distances due to the plasma density gradient. Putting electrons into the $n-$th wake period behind the driving laser pulse, the maximum energy gain is increased by the factor $2\pi n$ over that in the case of uniform plasma. 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.