Acceleration by the wakefield in the plasma can provide compact sources of relativistic electron bunches of high brightness. Free electron lasers and particle colliders, for using plasma wakefield accelerators, require high efficiency and bunches with low energy spread. The best way to achieve low energy spread is using profiled bunches which form plateau on the wakefield. However, in experimental setups it is easier to use gaussian-kind bunches. Our numerical investigations show that thus form of bunches can assure plateau on the central part of the bunch, higher accelerating field on the tail of the bunch and lower accelerating field on its head. This field distribution leads to decreasing of the energy spread of bunches.

Acceleration by plasma wakefield accelerators enables compact sources of high-brightness relativistic electron bunches. Applications like free electron lasers and particle colliders require high efficiency and low energy spread, achievable in the blowout regime, where the radial wake force is linear and independent of the longitudinal coordinate over much of the wakefield bubble. However, this regime introduces hose instability due to harmonic oscillations of electrons in the bunch. Studies show that anharmonic oscillations, caused by inhomogeneous focusing force along the wakefield bubble, suppress this instability. In the weakly nonlinear regime, where some plasma electrons remain in the bubble, their inhomogeneous density widens the stability region. Radial inhomogeneity in the residual plasma electron distribution further leads to anharmonicity of oscillations, stabilizing the bunch. We evaluated the oscillation period and found that the large radial and longitudinal gradients of the focusing force in the driver and witness bunch regions satisfy stochastic stabilization conditions. This enhances the stability of both bunches.

Acceleration by the wakefield in the plasma can provide compact sources of relativistic electron beams of high brightness. Free electron lasers and particle colliders, using plasma wakefield accelerators, require high quality bunches with predictable profile. Previous studies showed that the resonant sequence of electron bunches appears to be unstable due to the destruction of the bunches. In this paper we discuss the mechanism of this destruction due to the focusing field phase shift which appears during this time evolution. We numerically and analytically showed the possible way of suppressing this instability, shifting all bunches on some distance.