In laser-plasma wakefield acceleration, an actual and widely studied issue is the obtaining small self-injected bunches and enhancement of their energy and accelerating gradient by variation the parameters of laser pulses and
plasma. In particular, using the special plasma profiles has a significant effect. Earlier it has been shown that with a longitudinal linearly increasing plasma density profile, due to compression of the wakefield bubble, synchronism of the maximum accelerating field at the rear wall of the wakefield bubble and the self-injected bunch is achieved. In
this work, the wakefield acceleration in a non-monotonically inhomogeneous plasma was investigated by numerical simulation using the OSIRIS code. In the first short section, the plasma density decreases, which ensures controlled self-injection of the electron bunch even at a low intensity of the laser pulse. Then, in a long section, the plasma density increases in order to prolong the time of movement of the self-injected bunch in the wakefield acceleration phase and increase the energy of the bunch. The article shows an increase in the effect of energy growth and an increase in the bunch charge compared to the previously obtained results. In addition, the effects of the formation of self-injected bunches with their subsequent retention for lasers of lower amplitude than in previous studies have been demonstrated, which expands the experimental possibilities.