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An active plasma lens focuses the beam in both the horizontal and vertical planes simultaneously using a magnetic field generated by a discharge current through the plasma. A beam size of 5--10 $mu$m can be achieved using an focusing gradient on the order of 100 T/m. The active plasma lens is therefore an attractive element for plasma wakefield acceleration, because an ultra-small size of the witness electron beam is required for injection into the plasma wakefield to minimize emittance growth and to enhance the capturing efficiency. When the driving beam and witness electron beam co-propagate through the active plasma lens, interactions between the driving and witness beams and the plasma must be considered. In this paper, through particle-in-cell simulations, we discuss the possibility of using an active plasma lens for the final focusing of the electron beam in the presence of driving proton bunches. The beam parameters for AWAKE Run 2 are taken as an example for this type of application. It is confirmed that the amplitude of the plasma wakefield excited by proton bunches remains the same even after propagation through the active plasma lens. The emittance of the witness electron beam increases rapidly in the plasma density ramp regions of the lens. Nevertheless, when the witness electron beam has a charge of 100 pC, emittance of 10 mm mrad, and bunch length of 60 $mu$m, its emittance growth is not significant along the active plasma lens. For small emittance, such as 2 mm mrad, the emittance growth is found to be strongly dependent on the plasma density.
Plasma injection schemes are crucial for producing high-quality electron beams in laser-plasma accelerators. This article introduces the general concepts of plasma injection. First, a Hamiltonian model for particle trapping and acceleration in plasma
The proposal of generating high quality electron bunches via ionization injection triggered by an counter propagating laser pulse inside a beam driven plasma wake is examined via two-dimensional particle-in-cell simulations. It is shown that electron
Next-generation plasma-based accelerators can push electron bunches to gigaelectronvolt energies within centimetre distances. The plasma, excited by a driver pulse, generates large electric fields that can efficiently accelerate a trailing witness bu
We investigate beam loading and emittance preservation for a high-charge electron beam being accelerated in quasi-linear plasma wakefields driven by a short proton beam. The structure of the studied wakefields are similar to those of a long, modulate
Next-generation plasma-based accelerators can push electron beams to GeV energies within centimetre distances. The plasma, excited by a driver pulse, is indeed able to sustain huge electric fields that can efficiently accelerate a trailing witness bu