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An active plasma lens focuses the beam in both the horizontal and verticalplanes simultaneously using a magnetic field generated by a discharge currentthrough the plasma. A beam size of 5--10 $\mu$m can be achieved within a shortdistance using a focusing gradient on the order of 100 T/m. The active plasmalens is therefore an attractive element for plasma wakefield acceleration,because an ultra-small size of the witness electron beam is required forinjection into the plasma wakefield to minimize emittance growth and to enhancethe capturing efficiency. When the drive beam and witness electron beamco-propagate through the active plasma lens, interactions between the drive andwitness beams, and the plasma must be considered. In this paper, throughparticle-in-cell simulations, we discuss the possibility of using an activeplasma lens for the final focusing of the electron beam for the AWAKE RUN 2experiments. It is confirmed that the amplitude of the plasma wakefield excitedby proton bunches remains the same even after propagation through the activeplasma lens. The emittance of the witness electron beam increases rapidly inthe plasma density ramp regions of the lens. Nevertheless, when the witnesselectron beam has a charge of 100 pC, emittance of 10 mm mrad, and bunch lengthof 60 $\mu$m, its emittance growth is not significant along the active plasmalens. For small emittance, such as 2 mm mrad, the emittance growth is found tobe strongly dependent on the RMS beam size, plasma density, and multipleCoulomb scattering.

Witness electron beam injection using an active plasma lens for a proton beam-driven plasma wakefield accelerator