LAUSR

Active plasma lenses (APLs) have been proved as an effective device for focusing charged particles. In this paper, we have theoretically studied the feasibility of using a discharged-capillary based high gradient APL to focus laser accelerated pulsed proton beams. We specify equations of motion of proton beams in both straight and curved discharge-capillary APLs, on which the regulation law of a specific APL focusing and tuning protons can be calculated. Then, we summarize several constraints of APLs. Confirmed by a 2D PIC simulation, we find that with a proper plasma state, the proton energy loss, the transverse current distribution, and the Z-pinch effect do not significantly affect the beam transport, while the passive plasma lens (PPL) effect can promote the APL focusing within an acceptable extent. The regime of working parameters, including the plasma density ${n}_{0}$, the discharge current $I$, the length $L$ and the radius $R$ of APLs are given for different aimed proton energy. The results show that APL, whose parameters can be adjusted flexibly, is suitable for focusing and transporting proton beams with energy of 1--100 MeV. It is expected to build a beam-line based on plasma with centimeter length scale for pulsed proton beams. Such compact beam-line can have significant impact on various applications.