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.

中文翻译：

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用于聚焦激光等离子体加速脉冲质子束的有源等离子体透镜的设计

有源等离子透镜（APL）已被证明是一种用于聚焦带电粒子的有效装置。在本文中，我们从理论上研究了使用基于放电毛细管的高梯度APL聚焦激光加速脉冲质子束的可行性。我们指定了质子束在直线和弯曲放电毛细管APL中的运动方程，在此方程上可以计算特定APL聚焦和调整质子的调节律。然后，我们总结了APL的几个约束。通过2D PIC仿真确认，我们发现在适当的等离子体状态下，质子能量损失，横向电流分布和Z捏效应不会显着影响束传输，而被动等离子透镜（PPL）效应可以在可接受的范围内促进APL重点关注。工作参数的范围，${ñ}_0$，放电电流 $\mathrm{一世}$， 长度 $\mathrm{大号}$ 和半径 $\mathrm{[R}$的APL是针对不同的目标质子能量给出的。结果表明，APL的参数可以灵活调整，适用于聚焦和传输能量为1–100 MeV的质子束。期望建立基于等离子体的束线，该等离子体束具有厘米的长度尺度，用于脉冲质子束。这种紧凑的光束线可能会对各种应用产生重大影响。