Designing of active plasma lens for focusing laser-plasma-accelerated pulsed proton beams

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Designing of active plasma lens for focusing laser-plasma-accelerated pulsed proton beams

Tong Yang, Hao Cheng, Yang Yan, Minjian Wu, Dongyu Li, Yuze Li, Yadong Xia, Chen Lin, and Xueqing Yan

Phys. Rev. Accel. Beams 24, 031301 – Published 8 March 2021

Abstract

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.

Received 21 September 2020
Accepted 9 February 2021

DOI:https://doi.org/10.1103/PhysRevAccelBeams.24.031301

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Beam countermeasures Beam injection, extraction & transport Beam optics transport Collimation Plasma production & heating by high-voltage diodes Plasma transport

Accelerators & Beams

Authors & Affiliations

Tong Yang , Hao Cheng, Yang Yan, Minjian Wu , Dongyu Li, Yuze Li, and Yadong Xia

State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, 100871, China and Beijing Laser Acceleration Innovation Center, Huairou, Beijing,101400, China

Chen Lin^* and Xueqing Yan

State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, 100871, China; Beijing Laser Acceleration Innovation Center, Huairou, Beijing, 101400, China; and Institute of Guangdong Laser Plasma Techology, Baiyun, Guangzhou, 510540, China

^*lc0812@pku.edu.cn

Article Text

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Issue

Vol. 24, Iss. 3 — March 2021

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Images

Figure 1
Schematic concept of a proton beam focusing propagating in a straight (a) and a curved (b) APL. In the case of the curved APL, the coordinate system is transformed from the Cartesian coordinate system to the orthogonal toroidal one $(ξ, η, ζ)$ as shown in (b).
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Figure 2
(a) The chromatic dependence $| Δ F |$ is displayed for a solenoid (black line), a quadrupole triplet (blue line) and an APL (red line) designed for 50 MeV protons. The focal spot of an initial collimated proton beam with energy spread of 30% around 50 MeV is displayed on the right side, after focused by the solenoid (b), the quadrupole triplet (c) and the APL (d) with the marked parameters values, respectively. The rms transverse radius of the initial beam with a bi-Gaussian distribution is $300 μ m$ .
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Figure 3
Two different adjustment methods for an APL with $L = 3 cm$ and $r = 300 μ m$ . The parameters involved in the figure are APL length $L$ , object distance $l$ (the distance between the object point and the entrance of APL), image distance $d$ (the distance between the image point and the exit of APL) and distance between object and image point $S$ . (a) Scaling of the image distance $d$ with discharged current and aimed beam energy. The object distance is fixed at $l = 4 mm$ . The black dotted line is the lower boundary of $I$ demarcated from unfocused beams, where $d = 1 m$ . (b) Scaling of the object distance with the aimed proton energy when the distance between the object and image point is fixed at $S = 0.5 m$ and the discharge current is also fixed at $I = 1 kA$ . The inset subgraphs show two different adjustment methods corresponding to Fig. 3 and 3, respectively.
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Figure 4
(a) The magnetic field profile calculated by the model based on $J \propto T_{e}^{3 / 2}$ (red curve) and by the uniform current assumption (blue curve) for a capillary with radius $r = 300 μ m$ and discharge current $I = 1 kA$ . (b) The scaling of emittance increase $Δ ϵ$ (blue curve) and actual focal length $f_{ac}$ (red curve) with incident spot size of an ideal parallel beam in the case of the magnetic strength distribution shown by the red curve in (a).
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Figure 5
The 2D PIC simulation for a proton beam with a broad energy spectrum focused by an APL located from $z = 0$ to 2 cm. (a) Scaling of the density profiles of the entire beam at different $z$ , from the initial $z = 0$ (before entering the APL) to $z = 2.3$ , 2.5, and 3 cm (different detection planes behind the APL). The waist of the beam is at focal plane $z = 2.3 cm$ . (b) The density distribution of the proton beam shown in the moving window when it propagating close to the exit of the APL at $z = 1.9 mm$ . The electric field caused by the background electron disturbance (wakefield) is also superimposed. (c) Phase diagram $y^{'} - y$ of the proton beam at $z = 2.3 cm$ . Protons with 10% energy spread around 11 MeV, 10 MeV and 9 MeV are marked with blue, green, and red colors. (d) Scaling of the rms beam radius $σ_{r}$ with the protons energy at $z = 2.3 cm$ .
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Figure 6
The optimization result of the maximum collection angle (a), upper limit of current (b), lower limit of length (c) and upper limit of radius (d) for a working-state APL scaling with energy.
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