Relativistic modified Bessel-Gaussian beam generated from plasma-based beam braiding

Letter

Relativistic modified Bessel-Gaussian beam generated from plasma-based beam braiding

Bifeng Lei, Daniel Seipt, Mingyuan Shi, Bin Liu, Jingwei Wang, Matt Zepf, and Sergey G. Rykovanov

Phys. Rev. A 104, L021501 – Published 20 August 2021

Abstract

We theoretically and numerically demonstrate the generation of a relativistic modified Bessel-Gaussian beam (MBGB) via plasma-based beam braiding. It is realized by injecting several intense Gaussian pulses with well-designed offsets and angles into an underdense plasma channel which acts as a laser-pulse combiner via refractive coupling. The MBGB propagates stably in the plasma channel with a well-controlled orbital angular momentum of large value, exciting a twisted plasma wave. After leaving the plasma, it becomes unguided and survives in vacuum for at least hundreds of femtoseconds. This method is insensitive to the initial laser injection conditions and thus should be robust for experimental implementation. It provides an alternative approach in generating high-quality tunable intense optical vortex beams which are desired for various applications.

Received 27 January 2021
Revised 21 May 2021
Accepted 10 August 2021

DOI:https://doi.org/10.1103/PhysRevA.104.L021501

Physics Subject Headings (PhySH)

Laser driven electron acceleration Laser wakefield acceleration Laser-plasma interactions Plasma acceleration & new acceleration techniques

Accelerators & BeamsPlasma Physics

Authors & Affiliations

Bifeng Lei ^1,2,3,*, Daniel Seipt ^1,2,3, Mingyuan Shi^1,2,3, Bin Liu^1,2,†, Jingwei Wang⁴, Matt Zepf^1,2,3, and Sergey G. Rykovanov^5,‡

¹Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany
²GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt, Germany
³Faculty of Physics and Astronomy, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
⁴Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, 201800 Shanghai, China
⁵Center for Computational and Data-Intensive Science and Engineering, Skolkovo Institute of Science and Technology, Moscow 121205, Russia

^*b.lei@hi-jena.gsi.de
^†bin.liu@gsi.de
^‡S.Rykovanov@skoltech.ru

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Issue

Vol. 104, Iss. 2 — August 2021

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Images

Figure 1
(a) Schematic of PBB scheme in a parabolic plasma channel with three Gaussian pulses (green beamlets). Each pulse undergoes a centroid oscillation around the channel center along the $z$ axis (green arrow) with a helical trajectory (orange line). A plasma wave is excited with a twisted structure (blue surface). Electrons can be trapped and accelerated to form the structured beam (yellow beamlets at the back). (b) Transverse slice at the position indicated by the gray frame in (a). One of the laser pulses (green spots) is indicated with its initial offset $r_{c 0}$ and centroid tilt $ψ_{j}$ . The transverse density gradient of the plasma channel is indicated by the blue-white color. (c), (d) Numerical result of the initial field structure of the first two vortex submodes. of the MBGB, $| n | = 0, 1$ . The white curves are the plots of the field along the $x$ axis at $y = 0$ .
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Figure 2
3D PIC results of MBGB with the following parameters: $a_{0} = 3, n_{0} = 1 \times 10^{18} {cm}^{- 3}, w_{0} = 1$ , and $r_{c 0} = 1.5$ . (a), (d) Evolution of total OAM $L_{z}$ as transiting from the plasma into vacuum. $L_{z}$ is in units of $L_{z 0} = k_{p 0}^{4} E_{w b}^{2} / c$ . With the parameters used here, $L_{z 0} = 1.9 \times 10^{18} ℏ$ , where $ℏ$ is the reduced Planck constant. The analytical result is obtained by using Eq. (4) with an initial $w_{0}$ . The evolution of the spot size $w$ of a single subpulse as a function of propagation distance is shown in the inserted figure, which is calculated by helically propagating one of the subpulses in the plasma with the same injection condition. (b), (c) Electric field of four pulses after propagating $z = 27$ (or $140 μ m$ ) in a plasma channel and $z = 38$ (or $200 μ m$ ) in vacuum after leaving the plasma. The small dashed circles in (b) and (c) indicate the initial center of the subpulses. The outer circle in (c) indicates the center in vacuum at this point $z = 57$ . The radius is increased by 0.57 (or $3 μ m$ ).
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Figure 3
Plasma wakefield at at $τ = 32$ (or $z^{'} = 170 μ m$ ). (a) Initial intensity structure of MBGB in the plasma. The field along the $x$ axis at $y = 0$ is plotted by a white curve on the bottom. (b) Longitudinal slice of the background plasma density distribution in the $x z$ plane at $y = 0$ . Red and blue curves present the plot along the $z$ axis at $x = 0$ and $x = 1.5$ , respectively. The dashed red ellipses indicate the region of the lobe structure of the plasma wave. (c) Slice of longitudinal field $E_{z}$ . The solid black curve shows the plot of $E_{z}$ along the $z$ axis at $x = 0$ and the dashed magenta line shows the numerical approximation in the first bubble region. (d) Slice of transverse focusing field $W_{r}$ . (e) Density distribution of a twisted electron beam at $τ = 72$ in 3D. (f) Slice of an axial magnetic field after the MBGB. The field along the $z$ axis at $x = 0$ (indicated by the dashed line) is plotted by the blue curve, with a maximum value close to $10 MG$ .
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Figure 4
(a) Ratio of MBGB field amplitude perturbation $| δ {\tilde{a}}_{j} | / | \tilde{a} |$ on the dominating vortex mode $| n | = 1$ due to the inaccuracy on the laser injection offset $δ y_{j, 0}$ , calculated at $r = r_{c 0}$ by Eq. (6). (b) Field amplitude in the azimuthal direction at different propagation times along the path $r = r_{c 0}$ indicated by the white dashed lines in (c) and (d). Black solid line: Analytical result with $δ y_{j, 0} = 0$ . (c) and (d) Transverse MBGB field with initial $δ y_{j, 0} = 0.25 r_{c 0}$ at longitudinal positions $z = 3.8$ and 22.8, respectively.
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