Restoring betatron phase coherence in a beam-loaded laser-wakefield accelerator

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Restoring betatron phase coherence in a beam-loaded laser-wakefield accelerator

A. Koehler, R. Pausch, M. Bussmann, J. P. Couperus Cabadağ, A. Debus, J. M. Krämer, S. Schöbel, O. Zarini, U. Schramm, and A. Irman

Phys. Rev. Accel. Beams 24, 091302 – Published 20 September 2021

Abstract

Matched beam loading in laser wakefield acceleration, characterizing the state of flattening the accelerating electric field along the bunch, leads to the minimization of energy spread at high-bunch charges. Here, we experimentally demonstrate by independently controlling injected charge and accelerating gradients, using the self-truncated ionization injection scheme, that minimal energy spread coincides with a reduction of the normalized beam divergence. With the simultaneous confirmation of the micrometer-small beam radius at the plasma exit, deduced from betatron radiation spectroscopy, we attribute this effect to the minimization of chromatic betatron decoherence. These findings are supported by rigorous three-dimensional particle-in-cell simulations tracking self-consistently particle trajectories from injection, acceleration until beam extraction to vacuum. We conclude that beam-loaded laser wakefield acceleration enables highest longitudinal and transverse phase space densities.

Received 9 July 2021
Accepted 16 August 2021

DOI:https://doi.org/10.1103/PhysRevAccelBeams.24.091302

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 dynamics High intensity laser-plasma interactions Laser-plasma interactions

Laser driven electron acceleration Laser wakefield acceleration Plasma acceleration & new acceleration techniques

Accelerators & Beams

Authors & Affiliations

A. Koehler ^1,*, R. Pausch ¹, M. Bussmann ^2,1, J. P. Couperus Cabadağ ¹, A. Debus ¹, J. M. Krämer ¹, S. Schöbel ^1,3, O. Zarini¹, U. Schramm ^1,3, and A. Irman ¹

¹Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstrasse 400, 01328 Dresden, Germany
²Center for Advanced Systems Understanding, 02826 Görlitz, Germany
³Technische Universität Dresden, 01062 Dresden, Germany

^*a.koehler@hzdr.de

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Issue

Vol. 24, Iss. 9 — September 2021

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Images

Figure 1
Beam decoherence: (a) illustrates the transverse phase space of a bunch with finite energy spread consisting of many slices of different electron energy which rotate in phase space with the energy-dependent betatron frequency directed by the focusing force. The beam envelope encircles the sum of all slices, (b) shows the projection $d Q / d p_{x}$ of the beam on $p_{x}$ , which is typically recorded in experiments and used for determining the normalized beam divergence $γ σ_{Θ}$ , and (c) shows the time-dependence that is caused by the phase-space rotation of the beam envelope. When the slices in (a) span over $Δ ϕ \geq π$ , full decoherence is reached and the modulation in (c) vanishes. For $Δ ϕ < π$ , the beam can be extracted at a phase with reduced momentum spread and small $σ_{Θ}$ .
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Figure 2
The experimental setup is presented in (a) the laser is focused on a gas jet and drives a wakefield. Accelerated electrons are energy-analyzed in a magnet spectrometer, (b) illustrates a typical angle-resolved energy spectrum of electrons. An aluminum foil reflects residual laser light to a beam dump behind the spectrometer. As shown in (c), the betatron profiler intercepts the angular profile of the betatron radiation and on axis betatron radiation passes through a hole in the scintillator which is indicated by the black circular area in the center. Only the on axis part of the betatron spectra is detected by the x-ray camera, which is separated from the interaction chamber by a beryllium window. The reconstructed betatron spectrum is shown in (d). The gray area indicates photon energies that are not transmitted by the beam line. An aluminum filter foil attenuates the betatron flux.
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Figure 3
Measured relative energy spread $Δ E / E$ (a), normalized divergence $γ σ_{Θ}$ (b), betatron radius $r_{β} γ^{- 1 / 4}$ , (c) and calculated betatron phase difference $Δ ϕ$ according to Eq. (2) (d) obtained from electron bunches with different charges and at three different plasma densities, $3.7 \times 10^{18} {cm}^{- 3}$ (red line), $4.4 \times 10^{18} {cm}^{- 3}$ (blue line), and $5.0 \times 10^{18} {cm}^{- 3}$ (green line). Every data point represents the average of up to 15 shots with constant experimental parameters and the error bars denote the standard error of the mean. The error bars in (c) include the systematic error obtained from sensitivity analysis [14]. The maximum beam energy ranges from 300 MeV to 450 MeV.
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Figure 4
$K$ -shell ionization and electron injection: (a) shows the injection rate $d Q / d z$ of all trapped electrons and three distinct injections (I, II, and III). (b) indicates the evolution of the laser peak intensity $a_{0}$ . The gray dashed lines indicate the ionization threshold for the first and second nitrogen $K$ -shell electrons. (c)–(f) presents the electron transverse phase space distribution $(x, p_{x})$ in the laser polarization plane for the 0.5% nitrogen doping at $z = 0.87, 0.89, 0.92$ , and 0.94 mm. The gray scale represents macroparticles from region II marked in (a). The red and green scale represent slices of earliest and latest injected electrons as indicated in (a), respectively. Extracted from the simulation, the red line represents the path of sample macroparticles that are injected (dot) in the earliest slice at (c) and rotation until the actual time (cross) shown in (d), (e), and (f). The simulations were performed for a plasma density of $4.4 \times 10^{18} {cm}^{- 3}$ .
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Figure 5
Beam loading in PIC simulation: (a) illustrates the focusing field map $F = e (E - c B)$ for an injected charge of 100 p C at $z = 1.7 mm$ . The density of injected electrons and the focusing force are indicated by the gray and color scale at the bottom right, respectively, (b) presents two line outs of the focusing force in front of the bunch (orange) and at the bunch (blue) emphasizing its linearity. The black dashed line in (b) indicates the theoretically predicted value $- E_{0} / 2 k_{p} r$ [61], and (c) shows the beam size $σ_{beam} (ζ)$ (red line) and the matched beam size $σ_{match} (ζ)$ (green line) after injection ( $z = 1.1 mm$ ).
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Figure 6
PIC particle tracking for 50 pC charge, (a) and (b) showcase the evolution of transverse momentum $p_{x}$ and coordinate $x$ , respectively. The green line indicates one standard deviation $σ_{p} (z)$ and $σ_{x} (z)$ . The vertical gray dashed lines indicate the plasma density up- and down-ramp. In (c), the red and green line represent particle orbits in $(x, p_{x})$ from the earlier and later injected slice in Fig. 4. (d) shows the phase $ϕ = \arctan p_{x} / x γ^{1 / 2}$ of the two orbits from (c). The gray shaded area $z > 2.5 mm$ indicates the field-free space outside the plasma accelerator. The thick blue line shows the phase difference $Δ ϕ$ , which indicates a decreasing decoherence during acceleration. The dashed blue line is calculated with Eq. (2) using an averaged $γ^{'}$ . The vertical gray dashed line indicates the beginning of the plasma density down-ramp. Close to the end of acceleration ( $z = 2.0 mm$ ), (e), (f), and (g) present the beam energy bandwidth $Δ E / E$ , the normalized divergence $γ σ_{Θ}$ , and the normalized beam radius $σ_{r} γ^{- 1 / 4}$ , respectively. Error bars indicate one standard deviation in (g).
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