Stability of the modulator in a plasma-modulated plasma accelerator

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Stability of the modulator in a plasma-modulated plasma accelerator

J. J. van de Wetering, S. M. Hooker, and R. Walczak

Phys. Rev. E 108, 015204 – Published 19 July 2023

Abstract

We explore the regime of operation of the modulator stage of a recently proposed laser-plasma accelerator scheme [Phys. Rev. Lett. 127, 184801 (2021)], dubbed the plasma-modulated plasma accelerator (P-MoPA). The P-MoPA scheme offers a potential route to high-repetition-rate, GeV-scale plasma accelerators driven by picosecond-duration laser pulses from, for example, kilohertz thin-disk lasers. The first stage of the P-MoPA scheme is a plasma modulator in which a long, high-energy “drive” pulse is spectrally modulated by copropagating in a plasma channel with the low-amplitude plasma wave driven by a short, low-energy “seed” pulse. The spectrally modulated drive pulse is converted to a train of short pulses, by introducing dispersion, which can resonantly drive a large wakefield in a subsequent accelerator stage with the same on-axis plasma density as the modulator. In this paper we derive the 3D analytic theory for the evolution of the drive pulse in the plasma modulator and show that the spectral modulation is independent of transverse coordinate, which is ideal for compression into a pulse train. We then identify a transverse mode instability (TMI), similar to the TMI observed in optical fiber lasers, which sets limits on the energy of the drive pulse for a given set of laser-plasma parameters. We compare this analytic theory with particle-in-cell (PIC) simulations and find that even higher energy drive pulses can be modulated than those demonstrated in the original proposal.

Received 27 March 2023
Accepted 19 May 2023

DOI:https://doi.org/10.1103/PhysRevE.108.015204

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)

Laser wakefield acceleration Laser-plasma interactions Plasma acceleration & new acceleration techniques Plasma instabilities

Plasma PhysicsAccelerators & Beams

Authors & Affiliations

J. J. van de Wetering ^1,*, S. M. Hooker ¹, and R. Walczak ^1,2

¹John Adams Institute for Accelerator Science and Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom
²Somerville College, Woodstock Road, Oxford OX2 6HD, United Kingdom

^*johannes.vandewetering@physics.ox.ac.uk

Article Text

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Supplemental Material

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References

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Issue

Vol. 108, Iss. 1 — July 2023

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Images

Figure 1
Outline of the P-MoPA scheme from the original proposal [12]. A short, low-energy seed pulse excites a small wake in the modulator stage which spectrally modulates a long, high-energy drive pulse into interleaving redshifted (Stokes) and blueshifted (anti-Stokes) pulse trains while maintaining a smooth envelope. Chromatic dispersion is then applied to the spectrally modulated drive pulse to compress it into a multipulse train, which can then be used to resonantly drive a wakefield in the accelerator stage with the same density as the modulator.
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Figure 2
2D PIC simulation of the modulator stage in a matched parabolic plasma channel of matched spot size $w_{0} = 30 µ m$ with $W_{seed} = 50 mJ$ and $W_{drive} = 0.6 J$ , $τ_{drive} = 1 ps$ . The top panel shows the on-axis longitudinal intensity profiles ${| a |}^{2}$ for the seed and drive pulses. The middle panel plots the on-axis instantaneous frequency calculated by a Hilbert transform. The bottom panel displays the full 2D distributions of the relative amplitude $δ n / n_{00}$ of the plasma wave and the relative frequency modulation $Δ ω / ω_{L}$ .
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Figure 3
Comparison of the performance of modulators with plasma channels of different transverse profiles each with wall thicknesses of $20 µ m$ (see Supplemental Material for their parametrizations [22]). The left panels show the transverse electron density (blue) and normalized guided intensity (black) profiles of the channels for: top, a square channel of diameter $30 µ m$ ; middle, a parabolic channel of matched spot size $30 µ m$ ; bottom, a parabolic channel of matched spot size $50 µ m$ (with ${(50 / 30)}^{2} \times$ more seed and drive pulse energy to account for the larger spot size). The middle panels show the relative wake amplitudes $δ n / n_{00}$ at the end of the modulator, calculated by 2D PIC simulations. The right panels show the on-axis pulse envelopes $| a |$ at the end of the modulator before (dashed blue) and after (solid orange) the expected [28] sideband spectral phase $ψ_{m}$ was removed (see Supplemental Material [22]).
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Figure 4
2D PIC simulations of the intensity profiles, ${| a |}^{2}$ , of drive pulses at the exit of the modulator with a channel of square cross-section with $w_{0} = 30 µ m$ and $W_{seed} = 50 mJ$ , for various energies and durations of the drive pulse. The top row displays the intensity profiles decomposed into its redshifted Stokes $(ω - ω_{L}) < - ω_{p 0} / 2$ , central $| ω - ω_{L} | < ω_{p 0} / 2$ , and blueshifted anti-Stokes $(ω - ω_{L}) > ω_{p 0} / 2$ components; the bottom panel displays the full intensity profile of the drive pulse.
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Figure 5
Calculated intensity profiles, ${| a |}^{2}$ , of drive pulses at the exit of the modulator before (top) and after (bottom) compression into a pulse train for drive pulses of energy $W_{drive} = 1.2 J$ and FWHM duration: (a) $0.25 ps$ , (b) $1 ps$ , (c) $2 ps$ , and (d) $4 ps$ . For these 2D PIC simulations the modulator was taken to have a square cross-section with $w_{0} = 30 µ m$ , and the seed pulse to have an energy of $W_{seed} = 50 mJ$ .
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