Reconstructing nonlinear plasma wakefields using a generalized temporally encoded spectral shifting analysis

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Reconstructing nonlinear plasma wakefields using a generalized temporally encoded spectral shifting analysis

C. Arran, N. H. Matlis, R. Walczak, and S. M. Hooker

Phys. Rev. Accel. Beams 21, 103501 – Published 12 October 2018

Abstract

We generalize the temporally encoded spectral shifting (TESS) analysis for measuring plasma wakefields using spectral interferometry to dissimilar probe pulses of arbitrary spectral profile and to measuring nonlinear wakefields. We demonstrate that the Gaussian approximation used up until now results in a substantial miscalculation of the wakefield amplitude, by a factor of up to two. A method to accurately measure higher amplitude quasilinear and nonlinear wakefields is suggested, using an extension to the TESS procedure, and we place some limits on its accuracy in these regimes. These extensions and improvements to the analysis demonstrate its potential for rapid and accurate on-shot diagnosis of plasma wakefields, even at low plasma densities.

Received 20 June 2018

DOI:https://doi.org/10.1103/PhysRevAccelBeams.21.103501

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 Plasma acceleration & new acceleration techniques

Holography Optical plasma measurements Plasma diagnostic techniques

Accelerators & BeamsPlasma Physics

Authors & Affiliations

C. Arran¹, N. H. Matlis², R. Walczak¹, and S. M. Hooker¹

¹John Adams Institute for Accelerator Science, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom
²Deutsches Elektronen-Synchrotron (DESY), Notkestraße 85, Hamburg 22607, Germany

Article Text

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Issue

Vol. 21, Iss. 10 — October 2018

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Images

Figure 1
(a) Frequency-time domain plots of the reference pulse, and the probe pulse after it has interacted with a sinusoidal plasma wave of frequency $ω_{p 0}$ . Modulation of the probe pulse generates copies of the incident probe pulse, spectrally shifted by multiples of $ω_{p 0}$ . (b) The TESS signal, obtained by a Fourier transform of the recorded spectrum of the transmitted probe and reference pulses. The temporal separation of the probe and reference pulses yields a DC term at $t = 0$ and a sideband at $t = Δ t$ , and modulation of the probe causes a series of satellites (lighter blue) separated from the sideband by multiples of $ω_{p 0} ψ^{(2)}$ .
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Figure 2
(a) The measured spectrum of the probe pulse in a recent experiment [21] (solid red line) and a Gaussian fit to it (dashed black line). (b) Comparison of the spectral overlap factors $F (ω_{p 0})$ (solid, red) and $F_{Gauss} (ω_{p 0})$ (dashed, black) evaluated at the first order TESS peak as a function of gas cell pressure, assuming that the hydrogen gas was fully ionized by the driving laser. (c) Deduced wakefield amplitude as a function of cell pressure assuming spectral overlap factors $F (ω_{p 0})$ (solid, red) and $f (ω_{p 0})$ (dashed, black), showing the mismeasurement of an example wakefield amplitude when assuming a Gaussian profile.
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Figure 3
(a) Calculated temporal behaviour of the relative density of quasi-linear plasma waves for $β_{m} = 0.3$ (blue) and $β_{m} = 0.6$ (red). (b) Harmonic amplitudes $ϕ_{n}$ of the phase shift experienced by a 400 nm probe pulse copropagating for 1 mm with the plasma waves shown in (a). (c) Calculated TESS signals for the plasma waves in (a) and the phase shifts shown in (b) at $β_{m} = 0.3$ (blue) and $β_{m} = 0.6$ (red).
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Figure 4
(a) The calculated ratios $| Z_{κ} / Z_{0} |$ against plasma wave amplitude $β_{m}$ for (i) the $κ = 1$ and (ii) $κ = 2$ satellite peaks. The ratios are approximated using $N = 1$ (blue), $N = 5$ (green) and $N = 10$ (red) and are compared to simulations of the ideal ratios (black). (b) The wakefield amplitude retrieved using the peak ratios $| Z_{κ} / Z_{0} |$ against the simulated plasma wave amplitude.
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Figure 5
(a) Simulated electron density maps of a wakefield in (i) a weakly nonlinear regime and (ii) the strongly non-linear bubble regime. (b) Maps of the calculated TESS signal resulting from these density profiles, plotted in both space and in time against the expected peak positions. The magnitude of the TESS signal is plotted on a logarithmic scale. (c) A reconstruction of the electron density map of the wakefield using the TESS analysis, using $N = 4$ peaks from the TESS signal. In all plots the profile on-axis is shown below.
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