• High Power Laser Science and Engineering
  • Vol. 9, Issue 2, 02000e17 (2021)
M. Turner1, A. J. Gonsalves1、*, S. S. Bulanov1, C. Benedetti1, N. A. Bobrova2, V. A. Gasilov2, P. V. Sasorov2、3, G. Korn3, K. Nakamura1, J. van Tilborg1, C. G. Geddes1, C. B. Schroeder1, and E. Esarey1
Author Affiliations
  • 1Lawrence Berkeley National Laboratory, Berkeley, CA, USA
  • 2Keldysh Institute of Applied Mathematics RAS, Moscow, Russia
  • 3ELI Beamlines, Dolní Břežany, Czech Republic
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    DOI: 10.1017/hpl.2021.6 Cite this Article Set citation alerts
    M. Turner, A. J. Gonsalves, S. S. Bulanov, C. Benedetti, N. A. Bobrova, V. A. Gasilov, P. V. Sasorov, G. Korn, K. Nakamura, J. van Tilborg, C. G. Geddes, C. B. Schroeder, E. Esarey. Radial density profile and stability of capillary discharge plasma waveguides of lengths up to 40 cm[J]. High Power Laser Science and Engineering, 2021, 9(2): 02000e17 Copy Citation Text show less

    Abstract

    We measured the parameter reproducibility and radial electron density profile of capillary discharge waveguides with diameters of 650 $\mathrm{\mu} \mathrm{m}$ to 2 mm and lengths of 9 to 40 cm. To the best of the authors’ knowledge, 40 cm is the longest discharge capillary plasma waveguide to date. This length is important for $\ge$10 GeV electron energy gain in a single laser-driven plasma wakefield acceleration stage. Evaluation of waveguide parameter variations showed that their focusing strength was stable and reproducible to $<0.2$% and their average on-axis plasma electron density to $<1$%. These variations explain only a small fraction of laser-driven plasma wakefield acceleration electron bunch variations observed in experiments to date. Measurements of laser pulse centroid oscillations revealed that the radial channel profile rises faster than parabolic and is in excellent agreement with magnetohydrodynamic simulation results. We show that the effects of non-parabolic contributions on Gaussian pulse propagation were negligible when the pulse was approximately matched to the channel. However, they affected pulse propagation for a non-matched configuration in which the waveguide was used as a plasma telescope to change the focused laser pulse spot size.
    $$\begin{align}\nonumber{n}_e(r)={n}_e(0)+\Delta {n}_e(r),\nonumber\end{align}$$((1))

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    $$\begin{align}\nonumber\Delta {n}_e(r)=\frac{r^2}{\pi {r}_e{w}_m^4},\nonumber\end{align}$$((2))

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    $$\begin{align}8\pi {r}_e{\int}_0^{\infty}\left[{n}_e(r)\left(\frac{2{r}^2}{w_m^2}-1\right){e}^{-\frac{2{r}^2}{w_m^2}}\right]r\; \mathrm{d}r-1=0,\end{align}$$((3))

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    $$\begin{align}{w}^2(z)=\frac{w_i^2}{2}\left[1+\frac{w_m^4}{w_i^4}+\left(1-\frac{w_m^4}{w_i^4}\right)\cos \left(\frac{2\pi z}{\lambda_{\mathrm{osc}}}\right)\right],\end{align}$$((4))

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    $$\begin{align}{x}_c={x}_i\kern0.1em \cos \left(\frac{4\pi z}{\lambda_{\mathrm{osc}}}\right),\end{align}$$((5))

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    $$\begin{align}{w}_m=\sqrt{\frac{2z}{k\left[{\mathrm{arccos}}\left(\mathrm{d}{O}_{\mathrm{pulse}}/\mathrm{d}{O}_{\mathrm{cap}}\right)+2\pi j\right]}},\end{align}$$((6))

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    $$\begin{align}{n}_e(r)={n}_e(0)+\frac{1-{E}_{\psi}}{\pi {r}_e{w}_m^4}{r}^2+\frac{E_{\psi }}{2\pi {r}_e{w}_m^6}{r}^4,\end{align}$$((7))

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    M. Turner, A. J. Gonsalves, S. S. Bulanov, C. Benedetti, N. A. Bobrova, V. A. Gasilov, P. V. Sasorov, G. Korn, K. Nakamura, J. van Tilborg, C. G. Geddes, C. B. Schroeder, E. Esarey. Radial density profile and stability of capillary discharge plasma waveguides of lengths up to 40 cm[J]. High Power Laser Science and Engineering, 2021, 9(2): 02000e17
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