A numerical study on plasma acceleration processes with ion dynamics at the sub-nanosecond timescale

TL;DR

This paper investigates the recovery time of a hydrogen plasma under SPARC_LAB pump–probe conditions to understand how ion dynamics influence plasma wakefield properties at sub-nanosecond timescales. It performs spatially resolved simulations using both collisionless PIC (FBPIC with PSATD) and fluid (FDTD+LBM) models, explicitly including ion motion, allowing a direct assessment of fluid closures' validity in a regime where kinetic effects are relevant. The key finding is a non-monotonic dependence of on-axis ion accumulation on the initial density $n_0$, with a peak around $n_0 \sim 4{-}5\times 10^{14}$ cm$^{-3}$, which qualitatively reproduces the experimental ΔE trend and highlights model differences near the axis. The results guide modeling strategies for high-repetition-rate PWFA, suggesting improvements like including finite temperature and evolving pump dynamics to achieve quantitative agreement with experiments and enable better extrapolation to longer times.

Abstract

Plasma wakefield acceleration is a groundbreaking technique for accelerating particles, capable of sustaining gigavolt-per-meter accelerating fields. Understanding the physical mechanisms governing the recovery of plasma accelerating properties over time is essential for successfully achieving high-repetition-rate plasma acceleration, a key requirement for applicability in both research and commercial settings. In this paper, we present numerical simulations of the early-stage plasma evolution based on the parameters of the SPARC_LAB hydrogen plasma recovery time experiment (Pompili et al., Comm. Phys. 7, 241 (2024)), employing spatially resolved Particle-in-Cell and fluid models. The experiment reports on a non-monotonic dependence of the plasma recovery time on the initial plasma density, an effect for which ion motion has been invoked as a contributing factor. The simulations presented here provide further insight into the role of ion dynamics in shaping this behavior. Furthermore, comparing Particle-in-Cell and fluid approaches allows us to assess the quality of fluid models for describing this class of plasma dynamics.

Figures (5)

• Figure 1: (a) Sketch of the pump-and-probe configuration for the recovery time experiment performed in pompili2024recoverytime. A plasma wakefield is generated by a charged bunch (pump) in a plasma with density $n_0$. Another charged bunch (probe) enters the plasma after a time delay $\Delta t$. (b) The probe energy, $E_{\rm{P}}$, is measured downstream of the channel. (c) Additional measurement as in (a)-(b), but with a plasma unperturbed by the pump, resulting in a probe energy $E_{\rm{U}}$. (d) experimental results on the characterization of $\Delta E=E_{\rm{P}}-E_{\rm{U}}$ as a function of $n_0$ for different values of the delay time $\Delta t$. Vertical dashed lines mark selected values of $n_0$ for which plasma waves are analyzed in Fig. \ref{['fig:splot_fluid_vs_pic']}. The dashed-dotted horizontal line represents $\Delta E = 0$.
• Figure 2: color map in the $\rm{z}-\rm{r}$ plane for the normalized electron density $n_{\rm{e}}/n_0$ and bunch pump density $n_{\rm{b}}/n_{\rm{b,max}}$ ((a)-(c)), and for ion density $n_{\rm{i}}/n_0$ ((d)-(f)) after $0.78~\hbox{mm}$ ($~\sim 0.025~\rm{ns}$) of propagation of the pump into the plasma, moving from left to right. We report both data from fluid (bottom-half) and PIC (top-half) simulations for three different values of the initial unperturbed plasma density $n_0$ (see dashed vertical lines in Fig. \ref{['fig:sketch_ion_accumulation']}(d)). The dashed boxes represent the window where the maximum of the focusing field, $W_{\rm{r,max}}=E_{\rm{r}} - cB_{\rm{\phi}}$, analyzed in Fig. \ref{['fig:wave-breaking_estimation']} is computed. Horizontal segments in (d) represent the values of $r$ used to compute ion density analyzed in Fig. \ref{['fig:ions_density_non_monodromy_plot']}.
• Figure 3: Data from simulations with an initial plasma density $n_0 = 4 \cdot 10^{14}~\rm{cm}^{-3}$. (a) Normalized electron (blue line) and ion (yellow line) density as a function of $z$, computed at $r=3~\rm{\mu m}$ from the axis. (b) Radial integration of the electromagnetic energy, $\langle E_{\rm{W}} \rangle_{\rm{r}}$ (dashed green line), and its mean value over a plasma period, $\langle E_{\rm{W}}\rangle_{\rm{r,p}}$ (solid green line), as a function of $z$. The wave-breaking point is indicated with a red bullet.
• Figure 4: Electron wave-breaking length, $L_{\rm{wb}}$ (red dots), and maximum of the focusing wakefield, $W_{\rm{r,max}}=E_{\rm{r}} - cB_{\rm{\phi}}$ (blue squares), as a function of the initial plasma density $n_0$, computed from PIC simulations (see text for details).
• Figure 5: The normalized ion density $n_{\rm{i}}/n_0$ as a function of $n_0$. We report data for both the PIC (yellow squares) and fluid (light blue circles) simulations, at a fixed value of the longitudinal coordinate $z_0 = 0.78~\rm{cm}$ and for two different values of transversal coordinate: $r_1 = 3~\mu \rm{m}$ (a) and $r_2=6~\mu \rm{m}$ (b).