Measurement of the Saturation Length of the Self-Modulation Instability

Abstract

The self-modulation (SM) instability transforms a long charged particle bunch traveling in plasma into a train of microbunches that resonantly drives large-amplitude wakefields. We present the first determination of the saturation length of SM using experimental and numerical results. The saturation length is the distance over which wakefields reach their maximum amplitude along the plasma. By varying the plasma length and measuring the radius of the transverse distribution of the bunch, we find that the saturation length of SM decreases with plasma density and initial field amplitude, e.g., when seeding. The saturation length is a fundamental parameter of the instability, and these results are key for understanding SM and designing plasma wakefield accelerators driven by long bunches, such as AWAKE, or by long laser pulses for radiation production.

Figures (4)

• Figure 1: Schematic of the experimental setup (not to scale). Inset: Transverse distribution of the bunch at the screen for single events after propagating through (a) Rubidium vapor, (b) $9.5\,$m of plasma. Colormap: logarithmic scale.
• Figure 2: Radial slices of the transverse distribution of the bunch at the screen for different propagation distances in plasma ($L_p$). (a) $n_{pe}=(1.06 \pm 0.01)\times10^{14}\,$cm$^{-3}$, (b) $(1.98\pm 0.01)\times10^{14}\,$cm$^{-3}$, (c) $(3.90\pm 0.02)\times10^{14}\,$cm$^{-3}$, (d) $(7.42\pm 0.03)\times10^{14}\,$cm$^{-3}$. Colormap: logarithmic scale. White symbols: average radius of the halo $r_h$ for the corresponding $L_p$, error bars: standard deviation of $\sim10$ events. Pink diamonds: saturation point of the radius ($r_h = 0.9 \,r_{h,\mathrm{max}}$). $t_\mathrm{RIF} = 100\,$ps ($\sim0.6\sigma_t$). (a) $N_b =(2.98 \pm 0.08)\times10^{11}$, (b) $(2.98 \pm 0.03)\times10^{11}$, (c) $(2.86 \pm 0.05)\times10^{11}$, (d) $(2.87 \pm 0.05)\times10^{11}$.
• Figure 3: (a) Saturation length $L_{sat}$ as a function of $n_{pe}$ (same values as on Fig. \ref{['fig:waterfall']}) labeled with the quantity it is determined from. Inset: $r_{h,\mathrm{avg}}(L_p=9.5\,\text{m})$ as a function of $n_{pe} \, [\times 10^{14}\,$cm$^{-3}]$. (b) Normalized transverse wakefield amplitude $W_{\perp,\mathrm{max}}$ along the plasma for the four $n_{pe}$ values of Fig. \ref{['fig:waterfall']}. Black dashed line: $90\%$ of peak value.
• Figure 4: Radial slices of the transverse distribution of the bunch at the screen for different propagation distance in plasma ($L_p$). (a) SSM ($t_\mathrm{RIF}=350\,$ps ($\sim2.1\sigma_t$)), (b) SMI ($t_\mathrm{RIF}=550\,$ps ($\sim3.2\sigma_t$)). Colormap: logarithmic scale. White symbols: average radius of the halo $r_h$ for the corresponding $L_p$, error bars: standard deviation of $\sim20$ events. Pink diamonds: saturation point of the radius ($r_h = 0.9 \,r_{h,\mathrm{max}}$). (a) $n_{pe} = (1.02 \pm 0.01)\times10^{14}\,$cm$^{-3}$ , $N_b = (2.92 \pm 0.02)\times10^{11}$, (b) $n_{pe} = (1.08 \pm 0.01)\times10^{14}\,$cm$^{-3}$ , $N_b = (2.87 \pm 0.02)\times10^{11}$.