Controlled Growth of the Self-Modulation of a Relativistic Proton Bunch in Plasma

A long, narrow, relativistic charged particle bunch propagating in plasma is subject to the self-modulation (SM) instability. We show that SM of a proton bunch can be seeded by the wakefields driven by a preceding electron bunch. SM timing reproducibility and control are at the level of a small fraction of the modulation period. With this seeding method, we independently control the amplitude of the seed wakefields with the charge of the electron bunch and the growth rate of SM with the charge of the proton bunch. Seeding leads to larger growth of the wakefields than in the instability case.

Figure 1

Schematic of the experimental setup: the ionizing laser pulse enters the vapor source $t_p$ ahead of the $p^{+}$ bunch center and ionizes the rubidium atoms, creating the plasma. The seed $e^{-}$ bunch follows, $t_{\mathrm{seed}}$ ahead of the $p^{+}$ bunch. The optical transition radiation produced at a screen positioned 3.5 m downstream of the plasma exit is imaged on the entrance slit of a streak camera. A schematic example of a time-resolved image of the self-modulated $p^{+}$ bunch provided by the streak camera is shown in the inset. The magnetic spectrometer is located downstream of the screen.

Figure 2

Time-resolved images ($t$, $y$) of the $p^{+}$ bunch at the OTR screen obtained by averaging 10 single-event images (210 ps, $Q_p=14.7\mathrm{nC}$). Bunch center at $t=0\mathrm{ps}$, the bunch travels from left to right. Horizontal axis: time along the bunch normalized to the incoming bunch duration ${\sigma }_t$. (a) No plasma (incoming bunch). (b) Plasma ($n_{pe}=1.02\times {10}^{14}{\mathrm{cm}}^{-3}$) and $e^{-}$ bunch with $Q_e=249\mathrm{pC}$, $t_{\mathrm{seed}}=614\mathrm{ps}$ ahead of the $p^{+}$ bunch center. (c) Same as (b) but $e^{-}$ bunch delayed by 6.7 ps ($t_{\mathrm{seed}}=607.3\mathrm{ps}$). All images have the same color scale. (d) On-axis time profiles of (b) (blue line) and (c) (red line) obtained by summing counts over $-0.217\le y\le 0.217\mathrm{mm}$.

Figure 3

Time-resolved images ($t$, $y$) of the $p^{+}$ bunch (1.1 ns, $Q_p=14.7\mathrm{nC}$) obtained by averaging 10 single-event images. (a) No plasma (incoming bunch). (b) Plasma ($n_{pe}=0.97\times {10}^{14}{\mathrm{cm}}^{-3}$) and no $e^{-}$ bunch (SMI). (c) Plasma and $e^{-}$ bunch with $Q_e=249\mathrm{pC}$ (seeded SM). All images have the same color scale. Black dashed lines in (a) and continuous lines in (b) and (c) indicate, for each time column of the images, the points where the transverse distribution reaches 20% of its peak value. The distance between the lines is the transverse extent $w_{\mathrm{off}}$ (a) and $w$ (b), (c). Dashed lines of (a) also plotted in (b) and (c) for reference.

Figure 4

Top row: transverse extent $w$ along the $p^{+}$ bunch as a function of time along the bunch normalized to the incoming bunch duration ${\sigma }_t$. (a) Varying the $e^{-}$ bunch charge (see legend), $Q_e=0$ (SMI), $Q_e>0$ (seeded SM), $Q_p=14.7\mathrm{nC}$. (c) Varying the $p^{+}$ bunch charge $Q_p$ (see legend), $Q_e=249\mathrm{pC}$. Red points indicate the time along the bunch when $w=w_{\mathrm{off}}$. Bottom row: (b) $w$ as a function of $Q_e$ at $t=-1.19$ (blue points) and $t=-0.84{\sigma }_t$ (red points). (d) $w$ as a function of $Q_p$ at $t=-1.48$ (blue points) and $t=-1.30{\sigma }_t$ (red points). The error bars indicate the standard deviation of $w$, and of $Q_e$ and $Q_p$. Note: blue line: same data on (a) and (c).