Hosing of a Long Relativistic Particle Bunch in Plasma

Experimental results show that hosing of a long particle bunch in plasma can be induced by wakefields driven by a short, misaligned preceding bunch. Hosing develops in the plane of misalignment, self-modulation in the perpendicular plane, at frequencies close to the plasma electron frequency, and are reproducible. Development of hosing depends on misalignment direction, its growth on misalignment extent and on proton bunch charge. Results have the main characteristics of a theoretical model, are relevant to other plasma-based accelerators and represent the first characterization of hosing.

Figure 1

Schematic of the experimental setup (not to scale) showing main components used for the measurements. Inset: sketch of the images recorded—time-integrated ($x$, $y$), time-resolved ($x$, $t$), ($y$, $t$) images when hosing and SM develop simultaneously.

Figure 2

Time-resolved images of the proton bunch ($n_{\mathrm{pe}}=0.96\times {10}^{14}{\mathrm{cm}}^{-3}$, $Q_p=(14.9\pm 0.1)$ nC, $\mathrm{\Delta }x=(0.95\pm 0.16)c/{\omega }_{\mathrm{pe}}$). (a) $x$ plane, hosing; (b) $y$ plane, SM. Images—averages of ten consecutive single events recorded simultaneously, same color scale. Inset (a): single-event $3\sigma$ contours of time-integrated proton bunch charge distribution for the same ten events. Dashed red lines: position of the slit of the streak cameras. Elongation of the distribution indicates the plane of hosing. (c) Centroid position along the bunch in vacuum (gray line), undergoing SM (solid green line) and hosing (dashed black line).

Figure 3

Time-resolved images ($n_{\text{pe}}=0.96\times {10}^{14}{\mathrm{cm}}^{-3}$, $Q_p=(14.9\pm 0.1)\mathrm{nC}$). (a) $\mathrm{\Delta }x=(0.95\pm 0.16)c/{\omega }_{\mathrm{pe}}$. (b) $\mathrm{\Delta }x=(-0.93\pm 0.18)c/{\omega }_{\mathrm{pe}}$. Images have the same color scale. Reflection of $x_c$ oscillation visible, e.g., at $t\approx 124\mathrm{ps}$ (dashed red line). (c) $x_c$ oscillation curves: dashed black line, top image; solid blue line, bottom image. Insets (a),(b): single-event $3\sigma$ contours of time-integrated bunch charge distribution.

Figure 4

Proton bunch centroid position $x_c(t)$ ($n_{\text{pe}}=0.96\times {10}^{14}{\mathrm{cm}}^{-3}$). (a) $Q_p=(14.9\pm 0.1)\mathrm{nC}$. $\mathrm{\Delta }x=(0.53\pm 0.15)c/{\omega }_{\mathrm{pe}}$, green line; $\mathrm{\Delta }x=(0.95\pm 0.16)c/{\omega }_{\mathrm{pe}}$, black line; $\mathrm{\Delta }x=(1.47\pm 0.16)c/{\omega }_{\mathrm{pe}}$, red line. (b) $\mathrm{\Delta }x\approx 1c/{\omega }_{\mathrm{pe}}$. $Q_p=(46.5\pm 0.6)\mathrm{nC}$ ($n_{b0}=(7.0\pm 0.9)\times {10}^{12}{\mathrm{cm}}^{-3}$), red line; $Q_p=(14.9\pm 0.1)\mathrm{nC}$ ($n_{b0}=(4.3\pm 0.2)\times {10}^{12}{\mathrm{cm}}^{-3}$), black line. (c) Same as red line of (b) with rms variation of the data—red bars and result of the fit of Eq. (1), blue line. $R^2=0.84$.