Experimental Observation of Proton Bunch Modulation in a Plasma at Varying Plasma Densities

We give direct experimental evidence for the observation of the full transverse self-modulation of a long, relativistic proton bunch propagating through a dense plasma. The bunch exits the plasma with a periodic density modulation resulting from radial wakefield effects. We show that the modulation is seeded by a relativistic ionization front created using an intense laser pulse copropagating with the proton bunch. The modulation extends over the length of the proton bunch following the seed point. By varying the plasma density over one order of magnitude, we show that the modulation frequency scales with the expected dependence on the plasma density, i.e., it is equal to the plasma frequency, as expected from theory.

Figure 1

The protons together with the laser pulse (red marker in the depicted proton bunches) enter the plasma. The first half of the bunch propagates in neutral Rubidium while the second half propagates in plasma. After the plasma, the laser hits a beam dump and the modulated bunch hits a foil where optical transition radiation (OTR) is created. The light is imaged onto the slit of a streak camera and is streaked to obtain a time resolved image. The optical filters limit the bandwidth of the light to ensure time resolution.

Figure 2

(a) Streak camera image of the proton bunch without plasma. The bunch is on the right hand side of the image and the short laser pulse on the left hand side (see text). The green temporal profile is fitted with a Gaussian function (dotted black line, ${\sigma }_t=437\mathrm{ps}$, $1.5\times {10}^{11}\mathrm{protons}$). The laser timing is marked by the red line ($t=0$). (b) Image with plasma ($n_{\mathrm{Rb}}=2.092\times {10}^{14}{\mathrm{cm}}^{-3}$, $3\times {10}^{11}\mathrm{protons}$) and ionizing laser pulse (blocked, not visible) placed as in (a). The effect of the plasma ($t>0$) is visible in the image and on the bunch profile (green line). (c) Image as in (b), but with $n_{\mathrm{Rb}}=2.558\times {10}^{14}{\mathrm{cm}}^{-3}$ and the ionizing laser pulse in the front of the bunch at $-390\mathrm{ps}$. The SSM effect and streak camera setting are such that the bunch charge behind the laser pulse is not visible. The spatial dimension displayed is that at the OTR wafer.

Figure 3

Streak camera images on the fast (73 ps) timescale (a) at low ($n_{\mathrm{Rb}}=2.457\times {10}^{14}{\mathrm{cm}}^{-3}$) and (c) at high ($n_{\mathrm{Rb}}=6.994\times {10}^{14}{\mathrm{cm}}^{-3}$) plasma densities. Profiles obtained by summing the images along the spatial axis from $-0.4$ to 0.6 mm are displayed on the left-hand side of each image. The profile of image (a) shows the defocusing effect of SSM starting at the laser pulse time ($\sim 10\mathrm{ps}$). Image (c) is obtained $\sim 10\mathrm{ps}$ behind the ionizing laser pulse that is placed in the middle of the bunch as in Fig. 2. It is also obtained with a narrower band-pass filter (25 nm) than for image (a) and (e) (50 nm) to reduce the intensity of the light and decrease time resolution limitations originating from a broad OTR spectrum reaching the streak photocathode [26]. Figures (b) and (d) show the DFT power spectrum for the two profiles (black diamonds, no padding) as well as for background images (orange lines). The green lines depict the interpolated power spectrum (with padding). The blue lines show a noise threshold used for automatically detecting frequencies. Image (e) shows a low density case ($n_{\mathrm{Rb}}=2.190\times {10}^{14}{\mathrm{cm}}^{-3}$) where the full train of microbunches is shown. The Rubidium (and thus plasma) density for image (e) has an upwards density gradient of $3.4\%/10\mathrm{m}$.

Figure 4

Measured mean modulation frequencies (red dots, with standard deviation of the measured frequencies) as a function of the Rb vapor density $n_{\mathrm{Rb}}$ on a log-log plot. The orange dotted line corresponds to the expected $\alpha =0.5$, $\beta =1$ dependency of the modulation frequency. The mode values of the posterior distribution are plotted as the blue line.