Observation of the Self-Modulation Instability via Time-Resolved Measurements

Self-modulation of an electron beam in a plasma has been observed. The propagation of a long (several plasma wavelengths) electron bunch in an overdense plasma resulted in the production of multiple bunches via the self-modulation instability. Using a combination of a radio-frequency deflector and a dipole spectrometer, the time and energy structure of the self-modulated beam was measured. The longitudinal phase space measurement showed the modulation of a long electron bunch into three bunches with an approximately $200\mathrm{keV}/c$ amplitude momentum modulation. Demonstrating this effect is a breakthrough for proton-driven plasma accelerator schemes aiming to utilize the same physical effect.

Figure 1

Schematic of the experimental setup. After passing through the plasma the electron bunch enters a diagnostics section. The bunch is streaked by a rf deflector vertically and its longitudinal charge distribution can then be observed on a removable $\mathrm{Ce}:\mathrm{YAG}$ scintillator screen. Alternatively, the bunch can be further transported to a dipole spectrometer where the bunch is energy dispersed horizontally. This allows one to observe the longitudinal phase space of the bunch on a second $\mathrm{Ce}:\mathrm{YAG}$ screen.

Figure 2

Measured time-resolved electron bunch—the head of the bunch is on the right side; the color bar indicates measured intensity up to the maximal output value of the observing camera. Examples of bunches streaked with the rf deflector after passing the plasma cell with (a) a pure lithium vapor and (b) 8 cm of plasma with a density of $\sim {10}^{14}{\mathrm{cm}}^{-3}$. Without plasma the longitudinal bunch shape is a flat top, as generated in the accelerator. When the bunch is passing through the plasma it is self-modulated at the plasma period of $\sim 10\mathrm{ps}$, corresponding to a plasma wavelength of $\sim 3\mathrm{mm}$. Two modulation periods are visible.

Figure 3

Measured longitudinal phase space of an electron bunch—the head of the bunch is on the right side; the color bar indicates measured intensity up to the maximal output value of the observing camera. Examples of bunches streaked with the rf deflector and energy dispersed with the dipole after passing through the plasma cell with (a) a pure lithium vapor and (b) 8 cm of plasma with a density of slightly higher than ${10}^{14}{\mathrm{cm}}^{-3}$. Without plasma the longitudinal phase space is nearly linear. When the bunch is passing through the plasma it shows evidence of self-modulation: transverse electric fields in the plasma wake are causing alternate focusing and defocusing, while the corresponding longitudinal electric fields lead to a momentum modulation. Three modulation periods are visible—one more than in Fig. 2 due to the higher plasma density in this case.

Figure 4

Simulated electromagnetic fields along the plasma channel with electron bunch and plasma conditions as in the experiment. Shown are maximum transverse wakefields along the simulation box (solid lines, left axis) and the longitudinal electric field of the first modulation maximum (dashed lines, right axis).