Ionization-Induced Electron Trapping in Ultrarelativistic Plasma Wakes

The onset of trapping of electrons born inside a highly relativistic, 3D beam-driven plasma wake is investigated. Trapping occurs in the transition regions of a Li plasma confined by He gas. Li plasma electrons support the wake, and higher ionization potential He atoms are ionized as the beam is focused by Li ions and can be trapped. As the wake amplitude is increased, the onset of trapping is observed. Some electrons gain up to 7.6 GeV in a 30.5 cm plasma. The experimentally inferred trapping threshold is at a wake amplitude of $36\mathrm{GV}/\mathrm{m}$, in good agreement with an analytical model and PIC simulations.

Figure 1

(a) Schematic of the experimental setup. (b) Measured longitudinal density of Li vapor (red circles) and inferred He gas density (blue circles) in the heat-pipe oven for $n_0=1.6\times {10}^{17}{\mathrm{cm}}^{-3}$. The gray curve is the calculated maximum radial field of the bunch as it is focused and propagates along the plasma. The multiple peaks are due to the periodic oscillations of the beam’s transverse envelope. The red, blue, magenta, and black lines are the field ionization thresholds for Li, He, ${\mathrm{He}}^{+}$, and ${\mathrm{Li}}^{+}$, respectively.

Figure 2

(a) Number of electrons measured after the plasma and (b) relative amount of visible continuum light emitted by these particles versus the average beam energy loss. Note, the charge fluctuations below threshold on (a) are also present in the incoming charge as measured before the plasma. The plasma density is $1.6\times {10}^{17}{\mathrm{cm}}^{-3}$ [corresponding to the plasma density profile of Fig. 1b].

Figure 3

2D OSIRIS simulation results using the Li vapor and He gas profiles and density of Fig. 1b. The left panels correspond to Li and the right to He electrons. Figures (a) and (b) are real space densities ($r\mathrm{\text{−}}z$) at $z=11.3\mathrm{cm}$ [Fig. 1b] and (c) and (d) are the corresponding phase space densities ($p_z\mathrm{\text{−}}z$) at $z=11.3\mathrm{cm}$ and $z=22\mathrm{cm}$, respectively. The line plot in (c) is the on-axis wakefield $E_z$. The beam [black line in (a)] has $1.88\times {10}^{10}$ electrons, a Gaussian transverse profile with ${\sigma }_r=10\mu \mathrm{m}$, and a longitudinal profile with FWHM $\approx 65\mu \mathrm{m}$. The simulation was performed on a moving $500\times 600$ grid ($\Delta z\times \Delta r$, $1\mu \mathrm{m}\times 0.5\mu \mathrm{m}$) with 25 beam particles/cell and 1 of each gas atoms/cell. Simulations with higher spatial resolution and more particles/cell gave similar results.

Figure 4

(a) On-axis wakefield (continuous red line), $E_z$, the same as in Fig. 3c and fit to the linear part of $E_z$ (black dashed line) between ${\xi }_{\min }$ and ${\xi }_{\max }$. (b) Wake potential $\Psi$. (c) Number of trapped He electrons (circles) as a function of the peak accelerating field from short simulations with $n_0=1.6\times {10}^{17}{\mathrm{cm}}^{-3}$, and a number of electrons increasing from 0.4 to 1 times $1.8\times {10}^{10}{e}^{-}$. The dashed vertical lines show the trapping threshold calculated from Eq. (3). Circles and lines of the same color correspond to the same simulation. The same current profile as in Fig. 3 has been used but ${\sigma }_r=2.4\mu \mathrm{m}$.