Demonstration of passive plasma lensing of a laser wakefield accelerated electron bunch

We report on the first demonstration of passive all-optical plasma lensing using a two-stage setup. An intense femtosecond laser accelerates electrons in a laser wakefield accelerator (LWFA) to 100 MeV over millimeter length scales. By adding a second gas target behind the initial LWFA stage we introduce a robust and independently tunable plasma lens. We observe a density dependent reduction of the LWFA electron beam divergence from an initial value of 2.3 mrad, down to 1.4 mrad (rms), when the plasma lens is in operation. Such a plasma lens provides a simple and compact approach for divergence reduction well matched to the mm-scale length of the LWFA accelerator. The focusing forces are provided solely by the plasma and driven by the bunch itself only, making this a highly useful and conceptually new approach to electron beam focusing. Possible applications of this lens are not limited to laser plasma accelerators. Since no active driver is needed the passive plasma lens is also suited for high repetition rate focusing of electron bunches. Its understanding is also required for modeling the evolution of the driving particle bunch in particle driven wake field acceleration.

Figure 1

Photograph of the experimental setup: the laser pulse, incident from the left, drives an LWFA stage in a mixed-species gas cell, and the generated electron beam expands in vacuum according to its divergence. If the second gas jet is turned on, the transmitted diverging laser pulse (${\theta }_{\mathrm{div}}\approx 80\mathrm{mrad}$) preionizes the ${\mathrm{H}}_2$ gas and the trailing electron beam (${\theta }_{\mathrm{div}}\approx 2.5\mathrm{mrad}$) experiences plasma lensing, which reduces the divergence substantially as observed on a scintillation screen (Figs. 2 and 2).

Figure 2

Beam profiles as seen on the scintillation screen: Inset (a) shows the averaged and center aligned beam profile of 227 reference shots with the acceleration stage only. Inset (b) shows the averaged and center aligned beam profile of 175 shots with the focusing stage using an electron density of $1.6\times 10^{19}{\mathrm{cm}}^{-3}$ and a separation of $L_g=8.75\mathrm{mm}$. In both pictures the black ellipse encloses the standard deviation of a 2D gaussian fit function to the beam profile. The black ellipse reduces its area from $16\mu \mathrm{sr}$ (left) to $6\mu \mathrm{sr}$ (right) as the focusing stage is turned on. (c) and (d) show the corresponding data from the epoch3d Simulation: The bunch’s initial divergence is set up to match the experimentally measured divergence of $16\mu \mathrm{sr}$ (c). The encircled solid angle reduces to $7.3\mu \mathrm{sr}$ after propagation through 2.5 mm plasma with a density of $n_p=1\times 10^{19}/{\mathrm{cm}}^3$ with 0.5 mm linear ramps on both sides.

Figure 3

Solid angle and maximum electron flux depending on the density of the focusing plasma: The solid angle (left axis, blue) of the electron beam decreases as the plasma density increases. The gap length was kept constant at $L_g=8.75\mathrm{mm}$ for all measurements. Each point is calculated from an averaged and center-aligned (see text) beam profile over 150 to 250 shots. The reference with the lensing stage turned off ($\mathrm{density}=0$) has been measured at the beginning, middle and end of the scan. The error bars indicate the standard deviation ($\pm 1\sigma$) of these measurements. The error is similar for all measurements. The density measurements were taken using a wavefront sensor, resulting in an error of $\pm 0.5\times 10^{19}/{\mathrm{cm}}^3$. The red curve (right axis) shows the peak electron flux on the scintillation screen.

Figure 4

Single shot data analysis of the plasma lensing effect: Each dot represents a single laser shot without the plasma lens (green) or with the plasma lens in operation (black). The shift of the point clouds is clearly visible. The same data sets are shown in Figs. 2 (green, no plasma lens) and 2 (black, plasma lens density $1.6\times 10^{19}/{\mathrm{cm}}^3$). The red arrows therefore indicate the values obtained from the averaged analysis in Fig. 2. The gap length was constant at $L_g=8.75\mathrm{mm}$ Top: As the average solid angle reduces from $16\mu \mathrm{sr}$ to $6.8\mu \mathrm{sr}$, the charge in the beam’s central region drops to 75%. A linear fit reveals the increase of the beam’s angular fluence from $(96\pm 2)\times 10^3[\mathrm{a}.\mathrm{u}.]$ to $(160\pm 4)\times 10^3[\mathrm{a}.\mathrm{u}.]$ with the lensing stage enabled. The dashed lines show the standard deviation of the fit. Bottom: Together with the reduction of the solid angle an increase in the amplitude of the 2D Gaussian fit by a factor of 1.65 is observed.

Figure 5

The Lorentz force focusing the electron bunch: A central slice of the 3D simulation data is shown along $z=0$ after a propagation of $500\mu \mathrm{m}$ through the plasma. The gray contour lines indicate $1/\sqrt{2}$, $1/2$ and $1/4$ of the maximum bunch density. The electron bunch is moving towards $+x$ direction and experiences a focusing Lorentz force (color scale). Although the strongest fields are present in the tail of the bunch, the first half of it still experiences a significant amount of focusing.

Figure 6

Spectral dependence of the plasma lens: Each of the three spectra is aligned and averaged over 40–50 shots. The spectra show a comparison between the divergence of the electrons without (left) and with plasma lens (middle and right). The plasma lens uses an electron density of $(1.2\pm 0.8)\times 10^{19}{\mathrm{cm}}^{-3}$. Profiles of the high energy part (90–100 MeV) and the low energy part (40–42 MeV) are shown on top and bottom. It is shown that the high energy electrons are focused at 8 mm gap length (blue), whereas the low energetic electrons are focused at 24 mm gap length (red).

Figure 7

Spectral dependence of the lens for three single shots: The plots are equal to Fig. 6, but with only three single shots presented. The same behavior as in Fig. 6 can be observed: The high energy electrons are focused at 8 mm gap length (blue) whereas the low energetic electrons are focused at 24 mm gap length (red). This shows that the effect of plasma lensing can be observed in the single-shot data and the averaged data.

Figure 8

The spectral dependence of the plasma lens measured with five different gap lengths: The color maps show the divergence reduction ($={\theta }_{\mathrm{div}}^{\text{without lens}}/{\theta }_{\mathrm{div}}^{\text{with lens}}$, upper panel) and the relative intensity change on the lanex screen (lower panel). Both measurements are in good agreement, since a divergence reduction is followed by an increase in spectral intensity. The data is obtained by an average over 40–50 shots for each gap length using the same data set as in Fig. 6.