Laser and electron deflection from transverse asymmetries in laser-plasma accelerators

We report on the deflection of laser pulses and accelerated electrons in a laser-plasma accelerator (LPA) by the effects of laser pulse front tilt and transverse density gradients. Asymmetry in the plasma index of refraction leads to laser steering, which can be due to a density gradient or spatiotemporal coupling of the laser pulse. The transverse forces from the skewed plasma wave can also lead to electron deflection relative to the laser. Quantitative models are proposed for both the laser and electron steering, which are confirmed by particle-in-cell simulations. Experiments with the BELLA Petawatt Laser are presented which show controllable 0.1–1 mrad laser and electron beam deflection from laser pulse front tilt. This has potential applications for electron beam pointing control, which is of paramount importance for LPA applications.

Figure 1

Illustration of parameters relevant for this study. Pulse front tilt (PFT) from temporal chirp, spatial chirp, and angular dispersion is given by Eq. (4). The dashed line shows the propagation axis along which the laser pulse propagates to the right. Colors indicate different spectral components.

Figure 2

Laser-induced gradient of refractive index in a 2D LPA simulation with a 60 fs laser pulse propagating along $z$ with $a_0=0.01$ focused to a $w_0=50\mu \mathrm{m}$ waist in a uniform plasma with initial density ${10}^{16}{\mathrm{cm}}^{-3}$ (${\lambda }_p=330\mu \mathrm{m}$). PFT is due to ${\zeta }_0=1\mathrm{mm}$ fs and ${\phi }_0^{\left(2\right)}=-500{\text{fs}}^2$ at focus ($\psi =-46$ mrad). The black solid-line ellipse is an isocontour of laser intensity where the intensity is half of the peak intensity.

Figure 3

Laser steering rate from 2D PIC simulations with warp (blue crosses) and theory (red line) as a function of main physical parameters. Unless specified otherwise, nominal parameters are as follows: the background plasma density is $n_0=1\times {10}^{18}{\mathrm{cm}}^{-3}$, the laser normalized amplitude is $a_0=0.5$, the waist is $w_0=150\mu \mathrm{m}$ so that the pulse remains roughly collimated during the 5 mm propagation ($z_R\simeq 90\mathrm{mm}$), and PFT around focus is introduced with $\beta =5$ as at focus (i.e., in the far field) with $\lambda =800\mathrm{nm}$. The pulse duration is ${\tau }_0=30$ fs without PFT. The steering rate $\langle d{\theta }_e/dz\rangle$ is obtained by averaging $d^2{x}_c/\left(c^{2}d{t}^2\right)$ over the 5 mm propagation where $x_c$ is the transverse position of the laser pulse centroid. Subplots show the steering rate as a function of the following parameters: (a) PFT angle, (b) laser field amplitude, (c) pulse duration (for this scan, the parameters were slightly different, with $a_0=0.8$ and $n_0=2\times {10}^{17}{\mathrm{cm}}^{-3}$), and (d) plasma density.

Figure 4

(a) Transverse electric field $E_x$ for a $y$-polarized Gaussian laser pulse with $a_0=0.01$, $w_0=50\mu \mathrm{m}$, ${\tau }_0=60\mathrm{fs}$, and focused at $z=100\mu \mathrm{m}$ . The laser has no PFT. The plasma density is $n_e={10}^{17}{\text{cm}}^{-3}$ with a transverse linear gradient with characteristic length $L_t=1\mathrm{mm}$. The 2D $x\text{−}z$ simulation box is $300\mu \mathrm{m}\times 300\mu \mathrm{m}$ with $256\times 4096$ grid points. The simulation was performed with the PIC code warpx [31] in a Lorentz boosted frame [30]. Black ellipse: isocontour of the laser pulse envelope. Red line: $E_x=0$ from the PIC simulation. Black dashed line: model for $E_x=0$. White lines: isocontours of the pseudopotential $\mathrm{\Psi }$. (b) Same quantities in the presence of PFT due to ${\phi }_0^{\left(2\right)}=-500{\text{fs}}^2$ and ${\zeta }_0=1\mathrm{mm}$ fs, with no transverse density gradient. Note that in (b) the line where $E_x=0$ (black dashed line) is the same in each bucket, whereas in (a) the angle of the line increases with subsequent buckets behind the laser pulse.

Figure 5

The BELLA experimental setup for these experiments. Accelerated electrons were separated from the postinteraction laser pulse by optics with $\pm 1.2$ mrad clearance. The first optic after the interaction (wedge with hole) was imaged to determine laser deflection. An imaging phosphor was used to determine electron deflection.

Figure 6

Plots of electron charge distribution (normalized to unity) measured by the insertable phosphor. The laser group delay dispersion (shown above each plot) was varied with fixed near field $\beta =9.7$ zs, resulting in electron deflection due to pulse front tilt. The radius of the circle is 1.2 mrad, set by the hole in the upstream laser optics. The electron beams maintain a consistently elliptical shape, which allows the use of contour fitting for electron pointing determination [provided less than 50% of the charge (ellipse) area is clipped].

Figure 7

Evolution of the PFT of a laser pulse along propagation in vacuum (black dashed line) and in a uniform plasma (red solid line). The plasma density is $n_0={10}^{18}{\text{cm}}^{-3}$, and the Gaussian laser pulse is focused at $z=10\text{mm}$ with $a_0=3$, $w_0=35\mu \mathrm{m}$ and duration ${\tau }_0=40\text{fs}$. PFT is due to ${\zeta }_0=0.7\mathrm{mm}$ fs at focus with ${\phi }_0^{\left(2\right)}={\beta }_0=0$ [see Eq. (4)]. These 3D simulations were performed with warpx in a boosted frame with ${\gamma }_{\mathrm{boost}}=15$.

Figure 8

Experimental results and comparison with theory. (a) Final laser angle in the experiment as a function of group delay dispersion ${\phi }^{\left(2\right)}$ for several values of near-field angular dispersion $\beta$. (b) Laser deflection calculated from the model for the same parameters as the experiment. The nonzero ${\phi }^{\left(2\right)}$ crossing point and deflection amplitude agree between experiment and theory.

Figure 9

Measured electron pointing as a function of ${\phi }^{\left(2\right)}$ for several values of $\beta$. The electron beam direction differs from the laser in Fig. 8, indicating a distinct mechanism is deflecting the electrons.

Figure 10

The effect of laser analysis threshold on laser pointing determination is plotted for $\beta =$ 20, 4.9, and $-9.7$ zs.