Compton recoil effects in staging of laser wakefield accelerators

Laser plasma accelerators capable of generating $>10\mathrm{GeV}$ electron beams may require plasma mirrors to remove undepleted laser energy at the end of each accelerator stage. Near the plasma mirror surface, the electron bunch can interact with the reflected light, resulting in inverse Compton scattering. For realistic conditions, we show that a significant fraction of electrons emit one or more photons, increasing the energy spread of the electron bunch. We provide an analytical expression for calculating this effect, and use it to estimate the minimum drift space required before the plasma mirror to meet given energy spread specifications. Mitigation strategies, necessary to achieve sub-percent energy spread in multi-GeV laser wakefield electron sources, are proposed and explored.

Figure 1

Schematic of the interaction of an LWFA electron bunch (blue) with the laser pulse (red) reflected from a thin foil (gray): (a) Electron beam trails laser pulse propagating in the positive $x$ direction. (b) Laser pulse is reflected from foil and interacts with electron beam. (c) Electron beam passes through foil and is separated from the laser field.

Figure 2

Illustrations of the ICS geometry in the lab- and electron rest-frames. With the assumptions $\gamma \gg 1$ and $\theta \gg 1/\gamma$, relativistic beaming means that we can define the polar scattering angle ${\varphi }^{\prime }$ relative to the axis of the Lorentz boost.

Figure 3

Plot of (a) total cross section and (b) average photon energy calculated using [28] for the given electron energies. The approximation used in the simplified model is plotted as the red dashed line for comparison.

Figure 4

(a) Electron beam spectrum after 90° collision with a Gaussian laser pulse from Monte Carlo simulations with differing values of $a_0$. The initial electron beam had a mean energy of 50 GeV with ${\overline{\sigma }}_{\gamma 0}=1\%$. The resultant electron beam energy spread was calculated from the results of the Monte Carlo simulation (blue) and the analytical model (red). (b) Plots of the final electron spectrum for selected values of $a_0$.

Figure 5

Relative energy spread increase due to ICS at 90° for varying $a_0$ and electron energy $\gamma m_e{c}^2$. The Gaussian laser pulse had a wavelength of 800 nm, $\tau =50\mathrm{fs}$ and infinite transverse extent. The red isolines give the combination of electron energy and $a_0$ which results in the given percentage increase in energy spread.

Figure 6

Interaction geometry of electron beam (purple) trailing a laser pulse (blue). The laser pulse after reflection (red) from the planar surface interacts with the electron bunch.

Figure 7

Relative energy spread increase due to ICS with the drive laser of a “bubble” regime LWFA removed by a 45° plasma mirror. The laser is allowed to freely diffract from the guided value of $a_0=5$ at $z=0$. The required drift space to achieve a given percentage increase in energy spread as functions of electron energy are overlaid as red lines.

Figure 8

Relative increase in energy spread per stage due to ICS with the drive laser removed by a 45° plasma mirror. The $\lambda =1\mu \mathrm{m}$ laser is assumed to be externally guided in each stage with a matched spot size of ${\sigma }_x=70\mu \mathrm{m}$ and $a_0=1.5$. Isolines of 1% and 2% relative energy spread increase per stage are marked alongside the required value (0.45%) to achieve a final energy spread of 1% at 50 GeV.

Figure 9

Conceptual drawing for mitigating ICS energy spread increase through shaping of the reflecting surface. By deflecting as much energy as possible out of the path of the electron beam, it may be possible to reduce the collision overlap.

Figure 10

Relative energy spread increase due to ICS at the output of the final stage of a staged 50 GeV LWFA (see Sec. 5b) using a shaped profile reflector. The corner of the profile is $\mathrm{\Delta }x$ from the electron beam axis at a drift distance of $z$. The $\lambda =1\mu \mathrm{m}$, $a_0=1.5$ laser pulse had a transverse size ${\sigma }_x(0)=70\mu \mathrm{m}$ at the exit of a plasma of density ${10}^{17}{\mathrm{cm}}^{-3}$.

Figure 11

Energy spread increase as a function of reflector angle and drift distance from the exit of a 5 GeV accelerator operating in the highly nonlinear regime with $a_0=5$.

Figure 12

Relative increase in energy spread per stage due to ICS with the drive laser when accelerating in the 3rd plasma period. The $\lambda =1\mu \mathrm{m}$ laser is assumed to be externally guided in each stage with ${\sigma }_x=70\mu \mathrm{m}$ and $a_0=1.5$. Contours of 1% and 2% relative energy spread increase per stage are marked alongside the required values (0.45% and 0.04%) to achieve a final energy spread of 1% and 0.1% at 50 GeV.