Asymmetry in laser wakefields driven by intense pulses

Abstract

Laser wakefield theories rely on the laser envelope function, which is radially symmetric, and predict zero transverse momentum for the electrons along the propagation axis. Exact description of laser wakefields, beyond the envelope approximation, requires a more general formula for the Lorentz force acting on the electrons. Here we present a fundamental approach to express the transverse momentum of an electron crossing the laser pulse, and we show that an exact analytical formula can be derived for the non-zero transverse momentum of electrons initially lying along the axis of symmetry. The results outlined here shed light on the details of the electron motion inside an intense laser pulse and explain the strong wakefield asymmetry observed in simulations.

Figures (3)

• Figure 1: (a) Comparison of $p_x$ (blue, solution of Eq. (\ref{['eq:motion']})) and $\mathcal{P}$ (red, solution of Eq. (\ref{['eq:dpxcoord']})) for two values of initial electron position $x_0$. The parameters of the laser pulse are: $w_0=12\pi$, $N=2$ and $a_0=3$. (b) Final values of $\mathcal{P}$ and $p_x$ as a function of initial electron position for two CEP values: $\varphi_0=0$ and $\varphi_0=\pi/2$.
• Figure 2: (a) Assymetry parameter ($\Gamma$) for $w_0=24\pi$, $N=2$ and $a_0=3$ calculated with Eq. (\ref{['eq:motion']}). (b) The same is shown, but with a larger phase velocity. (c) The green line correspond to Eq. (\ref{['eq:motion']}), with the same parameters as in (a), where $\varphi_0=\pi/2$. The blue line represents the solution of Eq. (\ref{['eq:dpxcoord']}), with $\phi=0$, and the red dashed line correspond to the analytical solution of Eq. (\ref{['eq:dpxcoordsimpl']}). In (d) the pulse length dependence of the coefficients used in Eq. (\ref{['eq:dpanalit']}) are shown.
• Figure 3: (a) Final momentum of on-axis electrons, given by Eq. (\ref{['eq:dpanalit']}), after crossing the laser pulse for $a_0=9$ and $w_0=40\pi$. The results of PIC simulations with the same parameters, but varying the CEP phase, are shown with the circles. (b) Comparison of numerical (Eq. (\ref{['eq:motion']})) and analytical (Eq. (\ref{['eq:dpanalit']}), dashed lines) results. (c) Transverse electric field measured on axis (full lines) behind the laser pulse in 3D PIC simulation with the parameters presented in the text. The dashed lines show the theoretical prediction, including the variation of the wavelength. (d) Absolute value of the maximum electric field in the laser (full lines) and the variation of the central wavelength (dashed lines) versus propagation distance in the simulations presented in (c).