Speaker
Description
We propose and test a multi-step preliminary analytical procedure that tailors the initial density $\widetilde{n_0}$ of a cold diluted collisionless plasma to a very short and intense plane-wave laser pulse travelling in the $z$ direction, so as to maximize the early laser wakefield acceleration (LWFA) of bunches of plasma electrons self-injected in the plasma wave (PW) by the first wave-breaking (WB) at the density down-ramp. The procedure partially inverts the determination of the motion of the plasma electrons for a given pulse and (for simplicity, slowly varying) $\widetilde{n_0}(Z)$: the motion of every infinitesimal layer of electrons having coordinate $z\!=\!Z\!>\!0$ for $t\!\le\!0$ is determined using a fully relativistic multi-stream plane model (encompassing the Lorentz-Maxwell equations) that is valid as long as the pulse depletion can be negleted; up to WB, its equations reduce to a family (parametrized by $Z$) of decoupled pairs of Hamilton equations for a 1-dimensional system where $\xi=ct\!-\!z$ replaces time $t$ as the independent variable. We apply the procedure to a Gaussian laser pulse with $l_{fwhm}=10.5\lambda$ and $a_0=2$; using the latter and two associated $\widetilde{n_0}(Z)$ as inputs, we then determine the detailed plasma dynamics by FB-PIC simulations, confirming the predicted maximal acceleration in the early LWFA stages.
