Propagation of ultrastrong femtosecond laser pulses in PLASMON-X

TL;DR

This paper derives nonlinear equations describing ultrashort laser pulse propagation in plasma for the Plasmon-X device, highlighting conditions where 1-D approximation is valid and discussing effects of different spot sizes on pulse behavior.

Contribution

It presents a derivation of nonlinear equations for ultrashort laser pulses in plasma, including a nonlinear Schrödinger equation with nonlocal nonlinearity, tailored for the Plasmon-X setup.

Findings

1-D approximation valid for large spot sizes with weak nonlinearity.

Nonlocal nonlinear Schrödinger equation describes wake oscillations.

Small spot sizes lead to plasma channeling and local depletion.

Abstract

The derivation is presented of the nonlinear equations that describe the propagation of ultrashort laser pulses in a plasma, in the Plasmon-X device. It is shown that the Plasmon-X scheme used for the electron acceleration uses a sufficiently broad beam ($L_\bot\sim 130\,\,\mu{\rm m}$) that justifies the use of the standard stationary 1-D approximation in the electron hydrodynamic equations, since the pulse width is sufficiently bigger than the pulse length ($\sim 7.5\,\,\mu{\rm m}$). Furthermore, with the laser power of $W\leq 250$ TW and the $130\,\,\mu{\rm m}$ spot size, the dimensionless laser vector potential is sufficiently small $|A_{\bot_0}|^2/{2} = ({W}/{c^2\epsilon_0})({\lambda^2}/{8 \pi^2 c})({4}/{\pi L_\bot^2})({e}/{m_0 c})^2 \sim 0.26$, the nonlinearity is sufficiently weak to allow the power expansion in the nonlinear Poissons's equation. Such approximation yields a nonlinear Schr\" odinger equation with a reactive nonlocal nonlinear term. The nonlocality contains a cosine function under the integral, indicating the oscillating wake. For a smaller spot size that is used for the Thomson scattering, $L_\bot = 10\,\, \mu$m, the length and the width of the pulse are comparable, and it is not possible to use the 1-D approximation in the hydrodynamic equations. With such small spot size, the laser intensity is very large, and most likely some sort of chanelling in the plasma would take place (the plasma gets locally depleted so much that the electromagnetic wave practically propagates in vacuum).