Compact LWFA-Based Extreme Ultraviolet Free Electron Laser: design constraints

Combination of advanced high power laser technology, new acceleration methods and achievements in undulator development opens a way to build compact, high brilliance Free Electron Laser (FEL) driven by a laser wakefield accelerator (LWFA). Here we present a study outlining main requirements on the LWFA based Extreme Ultra Violet (EUV) FEL setup with the aim to reach saturation of photon pulse energy in a single unit commercially available undulator with the deflection parameter $K_0$ in a range of (1{\div}1.5). A dedicated electron beam transport which allows to control the electron beam slice parameters, including collective effects, required by the self-amplified spontaneous emission (SASE) FEL regime is proposed. Finally, a set of coherent photon radiation parameters achievable in the undulator section utilizing best experimentally demonstrated electron beam parameters are analyzed. As a result we demonstrate that the ultra-short (few fs level) pulse of the photon radiation with the wavelength in the EUV range can be obtained with the peak brilliance of $\sim$2$\times$10$^{30}$ photons/s/mm$^2$/mrad$^2$/0.1%bw if the driver laser operates at the repetition rate of 25 Hz.