  Multi-GeV-class laser plasma accelerating modules are key components of laser
plasma accelerators, because they can be used as a booster of an upstream
plasma or conventional injector or as modular acceleration sections of a
multi-staged high energy plasma linac. Such a plasma module, operating in the
quasi-linear regime, has been designed for the 5 GeV laser plasma accelerator
stage (LPAS) of the EuPRAXIA project. The laser pulse ($\sim$150 TW, $\sim$ 15
J) is quasi-matched into a plasma channel ($n_{\rm p} = 1.5\times 10^{17}$
cm$^{-3}$, $L\sim$ 30 cm) and the bi-Gaussian electron beam is externally
injected into the wakefield. The beam emittance is preserved through the
acceleration by matching the beam size to the transverse focusing fields. And a
final energy spread of $<$1\% has been achieved by optimizing the beam loading
effect. Several methods have been proposed to reduce the slice energy spread
and are found to be effective. The simulations were conducted with the 3D PIC
code Warp in the Lorentz boosted frame.
