  A novel method for generating GigaGauss solenoidal field in laser-plasma
bubble, using screw-shaped laser pulses, has been recently presented in
arXiv:1604.01259 [physics.plasm-ph]. Such magnetic fields enable fast
synchrotron radiation cooling of the beam emittance of laser-plasma accelerated
leptons. This recent finding opens a novel approach for design of laser-plasma
FELs or colliders, where the acceleration stages are interleaved with
laser-plasma emittance cooling stages. In this concept paper we present an
outline of how a staged plasma-acceleration FEL could look like and discuss
further studies needed to investigate the feasibility of the concept in detail.
