  We report here the results of a one week long investigation into the
conceptual design of an X-ray source based on a compact ring with on-orbit and
on-energy laser-plasma accelerator. We performed these studies during the June
2016 USPAS class "Physics of Accelerators, Lasers, and Plasma..." applying the
art of inventiveness TRIZ. We describe three versions of the light source with
the constraints of the electron beam with energy $1\,\rm{GeV}$ or $3\,\rm{GeV}$
and a magnetic lattice design being normal conducting (only for the
$1\,\rm{GeV}$ beam) or superconducting (for either beam). The electron beam
recirculates in the ring, to increase the effective photon flux. We describe
the design choices, present relevant parameters, and describe insights into
such machines.
