  We present the results of a theoretical study investigating the effects of
photoionization and heating by X-rays on discs around low-mass stars. In
particular we address the question of whether or not X-rays can drive a disc
wind. First, we construct a 1-dimensional ``quasi-hydrostatic'' model, which
solves for the vertical structure introduced by X-ray heating. We consider
uniform X-ray illumination of the disc, but the X-ray fluxes required to heat
the disc significantly are much greater than those seen by recent observations.
When the model is extended to consider heating from a central X-ray source we
find that the 1-dimensional model is only valid very close to the star. We
extend our analysis to consider a simple 2-dimensional model, treating the disc
as a two-layered structure and solving for its density profile
self-consistently. For T Tauri stars we are able to set a crude upper limit on
the mass-loss rate that can be driven by X-ray photoevaporation, with a value
of ~10^-13 g/cm^2/s. Our model is designed to maximise this value, and most
likely over-estimates it significantly. However we still find a mass-loss rate
which is less than that found in studies of ultraviolet photoevaporation. We
conclude that in the presence of a significant UV field, X-ray driven disc
winds are unlikely to play a significant role in the evolution of discs around
low-mass stars.
