  The physical properties of the faint and extremely tenuous plasma in the far
outskirts of galaxy clusters, the circumgalactic media of normal galaxies, and
filaments of the cosmic web, remain one of the biggest unknowns in our story of
large-scale structure evolution. Modelling the spectral features due to
emission and absorption from this very diffuse plasma poses a challenge, as
both collisional and photo-ionisation processes must be accounted for. In this
paper, we study the ionisation by photons emitted by the intra-cluster medium
in addition to the photo-ionisation by the cosmic UV/X-ray background on gas in
the vicinity of galaxy clusters. For near massive clusters such as A2029, the
ionisation parameter can no longer describe the ionisation balance uniquely.
The ionisation fractions (in particular of C IV, C V, C VI, N VII, O VI, O VII,
O VIII, Ne VIII, Ne IX, and Fe XVII) obtained by taking into account the
photoionisation by the cosmic background are either an upper or lower limit to
the ionisation fraction calculated as a function of distance from the emission
from the cluster. Using a toy model of a cosmic web filament, we predict how
the cluster illumination changes the column densities for two different
orientations of the line of sight. For lines of sight passing close to the
cluster outskirts, O VI can be suppressed by a factor of up to $4.5$, O VII by
a factor of $2.2$, C V by a factor of $3$, and Ne VIII can be boosted by a
factor of $2$, for low density gas.
