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 photoionization processes must be accounted for. In this paper, we study the ionization by photons emitted by the intracluster medium in addition to the photoionization by the cosmic ultraviolet/X-ray background on gas in the vicinity of galaxy clusters. For near-massive clusters such as A2029, the ionization parameter can no longer describe the ionization balance uniquely. The ionization 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 photoionization by the cosmic background are either an upper or lower limit to the ionization 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.
