Charm and longitudinal structure functions with the Kharzeev-Levin-Nardi model

We use the Kharzeev-Levin-Nardi model of the low $x$ gluon distributions to fit recent HERA data on charm and longitudinal structure functions. Having checked that this model gives a good description of the data, we use it to predict $F^c_2$ and $F_L$ to be measured in a future electron-ion collider. The results interpolate between those obtained with the de Florian-Sassot and Eskola-Paukkunen-Salgado nuclear gluon distributions. The conclusion of this exercise is that the KLN model, simple as it is, may still be used as an auxiliary tool to make estimates both for heavy ion and electron-ion collisions.