A simple illustrative physical model is presented to describe the kinetics of damage and amorphization by swift heavy ions (SHI) in LiNbO3. The model considers that every ion impact generates initially a defective region (halo) and a full amorphous core whose relative size depends on the electronic stopping power. Below a given stopping power threshold only a halo is generated. For increasing fluences the amorphized area grows monotonically via overlapping of a fixed number N of halos. In spite of its simplicity the model, which provides analytical solutions, describes many relevant features of the kinetic behaviour. In particular, it predicts approximate Avrami curves with parameters depending on stopping power in qualitative accordance with experiment that turn into Poisson laws well above the threshold value.