  Since a few breakthroughs in the fundamental understanding of the effects of
swift heavy ions (SHI) decelerating in the electronic stopping regime in the
matter have been achieved in the last decade, it motivated us to review the
state-of-the-art approaches in the modeling of SHI effects. The SHI track
kinetics occurs via several well-separated stages: from attoseconds in
ion-impact ionization depositing energy in a target, to femtoseconds of
electron transport and hole cascades, to picoseconds of lattice excitation and
response, to nanoseconds of atomic relaxation, and even longer macroscopic
reaction. Each stage requires its own approaches for quantitative description.
We discuss that understanding the links between the stages makes it possible to
describe the entire track kinetics within a multiscale model without fitting
procedures. The review focuses on the underlying physical mechanisms of each
process, the dominant effects they produce, and the limitations of the existing
approaches as well as various numerical techniques implementing these models.
It provides an overview of ab-initio-based modeling of the evolution of the
electronic properties; Monte Carlo simulations of nonequilibrium electronic
transport; molecular dynamics modeling of atomic reaction on the surface and in
the bulk; kinetic Mote Carlo of atomic defect kinetics; finite-difference
methods of tracks interaction with chemical solvents describing etching
kinetics. We outline the modern methods that couple these approaches into
multiscale multidisciplinary models and point to their bottlenecks, strengths,
and weaknesses. The analysis is accompanied by examples of important results
improving the understanding of track formation in various materials.
Summarizing the most recent advances in the field of the track formation
process, the review delivers a comprehensive picture and detailed understanding
of the phenomena.

Materials Science;Mesoscale and Nanoscale Physics