# Radial doses around energetic ion tracks and the onset of shock waves on the nanoscale

## TL;DR

This study investigates how realistic radial dose distributions from energetic ions influence the formation and strength of shock waves in tissue, using molecular dynamics simulations to compare different energy deposition models.

## Contribution

It introduces a method to incorporate detailed radial dose profiles into shock wave simulations, improving understanding of ion-induced damage at the nanoscale.

## Key findings

- Radial dose distributions significantly affect shock wave strength.
- Realistic energy deposition models produce different shock dynamics than uniform models.
- Shock waves are more intense near the Bragg peak region.

## Abstract

Energetic ions lose their energy in tissue mainly by ionising its molecules. This produces secondary electrons which transport this energy radially away from the ion path. The ranges of most of these electrons do not exceed a few nanometres, therefore large energy densities (radial doses) are produced within a narrow region around the ion trajectory. Large energy density gradients correspond to large pressure gradients and this brings about shock waves propagating away from the ion path. Previous works have studied these waves by molecular dynamics simulations investigating their damaging effects on DNA molecules. However, these simulations where performed assuming that all energy lost by ions is deposited uniformly in thin cylinders around their path. In the present work the radial dose distributions, calculated by solving the diffusion equation for the low energy electrons and complemented with a semi-empirical inclusion of more energetic $\delta$-electrons, are used to set up initial conditions for the shock wave simulation. The effect of these energy distributions vs. stepwise energy distributions in tracks on the strength of shock waves induced by carbon ions both in the Bragg peak region and out of it is studied by molecular dynamics simulations.