# Introduction

## Assumptions

This is a work-in-progress list of physical assumptions implemented in the numerics of ImpactX.

### Tracking and Lattice Optics

**tracking through lattice optics:**is treated through linear order with respect to the reference particle**velocity spread:**the above linearization implies that, when solving space-charge effects, we assume that the relative spread of velocities of particles in the beam is negligible compared to the velocity of the reference particle

### Space Charge (Poisson Solver)

**electrostatic in the bunch frame:**we assume there are no retardation effects and we solve the Poisson equation in the bunch frame