  Experimentalists use particles as tracers in liquid helium. The intrusive
effects of particles on the dynamics of vortices remain poorly understood. We
implement a study of how basic well understood vortex states, such as a
propagating pair of oppositely signed vortices, change in the presence of
particles by using a simple model based on the Magnus force. We focus on the 2D
case, and compare the analytic and semi-analytic model with simulations of the
Gross-Pitaevskii (GP) equation with particles modelled by dynamic external
potentials. The results confirm that the Magnus force model is an effective way
to approximate vortex-particle motion either with closed-form simplified
solutions or with a more accurate numerically solvable ordinary differential
equations (ODEs). Furthermore, we increase the complexity of the vortex states
and show that the suggested semi-analytical model remains robust in capturing
the dynamics observed in the GP simulations.
