Phase-space structures and the equilibrium plasma ion density in a dipole magnetic field

Charged particles moving in a dipole magnetic field are known to exhibit dynamical chaos [Dragt and Finn, J. Geophys. Res. 81, 2327 (1976) and Jung and Scholz, J. Phys. A 21, 2301 (1988)]. The equilibrium ion velocity distribution functions were recently measured in a low-temperature Ar plasma discharge [McLaughlin et al., Phys. Plasmas 32, 033502 (2025)]. The measured ion density as a function of radius in the equatorial plane was shown to agree well with a Monte Carlo simulation. Here, methods of dynamical systems and transient chaos are used to map families of orbits from nondimensional to laboratory coordinates. Basic thermodynamical assumptions are then made to recover the general ion density profile and other phase-space characteristics. A charged particle beam is simulated to demonstrate how an experimenter can populate an area of the near-field region with chaotically scattered orbits.