  Ions in Hall effect thrusters are often characterized by a low
collisionality. In the presence of acceleration fields and azimuthal electric
field waves, this results in strong deviations from thermodynamic equilibrium,
introducing kinetic effects. This work investigates the application of the
14-moment maximum-entropy model to this problem. This method consists in a set
of 14 PDEs for the density, momentum, pressure tensor components, heat flux
vector and fourth-order moment associated to the particle velocity distribution
function. The model is applied to the study of collisionless ion dynamics in a
Hall thruster-like configuration, and its accuracy is assessed against
different models, including the Vlasov kinetic equation. Three test cases are
considered: a purely axial acceleration problem, the problem of ion-wave
trapping and finally the evolution of ions in the axial-azimuthal plane.
  Most of this work considers ions only, and the coupling with electrons is
removed by prescribing reasonable values of the electric field. This allows us
to obtain a direct comparison among different ion models. However, the
possibility to run self-consistent plasma simulations is also briefly
discussed, considering quasi-neutral or multi-fluid models. The maximum-entropy
system appears to be a robust and accurate option for the considered test
cases. The accuracy is improved over the simpler pressureless gas model (cold
ions) and the Euler equations for gas dynamics, while the computational cost
shows to remain much lower than direct kinetic simulations.
