Hyperbolicity analysis of multimoment plasma models: application to auroral plasma outflows along magnetic field lines

As evidence of large field-aligned ion outflows from the high latitude ionosphere has been accumulated both above the polar cusp and auroral regions, numerous models were developed in the recent years to investigate the transport of plasma along magnetic field lines between the ionosphere and the magnetosphere. The description of such large scale dynamic phenomena usually requires the implementation of fluid type numerical models, although the basic assumptions for such fluid models are not appropriate at high altitudes in the collisionless magnetosphere. One-dimensional modelling was based on multifluid and multimoment fluid models with higher order moments involved to account for the multiple transitions occurring with altitude and particularly, the transition from collision dominated to collisionless plasma. In such models, the plasma dynamics is described by an appropriate set of transport equations involving density number, bulk velocity, temperatures and heat fluxes. The stability of the solutions of linearized systems of such one-dimensional transport equations requires the hyperbolicity condition. This condition leads to a heat flux limitation for the third-order approximation systems (i.e. the systems that solve heat flux equations self consistently). This criterion fails in auroral zones at high altitudes and this could explain some numerical instabilities. The case of multifluid models is also investigated. The hyperbolicity analysis leads in this case to a limitation of the relative velocity. These conditions are discussed from a kinetic point of view. These criteria are applied to polar wind models and lead to an explicit and qualitative limitation of the altitude range for the validity of the models which is compared with the altitude range already reported from phenomenological considerations.