COMPARISON OF GENERALIZED TRANSPORT AND MONTE-CARLO MODELS OF THE ESCAPE OF A MINOR SPECIES

In a wide variety of space physics problems (e.g. polar wind, solar wi nd), outflowing species pass through two different regions: (1) a coll ision-dominated region, in which hydrodynamic transport equations can be applied, and (2) a collisionless region. where kinetic models are a pplicable. These two regions are separated by a transition layer where more rigorous mathematical approaches should be used. One such approa ch is the Monte-Carlo method. The Monte-Carlo technique uses pseudo-ra ndom numbers to simulate the diffusion of a given species under the in fluence of gravitational and electromagnetic forces and interparticle collisions. A second possible approach is to use generalized transport equations. The 16-moment set of transport equations, considered here, is obtained by taking moments of Boltzmann's equation, assuming that the particle distribution function is an expansion about a bi-Maxwelli an with correction terms proportional to the stress and the parallel a nd perpendicular beat flows. The purpose of this study is not to provi de a new or better description of a particular flow in space. It is, r ather, to compare the Monte-Carlo and 16-moment generalized transport approaches for conditions corresponding to the transition from collisi on-dominated to collisionless flow and to draw conclusions about these two methods based on the results of the comparison. The 16-moment and Monte-Carlo approaches are compared for the case of a minor species d iffusing through a static background. First, the problem is cast in a form which makes the description independent of the way in which the b ackground density varies with distance. For this transformed problem, the 16-moment and Monte-Carlo models show close agreement. Then, the t ransformed problem is 'mapped' to a particular case that approximates conditions existing in the Earth's upper atmosphere. The general agree ment between the Monte-Carlo and 16-moment model solutions for the map ped problem is evidence that the 16-moment formalism is capable of suc cessfully describing transitions from collision-dominated to collision less flow.