With the track length estimator, one computes the quantities of interest along the free streaming trajectories of the test particles (straight lines in the case of neutral particles). A trivial example is the estimate of the neutral density which is given by

where *V* is the volume of a zone, *w* is the ``weight'' of a trajectory
expressed as particles per second, *l* is the length of a trajectory
segment and *v* is the speed of the particle. (Note that the summand is
proportional to the time a particle spends in a zone.)

A more complicated example is the momentum exchange between neutral and the background ions due to charge exchange. In this case the kernel of the summation would include a factor giving the mean momentum loss rate per neutral particle. This can be computed directly from the collision cross section by a suitable integration over the ion distribution function.

The key points are:

- the integral can be carried out exactly (assuming that exact cross section data is available)
- this estimate includes contributions in zones where the collision rate may be small and no ``real'' charge exchange collisions are included by the Monte Carlo code (because it only simulates a relatively small number of trajectories).

The way geometry is handled in Degas 2 allows track length estimators to be computed easily. (This is one of the areas where Degas 2 differs from the earlier Degas code.) Since the only ``cost'' is the additional table lookup on, e.g., the momentum loss rate, this leads to scores with reduced error for a given amount of CPU time. The neutral gas transport code EIRENE employs the same technique.

Fri Mar 29 16:26:47 EST 1996