Track length estimator

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.