In order to get the most realistic performance possible out of the FGT Slow Simulator, all important physical effects have to be incorporated. I did some digging in the literature to get information on two topics,

1. diffusion of electrons
2. range of produced delta electrons

Diffusion of Electrons

In general, the diffusion of electrons transversely to the drift direction leads to a widening of the charge cloud that gets recorded on the readout strips. This effect is extremely crucial for us so that we can get good results with a reasonable number of strips (spatial resolution quite a bit better than pitch/Sqrt(12)). Since diffusion is a statistical process (electrons scattering of gas atoms), the change of the center of gravity of the charge cloud, and thus the deterioration of the spatial resolution, depends on the number of electrons involved, and goes as 1/Sqrt(n). So diffusion only negatively affects the spatial resolution as long as only a small number of electrons is involved. In the case of the FGT, this is the case in the drift gap. After the first amplification stage (and much more so after subsequent amplification stages), we are dealing with thousands of electrons, and the error introduced by diffusion should be negligible. That said, here are some numbers to get a ballpark estimate:

For our electric fields the transverse diffusion is ~250 um (RMS) for one cm of drift (taken from NIM A438, 376 (1999)). The drift gap of the FGT is 3 mm thick, which means in that space the diffusion should be roughly 137 um (250 um * Sqrt(3) / Sqrt(10)). Now we have typically something like 30 e- produced in the drift gap, so the error on spatial resolution would be 137 um /Sqrt(30) = 25 um. Of course this is an overestimate, since I assumed above that all electrons drift the full 3 mm of the drift gap, which is not true. Anyway, depending on how much CPU time we want to invest there are a couple of ways to implement this in the slow simulator...

Range of Delta Electrons

The production of highly energetic electrons (so-called delta electrons) will reduce the spatial resolution by shifting a part of the primary ionization to one side of the track. These electrons typically get emitted transversely to the through going particle. Their practical range depends on their initial energy, the precise functional form of this dependence is not quite clear from the literature, especially in the most relevant region of energies below a few keV.

Taken from PR 170, 391 (1968), I get a mostly linear dependence of the practical range as a function of energy, which for the case of Ar translates into

r = 3.2 mm * E/keV (1 - 0.98/(1+ 3.12*10^-3 *E/keV))

That would mean ~70 um for a 1 keV electron.

On the other hand, taken from F. Sauli, CERN 77-09, for Ar

r = 4260 mm * (E/MeV)^1.72

That would mean ~29.5 um for 1 keV. The difference between those two formulas gets much bigger at lower energies, since one is linear, the other is exponential. I don't know which one to trust more, the linear one certainly would be a worst-case estimate for us.

This is an effect that could be included in the simulator for primary produced electrons above 100 eV or so. Those guys are already quite rare, so this should not be a serious CPU eater.