charge collecting / induced current

[nbassler]

Currently iontracks counts the carge reaching the electrodes. However, a current is already induced when charges move through the ionization chamber.

Possibly a more exact solution can be obtained if this is considered.

where I(t) is the current in the ionization chamber due moving the charge carriers N as a function of time t.

Let n(t) be the number of charge carriers per unit volume, so in principle that would N(t) / V, where V is the volume of the ionization chamber.

A is the area of the ionization chamber pi*r² electrodes.

v is the drift velocity of the charge carriers N. (Possibly constant as a function of time t, neglegting space charge effects?)

q is the charge per charge carrier in Coulomb.

So, the total accumulated charge Q(t) in the electrometer is rather:

This value will probably be slightly higher than what is collected at the electrodes, since charge carriers lost due to recombination may still contribute to a signal to the electrometer before they recombined.

[nbassler]

As a sanity test of your code, you could propagate all initial charge carriers n(t=0) without any recombination. The Q(t->infinty) integral should correspond to what was collected at the electrodes, equal to what was initally deposited at t=0, Q(t=0) = N(t=0) * q

[nbassler]

Apparently one should not elimiate the carges at the electrodes, however then Q(t->infinity) becomes divergent. Integration should be stopped when the last charge has left the I-chamber. Maybe n(t) could be split up into two components. if only counting n(t)_ionchamber, then it should be relative to the no-recombination case, where n(t)_ionchamber is exactly half of n(t)_total.

Still assuming a constant charge carrier velocity v(t).