Poisson equation for ions in the gas phase

Hello Freefem community !

I am trying to solve a transport equation of ions in the gas phase between two circular electrode plates. There is a small radioactive source that produces ions in the space, both positives and negatives ions. The drift of + ions is monitored at the cathode (0V) and by varrying the potential on the anode it is possible to extract the ion-ion recombination coefficient alpha.
At high potential near 1 kV there is almost no recombination because the ions only spend a millisecond or so in the space and there is not enough time to recombine. The current of cations is maximum at the cathode (~100 pA). However, at lower potential like 2V for instance the effect of recombination starts to be dominant and the current drops.
The problem I have is that at low potential the space charge is high and the system is not stable anymore due to the coupling beween the ion density and the electrostatic potential and I don’t know how to solve this problem.
Do you have an idea on how I can improve the stability?
Thanks for reading

The source code: