Plasma Sheath Lower than Expected

[gregstath99]

Hi

I'm trying to run a simulation where I observe the formation and stabilisation of a Debye plasma sheath. I am using the electrostatic solver and I have set the x and y boundaries to be periodic but the z boundaries to be Dirichlet such that they model 2 perfectly conducting plates. This simulation is being done as a validation that my code works so there is a specific sheath potential I expect to observe. At first I observe this potential but then after some time the sheath potential drastically drops. For context this is a proton/electron plasma. What I have noticed is when looking at the ion and electron densities across the domain (zmin to zmax) what happens is after some time the charge densities perfectly balance out but for a sheath to form and be sustained there needs to be a charge imbalance at both of the z ends where the proton density is higher than the electron density and then the rest of the plasma is quasineutral. This would lead to the sheath being much lower than expected but I'm trying to figure out why the simulation behaves like this and how to change it. My first thought is that I need to use a non linear electrostatic solver but it could also be something related to the boundary conditions. Has this issue occured before and are there any potential suggestions?

Thank You