Default initial condition for charged pdf & wall boundary condition does not satisfy Chodura.

[mrhardman]

The default initial condition for the charged pdf, set at this line

moment_kinetics/src/initial_conditions.jl

Line 584 in 7dda1ac

for iz ∈ zrange

(in master), does not appear to satisfy the kinetic Chodura condition calculated in the diagnostic here:

moment_kinetics/src/velocity_moments.jl

Line 705 in 993c88e

function update_chodura_integral_species!(ff,dffdr,ff_dummy,vpa,vperp,z,r,composition,geometry,vz,dens,del_vpa)

This may be an issue for production simulations.

[mrhardman]

@johnomotani is the kinetic Chodura condition satisfied in the initial condition of your simulations?

[johnomotani]

@johnomotani is the kinetic Chodura condition satisfied in the initial condition of your simulations?

In some runs I have now, using my diagnostic, the ratio I compute is starting at about 0.2, and increasing slowly to about 0.9 as the simulation reaches steady state.

Do we expect the Chodura condition to be satisfied by the initial condition anyway? I have the impression it's some sort of self-consistent thing between the distribution function and the parallel electric field, so even if the initial condition did not obey it, the simulation should rearrange itself (assuming everything is correct and well resolved!) to obey it?

[mrhardman]

Having tried varying resolutions in the master branch, I am very surprised that you can get values like 0.2 or 0.9. I find that the ratio (admittedly calculated using different code, but I think I checked that it gives the correct result for the MMS test) asymptotes to 1 from above for increasing resolution. I have not been able to get a value less than 1.

My understanding is that, if the condition is satisfied, a stable boundary layer sheath exists at the wall, permitting the quasineutral assumption at larger distances from the wall (i.e., we can neglect the nabla^2 term in Poisson's equation). If the Chodura condition is not satisfied, our simulations are invalid, and should include the Laplacian in quasineutrality. This statement could be overly harsh, and instead we could state that only the final steady state should obey the Chodura condition.

Either way, I have a problem with my simulations and I would like to do a comparison with yours!

Could you send me an input file which behaves as you say, for the standard DK case?

[johnomotani]

@mrhardman If you check out the (still very much in progress) recycling-fraction branch (https://github.com/mabarnes/moment_kinetics/tree/recycling-fraction), then the input files examples/wall-bc/wall-bc_volumerecycle.toml or examples/wall-bc/wall-bc_no-neutrals.toml should (if I haven't broken something since I ran them) show you what I'm seeing.

wall-bc_volumerecycle.toml should give

and wall-bc_no-neutrals.toml

[mrhardman]

So without neutrals, you do not satisfy Chodura in steady state? My suspicion now is that one can prevent Chodura being satisfied by sourcing ions too close to the wall -- what is your source in the second case without neutrals?

[johnomotani]

The source in the second case is a Gaussian peaked in the centre of the box like exp(-(8*z)^2)

[johnomotani]

So actually the first case has more of a source close to the wall (from ionisation/charge exchange) than the second one.

[johnomotani]

Oh, also those runs I posted plots from have Krook collisions in them. Don't know if that makes a difference to what you're interested in. I have a few PRs to make soon!

[mrhardman]

In principle, if the code captures properly the divergence of Ez as z -> z_wall, none of the other terms should matter, as the dominant physics should just be of acceleration by Ez. Using my new feature of unevenly spaced element boundaries improved matters by bringing the integral closer to 1, but it did not resolve it entirely!