Simulating the child-langmuir law

[JameyH]

Hello, I am a new to PIC but after spending a couple weeks looking around the different options I was impressed by warpx. I further was encouraged to find active discussions about it happening here.

I am interested in simulating a parallel plate diode and comparing my results to Child's Law. PIC is quite daunting and I was hoping to layout my general strategy for using warpx and seeing if it made sense to others.

• Start with a 2D sim

• Take my cathode surface to be thermionic emitter and then calculating current coming off of it by using Richardson's Law to calculate how many particles to inject each time step by calling picmi.UniformFluxDistribution

• Using picmi.ParticleBoundaryScrapingDiagnostic to keep track of how many macroparticles made it through the gap. Hopefully these can be used to keep track of the average current flowing through the diode.

The next step will be simulate some experimental tricks to increase the current going through my diode.

• adding some Ar+ ions to cancel out some of the space charge, thereby increasing the current density. This Seems doable by spawning in a background amount ions. Maybe later I can be more realistic and assume a low density fluid of Argon neutrals that are sometimes ionized by the electrons and model this using picmi.MCCCollision

• adding in positively charge grids in the gap between the diodes to further reduce the space charge seen by the electrons leaving the cathode surface. This could likely be done by using something like picmi.EmbeddedBoundary( implicit_function = eb_func,...)

I would appreciate any feedback on these ideas. I have tried to read the docs, but I there is still much I do not understand. If there some textbook that maps on well to warpx that would also be a lifesaver.

Thanks!

[roelof-groenewald]

Hi @JameyH. Your plan sounds reasonable. There was actually quite a bit of work done a few years ago on using WarpX to simulate thermionic diodes. The public version of WarpX used for that work can be found from this link. I would say that would be a good place to start from. Note that the WarpX version in that repo has not been updated for quite a while so it would be good to just use the functionality shown there as a guide of how to get started.