HybridPIC vs implicit PIC planar pinch: why are shocks/discontinuities missing?

[pimanov]

Dear WarpX Community,

I’m trying to understand a physics/modeling difference between the implicit PIC planar pinch test and a HybridPIC version.

Starting from the 1D theta-implicit planar pinch example
Examples/Tests/implicit/inputs_test_1d_theta_implicit_planar_pinch (by @JustinRayAngus), the PIC run shows a strong shock-like/discontinuous structure that oscillates back and forth. In my HybridPIC run, the solution stays smooth: with low resistivity the magnetic field barely penetrates the domain, and with high resistivity it becomes nearly linear. I don’t see an intermediate resistivity that produces a strong discontinuity.

Question: Is this expected because HybridPIC omits key physics responsible for the PIC “shock” (e.g., electron kinetic effects / electron inertia / displacement current), or am I missing a required HybridPIC term/setting (electron pressure via elec_temp/gamma, hyper-resistivity, etc.) to recover similar behavior?

Input decks:
inputs_test_1d_theta_hybrid_planar_pinch.txt
inputs_test_1d_theta_implicit_planar_pinch.txt
visualization.ipynb

[JustinRayAngus]

I don't think the HybridPIC method in WarpX has sufficient physics to do this problem. This problem can be simulated with a resistive MHD model (https://doi.org/10.1063/1.5104340), but you need a vacuum resistivity model to get the magnetic field to diffuse through the vacuum regions and into a skin layer at the edge of the plasma, where it then will produce a JxB force that drives the shock. With a uniform resistivity, I think the behavior you see is as expected. I also do not believe that the HybridPIC model includes a temperature equation for the electrons nor does it include thermal energy exchange with ions. Both of these are important for getting the shock physics correct.

@roelof-groenewald can comment more on what physics is and is not included in the HybridPIC model.

[pimanov]

@JustinRayAngus or @roelof-groenewald do you know if anyone is working on an advanced resistivity model for HybridPIC, like the one used in the paper (https://doi.org/10.1063/1.5104340)?

[roelof-groenewald]

@pimanov I'm not aware of anyone actively working on advanced resistivity models, but we would welcome any contributions if you are interested in adding such models to the code.