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Add Dan Barnes' semi-implicit Poisson solver
This PR adds a new electrostatic solver based on the semi-implicit scheme developed by Barnes, Journal of Comp. Phys., 424 (2021), 109852 (see Appendix A of reference).
The implementation was tested through the simulation of a Langmuir probe placed inside a uniform plasma. To this end a 2d simulation was performed with an initial uniform plasma with a conducting disk inserted in the center of the domain. The disk is kept at 0 V while Neumann boundary conditions are used for the domain boundary. Electrons and hydrogen ions were injected from all the domain boundaries using the UniformFluxDistribution
in order to simulate the particle flux from a uniform plasma. Thermal boundaries were used for the particles with the same temperatures as the initial plasma particles. The expected outcome of this simulation is that a sheath develops around the "Langmuir probe" with value
$V_s = 0.5T_e\ln\left(2\pi\frac{m_e}{2m_p}(1 + \frac{T_i}{T_e})\right) $.
A pre-sheath of roughly $0.7T_e$ is also expected to form but the exact value of this depends on the domain size since the pre-sheath extends for many Debye lengths.
The figure below shows an example outcome from a simulation as described above in which the semi-implicit factor was set to $C_{SI} = 10$.
Required before merging:
- [x] Merging of https://github.com/AMReX-Codes/amrex/pull/3968
- [x] Add example to CI tests
- [x] Update documentation