Implement particle pusher by Higuera and Cary

[MaxThevenet]

It could be interesting to explore this particle pusher.
Here are the main references:
https://aip.scitation.org/doi/full/10.1063/1.4979989
http://accelconf.web.cern.ch/AccelConf/ipac2018/papers/thpml042.pdf
One could for instance mimic what is done for Boris and Vay pusher.

[jlvay]

We want to implement for sure the one described in the Phys. Plasmas paper. A reference of the paper on arXiv is available at https://arxiv.org/abs/1701.05605v1
The conference paper describes a different pusher.

[RemiLehe]

@Yin-YinjianZhao
Here is a bit more info on the implementation in WarpX:

• The particle pusher is called here:
  https://github.com/ECP-WarpX/WarpX/blob/master/Source/Particles/PhysicalParticleContainer.cpp#L1486
  https://github.com/ECP-WarpX/WarpX/blob/master/Source/Particles/PhysicalParticleContainer.cpp#L1593
  https://github.com/ECP-WarpX/WarpX/blob/master/Source/Particles/RigidInjectedParticleContainer.cpp#L429
  using the usual ParallelFor syntax which allows the code to work for both CPU and GPU.

• The definition of the Boris and Vay pusher (for single particle) are here:
  https://github.com/ECP-WarpX/WarpX/blob/master/Source/Particles/Pusher/UpdateMomentumBoris.H
  https://github.com/ECP-WarpX/WarpX/blob/master/Source/Particles/Pusher/UpdateMomentumVay.H
  One would need to create a new file for the Higuera-Cary pusher.

• The pusher which is selected during a given simulation (i.e. Boris or Vay) depends on the user input. The code that does this is here:
  https://github.com/ECP-WarpX/WarpX/blob/master/Source/Utils/WarpXAlgorithmSelection.cpp
  https://github.com/ECP-WarpX/WarpX/blob/master/Source/Utils/WarpXAlgorithmSelection.H
  This would need to be updated.

• Finally, the documentation would need to be updated here:
  https://github.com/ECP-WarpX/WarpX/blob/master/Docs/source/running_cpp/parameters.rst
  (Search for algo.particle_pusher in that file.)

[RemiLehe]

@jlvay also pointed out a recent article that compares the different solvers:
https://iopscience.iop.org/article/10.3847/1538-4365/aab114/meta

[Yin-YinjianZhao]

When reading the papers and implementing the methods, I found two typos in two papers, which made me suffer for some time before figuring them out...
So, I'd like to share them here. See the two photos below.

For testing, I followed Ripperda's paper and tested Boris's, Vay's, and Higuera's methods using five cases (uniform E, uniform B, force-free, E x B, magnetic mirror). Although I couldn't get exactly the same results as those shown in Ripperda's paper, my results are good enough to indicate that my implementation is correct.
The next step will be to add the Higuera's solver into WarpX.
And if we want to add some automated tests for WarpX for the pushers, the ones in Ripperda's paper are good candidates.

[Yin-YinjianZhao]

The pusher has been added into WarpX, and one automatic test of the free-force field case is added.