Add Higuera-Cary pusher

[steindev]

Add Higuera-Cary pusher as presented in doi:10.1063/1.4979989.
The HC method is 2nd order, structure preserving, and relativistically correct.
Compared to Vay's method, the HC method has the additional property of being structure preserving while it correctly calculates the velocity in ExB direction when E·B=0 in contrast to Boris' method.
A correction to the formulas given in the original article is applied as documented by the WarpX team: (ECP-WarpX/WarpX#320).

Further references:

• Higuera's article on arxiv
• Riperda's comparison of relativistic particle integrators

Tests performed so far

• Single particle acceleration in constant electric field

  • HC produces the exact same result as Boris

• Single particle turning circles in a constant magnetic field

  • particle sticks closer to (expected) circular trajectory than Boris' or Vay's method

• Single particle movement with constant velocity in a force-free field composed of constant magnetic and electric fields

  • HC performs better than Boris, but the deviation from the expected straight line motion is still large.
    Only Vay produces the expected result, but it was Vay's design goal to reproduce the correct behavior truthfully.
    HC's issue arises mainly due to insufficient precision of the input values (i.e. fields), as it relies on the cancellation of two very large equal but opposite numbers when calculating the new momentum, in this test case.
  • UPDATE: I experimented a bit with precisionCasts and finally figured how to reduce errors due to upcasting while calculating with the necessary high precision, too.
    The HC pusher now performs as good as the Vay pusher and reproduces the trajectory.
    (Therefore, I would like to spare discussions on that)

• Kelvin-Helmholtz instability

  • Virtually no difference in electron distribution between Boris and HC at step 800. See the plot below showing where the distributions differ.
    
    Note, this picture amplifies the real difference. White pixels just mark that there is a change in that pixel, but not how large it is. Drawing the absolute difference in electron distributions results in a black void only.
  • Charge conservation: for HC is about the same as for Boris, i.e. max|d|/ρ_0=3.8e-5 and 4.0e-5, respectively, at the end of the simulation
  • Numerical heating: curves of particle energy over time relative to initial energy are identical for Boris and HC

To Do

• figure out if HC pusher gives expected results in force-free test
• perform many particle test (e.g. KHI)
• add option of the new HC pusher in list of available pushers in species.param in all examples

Big THANKS to @aroeszler who implemented most of the method.

This will close #2589.

[PrometheusPi]

• A minor typo in @aroeszler name.
• some question regrading naming
• could you please add a comment in the pusher implementation to highlight where the floating point precision becomes an issue so that your solution is documented

[sbastrakov]

Nice work @aroeszler and @steindev ! Just some small suggestions above on code style.

[sbastrakov]

I asked @psychocoderHPC and he trusts our reviews of this PR. So I assume you did not plan to add anything more to this PR @steindev and we can press the merge button now?

[steindev]

@steindev and we can press the merge button now?

Squash and merge probably, but YES you can do so. From my point of view everything is fine. Once we change the default pusher in a separate PR I will add a magnetic bottle test as suggested by @BeyondEspresso.