Space Charge Solver

[ax3l]

Implement the space charge solver.
Close #101

• update exact charge: https://github.com/ECP-WarpX/impactx/blob/81684134057d43b9f4ecf8b6dcf9221b84e4b9f8/src/particles/ChargeDeposition.cpp#L69
• Poisson solve
  • depends on ABLASTR: Update Poisson Solver API ECP-WarpX/WarpX#3243 (via Update ABLASTR: Poisson API #164)
  • depends on ABLASTR: Add Nodal Gather Functions ECP-WarpX/WarpX#3357 (via Update ABLASTR: Nodal Gather #235)
  • depends on Fix: ABLASTR nvcc Phi Fine/Coarse ECP-WarpX/WarpX#3374 (via ABLASTR: Update #246)
  • depends on Modified and renamed coordinate transformations (to fixed t, to fixed s). #242
  • debug why this is zero - mismatched phi and rho in the call
  • fix sign of deposited charge Charge Deposition: Fix Sign #251
• space charge force: via stencil on phi Add Space Charge Forces ax3l/impactx#1
• space charge kick: gather fields and
  • push particles (in momentum): dt = ds / v_ref
    • Skip space charge calc for zero-sized elements
    • Skip position push? (because it is handled in the external elements)
• expose control over number of cells to use to user: Expose Control over Domain Resolution & MR Gridding #240
• follow-up PR: MR Space-Charge: MR #102
• tests
  • Added examples for 3D space charge benchmarking. #141
  • Added cold expanding beam benchmark example (with space charge). #244
  • make sure the test's bunch charge is non-zero, otherwise weighting & thus charge deposited is zero: https://github.com/ECP-WarpX/impactx/blob/81684134057d43b9f4ecf8b6dcf9221b84e4b9f8/src/particles/ChargeDeposition.cpp#L51 -> Test: Charge Deposition #165

Update Evolve Loop for Leap-Frog

• Modified ordering of evolve/push loop. #160

Loop over elements in the lattice
     Loop over steps through element
          Loop over all particles to apply element map half-step
          Z-to-T transformation
                Solve Poisson equation
          T-to-Z transformation
          Loop over all particles to apply space charge full step
          Loop over all particles to apply element half-step
     End loop over steps through element
End loop over elements

[ax3l]

@cemitch99 @RemiLehe this PR is ready for review & merge.

All other open points in the PR description will be done in follow-up PRs, to keep the lines in this PR small and quick to review.

[ax3l]

@RemiLehe let's discuss this again, this might currently be too large (can be performance-optimized in a follow-up PR as well)

[cemitch99]

Looks ok to me; I don't see any obvious problems. Thanks a lot.