impactx

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This PR refers to:

C. E. Mayes, R. D. Ryne, and D. C. Sagan, "3D Space Charge in BMAD," in proc. IPAC2018, DOI:10.18429/JACoW-IPAC2018-THPAK085

This is a replacement for PR #257 Closes @ChristopherMayes' #256.

Added the expanding Gaussian beam test and plot script corresponding to phase space shown in Fig. 4.

• [x] add expanding Gaussian beam test
• [x] add plot script to reproduce Fig. 4
• [x] add static Gaussian beam field calculation
• [x] add plot script to reproduce Fig. 1
• [x] add documentation
• [ ] verify resolution and convergence
• [ ] potentially use IGF solver (with much smaller grid) #605

Could the plot(s) be created and checked in, or at least put in docs somewhere?

@ChristopherMayes Thank you for your comment. Yes, absolutely. We still finalize a few space charge benchmarks for HB 2023 right now and this is one of them. As stated in your IPAC2018 paper, the non-IGF method starts to fail for large aspect ratios (w/o pushing resolution much further up). We added a preview to the PR description.

We will clean this PR up further once final, e.g., replacing the data files from the analytical solution with results calculated on the fly.

Yes, on the plots, too. The docs will get a readme file for the new case and we will include the plot, similar to https://impactx.readthedocs.io/en/latest/usage/examples/fodo/README.html

@ChristopherMayes commented that if we also plot Fig 2 of https://accelconf.web.cern.ch/ipac2018/papers/thpak085.pdf, we can see more precision details (e.g., for fixed precision and infinite number of steps in the MLMG, do different aspect ratios converge to the same result). For instance, GPT sometimes gets this wrong for some aspect ratios.