[ET Trac] #2952: GRHayLET/IllinoisGRMHD convert_*_to_*.c magnetic sector subleties

[Leonardo Rosa Werneck]

#2952: GRHayLET/IllinoisGRMHD convert_*_to_*.c magnetic sector subleties

 Reporter: Maxwell Rizzo
   Status: new
Milestone: 
  Version: 
     Type: bug
 Priority: minor
Component: EinsteinToolkit thorn

Comment (by Leonardo Rosa Werneck):

Hi Maxwell! Thanks for pointing these out!

* Regarding `phitilde = Aphi`, I agree that this is misleading. Although I don't see anything in the `HydroBase` documentation that states that `Aphi` is defined without the `sqrt{gamma}` factor in it, intuitively that's what I would expect. This has been likely not been a problem because most of our ID thorns set `Aphi` to zero initially. This can definitely be fixed.
* Regarding the factor of `1/sqrt(4pi)`, I would point to the discussion surrounding Eqs. (A9) and (A10) of the [GRHayL paper](https://arxiv.org/pdf/2512.15846). Since this affects only the definition of the magnetic field itself, I think rescaling only `Avec` is correct, but let me know if you find a reasoning to also rescale `Aphi`.
* Regarding `Ax`/`Ay`/`Az` being staggered, I don't know of a way to remedy this. Our initial data thorns (such as `Seed_Magnetic_Fields`) "borrow" `Avec` as auxiliary storage. Although one can argue this is incorrect and that they could initialize `Ax`/`Ay`/`Az` directly instead, doing that would make it difficult for users to utilize our initial data in their own evolution thorns. Our "solution" was to add a parameter to the ID thorns that allows users to initialize `Avec` with either staggered or vertex-centered data. We'd be happy to discuss alternatives, if you'd like to propose any.
* Regarding repopulating `Avec`/`Aphi`, this can be added, but the usefulness is less clear to me. While having them in the `HydroBase -> GRHayLET` conversion enables users to more easily utilize our initial data thorns, having them in the `GRHayLET -> HydroBase` seems less useful/redundant, as users can output `Ax`/`Ay`/`Az`/`phitilde` instead of the `HydroBase` quantities. The centering mismatch also makes things a bit trickier, as you pointed out. That being said, we'd be happy to add the copy if folks think it would be useful.

Let me know what you think. I'd be happy to create a PR to address issues we agree on.

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Ticket URL: https://bitbucket.org/einsteintoolkit/tickets/issues/2952/grhaylet-illinoisgrmhd-convert_-_to_-c
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