Investigation into using RADIA for Bfield computation.

Opt-ID does not consider material types, and both Opt-ID and Radia do not consider interactions between magnets for the "sum of bfield" approaches.

All errors are computed relative to using Radia with a magnet group and directly using the magnetic field vectors for the magnet (no rotation matrices).

The magnetic field vector plots (top row) are colour normalized the same as one another, you can see that Opt-ID is brighter (overestimating) for Ferrite and is darker (underestimating) for NdFeB materials.

The error plots are colour normalized down the columns (bfield errors in each axis for the same calculation methods) but are scaled independently between columns (different calculation methods) to highlight details. The colourbars denote the magnitudes being shown. If the error plots are scaled globally like the top row then the Radia sum of bfield methods are completely washed out as they are a couple of orders of magnitude closer to the Radia grouped bfields.

Radia with the sum of bfield method is pretty accurate even when considering Ferrite material magnets without an interaction matrix. I think we will be able to get away with not considering the interaction matrices, at least for now.

# No Material
- All methods are consistent.
- Sum of bfield error is on the order of 1e-9

## No Material - Z Aligned Fields


## No Material - Canted Fields


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# Sm2Co17 Material
- Opt-ID gives a reasonable approximation over the sample space but is off by quite a bit everywhere.
- Opt-ID sum of bfield error is on the order of 1e-2
- Radia sum of bfield error is on the order of 1e-5

## Sm2Co17 Material - Z Aligned Fields


## Sm2Co17 Material - Canted Fields


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# NdFeB Material
- Opt-ID underestimates the field strength pretty much everywhere.
- Opt-ID sum of bfield error is on the order of 1e-1 to 1e-2
- Radia sum of bfield is less accurate for NdFeB than for Sm2Co17 but is still consistent.
- Radia sum of bfield error is on the order of 1e-4

## NdFeB Material - Z Aligned Fields


## NdFeB Material - Canted Fields


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# Ferrite Material
- Opt-ID overestimates the field strength pretty much everywhere.
- Opt-ID sum of bfield error is on the order of 1e-1
- Radia sum of bfield is reasonably accurate pretty much everywhere.
- Radia sum of bfield error is on the order of 1e-4

## Ferrite Material - Z Aligned Fields

## Ferrite Material - Canted Fields