Strain optimization

[ejpaul]

This PR is based on work by @phuslage for the optimization of coil curves and the HTS winding angle to reduce torsional and hard-way bending strain as defined in :

Paz Soldan, "Non-planar coil winding angle optimization for compatibility with 
non-insulated high-temperature superconducting magnets", Journal of Plasma Physics 
86 (2020), doi:10.1017/S0022377820001208. 

The orientation of the HTS tape normal is defined by the FramedCurve class, which is inherited by FramedCurveFrenet or FramedCurveCentroid. The FramedCurve defines a curve and an orthonormal frame, where the tangent vector is aligned with the curve tangent. The frame can be rotated by an angle alpha with respect to the Frenet or centroid reference frames. The FramedCurve class evaluates geometric properties of the frame, such as the torsion and binormal curvature. This class is also used to set up a multi-filament coil using the CurveFilament class.

The strains are evaluated in the StrainOpt class, which is defined by a FramedCurve and a tape width. The objective functions LPTorsionalStrainPenalty and LPBinormalCurvatureStrainPenalty can be used for optimization with respect to the coil or rotation dofs.

An example of optimization with respect to the rotation dofs is provided in strain_optimization_simple.py

[codecov]

Codecov Report

All modified lines are covered by tests ✅

Comparison is base (f8f9d59) 91.07% compared to head (60329b3) 90.93%.
Report is 18 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #346      +/-   ##
==========================================
- Coverage   91.07%   90.93%   -0.14%     
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  Files          70       72       +2     
  Lines       12367    12681     +314     
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+ Hits        11263    11532     +269     
- Misses       1104     1149      +45     

Flag	Coverage Δ
unittests	90.93% <100.00%> (-0.14%)	⬇️

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Files	Coverage Δ
src/simsopt/geo/__init__.py	100.00% <100.00%> (ø)
src/simsopt/geo/finitebuild.py	100.00% <100.00%> (+0.64%)	⬆️
src/simsopt/geo/framedcurve.py	100.00% <100.00%> (ø)
src/simsopt/geo/strain_optimization.py	100.00% <100.00%> (ø)

... and 10 files with indirect coverage changes

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[phuslage]

Maybe we add a test that checks whether the cost functions vanish for a circular coil.

[landreman]

Is this PR ready for another review? If so can you merge master in and resolve merge conflicts?

[ejpaul]

Is this PR ready for another review? If so can you merge master in and resolve merge conflicts?

@landreman Yes, it is ready. I have merged in master.

[landreman]

Looks good. Since StrainOpt was not intended to be used as an objective function in optimization, the Opt in the name might be confusing to users. So I took the liberty of renaming it to CoilStrain, and adding to the docs to clarify. Hope that's ok. Feel free to merge whenever you're ready.

[ejpaul]

Looks good. Since StrainOpt was not intended to be used as an objective function in optimization, the Opt in the name might be confusing to users. So I took the liberty of renaming it to CoilStrain, and adding to the docs to clarify. Hope that's ok. Feel free to merge whenever you're ready.

Thanks, Matt!