Stellarator symmetry available for testing

[zhucaoxiang]

For a long time, FOCUS ignores periodicity and stellarator symmetry, as the computation speed was never an issue and generally, FOCUS results followed periodicity and stellarator symmetry if the target plasma does. I implemented the periodicity some time ago. A recent presentation by J. Schmitt indicates that finite asymmetry in coils may cause sizable differences in Boozer harmonics. The results motivate me to really consider finishing the stellarator symmetry.

Now the new function is ready for testing in the branch symmetry. Anyone who is interested should take a look. I will merge it into develop (and master) after the recent pull request is merged.

Some key points:

• It is developed based on the develop branch, which means it has the ability to specify a secondary limiter surface by using limiter_surf when using coil-surface separation. More details can be checked #42.
• The main change is to enable stellarator symmetry while re-implementing the periodicity.
• *.focus file for coil parameters now has a slightly different I/O. An additional parameter symm will be read to indicate the symmetry property of this particular coil. Old executables can still read this new format, but the new executable cannot read old formats.

# coil_type  coil_symm   coil_name
   1  2  Mod_001   
# Nseg        current         Ifree         Length         Lfree  target_length
 128  1.009791754928605E+06     1  8.670505423971651E+00     1  5.000000000000000E+00

• Re-implement the calculation of minimum coil-coil distance, but might need further checkings.
• Add an output for calculating surface averaged Bn error.
• Bug fixes.

There is a detailed developing note available at https://princetonuniversity.github.io/FOCUS/notes/FOCUS_stellarator_symmetry_and_periodicity.html. Please take a look. Some key information: Section 1.4 How to use, Section 3 Summary.

Please feel free to test and report issues.