Use density and asymmetry profile to determine mid-Z and high-Z together

[k-collie]

Principle

After the SXR inversion we get a symmetric density and an asymmetry profile. Using the toroidal rotation from CXRS we can get the predicted asymmetry profiles for the two species. Therefore the asymmetry parameter should give us the ratios of the two species and the density profile will give us an absolute magnitude. We can likely use an optimization routine to find the symmetric density profile for mid-Z and high-Z.

Implementation

• factor out reused functionality from invert_radiation
• allow fixing asymmetry parameter for invert_radiation
• reconstruct density rather than emissivity
  • pass in loss function and electron density to invert call
  • write closure for init_guess_bounds that returns densities
  • write closure for emissivity_from_knotvals that converts densities to EmissivityProfiles
    • asym_profile + asym_profile != asym_profile => problem
• allow reconstruction of multiple elements