Photosphere versus corona force-free assumption
The force-free approximation is much better suited to the corona than to the photosphere.
That is awkward, because the photosphere is where routine vector magnetograms are measured.
The physical reason
The key parameter is plasma beta:
When , magnetic pressure dominates gas pressure. In that regime, non-magnetic forces are small and a force-free model is plausible.
The corona is often low-, so the force-free approximation can work reasonably well there.
The photosphere is denser and more dynamic. Gas pressure, gravity, flows, and non-force-free stresses matter. It is not a clean force-free boundary.
The modelling tension
NLFFF extrapolation uses a photospheric vector magnetogram as the lower boundary, but the mathematical model is meant for the low- corona above it.
So the basic mismatch is:
This is not a small bookkeeping issue. It is one of the central difficulties in coronal extrapolation.
Practical consequences
A model can behave badly in either direction:
- It can overfit the photospheric boundary and drag non-force-free structure into the corona.
- It can satisfy force-free residuals in the volume while drifting away from the measured boundary.
This is why preprocessing, boundary weighting, and careful diagnostics matter.
Why this matters for NF2
NF2 does not remove the photosphere-corona mismatch. It changes how the mismatch is handled.
Because the boundary is a soft loss term, NF2 can trade boundary agreement against force-free and divergence residuals. That makes the method flexible, but it also means the individual loss terms must be monitored separately.
The useful question is not whether NF2 achieves perfect boundary agreement and perfect force-freeness at the same time. The useful question is how well it balances boundary agreement, force-freeness, divergence control, and magnetic-energy behaviour.