Refactor constraint_equation_2 to use total plasma power balance in MW

[chris-ashe]

This pull request updates the plasma power balance constraint equation in constraints.py to use total power units (MW) instead of power density (MW/m³), and simplifies the calculation logic. The changes streamline the code by removing per-volume calculations and ignition model branching, and by using more descriptive variable names.

Constraint Equation Refactor:

• Changed the registered unit for constraint 2 from "MW/m³" to "MW" to reflect total plasma power rather than power per volume.
• Simplified the calculation of power loss and heating by removing the use of power density variables and ignition model branching; now uses p_plasma_loss and p_plasma_heating directly.
• Updated the handling of radiation loss models to add the appropriate radiation term to p_plasma_loss, using more consistent variable names.

Code Documentation and Cleanup:

• Removed outdated docstring details about input variables and ignition model logic, reflecting the new simplified approach.
• Cleaned up unused variables and redundant code paths for clarity and maintainability.## Description

Checklist

I confirm that I have completed the following checks:

• My changes follow the PROCESS style guide
• I have justified any large differences in the regression tests caused by this pull request in the comments.
• I have added new tests where appropriate for the changes I have made.
• If I have had to change any existing unit or integration tests, I have justified this change in the pull request comments.
• If I have made documentation changes, I have checked they render correctly.
• I have added documentation for my change, if appropriate.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 62.50000% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 49.74%. Comparing base (2eb62fb) to head (0ec7593).
⚠️ Report is 13 commits behind head on main.

Files with missing lines	Patch %	Lines
process/core/solver/constraints.py	62.50%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4631      +/-   ##
==========================================
- Coverage   50.01%   49.74%   -0.28%     
==========================================
  Files         151      151              
  Lines       30123    30297     +174     
==========================================
+ Hits        15066    15070       +4     
- Misses      15057    15227     +170     

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[grmtrkngtn]

I agree this is a good change in principle, one suggestion to clarify the name of the variable for transport from the core.

[mkovari]

I agree that the constraint should be modified to use power instead of power density.
Please check issue #4421, which raises a few distinct problems:

• The puzzling use of electron transport power per volume (MW/m3).
• Transport and confinement variables exist in two different namespaces
• Plasma power across separatrix not balancing

Where has the ignition logic gone? I never liked it but you seem to have just deleted it.

[chris-ashe]

I agree that the constraint should be modified to use power instead of power density. Please check issue #4421, which raises a few distinct problems:

• The puzzling use of electron transport power per volume (MW/m3).
• Transport and confinement variables exist in two different namespaces
• Plasma power across separatrix not balancing

Where has the ignition logic gone? I never liked it but you seem to have just deleted it.

The ignition check is now obsolete as the plasma heating term has the injected power term in it which would be zero in the ignited case

[mkovari]

The ignition check is now obsolete as the plasma heating term has the injected power term in it which would be zero in the ignited case

What about the ohmic heating - isn't that handled differently for the ignited case?

[chris-ashe]

The ignition check is now obsolete as the plasma heating term has the injected power term in it which would be zero in the ignited case

What about the ohmic heating - isn't that handled differently for the ignited case?

The ohmic term is in there also. There will still be ohmic power

[mkovari]

The ohmic term is in there also. There will still be ohmic power

By definition an ignited plasma has not external heating at all - not even ohmic heating.

[grmtrkngtn]

Now it looks good to me.