Add eich profile

[chris-ashe]

This pull request introduces significant new functionality and documentation for modeling plasma scrape-off layer (SOL) physics, particularly focusing on heat flux profiles and power spreading in tokamak divertors. The main changes include the addition of new physics models and plotting functions for SOL profiles, the implementation of the Scarabosio 2014 power spreading factor, and comprehensive documentation updates to explain the new models and their physical basis.

Key changes include:

New SOL Physics Models and Methods

• Added methods to ScrapeOffLayer for calculating the outboard midplane near-SOL radial heat flux profile (calculate_outboard_midplane_near_sol_radial_profile), the Eich target heat flux profile (calculate_eich_target_heat_flux_profile), and the Scarabosio 2014 H-mode power spreading factor (calculate_scarabosio2014_power_spreading_factor). These provide core physics calculations for SOL heat transport and divertor power spreading.
• Updated the run method in ScrapeOffLayer to compute and store the Scarabosio 2014 and general power spreading factors in the physics data structure.
• Added new physics variables to PhysicsData for storing the outboard lower divertor flux expansion and power spreading factors.

Plotting Enhancements

• Introduced new plotting functions in process/core/io/plot/summary.py to visualize the midplane near-SOL radial profile, the Eich target heat flux profile at the lower outboard divertor, and a summary of SOL power fluxes. These plots leverage the new physics models and are integrated into the summary plotting workflow.
• Registered ScrapeOffLayer in the plotting module for direct access to SOL physics calculations.

Documentation Improvements

• Expanded the documentation in plasma_scrape_off_layer.md to describe the upstream radial decay, the Eich target heat flux profile, and the physical meaning of the spreading parameter S, including the Scarabosio 2015 scaling law. Added new references to support these sections.

Output and Usability

• Enhanced the output of the ScrapeOffLayer model to include the new power spreading factors for traceability and user insight.
• Fixed the calculation of parallel power flux by including the outboard separatrix power fraction.

---

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 21.97802% with 71 lines in your changes missing coverage. Please review.
✅ Project coverage is 49.39%. Comparing base (a9358cc) to head (a47f2a2).
⚠️ Report is 4 commits behind head on main.

Files with missing lines	Patch %	Lines
process/core/io/plot/summary.py	6.45%	58 Missing ⚠️
process/models/physics/scrape_off_layer.py	43.47%	13 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4507      +/-   ##
==========================================
- Coverage   49.46%   49.39%   -0.08%     
==========================================
  Files         150      151       +1     
  Lines       30069    30169     +100     
==========================================
+ Hits        14874    14902      +28     
- Misses      15195    15267      +72     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[chris-ashe]

Can I ask someone from @ukaea/process-model-review to check if the $q_0$ term in the Eich target profile should be divided by the flux expansion factor, $f_x$. Currently the input is just the upstream $q_{\parallel,u}$

[grmtrkngtn]

There's a lot of typos for scrabosio instead of scarabosio

[grmtrkngtn]

Does the flux-expansion factor cancel here? If I change f_b_div_flux_expansion I get the same profile regardless

[chris-ashe]

I have seen several different variations of the same formula (all in Eich papers), so there is a discrepancy somehwere