i_confinement_time ITPA20-IL Scaling equation fix

[OceanNuclear]

Description

Closes #4017
reference [^23] is dereferenced into [^22].

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

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 49.44%. Comparing base (6980eb9) to head (2d82030).
⚠️ Report is 12 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4158      +/-   ##
==========================================
+ Coverage   47.97%   49.44%   +1.47%     
==========================================
  Files         143      149       +6     
  Lines       30125    29796     -329     
==========================================
+ Hits        14451    14734     +283     
+ Misses      15674    15062     -612     

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[OceanNuclear]

Before the PR, the documentation page looks like:

The top reference ([22]) shows this equation:

matching the top equation. It also shows the bottom equation:

However, the bottom reference ([23]) shows this equation:

But the [3] here is actually citing the first paper ([22]). This also explains the index rounding issue mentioned in #4017.

[OceanNuclear]

According to reference [22], the values (and the errors) for the top equation is:

and for the bottom equation is:

[OceanNuclear]

Regarding making the roundings more consistent, these are the values (α) and their uncertainties (σ) as recorded in the first paper ([22]):

ITPA20 scaling (H-mode)	$\alpha_0$	$\alpha_I$	$\alpha_B$	$\alpha_n$	$\alpha_P$	$\alpha_R$	$\alpha_{1+\delta}$	$\alpha_\kappa$	$\alpha_\epsilon$	$\alpha_M$
Mean	0.0534	0.976	0.218	0.2442	-0.6687	1.71	0.362	0.799	0.354	0.195
σ	0.0013	0.015	0.013	0.009	0.0063	0.023	0.033	0.027	0.031	0.016
Mean + 0.5 σ	0.05405	0.9835	0.2245	0.2487	-0.66555	1.7215	0.3785	0.8125	0.3695	0.203
Mean – 0.5 σ	0.05275	0.9685	0.2115	0.2397	-0.67185	1.6985	0.3455	0.7855	0.3385	0.187
Best rounding	0.053	0.98	0.22	0.24	-0.67	1.7	0.36	0.8	0.35	0.2

ITPA20-IL scaling (H-mode)	$\alpha_0$	$\alpha_I$	$\alpha_B$	$\alpha_n$	$\alpha_P$	$\alpha_R$	$\alpha_{1+\delta}$	$\alpha_\kappa$	$\alpha_\epsilon$	$\alpha_M$
Mean	0.067	1.291	-0.134	0.1473	-0.6442	1.194	0.56	0.673	0	0.302
σ	0.0021	0.017	0.017	0.0088	0.0063	0.027	0.032	0.039	0.033	0.016
Mean + 0.5 σ	0.06805	1.2995	-0.1255	0.1517	-0.64105	1.2075	0.576	0.6925	0.0165	0.31
Mean – 0.5 σ	0.06595	1.2825	-0.1425	0.1429	-0.64735	1.1805	0.544	0.6535	-0.0165	0.294
Best rounding	0.067	1.29	-0.13	0.15	-0.644	1.2	0.56	0.67	0	0.3

[OceanNuclear]

@stuartmuldrew can you identify what the (+0059 - 0.032) is doing in the first term of the top equation, and the (+0.030 - 0.018) in the first term of the bottom equation? I can't see these being the upper and lower bounds of that constant

[timothy-nunn]

@jonmaddock have you approved this as a maintainer as ready to be merged? Also are you managing this PR and should I put you as the assignee?