Table 1.

Summary of results for extrapolations from the minimum dataset for the high-$J_{\text{c}}$ OST-RRP^® conductor, showing the reductions in minimum-dataset extrapolation errors for the ESE relation given by equation-set (2) (indicated as red-italic RMSE and RMSFD values in the last two columns). Small differences in the overall RMSFD and RMS percentage errors indicate a considerable difference in the quality of the fit, as shown by comparing the relative RMSFD and RMSE values for cases 2–7 with the percentage errors at individual $I_{\text{c}}$ data points in the semi-logarithmic figures 3–5 that follow. Differences in parameters between corresponding cases are highlighted in red (‘var’ denotes ‘variable’).

Case #		OST Dataset (high-$J_{\text{c}}$ RRP® conductor): Extrapolation test cases	RMSFD (%)	RMSE (%)
Test case with all free parameters
1	All parameters simultaneously fitted (to show the large extrapolation errors when fitting all the scaling parameters)		58.1
Polynomial ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\mathit{\epsilon })$, Taylor (2005)
2	Durham:	polynomial ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\mu =2,\eta =\mathrm{var},w=2.2,s=1,v=1.5,p=0.5,q=2.0613$	15.7	0.200
3	ESE:	polynomial ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\mu =2,\eta =\mathrm{var},w=3.0,s=\mathrm{var},v=1.5,p=0.5,q=2.0613$	7.1	0.115
Deviatoric $b_{\text{c}2}(\epsilon )$, ten Haken (1994), Godeke et al (2006), Arbelaez et al (2009), Mentink (2008,2014)
4	G/ITER:	deviatoric ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\mu =1,\eta =2,w=3.0,s=1,v=1.52,p=0.5,q=2.0613$	11.7	0.156
5	ESE:	deviatoric ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\mu =1,\eta =\mathrm{var},w=3.0,s=\mathrm{var},v=1.5,p=0.5,q=2.0613$	7.0	0.114
6	MAG:	deviatoric ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\eta -\mu =1,\mu =\mathrm{var},w=3.0,s=1,v=1.52,p=0.5,q=2.0613$	9.5	0.130
7	ESE:	deviatoric ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\eta -\mu =1,\mu =\mathrm{var},w=3.0,s=\mathrm{var},v=1.5,p=0.5,q=2.0613$	7.7	0.114
Extended Power Law $b_{\text{c}2}(\epsilon )$, NIST (Ekin 2006)
8	ESE:	extended power law ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\mu =0,\eta =\mathrm{var},w=3.0,s=\mathrm{var},v=1.5,p=0.5,q=2.0613$	7.3	0.126
9	ESE:	extended power law ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\mu =1,\eta =\mathrm{var},w=3.0,s=\mathrm{var},v=1.5,p=0.5,q=2.0613$	6.8	0.110
10	ESE:	extended power law ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\mu =2,\eta =\mathrm{var},w=3.0,s=\mathrm{var},v=1.5,p=0.5,q=2.0613$	7.0	0.114
Invariant Strain Function $b_{\text{c}2}(\epsilon )$, Markiewicz (2006)
11	ESE:	invariant strain ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\mu =1,\eta =\mathrm{var},w=3.0,s=\mathrm{var},v=1.5,p=0.5,q=2.0613$	6.9	0.112
Exponential ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon )$, CERN (Bordini et al 2013)
12	ESE:	exponential ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\mu =0,\eta =\mathrm{var},w=3.0,s=\mathrm{var},v=1.5,p=0.5,q=2.0613$	8.7	0.131
13	ESE:	exponential ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\mu =1,\eta =\mathrm{var},w=3.0,s=\mathrm{var},v=1.5,p=0.5,q=2.0613$	8.3	0.121
14	ESE:	exponential ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\mu =1,\eta =\mathrm{var},w=3.0,s=\mathrm{var},v=1.5,p=0.5,q=2.0613$, $\text{fit only}{\mathbf{\epsilon }}_0\ge -0.48\text{\%}$	15.6	0.189
15	ESE:	exponential ${\mathit{b}}_{\mathbf{\text{c}}\mathbf{2}}(\epsilon ),\mu =2,\eta =\mathrm{var},w=3.0,s=\mathrm{var},v=1.5,p=0.5,q=2.0613$	8.5	0.128

$F_{\text{P}}$ was trimmed below 200 AT for table 1 and below 125 AT for table 2 to minimize flux creep effects at the lowest $F_{\text{P}}$ levels (near ${T_{\text{c}}}^{\ast }$ and ${B_{\text{c2}}}^{\ast }$). The specific trim level (discussed further in section 3.8) had negligible effect on the RMSE, but did affect the RMSFD results. Therefore, the RMSE results are general, whereas the RMSFD results are restricted to comparisons within each table. [The difference in table-to-table RMSFD levels depends on the $F_{\text{P}}$ trim level set relative to the conductor’s $F_{\text{Pmax}}$ or $K(0,0)$ value. That is, the relative trim level was lower (not as restrictive) for the OST-RRP^® conductor because it is normalized by significantly higher $J_{\text{c}}$ and $K(0,0)$ values, compared to the WST-ITER conductor ($F_{\text{Ptrim}}/K(0,0)=0.4\%$ for the OST-RRP^® dataset, versus 0.7% for the WST-ITER dataset). This resulted in the inclusion of more outlier data points for the OST-RRP^® dataset at the extremes.]