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trx/libnf.f90: the reactivity spline (linear sigma-v vs log10 T) returns negative values for D-He3 / T-He3 and is 5-11x off for D-T below 4 keV #271
Description
Summary
set_usigmav_nf (trx/libnf.f90:322-343) fits a natural cubic spline (SPL1D, ID=0) through the linear svnf_* values against log10(T), and sigmav_nf evaluates it with SPL1DF. The tables span five decades over ten points, so the spline overshoots between knots: it returns negative reactivities for D-He3 and T-He3 and is off by 5–11× for D-T below ~4 keV. trm/libsigma.f90:45-83 splines log10(σv) and exponentiates, which has none of this.
Found during the review of #269 by the domain reviewer; reproduced here with lib/libspl1d.f90 and the tables copied from libnf.f90 (300 log-spaced temperatures in [1, 1000) keV):
| table | negative samples | minimum | at |
|---|---|---|---|
svnf_dhe3 |
37 / 300 | −1.6e-20 cm³/s | 3.4 keV |
svnf_the3 |
53 / 300 | −4.9e-21 cm³/s | 6.9 keV |
svnf_dd, svnf_dt, svnf_tt |
0 | — | — |
D-T against Bosch-Hale (NF 32 (1992) 611), both in cm³/s:
| T [keV] | spline | Bosch-Hale | ratio |
|---|---|---|---|
| 1.5 | 3.57e-19 | 6.92e-20 | 5.2 |
| 2.5 | 7.74e-20 | 8.43e-19 | 0.09 |
| 3.0 | 6.85e-19 | 1.87e-18 | 0.37 |
| 4.0 | 5.05e-18 | 5.97e-18 | 0.84 |
| 10 | 1.10e-16 | 1.14e-16 | 0.97 |
| 50 | 8.70e-16 | 8.65e-16 | 1.01 |
Effect
tr_pnf (trx/trpnf.f90:84-89) uses RATE_NF=sigmav_nf(id_nf,PT1) per radial cell. A negative rate makes SNF negative: reactants are created, products destroyed, and PNF_NSNNFNR becomes a negative power, over parts of the 2–7 keV range (minima reproduced at 3.4 keV for D-He3 and 6.9 keV for T-He3) — temperatures any edge profile crosses. For D-T (model_pnf=1) the sign is right but the edge contribution is wrong by up to 11×. Independent of #236 (the cm³/s → m³/s factor) and of #269, which keep the interpolation as is.
Suggested fix
Spline LOG10(svnf_*) in set_usigmav_nf and return 10**value in sigmav_nf (the trm/libsigma.f90 pattern), keeping the *1.D-6 of #269; or replace the ten-point tables with the Bosch-Hale parametrisation. Either changes model_pnf>0 results below ~10 keV, so it needs the lead's confirmation, like the rest of the fusion-path fixes (#236, #269).
Test
sigmav_nf(id, T) >= 0 for all 13 channels over [1, 1000) keV (fails today for dhe31/32, the31..36), and sigmav_nf(id_nf_dt, T) within 25 % of Bosch-Hale at 1.5, 2.5, 3, 10, 50 keV (fails today at 1.5 and 2.5).
Activity