Processing steps

1. Match each state to the observed sample at its time.
2. Keep every matched sample, counting those flagged R_p_nonpositive (dropping them would bias Z upward); a non-positive mean V_R gives not_identifiable.
3. Scan R_p^model(Z) over the bounds; a non-monotonic response gives non_monotonic without a fit.
4. Minimise J(Z) = sum w (V_R^obs - R_p^model(Z) (I_p - I_ni))^2 with a bounded scalar search.
5. Uncertainty from the curvature of J and the residual scatter (None with one sample); a minimum within 0.1 % of the range from a bound gives bound_hit. The scan only brackets the search: its smallest J sitting at an end point says nothing by itself, since a clean plasma (Z_eff ~ 1.0-1.03) minimises inside the first scan interval without touching the bound.

Defaults

time_tolerance_s 50 us is a numerical convenience below the 1e-4 s rounding of the Lane K state key (#1454); scan_points 41 is a numerical convenience.

Applicability

Machine-independent.

Limitations

One amplitude only: Z_eff is constant across radius and time (#1214 Sec. 10). The uncertainty is statistical; the systematic part comes from resistive_zeff_sensitivity.

Provenance

1. #1214 Secs. 9-11.

Processing steps

1. sigma_par(psi) from parallel_conductivity.
2. <E.B> = (<J.B> - <J_bs.B>) / sigma_par – <J_bs.B> is zero when the state carries none.
3. P_Ohm = int <E.B><J.B>/<B^2> dV by the trapezoid rule on the enclosed volume.
4. R_p = P_Ohm / I_p^2.

Applicability

Machine-independent.

Limitations

<E.J> ~ <E.B><J.B>/<B^2> is exact only when J_par/B is a flux function; the poloidal variation of the Pfirsch-Schlueter current is dropped, which at VEST aspect ratio is part of the model-form uncertainty rather than a resolved term. Steady state is not assumed: the current profile is the equilibrium’s own, and only its parallel resistivity is modelled.

Provenance

1. S. P. Hirshman and D. J. Sigmar, Nucl. Fusion 21 (1981) 1079 – the flux-surface parallel Ohm’s law.
2. #1214 Sec. 7.

Processing steps

1. Smooth I_p, psi_B and L_i with smoothing.
2. psi_C = psi_B + L_i I_p (Romero eqs. 35-36) and run the balance with R_p = 0 so that its V_R is unused.
3. V_R = V_B - V_I; R_p = V_R / (I_p - I_ni).
4. Flag samples whose V_B or R_p is not positive.

Defaults

None. I_ni and smoothing have no default: an assumed value for either moves R_p and must be the caller’s stated choice.

Applicability

Machine-independent. Closed-flux phase only, as the balance it calls.

Limitations

R_p is a closure: it absorbs every error in V_B, L_i and I_ni. dL_i/dt from reconstructed li_3 is the noisiest term; where inductive_fraction is large the resistance is a small difference of large numbers and should not be fitted.

Provenance

1. J. A. Romero and JET-EFDA contributors, Nucl. Fusion 50 (2010) 115002, eqs. (23)-(27), (35)-(40).
2. #1214 Sec. 5 (observed path) and Sec. 4 (convention).

Applicability

Machine-independent.

Limitations

spitzer_nrl and sauter_spitzer differ by tens of percent at Z > 1 (linear Z against Z N(Z)); the model name is part of the result. The axis surface has epsilon = 0 and no trapped particles.

Provenance

1. O. Sauter, C. Angioni and Y. R. Lin-Liu, Phys. Plasmas 6 (1999) 2834; 9 (2002) 5140 (erratum).
2. A. Redl et al., Phys. Plasmas 28 (2021) 022502.
3. NRL Plasma Formulary (2019), p. 29.

Processing steps

1. Order the states in time.
2. Run infer_resistive_zeff on each state alone.
3. Keep the value only for ok and bound_hit; bound_hit keeps its bound value so the reader sees where it stuck.

Applicability

Machine-independent.

Limitations

Not the estimate: #1214 Sec. 9 fits one scalar over a window, because one sample carries the full noise of a differentiated V_R and no residual to judge it by. These values show whether that scalar hides a trend, and are labelled as a diagnostic wherever they are drawn.

Provenance

1. #1214 Secs. 9-10.

Processing steps

1. Nominal inference.
2. Re-infer with T_e, n_e and li_3 scaled by 1 +/- relative_perturbation.
3. Re-infer with the smoothing window scaled by each factor.
4. Re-infer with each alternative conductivity model, and without the bootstrap current if the states carry one.
5. delta = Z - Z_nominal; the largest absolute delta per input goes into nominal.sensitivity.

Defaults

relative_perturbation 0.1 and smoothing_factors (0.5, 2) are numerical-convenience probes of local sensitivity, not uncertainty estimates of VEST diagnostics; models is the conventional Spitzer/Sauter/Redl ladder of #1214 Sec. 3.

Applicability

Machine-independent.

Limitations

One-at-a-time perturbations; no correlation between inputs. NEO enters only as a callable model the caller supplies.

Provenance

1. #1214 Sec. 12 and Phase F.

Processing steps

1. For each sample, select the samples with |t - t_i| <= window_s/2.
2. Fit a polynomial of order in t - t_i by least squares.
3. Return its constant term.

Applicability

Machine-independent.

Limitations

The window shrinks to one side at the ends of the record, where the fit extrapolates and is least reliable; cut a margin of window_s / 2 off the inference window if the end samples matter.

Provenance

1. A. Savitzky and M. J. E. Golay, Anal. Chem. 36 (1964) 1627 – the uniform-grid special case.