Multi-diagnostic convergence: a single measurement in weakly collisional plasmas

When multiple electron temperature diagnostics converge on the same value, the standard inference is that the measurement is robust. We show that this convergence is a structural consequence of the shared ionization bottleneck in any plasma where the electron Knudsen number exceeds <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mo>∼</m:mo> <m:mn>0.01</m:mn> </m:math> ~ 0.01 : all diagnostics downstream of collisional ionization report the effective temperature T eff of the electron velocity distribution, not the core temperature T core . Their agreement is a single measurement reported N times. We introduce a diagnostic taxonomy classifying methods as ionization-gated (Type A, measures T eff ), bulk-sampling (Type B, measures T core ), or distribution-resolving (Type C). The ratio R = T A / T B yields κ = 3 R /[2( R − 1)] directly. We apply the framework to the solar corona ( R = 2.4, κ ≈ 2.5) and validate it quantitatively in the tokamak scrape-off layer, where single kappa distributions ( κ ≈ 2–10) reproduce published bi-Maxwellian EEDF decompositions to 3–8 % RMS with one fewer free parameter and Thomson scattering independently confirms the predicted Type B temperature. We test the framework’s boundary of applicability in planetary nebulae (the 80-year CEL–ORL abundance discrepancy). Knudsen number calculations, including the Shoub v 4 mean-free-path scaling for tail electrons, show that the ionizing population is collisionless in the corona even when the bulk is fluid; in planetary nebulae, both the ionizing electrons (∼55 eV) and the lower-energy excitation electrons (∼5 eV) that drive the CEL diagnostic are collisional over nebular scales, identifying PNe as the falsification boundary of the framework; in the tokamak SOL, non-local parallel transport maintains suprathermal tails even where local collisionality is high. For plasmas with κ ≈ 3–5, the raw Spitzer–Härm formula with spectroscopic T e as input overestimates parallel heat flux by factors of 3–25×; flux-limited transport models inherit the temperature bias through their boundary conditions, with direct relevance to ITER divertor predictions. Every diagnostic campaign on a weakly collisional plasma should include at least one Type B measurement.