Multi-diagnostic convergence: a single measurement in weakly collisional plasmas
arXiv:2605.21106 · doi:10.1515/ot-2026-0011
Abstract
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 : all diagnostics downstream of collisional ionization report the effective temperature , not the core temperature . Their agreement is a single measurement reported times. We introduce a taxonomy: Type A (ionization-gated, ), Type B (bulk-sampling, ), Type C (distribution-resolving). The ratio yields directly. Applied to the solar corona (, ) and the tokamak scrape-off layer, single kappa distributions (--) reproduce published bi-Maxwellian EEDF decompositions to 3--8\% RMS with one fewer parameter, and Thomson scattering confirms the predicted Type B temperature. We test applicability in planetary nebulae (the 80-year CEL--ORL abundance discrepancy). Knudsen calculations with the Shoub mean-free-path scaling show ionizing electrons are collisionless in the corona even when the bulk is fluid; in PNe, both ionizing ( eV) and excitation ( eV) electrons are collisional over nebular scales, identifying PNe as the falsification boundary; in the SOL, non-local parallel transport maintains tails even where local collisionality is high. For --, the raw Spitzer--Härm formula with spectroscopic overestimates parallel heat flux by factors of 3--25; flux-limited models inherit the bias through their boundary conditions, relevant to ITER divertor predictions. Every diagnostic campaign on a weakly collisional plasma should include at least one Type B measurement.