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

TL;DR

This paper reveals that convergence of multiple electron temperature diagnostics in weakly collisional plasmas indicates a shared ionization bottleneck, leading to effective temperature measurements that can misrepresent the core temperature.

Contribution

It introduces a taxonomy of diagnostics, derives a direct relation between temperature ratios and the kappa parameter, and applies this framework to solar, tokamak, and planetary nebulae plasmas.

Findings

Convergence of diagnostics reflects the effective temperature, not the core temperature.

Single kappa distributions fit observed data with fewer parameters.

Non-local transport affects heat flux estimates in plasma environments.

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 $\sim 0.01$: all diagnostics downstream of collisional ionization report the effective temperature $T_{\rm eff}$, not the core temperature $T_{\rm core}$. Their agreement is a single measurement reported $N$ times. We introduce a taxonomy: Type A (ionization-gated, $T_{\rm eff}$), Type B (bulk-sampling, $T_{\rm core}$), Type C (distribution-resolving). The ratio $R = T_A/T_B$ yields $\kappa = 3R/[2(R-1)]$ directly. Applied to the solar corona ($R = 2.4$, $\kappa \approx 2.5$) and the tokamak scrape-off layer, single kappa distributions ($\kappa \approx 2$--$10$) 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 $v^4$ mean-free-path scaling show ionizing electrons are collisionless in the corona even when the bulk is fluid; in PNe, both ionizing ($\sim 55$ eV) and excitation ($\sim 5$ 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 $\kappa \approx 3$--$5$, the raw Spitzer--H\"arm formula with spectroscopic $T_e$ overestimates parallel heat flux by factors of 3--25$\times$; 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.