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

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 $T_{\mathrm{eff}}$, not the core temperature $T_{\mathrm{core}}$. Their agreement is a single measurement reported $N$ times. We introduce a taxonomy: Type A (ionization-gated, $T_{\mathrm{eff}}$), Type B (bulk-sampling, $T_{\mathrm{core}}$), 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--Härm 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.

References in corpus (30)

• Kappa distributions: theory and applications in space plasmas
• Coronal Holes
• Ionisation state, excited populations and emission of impurities in dynamic finite density plasmas. I: The generalised collisional-radiative model for light elements
• Solar UV and X-Ray Spectral Diagnostics
• Resolving the electron temperature discrepancies in HII Regions and Planetary Nebulae: kappa-distributed electrons
• Electrons in the Young Solar Wind: First Results from the Parker Solar Probe
• Collision Strengths for [O III] Optical and Infrared Lines
• On the interpretation and applicability of $\kappa$-distributions
• Confirmation of the link between central star binarity and extreme abundance discrepancy factors in planetary nebulae
• Non-Equilibrium Processes in the Solar Corona, Transition Region, Flares, and Solar Wind \textit{(Invited Review)}
• KAPPA: A Package for Synthesis of optically thin spectra for the non-Maxwellian kappa-distributions based on the CHIANTI database
• Suprathermal Electrons in the Solar Corona: Can Nonlocal Transport Explain Heliospheric Charge States?
• H to Zn Ionization Equilibrium for the Non-Maxwellian Electron kappa-distributions: Updated Calculations
• Signatures of the non-Maxwellian $\kappa$-distributions in optically thin line spectra \subtitle{I. Theory and synthetic Fe IX--XIII spectra}
• LOFAR observations of the quiet solar corona
• A Simple Method for Modeling Collision Processes in Plasmas with a Kappa Energy Distribution
• Imaging and Spectroscopic Observations of a Transient Coronal Loop: Evidence for the Non-Maxwellian $\kappa$-Distributions
• Theory of gyroresonance and free-free emissions from non-Maxwellian quasi-steady-state electron distributions
• Propagation Effects in Quiet Sun Observations at Meter Wavelengths
• Electron Temperatures and Free-Electron Energy Distributions of Nebulae from C II Dielectronic Recombination Lines
• The Continuum Emission Spectrum of Hf 2-2 near the Balmer Limit and the ORL versus CEL abundance and temperature Discrepancy
• Spectroscopic diagnostics of the non-Maxwellian $\kappa$-distributions using SDO/EVE observations of the 2012 March 7 X-class flare
• SOL-KiT -- fully implicit code for kinetic simulation of parallel electron transport in the tokamak Scrape-Off Layer
• Electron Energy Distributions in HII Regions and Planetary Nebulae: kappa-Distributions Do Not Apply
• Effective collision strengths for excitation and de-excitation of nebular [O III] optical and infrared lines with kappa distributed electron energies
• Scaling laws for electron kinetic effects in tokamak scrape-off layer plasmas
• The ultraviolet CII lines as a diagnostic of kappa-distributed electrons in planetary nebulae
• Temperature inversion in a gravitationally bound plasma: Case of the solar corona
• The diagnostic temperature discrepancy as evidence for non-Maxwellian coronal electrons
• Kinetic collisionless model of the solar transition region and corona with spatially intermittent heating

Cited by in corpus (1)

• The Quiet-Sun DEM Under Kappa: Diagnostic Degeneracy and the Failure of the Conductive Closure