A Logical and Empirical Audit of Langmuir-Probe Plasma Diagnostics

Langmuir probes have supplied electron densities and temperatures for a century, and mission and facility archives now hold between 109 and 1011 reduced current–voltage sweeps. The size of this record is often taken as evidence that the method is accurate. We test that inference in two ways. First, we write a probe measurement as a first-order theory in the sense of Mendelson (2015). The reduction assumptions are proper axioms, the recorded trace supplies atomic sentences, and the plasma being measured is the intended interpretation. In that language, agreement among values reduced under the same axioms holds in every model of the theory, so it cannot show that the plasma is one of those models. Only a reference whose deduction does not depend on the probe axioms, evaluated at the same plasma state, with its discrepancy left unrescaled, can bound the probe’s error. This gives three conditions (C1, freedom from dependence on the probe axioms; C2, co-location; C3, disclosure) and a partition of reported values into anchored (A), calibrated (B) and self-referential (C) classes. Second, we apply the test in a pre-registered audit of 80 open-access papers drawn at random from OpenAlex and of ten facility and mission data pipelines. Of papers about probes, 77.5% are class C (Wilson 95% interval 62–88%). Of papers that use a probe in passing, 87.5% are (74–95%). None of the 52 papers that report a probe electron temperature anchors it. Weighted by traces, the class C share of the pipelines is 6–85% as registered and 41–93% when each anchor is confined to the conditions it sampled; in both readings the outcome turns on one fusion archive whose documentation reports no cross-check. Where anchors exist, the probe differs from the reference by 2% to a factor of three in density and by up to several hundred kelvin in temperature. Checking the analysis against Mendelson’s catalogue of paradoxes finds no contradiction. It finds one invalid quantifier step in the registered pipeline coding, which we correct, one hidden dependence in temperature references, and a self-application of Epimenides type: the audit is itself class C until a coder independent of the first repeats it.