2026-10-04 University of Michigan plasma theory group (author copy), via Chrome

URL: https://plasmatheory.engin.umich.edu/wp-content/uploads/sites/519/2021/01/BaalrudPRL2009a.pdf [web] (An alternative copy is at cptc.wisc.edu, per Bing.) This is a 4-page open author copy of Baalrud, Callen and Hegna, PRL 102, 245005 (2009). The PDF text layer could not be read through Chrome's viewer, so p.1 was read from a screenshot [web: page image p.1]. Pages 2-4 were not read. The file was not downloaded: downloads need the owner's approval (about 4 pages, size not shown).

Points on p.1 [web: page image p.1]: - It calls the scattering of electrons in low-pressure discharges an anomaly "since the earliest days of plasma physics research". Langmuir's seminal paper (their ref. [1]) reported an electron velocity distribution that equilibrated to a Maxwellian much closer to the walls than Coulomb-collision theory could explain. - In Langmuir's experiment the calculated electron-electron collision length was much longer than the tube diameter, yet the distribution was Maxwellian at all velocities. Langmuir expected the high-energy tail to be depleted, and it was not. - Langmuir's tube is described as a spherical discharge tube about 3 cm in diameter with a hot filament. This differs from the 18 cm bulb in the project document, so it may be a different (1925) apparatus. - The name "Langmuir's paradox" was given by Gabor et al. (their ref. [5]; see the Nature note). The paradox "today remain[s] a serious discrepancy in the kinetic theory of gas discharges". - Proposed explanations listed: circuit oscillations interfering with probe measurements and scattering of electrons by photons (both from Langmuir [1]), sheath oscillations (Gabor [5]), electronic polarizability of neutrals [7], and "nonlocal" kinetics [8], which claims there may be no paradox. "None of the previous work has given a definitive answer." - Their proposal is that ion-acoustic instabilities in the presheath amplify collective fluctuations and so enhance electron scattering. Bearing: claim 5 (oscillations as the cause of the scattering) and claim 3 (ion-acoustic waves, the "electric sound waves" of Tonks and Langmuir). A 2009 mainstream proposal ties the anomaly to the ion-acoustic branch that the 1929 paper derived. This is a different branch from the electron-oscillation mechanism Merrill and Webb favoured.