Trichel: Arbiter (Step 3)

Inputs weighed: facts.json, claims.md, deep/ read of the ESA paper, physicist.md, mathematician.md, contrarian.md, sites.md and research/ notes (including the saved Sattari 2011 thesis, which the reviewers quoted). Tags: [read] document, [web] URL, [memory] with confidence, [calc] my own arithmetic (project venv, numpy).

Source note

The folder holds one document: Sattari, Castle and Adamiak (SCA), ESA Annual Meeting on Electrostatics 2010, paper K4, a numerical simulation of Trichel pulses. Its text is fully readable (no source gap for it). Nothing written by G. W. Trichel is in the folder. Everything said here about his 1938 work rests on the SCA paper's description, on the Investigator's [web] abstract, or on [memory]. Statements about Lama and Gallo (1974) rest on how Sattari's 2011 thesis quotes them: nobody in this review has read the original paper. My own attempt to confirm its content found only bibliographic data (J. Appl. Phys. 45, 103-113; DOI 10.1063/1.1662943; the study relates pulse current, frequency and charge to tip radius, gap and voltage) [web] search result listing, https://doi.org/10.1063/1.1662943 (not opened).

Plain-language background

A sharp needle at several kilovolts negative in air, facing a plate 1 cm away, glows faintly. The current is a train of very short spikes (Trichel pulses), one every 3 to 20 microseconds (us). In the standard picture [memory, high]: a free electron near the tip, where the field is about 10^7 V/m, ionizes air molecules in an avalanche. Positive ions fall into the needle within nanoseconds. Electrons drift out and attach to oxygen, forming slow negative ions. That cloud lowers the tip field below the ionization threshold, so the current stops until the cloud drifts away and the field recovers. The SCA paper is a computer model of that picture. It is a modelling paper, not an inventor's claim, and there is no "mainstream rejects it" story.

Numbers I recomputed where the reviewers differ

1. Table 1 ratios (simulated/"experimental" period): 11.33/21.85 = 0.519, 6.31/13.32 = 0.474, 3.39/9.09 = 0.373, 2.46/5.07 = 0.485 [calc]. All three reviewers agree. "About half" holds at three voltages, not at 9 kV.
2. Lama-Gallo law as quoted in the thesis: f = K1 V (V - V0)/(r d^2), K1 about 27 kHz mm^3/kV^2, V0 = 2.3 kV [web] Sattari thesis Ch. 8.2 (research/files/Sattari-2011-PhD-thesis-UWO.pdf). For r = 0.1 mm, d = 10 mm: T = 11.26, 8.12, 6.14, 3.87 us at 7, 8, 9, 11 kV [calc]. The thesis column "Gallo's T" (11.3, 8.1, 6.1, 4.8 at 7 to 10 kV) is this law evaluated, so it is consistent with Lama and Gallo's own onset.
3. Fit of the ESA "experimental" column: regressing 1/(T V) on V gives slope 2.848 kHz/kV^2 (K1 = 28.5) and V0 = 4.705 kV; residuals are at most 0.008 kHz/kV [calc]. Against the same law with K1 = 27 and V0 = 4.7 kV the four values are uniformly 0.949 to 0.950 of it [calc]. The physicist, mathematician and contrarian differ only in how they describe this (the mathematician's "K = 350" is the same K1 in different units; the contrarian's "K1 = 28.5" matches mine). The three are therefore in agreement on the numbers. The ESA column sits exactly on the Lama-Gallo functional form with V0 = 4.7 kV, which equals the model's own computed onset [read: p.7].
4. The simulated periods fit the same form poorly: V0 = 4.64 kV, K1 = 62, residuals up to 5.7 kHz/kV (the 9 kV point is the outlier) [calc]. The model reproduces the direction of the voltage dependence, not Lama and Gallo's scaling.
5. Simulated divided by the law with Lama and Gallo's own V0 = 2.3 kV: 1.01, 0.78, 0.55, 0.64 at 7, 8, 9, 11 kV [calc] (contrarian's numbers, confirmed). So against that reference the 7 kV period is within 1%, and there is no uniform factor of two.
6. Physicist's tip-field estimate E_tip = 2V/(R ln(4d/R)) with R = 100 um, d = 1 cm, V = 7 kV: ln 400 = 5.99, E = 2.34e7 V/m [calc], matching the paper's Fig. 10 peak of 2.2 to 2.45e7 V/m [read: page image p.11, via deep read]. At 4.7 kV the same formula gives 1.57e7 V/m, well above the corrected ionization threshold of about 87 Td (2.1e6 V/m) [calc, from reviewers]. The model's "onset" of 4.7 kV therefore did not come from the model's own coefficients (the thesis says Peek's formula [web] thesis p.96, via the mathematician).
7. Ionization law: printed 10^(11.93 - 4.493/EN) gives ki about 7e11 /s at 41 Td and nearly constant above, against attachment ka = 6e6 /s, so no threshold. The thesis prints 449.3 [web] thesis Ch. 6, p.91; with that, ki = ka near 87 Td [calc, physicist and mathematician agree]. Misprint confirmed.
8. Magnetic confinement of Gallo's channel (the thesis authors' suggestion): B = mu0 I/(2 pi r). For I = 1.8 mA at r = 1 um that is 0.36 T (mathematician, contrarian); the physicist's "0.8 T" used r = 0.5 um and a garbled line, so the figures differ only by the assumed radius. Electron cyclotron frequency at 0.36 T is about 6e10 rad/s [calc], below an electron collision frequency of order 1e12 /s at 1 atm [memory, medium], so confinement is doubtful. Untested, unsupported by this estimate; not ruled out by experiment.
9. Charge check on the thesis: a triangular 1.8 mA pulse 0.3 us wide carries about 0.27 nC [calc], within a factor 2.5 of the thesis's 115 pC at r = 100 um. Same order; no more is claimed.

Where the three reviewers disagree, and my ruling

A. Does "only in electronegative gases" (claim 1) count as "Tested, not supported"? The contrarian says yes, the physicist and mathematician say never properly tested as a universal rule, contested. I rule for the latter. The single contrary source is Zhang, Xia, Jiang and Ouyang, Sci. Rep. 7:10135 (2017), whose abstract, as quoted by the Investigator, says Trichel pulses occur "in various gases rather than only in electronegative gases", with positive ions predominant and negative ions "not necessary" [web] https://pmc.ncbi.nlm.nih.gov/articles/PMC5579005/. It is one peer-reviewed experimental group, documented in one paper with no second source found. It is evidence and I keep it. But I could not read the full text: PMC and nature.com both blocked me again (reCAPTCHA, login redirect), and Europe PMC returned nothing. So I cannot say which gases were tested or how ion removal was done. That is a failed web check, stated as such. A single unreplicated paper is not a controlled test that the textbook statement fails.

B. Is claim 5 "Refuted by calculation" (contrarian)? No. The contrarian's own caveat is right: the evidence is a numerical coincidence (a 2-parameter law matching 4 points to within 0.01 kHz/kV), and the authors never say how the column was made. Gallo, thanked in the paper, may have supplied fitted values, or the authors may have rescaled for a different geometry. A calculation cannot refute a number whose origin is unknown. Strongest supportable statement: the column is indistinguishable from the Lama-Gallo form with V0 = 4.7 kV, not with Lama and Gallo's published V0 = 2.3 kV; the thesis (same authors) uses 2.3 kV and obtains the opposite sign of error. The "half" shortfall is therefore not a stable fact about the model. Verdict: Internally inconsistent across the authors' two documents (reference values for 7 kV differ 21.85 vs 11.3 us), and the stated cause is Never properly tested.

C. Internal consistency of claim 3. The mathematician and physicist call the printed system inconsistent; the contrarian says "misprint, so not inconsistent". All agree on the facts: Eqs. (6) and (7) have sources proportional to Np and Nn where ionization and attachment should be proportional to Ne [read: page image p.4, via mathematician]; ki exponent misprinted; the recombination term lacks a 1/e if N is charge density; D = kB T k/e has an undefined k; "N_O2" is the total air density 2.46e25 /m^3, not the O2 density (about 5e24) [calc]. Whether the 2010 code used the correct forms is unknown. I split: as printed, Internally inconsistent; as an unknown code, not shown wrong.

D. Does the pulse-shape mismatch matter? All three agree that the paper never compares rise time, width, amplitude or charge, and that it quotes "tens of ns" widths and a 1.3 ns rise [read: p.1] while its simulated pulses are hundreds of ns wide (thesis Table 8.3, 0.2 to 0.3 us) [web, via Investigator]. The 2017 experimental paper from the same group reports measured shape independent of radius, voltage and gap and "some discrepancies" with simulation [web] https://www.sciencedirect.com/science/article/abs/pii/S0304388616301735 (abstract). I weigh this as the strongest evidence against the "reproduces the measured pulses" reading. It rests partly on the thesis, which I did not independently open beyond the reviewers' quotes.

E. Mechanism (claim 2). Physicist and contrarian say plausible, untested for the strong form; mathematician agrees; all accept the weak form (ion space charge suppresses the tip field). My order-of-magnitude check agrees with theirs: a negative ion with mu = 2e-4 m^2/Vs moves 1 mm in about 0.5 to 5 us in fields of 1e6 to 1e5 V/m [calc], the right order for the 3 to 20 us period. Competing evidence, all kept: Zhang 2017 (positive-ion rebuild; negative ions not necessary); Gallo's micrometre-wide channel, reported in one source (Sattari thesis Ch. 8.3, relaying Gallo's own unpublished microscope observations, no independent publication found), which the thesis authors say is "not described by present theory or simulations"; and Trichel's 1938 statement that the pulses are not affected by external circuit constants [web] https://journals.aps.org/pr/abstract/10.1103/PhysRev.54.1078 (abstract, via Investigator) against the thesis simulations in which the period depends on R_ext. One fact to note: the R C time constant for 100 kOhm and 0.055 pF is 5.5 ns [calc], far below the microsecond period, so how R_ext changes the period in the model is not explained in what I read. Gallo's -2.3 kV onset also conflicts with Dordizadeh 2017's measured -4 to -6 kV for 19 to 55 um tips [web, abstract], so even the experimental record has two onsets (tip sizes differ, so this is a difference, not a proven contradiction).

Corrected claim list (with final verdicts)

Verdict scale from Step 2.

1. A negative point-plane corona in air emits a regular train of Trichel pulses, in a limited voltage range, only in electronegative gases. - Reviewers: all agree pulses in air are established. Split on the "only electronegative" part (see A). - Evidence: Trichel 1938 oscillograms; Loeb 1939 Figs. 243, 247, 248 [web] https://archive.org/stream/in.ernet.dli.2015.74804/2015.74804.Fundamental-Processes-Of-Electrical-Discharge-In-Gases_djvu.txt (via Investigator); Loeb, Kip and Hudson 1941, Lama and Gallo 1974, Dordizadeh 2017 [memory, high on the first two; the rest from SCA refs and the abstract]. - Tension kept: Trichel's "frequency independent of gap length" vs Lama and Gallo's f proportional to 1/d^2 [web, thesis Ch. 8.2]; probably different regimes [memory, medium]. Unresolved. - Final verdict: pulses in negative needle-plane air corona: Established. "Only in electronegative (attaching) gases": Established in the classical literature, provisionally; contested by one 2017 experimental paper [revised in QE revision R1; was "Never properly tested"].

2. The pulsing is space-charge dynamics: positive ions absorbed in nanoseconds switch ionization off; slow negative-ion drift sets the period. - Agreed: order of magnitude right; mechanism is Trichel's own (1938 abstract, "space-charge formation and clearing"). Models by several groups agree qualitatively, but they share assumptions, so that is agreement among models, not independent experimental proof. - Final verdict: weak form (ion space charge quenches the avalanche): Established. Strong form (negative-ion clearing alone sets the period): Plausible, untested (unchanged; QE revision R2 adds that this emphasis is Loeb's modification, not Trichel's own account as SCA report it). Competing claims kept in the record (Zhang 2017; Gallo's channel; circuit independence).

3. A 2D FEM-FCT three-species model reproduces a regular pulse train, a post-pulse and a large delayed first pulse; first such 2D simulation at several voltages. - (i) A drift-diffusion-Poisson model gives regular pulses: Plausible, untested as a quantitative predictor (the model reproduces the timescale order; others, Morrow 1985, Napartovich 1997, Soria 2007 per SCA's references [read: p.14-15], found pulsing too; I did not read them). - (ii) "Reproduces the measured pulses": Tested, not supported quantitatively where compared (QE revision R4 adds two more comparisons, one against and one for the model) (period depends on the reference; pulse width about 10 times the quoted literature values; onset 4.7 vs 2.3 kV measured by Gallo). - (iii) Large first pulse (25 to 37 mA against about 2 mA) and post-pulse: Never properly tested. No experiment cited; the first pulse depends on an unstated seed charge; the authors themselves say the post-pulse "can be a source of instability in the calculations" [read: p.8]. These may be numerical or physical; undecided. - (iv) Printed equations: Internally inconsistent as printed (typos listed in C); the code is unseen. - (v) "First successful": Never properly tested [relabelled in QE revision R5; was "Not testable as stated"]: a priority claim by the developers, checkable against named prior art (Napartovich 1997, MacAlpine and Yim 1995, Soria 2007), not yet checked. - Independent replication of this code: none found; follow-ups are by the same group.

4. Pulse frequency rises with voltage; simulated period falls from 11.33 us at -7 kV to 2.46 us at -11 kV, following Lama and Gallo (21.85 to 5.07 us). - Agreed: trend established. Averages recomputed: mean(13.38, 10.67, 10.85, 10.4) = 11.33 and mean(3.53, 3.30, 3.35) = 3.39 [calc]; the first interval is excluded. At 7 kV the first interval (11.5 us) is shorter than the second (13.38 us), contrary to the paper's text [read: p.7]. The 9 kV mean rests on three intervals; no uncertainties. - Final verdict: trend Established. The quoted "Lama and Gallo" numbers: Never properly tested [relabelled in QE revision R5; was "Not testable as stated"]: their origin is untraceable and nobody has compared them with Lama and Gallo's tables; they equal the Lama-Gallo form with the model's onset. The simulated numbers do not follow the Lama-Gallo scaling (item 4 above).

5. Simulated periods are about half the measured ones, cause "approximations in the numerical technique". - Final verdict: the stated cause: Never properly tested (the paper tests nothing; the thesis shows sensitivity to R_ext and mobility, little to the secondary-emission coefficient). The size of the gap: Never properly tested as a property of the model [relabelled in QE revision R5; was "Internally inconsistent across documents"]; the authors' two documents give different gaps and different simulated periods (see B and QE revision R3), so it is not a stable property. Candidate causes, all untested here: constant ion mobility, R_ext (unstated in the paper), tip geometry (Gallo's channel; a fitted 10 um effective radius brought the thesis period to within 15% and current within 23%, a tuned parameter) [web, thesis Ch. 8.4 via Investigator], reduced oxygen kinetics applied to air, 5 um mesh around a 25 to 50 um active layer.

What would settle it

• Claims 4 and 5, the reference data: read Lama and Gallo (J. Appl. Phys. 45, 103) and compare their tabulated periods at r = 100 um, d = 1 cm with 21.85, 13.32, 9.09, 5.07 us. Or ask the authors how the column was made. If the numbers are Gallo's data, then V0 depends on something not in the quoted law; if they are the formula with V0 = 4.7 kV, the "half" gap is an artefact.
• Claims 3 and 5, the model: rerun the code with the corrected ki, thesis circuit (R_ext = 100 kOhm, Cd = 0.055 pF), mesh and time-step refinement, and a different seed charge; see whether the first pulse and post-pulse survive. A pulse-shape comparison (rise, width, amplitude, charge) against a fast-scope measurement at -7 kV, 1 cm, 100 um tip would be the real test.
• Claim 2, mechanism: change negative-ion mobility or sweep the ions away (gas flow across the tip, or compare gases with different attachment) and see whether the period tracks the model or Zhang's positive-ion account.
• Claim 1, electronegativity: obtain the Zhang 2017 gas list and methods; replicate in purified nitrogen or argon with a clean needle.
• Gallo's channel: a microscope or imaging experiment on negative tips (0.12 to 2 um width claimed, wobble, -2.3 kV onset), done by a group other than Gallo's collaborators.
• Circuit dependence: measure the period against R_ext (and added capacitance) in one apparatus; Trichel 1938 says no effect, the thesis model says yes.

Absence-of-evidence analysis

Trichel's own research record goes quiet after 1939. This is an anomaly worth analysing, not a neutral gap. - Facts: Phys. Rev. 54, 1078 (negative corona, 1938) and Phys. Rev. 55, 382 (positive corona, 1939) [web] https://link.aps.org/doi/10.1103/PhysRev.54.1078, https://link.aps.org/doi/10.1103/PhysRev.55.382 (via Investigator). Gervais W. Trichel (1898-1990), Army officer: Berkeley Ph.D. 1938, "Captain, Ordnance Corps" in Loeb's 1939 preface, later Ordnance rocket development, Chrysler 1947-63 [web] Redmond and Smith, Project Whirlwind (archive.org); Loeb 1939 preface (archive.org); Prabook https://prabook.com/web/gervais_william.trichel/90642 (a compiled biography). - Competing explanations: 1. Career change to military service: strongly supported by three independent-looking sources; his doctorate was done while serving as an officer. 2. Wartime secrecy of later work: plausible for the 1940s ordnance and rocket work, but it explains why his later work is not in open physics literature, not why corona papers stopped. No document found. 3. Suppression or dismissal of the corona work: no evidence. Loeb thanked him and reproduced his oscillograms; later groups cited and extended the work for 85 years. 4. Commercial secrecy: no evidence. - Not found: the Berkeley dissertation itself (WorldCat blocked), the Library of Congress Vannevar Bush finding aid entry "Trichel, Gervais W., 1949", NASA, Find a Grave and Military Times pages. These would confirm the career timeline. - Verdict on this anomaly: best explained by explanation 1. Not proven by any one source; it is the best supported with what was found.

Second gap in the record: the 1997 TRINITI (Akishev et al.) report for ABB, from which the key rate constants come, is not online [read: p.4, p.15]. ABB is a commercial party with a stake in corona modelling. The report is the authors' source and is unverifiable by this review. What would decide: a copy, or the later Napartovich/Akishev publications (not reached). Third gap: Gallo's microscope observations appear in the 2011 thesis only; the 2010 paper thanks Gallo yet omits them [read: p.14]. Explanations: they were not yet written up; they conflict with the smooth-tip model; the observation was informal. Evidence for each is thin. Decided by finding Gallo's lab records or a later paper.

Open questions

1. What exactly are Lama and Gallo's measured periods at the 1 cm / 100 um geometry, and what is their V0 for it?
2. Did the 2010 code use ki with 449.3, an algebraic or ODE circuit, and what R_ext?
3. Is the 25 to 37 mA first pulse real? Do real needles show a start-up spike at turn-on?
4. Why is the simulated pulse about 0.2 to 0.3 us wide when measured pulses are tens of ns?
5. Is the narrow ionization channel at the tip real, and does it set the period (effective radius 10 um fit)?
6. Do negative ions matter (Zhang) or not (textbook)? Which gases did Zhang test?
7. Why is the period independent of R_ext in Trichel (1938) and dependent in the model?
8. Why do Gallo (-2.3 kV) and Dordizadeh (-4 to -6 kV) disagree on onset?

Failed or incomplete web checks

• Zhang 2017 full text: PMC reCAPTCHA, nature.com login redirect, Europe PMC no result (3 attempts). Facts about it rest on the abstract relayed by the Investigator.
• Lama-Gallo 1974: bibliographic data only [web] search; formulas from the thesis.
• Medium-confidence [memory] facts that no verdict depends on: electron drift speed in air about 2e5 m/s; electron collision frequency near 1e12 /s; Einstein relation at high E/N. Left as [memory, medium], used only as supporting caveats.
• Budget used: 4 web calls of 8.

QE revision

Prompted by qe.md (verdict MINOR) and the new deep read of the ESA paper's introduction and literature review (pp.1-3; deep/Trichel-Pulses-ESA2010-K4-Sattari-e5dd69.md, last section). I also re-checked the thesis (research/files/Sattari-2011-PhD-thesis-UWO.pdf, extracted text) for the numbers in R3 and R4, and used 2 more web calls (6 of 8 used in total). The deep read is by an agent reading the paper, and its reading of earlier theories is the SCA authors' characterisation (they have a stake in presenting prior work as limited), not a check of those papers.

R1. Claim 1, "only in electronegative gases": evidence for was left out; verdict revised

What the paper says [read: p.1-2, deep read A]: "The Trichel pulses only occur in electronegative gases ... In electropositive (non-attaching) gases such as nitrogen, the corona current in the external circuit would be continuous without pulses" (p.1, no reference number, and phrased conditionally, "would be"); "Loeb et al [6] confirmed that these regular pulses exist only in electronegative gases" (p.2). Ref [6] is Loeb, Kip, Hudson (and Bennett), Phys. Rev. 60, 714 (1941). The paper gives no gases or measurements for [6]. It also says pulses in SF6, a strongly attaching gas, are "more irregular" [read: p.1, citing Van Brunt and Leep 1981], so even in attaching gases the pulses are not uniformly regular.

New web evidence, each from a search listing and abstract summary only (full texts not opened): - Weissler, Phys. Rev. 63, 96 (1943), "Positive and Negative Point-to-Plane Corona in Pure and Impure Hydrogen, Nitrogen, and Argon": Trichel pulses "are not observed in pure H2 and N2 but are immediately produced upon the addition of traces of O2" [web] https://journals.aps.org/pr/abstract/10.1103/PhysRev.63.96 (abstract as relayed by search summary). This confirms the QE's [memory, medium] lead and is an independent, direct experiment on the nitrogen case. - Loeb, Kip, Hudson 1941: the abstract summary says Trichel's theory "is applicable except as modified by the influence of negative ions" [web] https://link.aps.org/doi/10.1103/PhysRev.60.714 (search summary). It does not state the gas result, so the SCA sentence about [6] is still carried by SCA alone. - Against, still on the record: Zhang, Xia, Jiang, Ouyang, Sci. Rep. 7:10135 (2017): pulses "in various gases rather than only in electronegative gases" [web] https://www.nature.com/articles/s41598-017-10118-2 (title and abstract; full text still unread by me, so the gas list, purity and ion-removal method are unknown). A further title I did not open and cannot weigh: "Pulsed mode of a negative corona in nitrogen: I. Experiment", Technical Physics (2001) [web] https://link.springer.com/article/10.1134/1.1378130 (title only). It suggests pulsing in nitrogen has been studied; whether in pure nitrogen is unknown.

Weighing. For: an old, direct, two-sided test (pure gas, then trace O2 added) plus SCA's report of Loeb. The theory also agrees (no attachment, no slow negative ion). Against: one modern experimental group, with unknown gas purity. A 1943 result that a trace of O2 switches pulses on also shows how Zhang's result could differ: contamination or ion production by other routes cannot be excluded from the abstracts. That is an explanation, not a finding, and I do not use it to dismiss Zhang.

Ruling: split. "Pulses require an electron-attaching component (O2 in air)": Established in the classical literature (Weissler 1943 abstract; Loeb 1941 as cited by SCA), provisional until the full texts are read. "Only in electronegative gases, in the strict universal sense": contested, not settled, because Zhang 2017 is an experimental claim against it that I cannot read. Because the scale needs one label, I use Established (provisional), contested by one 2017 experimental paper. What would revert it: Zhang's full text showing pure, non-attaching gas with a clean needle and pulses persisting. Change from the earlier arbiter text: I called this "Never properly tested". That was wrong: tests exist (Weissler; Loeb as cited), and I had not weighed them.

R2. Claim 2: whose mechanism is "the textbook one"?

SCA describe Trichel's own account [read: p.2] as: a negative cloud forms far from the point and a positive cloud near it; the positive cloud raises the field at the point and lowers it between the clouds, "so no ionization can take place beyond the positive ion cloud"; the positive ions move into the point, "narrow the region of enhanced electric field and finally the ionization process stops". On p.1 they credit Trichel with the "shielding effect produced by the positive ion cloud near the cathode". The deep read notes the two passages are not reconciled. The Loeb 1941 abstract (above) says Trichel's theory holds "except as modified by the influence of negative ions". So the emphasis on negative-ion clearing setting the period is at least partly later, and Zhang 2017's emphasis on positive ions is closer to Trichel's own wording than my earlier text suggested. Effect: the weak form stays Established; the strong form stays Plausible, untested; the Zhang dispute is a dispute about how Trichel's picture was later modified, not a clean "textbook against a newcomer". I keep my earlier statement that Trichel's 1938 abstract says "space-charge formation and clearing".

Citation problem found by the deep read [read: p.14]: SCA's reference [2] is printed as Trichel, "The mechanism of the positive point-to-plane corona in air at atmospheric pressure", Phys. Rev. 55, 382 (1938 as printed). My own Absence-of-evidence section lists Phys. Rev. 54, 1078 as the negative-corona paper and 55, 382 as the positive-corona paper (1939). So SCA seem to cite the positive-corona paper for a negative-point mechanism, or mis-print the title or year; the paper does not remark on it. Unresolved; I cannot tell which Trichel paper the quoted mechanism comes from.

R3. Claim 5 and open question 2: the simulated periods also differ between the two documents

Thesis Table 7.1 (Rext = 100 kOhm, -7 to -10 kV) [web] thesis p.111, research/files/Sattari-2011-PhD-thesis-UWO.pdf, text checked by me: simulated T = 13.5, 9.9, 6.6, 6.2 us; standard deviations 2.09, 0.81, 0.61, 0.80 us; "Gallo's T" 11.3, 8.1, 6.1, 4.8 us. ESA Table 1 simulated: 11.33, 6.31, 3.39 us at 7, 8, 9 kV. ESA divided by thesis: 0.84, 0.64, 0.51 [calc]. Thesis simulated divided by thesis "Gallo's T": 1.19, 1.22, 1.08, 1.29 [calc]. So both columns moved: the model gave periods about 0.5 to 0.84 times as long in 2010 as in the thesis (changed mobilities, circuit ODE with Rext = 100 kOhm and Cd = 0.055 pF, and the 449.3 ionization law, per the QE and thesis Ch. 6), and the reference moved from 21.85 to 11.3 us at 7 kV. The thesis's own scatter (0.6 to 2.1 us on an average of a few pulses) is as large as some of the differences discussed; the ESA paper gives no scatter. The ESA 9 kV point (3.39 us, three intervals) is the outlier of its set (my item 4 above) and the point that changed most. This reinforces ruling B: the "about half" gap is not a stable property of the model. It also widens open question 2: we cannot say which equations and parameters the 2010 code used, and the thesis cannot stand in for it. Limit: the thesis runs only to -10 kV, so the 11 kV point has no thesis counterpart.

R4. Claim 3(ii): two further comparisons from the thesis

• Against the model: the thesis's charge ratio Qi/Q (pulse charge over average pulse charge) is above 0.5 in simulation; Atten's paper [ref 32, Haidara, Denat, Atten] reports it below 0.5 in high-pressure air with no external resistance [web] thesis Ch. 8.6-8.7 (text lines checked by me). The authors say the conditions differ (they simulate atmospheric pressure with 10 to 100 kOhm), that the observation was "not confirmed", and extrapolate that at zero resistance the ratio could fall below 0.5 because it falls as Rext drops from 100 to 10 kOhm. So this is a mismatch at non-matched conditions and an untested extrapolation, not a clean failure. I record it as unresolved.
• Against the model: average current in thesis Table 7.1 is 13.6, 19.0, 28.1, 33.3 uA against Gallo's 17.1, 23.7, 31.4, 40.0 uA, that is 0.80, 0.80, 0.89, 0.83 of Gallo [calc]. The model is low on current and high on period in that table. (In the fitted 10 um-radius case of Ch. 8.4 it is 23% high on current, so the sign depends on the tuned geometry.)
• For the model: the thesis reports the simulated period rising with pressure and says this is compatible with experiment (ref 32) [web] thesis Ch. 8.5 and summary (I checked only that the thesis states it; I did not check the experimental data).
• Net: claim 3(ii) stays Tested, not supported quantitatively where compared, with the pressure trend kept as a point in the model's favour.
• Pulse width: the 0.2 to 0.3 us simulated widths are from thesis Table 8.3, a pressure study at -9 kV (0.30, 0.28, 0.19 us at 0.8, 1.0, 1.2 atm), not the 7 kV case; the comparison with "tens of ns" is therefore at 1 atm, -9 kV.

R5. Claim 3(v), and two labels that stretched the scale

• 3(v) "first successful" priority claim: the deep read gives the nearest prior art as SCA describe it: Napartovich et al. 1997 (1.5D model of Trichel pulse sequences in dry air for gaps under 1 cm), MacAlpine and Yim 1995 and Kekez et al. 1982 (simplified models of pulse chains), Soria et al. 2007 (particle-in-cell, pure oxygen), Morrow 1985 (1D, first pulse only, ion secondary emission ignored per SCA). SCA's claim is specifically for a 2D three-species model at several voltages, which is narrower than "first simulation of Trichel pulse trains". None of these papers has been read by this review. So the claim is checkable, and I relabel it Never properly tested (was "Not testable as stated").
• Claim 4 numbers: relabelled Never properly tested. QE is right that "Not testable as stated" is reserved for vague claims; the problem here is provenance and the lack of a comparison with Lama and Gallo's tables.
• Claim 5 gap: relabelled Never properly tested. "Internally inconsistent" is defined on the scale as contradicting its own equations, units or definitions. A mismatch between two documents by the same authors is a different thing; I describe it in words (R3) instead of using the label. The label "Internally inconsistent" stays for claim 3(iv), the printed equations, where it fits the definition.
• The ESA abstract says that with increased voltage the pulse frequency "decreases in agreement with previously reported experimental data" [read: p.1, deep read D]; the body (p.12) and Table 1 show the period falling, so frequency rising. I treat the abstract as a misstatement and the trend (claim 4) stays Established. The rise time appears as 1.3 ns (p.1, from Zentner [4]) and 1.5 ns (p.2, Loeb's theory, no reference); I do not resolve which.

R6. Additional leads kept (no verdict change)

• Trichel's empirical laws, as SCA report them [read: p.1]: frequency varies linearly with corona current; varies inversely with point radius at the same current; is independent of gap length. These sit beside Lama-Gallo's f proportional to 1/d^2 at fixed voltage (my claim 1 tension). They are not necessarily in conflict: one holds at fixed current and the other at fixed voltage [memory, low], not checked.
• Earlier theories and their reported failings [read: p.2], as characterised by SCA: Loeb's successive avalanches (could not explain the 1.5 ns rise); Aleksandrov 1963 parallel avalanches (predict fast rise and a slow foot); Kekez, Savic, Lougheed 1982 equivalent circuit; Ogasawara 1966 analytic early rise (exponential growth only); Morrow 1985; Napartovich 1997; MacAlpine and Yim 1995.
• From the QE retention table (not weighed by me): Amin 1954, pre-onset streamers "sought in vain by G. W. Trichel in 1937" (Google snippet, research/2026-10-04-google.md); Kokovin 2021, Ferreira 2025, Friebe 2021, Eindhoven 1987 thesis as unread related work.
• Interested parties unchanged: the SCA authors characterise prior work while introducing their own model; the TRINITI/ABB report remains the authors' source and is not online.

Changes to the verdicts (summary)

Still not done

• Full text of Zhang 2017, Weissler 1943, Loeb-Kip-Hudson 1941 and Lama-Gallo 1974 remain unread. Weissler and Loeb are from abstract-level web summaries. A Chrome run by the next Investigator should open these four, plus the 2001 Technical Physics nitrogen paper.
• Open question added: which Trichel paper does SCA's quoted mechanism come from (Phys. Rev. 54, 1078 or 55, 382)?