Trichel: Quality Engineering (Step 4b)

Inputs checked: _text/manifest.json, _textprep.log, digest/ (1 file, all read), deep/ (1 file, both parts read), facts.json, claims.md, sites.md, research/ (8 notes, plus the saved Sattari 2011 thesis, which I extracted to /tmp/trichel_qe and searched), physicist.md, mathematician.md, contrarian.md, arbiter.md, primer.md, example.py (run). I also read the extracted text of the ESA paper directly for the spot checks.

Verdict: MINOR

The work is thorough and honest. The deep read is unusually careful. The reviews reconstruct where the "experimental" column came from, and the arbiter and primer keep the competing evidence (Zhang 2017, Gallo's channel, circuit independence, the Trichel biography) with its source and stake. No central verdict looks likely to move by more than one step. The defects below are fixable by a QE revision section in arbiter.md and edits to primer.md. One of them changes a background verdict (claim 1b).

1. Coverage

• Manifest: 1 document (the ESA 2010 paper K4, 15 pages, 0 OCR pages, 1 chunk). Digested: yes (digest/...e5dd69.01.md). Nothing skipped. PASS.
• facts.json has one entry for the one document, with how_read stated accurately ("digest + deep read (pp.1-15 ...)"). PASS.
• The Investigator's saved thesis (research/files/Sattari-2011-PhD-thesis-UWO.pdf) is not a manifest document. It was read in part by the Investigator, the contrarian and the mathematician, and the arbiter quotes them. That is acceptable for a [web] secondary source, but see defect R1 below: part of what it says was not carried forward.

2. Shortcuts

• The one key document was deep-read in full, and the equations and figures were read from page images (pp.4-13). PASS.
• The paper's literature review (pp.1-3) was covered by the digest only. The deep read's questions covered pp.3-15. The introduction carries evidence on claim 1b ("only in electronegative gases") and on the history of the mechanism (claim 2). That evidence was not weighed (defect M1). It is a small shortcut, but it touches a verdict.
• Thesis: read selectively (Ch. 6, Table 7.1, Ch. 8). Acceptable for a secondary source. The selective reading missed two pertinent points (R1, R2).

3. Accuracy spot checks (against the extracted text)

I also checked the primer's image-charge formula ΔE = q(D + R)/[4πε₀R(D − R)²] by hand: a point charge plus its image in a sphere at fixed potential. It is correct. The Check-yourself answers 1 and 3 recompute correctly (3.25e7 V/m; 5.1 us).

4. Missed material and retention defects

M1. The paper's own evidence for "only in electronegative gases" was left out (claim 1b). This changes a verdict. The paper states: "In electropositive (non-attaching) gases such as nitrogen, the corona current in the external circuit would be continuous without pulses" [read: p.1]. It also states: "Loeb et al [6] confirmed that these regular pulses exist only in electronegative gases" [read: p.2] (Loeb, Kip and Hudson, Phys. Rev. 60, 714, 1941). The arbiter rules 1b "Never properly tested as a universal rule" and the primer's evidence table says "Not as a universal rule". Both weigh only Zhang 2017 against the claim and cite nothing for it. Under SOURCE HONESTY, evidence for a claim has to be stated as well as evidence against it. A 1941 experimental confirmation cited in the document is a test on record. Its quality is unknown: nobody has read Loeb-Kip-Hudson, and which gases they used and how pure those gases were is not known. A further lead, [memory, medium], is Weissler, Phys. Rev. 63, 96 (1943), on negative point corona in pure and impure H2, N2 and Ar. My recollection is that it found pulses tied to electronegative impurities. It needs a web check before anyone uses it. - Remediation: in an arbiter QE revision, weigh Loeb-Kip-Hudson 1941 (as cited by SCA) against Zhang 2017. A likely revised verdict for 1b is "Established in the classical literature (Loeb et al. 1941, as cited [read: p.2]); contested by one 2017 experimental paper whose gas list is unverified". The arbiter should decide. Add both to the primer's evidence table row 1b, to §3.1 and to Check-yourself answer 5.

M2. Trichel's own account gives the positive-ion cloud the central role. That bears on the Zhang contest (claim 2). SCA describe Trichel's mechanism as follows. A positive cloud near the point raises the field there and lowers it between the positive and negative clouds. The positive ions then move into the point and "narrow the region of enhanced electric field and finally the ionization process stops" [read: p.2]. They also credit Trichel with explaining "the shielding effect produced by the positive ion cloud near the cathode" [read: p.1]. The primer's §3.2 and §1 present negative-ion blocking as "his explanation, still the textbook one". The arbiter calls the strong form (negative-ion clearing sets the period) Trichel's. Zhang's positive-ion account is therefore partly closer to Trichel's own emphasis than the record now suggests. - Remediation: one sentence in the arbiter (claim 2) and in primer §3.1/§3.2 separating what Trichel said, as SCA report it, from the later negative-ion-clearing emphasis.

M3. History of theories omitted from the primer. The digest and text give the line of earlier explanations [read: p.2]: - Loeb's successive-avalanche theory, which failed to explain the 1.5 ns rise in air; - Aleksandrov's parallel avalanches (1963), which predict fast rises and a slow pre-pulse foot; - Kekez, Savic and Lougheed's equivalent circuit (1982); - Ogasawara's analytic early-stage solution (1966); - Morrow 1985, 1D FD-FCT, only the first pulse, ion secondary emission ignored; - Napartovich 1997, 1.5D, pulse sequences in dry air for gaps under 1 cm; - MacAlpine and Yim 1995.

This history is the context for SCA's priority claim 3(v) and for the "rise time" question that the model never answers. - Remediation: a short paragraph in primer §3 (or §4), with the facts as stated by SCA. Also note in the arbiter that claim 3(v) could be checked by a literature search (Napartovich's 1.5D work and MacAlpine 1995 are the nearest prior art), rather than being simply untestable.

R1. The model's own periods also changed between the paper and the thesis. The record attributes the sign flip to the reference alone. The arbiter (B) and the primer (§5 step 6, "the thesis ... uses the 2.3 kV values and reports the opposite sign of error") explain the flip from underestimate to overestimate as a change of reference. But the simulated periods changed too: at 7 / 8 / 9 kV they are 11.33 / 6.31 / 3.39 us in the ESA paper and 13.5 / 9.9 / 6.6 us in the thesis [web: thesis Table 7.1]. At 9 kV that is nearly a factor of 2. The thesis model also uses different mobilities (2.24e-4 and 2.16e-4 m²/Vs against 2e-4), a circuit ODE with R_ext = 100 kOhm and Cd = 0.055 pF, and the 449.3 ionization law [web: thesis Ch. 6]. So both columns moved. This strengthens the arbiter's point that the gap "is not a stable property of the model", and it widens the open question "what did the 2010 code use?" The thesis also gives standard deviations of 0.6-2.1 us on its averages (the contrarian noted this), and the arbiter and primer do not carry them. The ESA 9 kV outlier (3.39 us) is the point that moved most. - Remediation: arbiter QE revision under claim 5 and open question 2; primer §5 step 6 (one added column or one sentence) and §6 rows 5.

R2. A negative finding from the thesis is missing from every review: charge ratio against Haidara, Denat and Atten. The Investigator recorded that the thesis's ratio Qi/Q > 0.5 disagrees with Haidara, Denat and Atten's measurements (< 0.5, high-pressure air), and that the authors attribute this to the surge resistor [web: thesis Ch. 8.5-8.6, via research/2026-10-04-uwo-scholaris.md item 13]. The thesis also compares average current with Gallo's law and gets 13.6-33.3 uA simulated against 17.1-40.0 uA, so the model is low on current while high on period. Neither point appears in the arbiter or the primer. Both bear on claim 3(ii) ("reproduces measured pulses"). The pressure trend (simulated period rises with pressure, said to agree with experiment [32]) is a point in the model's favour and should be kept beside them. - Remediation: add these to the arbiter's claim 3(ii) evidence and to the primer's evidence table, row 3(ii).

R3. Minor leads not carried forward (retention, low weight). - Amin, J. Appl. Phys. 1954: pre-onset streamers "sought in vain by G. W. Trichel in 1937" (Google snippet; research/2026-10-04-google.md item 17). It bears on Trichel's own programme. - Related models listed by the Investigator but absent from the primer's Further reading: Kokovin et al. 2021, Ferreira et al. 2025, Friebe et al. 2021, the Eindhoven 1987 thesis. - Trichel-era empirical laws quoted by SCA: frequency "varies linearly with the corona current" and inversely with tip radius at fixed current [read: p.1]. These are in facts.json but not in the primer. - Remediation: one line each in the primer (§3.1 and §9). No verdict change.

5. Process

• Source tags: present and honest throughout. [calc] is used consistently for reproduced arithmetic. Thesis-derived facts are tagged [web] with the thesis URL, and "via Investigator" or "via reviewers" is stated. The arbiter states openly what it did not read itself (Lama-Gallo, the Zhang full text). PASS.
• Web checks: the reviewers and the arbiter recorded their attempts. Zhang 2017 full text failed four times (reCAPTCHA, login redirect). The AIP page for Lama-Gallo returned 403. These are stated as failures, not hidden. The [memory, medium] items left unchecked (electron drift speed, collision frequency, Einstein relation at high E/N) support caveats only, and no verdict depends on them. PASS. Recommendation: the next Investigator run should try Zhang 2017 and Lama-Gallo 1974 in Chrome, since four scripted attempts have failed. These two sources would settle claims 1b, 4 and 5.
• Verdict scale: mostly consistent. Two uses stretch the scale definitions:
• (a) Claim 4 (numbers): "Not testable as stated" is used for "the reference values' origin is untraceable". The scale reserves that verdict for vague claims or interpretations. The issue here is provenance, which "Never properly tested" (quantitative match) describes better, as the physicist and mathematician wrote.
• (b) Claim 5 (gap): "Internally inconsistent across the authors' two documents". The scale defines this verdict as a claim contradicting its own equations, units or definitions. Inconsistency across two documents is arguable, but acceptable if the arbiter states that this is how the verdict is used.
• Remediation: the arbiter should either relabel these or add one sentence justifying the use.
• Primer vs STEP 4: all nine sections are present and in order. Symbols are defined (E/N, Td, α, η, γ, FEM, FCT, SCA). There is a step-by-step worked example with real numbers, and example.py reproduces it. There are five Check-yourself questions with answers. Reader profile respected: no tensors or field theory are needed. PASS, with two wording points:
• (a) §7, second bullet: "a comparison with 'experiment' whose numbers turn out to be a formula evaluated with the model's own onset voltage" states as fact what the arbiter explicitly declined to rule (B: "a calculation cannot refute a number whose origin is unknown"). It should read "whose numbers are indistinguishable from a formula evaluated with...". The primer must add no verdicts.
• (b) §4 table and §6 row 3(ii): the 0.2-0.3 us simulated width comes from the thesis's pressure study at -9 kV (Table 8.3). Say so.
• example.py: runs cleanly in the venv. Its output matches the primer. PASS. (Small note: at s = 0.5 mm its "tip-field depression by 115 pC" is 2.9e7 V/m, which exceeds the 2.3e7 V/m tip field. This shows the point-charge model breaks down that close to the tip. The primer quotes only the 1 mm and 2 mm values, which is fine. A comment in example.py would help a learner.)
• Absence of evidence: the arbiter analyses Trichel's post-1939 silence with competing explanations, and also the TRINITI/ABB report and Gallo's unpublished observations, each with what record would decide it. PASS.
• Interested parties: ABB's stake in the TRINITI report, the developers' stake in the "first successful" claim, and Gallo's observations relayed by his collaborators are all labelled. PASS.

6. Retention check (summary)

No material was dropped because a reviewer judged it negatively. The omissions are oversights in carrying material forward. They are not suppression.

7. Remediation actions

Deep reads (most important first): 1. Sonnet: ESA paper (slug Trichel-Pulses-ESA2010-K4-Sattari-e5dd69), pp.1-3. Question: "List every factual statement in the introduction and literature review, with its reference number. In particular: (a) the statements that Trichel pulses occur only in electronegative gases, that nitrogen gives continuous current, and that Loeb et al. [6] 'confirmed' this; (b) how SCA describe Trichel's own mechanism, especially the roles of the positive and negative clouds; (c) each earlier theory or model (Loeb, Aleksandrov, Kekez, Ogasawara, Morrow, Napartovich, MacAlpine, Soria), what it explained and what it failed to explain; (d) the empirical laws attributed to Trichel (frequency against current, tip radius, gap). Tag each [read: p.N]."

No other deep reads are needed. The rest of the paper has been read in full, with page images.

File changes: - facts.json: in key_claims or summary, add the Loeb et al. 1941 confirmation and the nitrogen statement [read: p.1-2], and Trichel's positive-cloud account [read: p.1-2]. - claims.md: under claim 1, note that the document cites Loeb et al. 1941 as confirming the electronegative-only rule. Under claim 2, note that SCA's account of Trichel emphasises the positive-ion cloud. - arbiter.md: add a "QE revision" section: - (1) re-weigh claim 1b with Loeb et al. 1941 [read: p.2] against Zhang 2017, and state the revised verdict; - (2) claim 2: separate Trichel's positive-cloud account from the negative-ion-clearing strong form; - (3) claim 5 and open question 2: record that the simulated periods also changed between the ESA paper and the thesis (11.33/6.31/3.39 against 13.5/9.9/6.6 us; changed mobilities, circuit ODE, ki), with the thesis's standard deviations of 0.6-2.1 us; - (4) claim 3(ii): add the Qi/Q disagreement with Haidara-Denat-Atten, the low average current against Gallo's law, and, in the model's favour, the pressure trend; - (5) claim 3(v): say that the priority claim could be checked against Napartovich 1997 (1.5D), MacAlpine and Yim 1995 and Soria 2007; - (6) justify or relabel "Not testable as stated" (claim 4 numbers) and "Internally inconsistent across documents" (claim 5). - primer.md: - §3.1: add the Loeb 1941 and nitrogen statements, Trichel's empirical laws (linear in current, inverse in radius), and a short history of the earlier theories (M3); - §3.2 and §1: say that Trichel stressed the positive cloud; - §5 step 6: add the thesis's simulated periods; - §6: revise row 1b if the arbiter changes it, and add the R1 and R2 points to rows 3(ii) and 5; - §7 bullet 2: change "turn out to be" to "are indistinguishable from"; - §4 and §6: attribute the 0.2-0.3 us width to the thesis pressure study at -9 kV; - §9: add Kokovin 2021, Friebe 2021, Ferreira 2025 and the Eindhoven 1987 thesis as unread related work; - update Check-yourself answer 5 if row 1b changes. - example.py: optional comment at Step 5 that the point-charge image estimate is invalid when the cloud is within about one tip radius (s = 0.5 mm gives a depression larger than the tip field). - Next Investigator run (outside this remediation): Chrome attempts on Zhang 2017 (gas list, purity), Lama and Gallo 1974 (tabulated periods at r = 100 um, d = 1 cm), Loeb, Kip and Hudson 1941, and Weissler 1943 (Phys. Rev. 63, 96; [memory, medium]: pure N2, H2 and Ar negative corona).

Recheck

Checked against the current arbiter.md (new "QE revision" section), primer.md, facts.json, claims.md and example.py.

• M1 (Loeb 1941 / nitrogen evidence, claim 1b): FIXED. The arbiter weighs Loeb-Kip-Hudson (as cited by SCA) and Weissler 1943 against Zhang 2017, gives a split ruling ("Established (provisional), contested by one 2017 experimental paper") and admits the earlier "Never properly tested" was wrong. The primer has it in §3.1, row 1b, further reading and Check-yourself answer 5. facts.json and claims.md carry it with [read: p.1-2]. Weissler is tagged as an abstract-level web summary with the full text unread.
• M2 (Trichel's positive-cloud account): FIXED. Arbiter claim 2 and primer §1 and §3.2 separate Trichel's wording as SCA report it from the later negative-ion emphasis. facts.json and claims.md are updated.
• M3 (history of earlier theories): FIXED. The primer has the history paragraph (Loeb, Aleksandrov, Kekez, Ogasawara, Morrow, Napartovich, MacAlpine) and the arbiter and primer name the prior art for checking claim 3(v).
• R1 (model periods also changed between paper and thesis): FIXED. The arbiter and primer §5 step 6 give 11.33/6.31/3.39 against 13.5/9.9/6.6 us, with ratios, the changed mobilities, R_ext, Cd and 449.3 law, and the 0.6-2.1 us scatter.
• R2 (Qi/Q against Haidara-Denat-Atten; low current; pressure trend): FIXED. These are in arbiter claim 3(ii) and primer row 3(ii), with the pressure trend kept as a point for the model and the authors' surge-resistor explanation noted as untested.
• R3 (minor leads): FIXED. Amin 1954, Kokovin, Friebe, Ferreira and the Eindhoven 1987 thesis are in primer §9. Trichel's empirical laws are in facts.json and the primer.
• Verdict labels (claim 4, claim 5): FIXED. Both are relabelled "Never properly tested", the arbiter explains why, and a before/after table is included. One leftover: the arbiter's section B (about line 29) still prints the old phrase "Internally inconsistent across the authors' two documents". The QE revision and the label table supersede it, so this is cosmetic and does not count as a defect.
• Primer wording (§7 bullet 2 "indistinguishable from"; 0.2-0.3 us width tied to the -9 kV pressure study, §4 and §6): FIXED.
• example.py caution at Step 5 (optional): FIXED. A comment now says the point-charge estimate fails within about one tip radius (s = 0.5 mm).
• Remaining, not defects: Zhang 2017, Lama-Gallo 1974, Loeb-Kip-Hudson 1941 and Weissler 1943 full texts are still unread. The arbiter lists them for a Chrome run by the next Investigator, as this QE recommended.

Final: PASS