Energy Aperture

Value chain · CLM-0093

In plain terms

The thousand-fold disagreement between the two published versions was a lost micro prefix in the abstract I was working from. The papers agree.

The claim as recorded

The apparent factor of 1,034 between the Perkins and Goldman coefficient and the Duncan coefficient is a unit-prefix transcription artefact and not a disagreement: Duncan's 1980 precursor states the relation at a 2.4 GHz normalisation with a coefficient of 6 W/m2, which renormalises to 0.434 W/m2 at 1 GHz and matches the 2004 review's 0.43, and working backwards that implies about 1.465 microwatts per square metre at 15 MHz against the retrieved abstract's reading of 1.5 milliwatts, so the two relations agree to about 2 per cent.

T0 own calculation · high confidence · as of 2026-09 · VER-415 CONFIRMED 2026-09-04 · VC06

Scope and limits

Inferred from agreement when written; the published abstract, read on the publisher's page 2026-09-20, prints the F-region coefficient as 1.5 microwatts per square metre, so the lost prefix is now read from the abstract itself and not only inferred. The full text of Perkins and Goldman remains closed access.

What it assumes

that the OSTI abstract's "1.5 mW/m2" is a transcription of 1.5 microwatts per square metre, which the arithmetic strongly implies but the full text would confirm

Where it comes from

SRC-117 LA-UR-80-1562 / CONF-800672-1, SPS Environmental Effects on the Upper Atmosphere, Intl...
SRC-116 Self-focusing of radio waves in an underdense ionosphere, J. Geophys. Res. 86(A2) 600-608, 1981

This is the project's own working, shown in full:

CALC-012 The finished calculation, on measured data
CALC-012 The finished calculation, on measured data
6 / 2.4^3 = 0.434. And 0.434 x (15/1000)^3 = 1.465e-6 W/m2 = 1.465 microwatts per square metre. Arithmetic in CALC-012.
Related records
Answers question
QST-010 not published in this release
Supersedes
CLM-0091 not published in this release

Cite this

energyaperture.com/c/clm-0093

CLM-0093, Energy Aperture, as of 2026-09.

Connected records

Other published records linked to this one. A list, not a judgement.

Also from SRC-116
CLM-0088The published abstract of the original paper states a testable condition for whether self-focusing can happen at all, and gives the growth...
CLM-0157The published abstract of a 1981 physics paper on self-focusing gives its threshold formulas scaled to 15 MHz, about 160 times lower than...
Also from SRC-117
CLM-0092Duncan's own 1980 paper says the flawed earlier calculation was Holway and Meltz's, and praises Perkins and Roble's as the first thorough...
CLM-0693The formula used here for when a microwave beam starts to focus itself in the ionosphere has now been checked against the original 1980...
CLM-0694The scientist who published the threshold formula says a single threshold number does not really exist. Whether the beam becomes unstable...
CLM-0695The 1980 paper says the SPS beam is expected to cause the ionosphere to focus it. It backs this with radar measurements from Arecibo, made...