Energy Aperture

Value chain · CLM-0088

In plain terms

The published abstract of the original paper states a testable condition for whether self-focusing can happen at all, and gives the growth length as 25 km in the upper ionosphere and 1 km lower down. Its formulas are set at 15 MHz and carry two factors the abstract does not explain.

The claim as recorded

The OSTI abstract of Perkins and Goldman 1981 (record 6536431) states the self-focusing condition 2cf/(pi f_p^2 l) < 1 with l about 25 km in the F region and about 1 km in the E region, and gives F- and E-region threshold power flux formulas normalised to 15 MHz with factors C_F ~ 1 and C_E ~ 1 that the abstract says depend on spatial and temporal growth rates. The journal's own abstract, read 2026-09-20, prints the F-region coefficient as 1.5 microwatts per square metre where the OSTI transcription prints 1.5 milliwatts; with the microwatt prefix the F-region form renormalised to 1 GHz is about 0.44 W/m2, in agreement with the 0.43 form of the 2004 review.

Scope and limits

ABSTRACT ONLY. The full text is closed access with no legitimate open copy anywhere, confirmed by Unpaywall returning is_oa false with zero locations across 24 attempted routes. The abstract gives C_F ~ 1 and C_E ~ 1 without their functional form. The OSTI transcription's milliwatt prefix on the F-region coefficient is a transcription error: the published abstract prints microwatts (read on the publisher's page 2026-09-20), so the apparent thousandfold disagreement with the Duncan form recorded at the second reading is closed; the E-region coefficient is 1 mW/m2 in both. No explicit numerical bound on the frequency to plasma frequency ratio is stated. That Perkins and Goldman 1981 themselves state these results, as the claim first put it, is not checkable in the archive, which holds the abstract and not the paper: the full text was sought 2026-09-02 across the routes above and not obtained (claim narrowed 2026-09-20 to the abstract).

What it assumes

No assumptions are recorded against this claim.

Where it comes from

SRC-116 Self-focusing of radio waves in an underdense ionosphere, J. Geophys. Res. 86(A2) 600-608, 1981
SRC-116 Self-focusing of radio waves in an underdense ionosphere, J. Geophys. Res. 86(A2) 600-608, 1981
Abstract quoted verbatim from OSTI record 6536431, cross-checked against an independent Google Scholar snippet for one corrupted symbol. The condition is "2cf/[pi]f_p^2 l < 1" with the abstract's parenthesis "(In the F region, l ~ 25 km is used, while in the E region l ~ 1 km.)". The formulas are P_c,F ~ 1.5 mW/m2 (f/15MHz)^3 (T_e/1000K)^4 (10^6 cm^-3/n_e)^3 C_F and P_c,E ~ 1 mW/m2 (f/15MHz)^3 (10^5 cm^-3/n_e) C_E. Dimensional check: the condition is dimensionless.
Related records
Answers question
QST-009 not published in this release
QST-010 not published in this release

Cite this

energyaperture.com/c/clm-0088

CLM-0088, Energy Aperture, as of 1981.

Connected records

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

Also from SRC-116
CLM-0093The thousand-fold disagreement between the two published versions was a lost micro prefix in the abstract I was working from. The papers...
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...