Value chain · CLM-0693
In plain terms
The formula used here for when a microwave beam starts to focus itself in the ionosphere has now been checked against the original 1980 paper that first published it. Every part matches: the constant, the way it scales with frequency, density and temperature, and the assumption that one correction factor is about one.
The claim as recorded
The thermal self-focusing threshold relation used here throughout is now confirmed at its primary source. Duncan (1980) states it as P_thresh (W/m2) ~ (6 W/m2)(10^6/n)^3(T_0/1000 K)^4(f/2.4 GHz)^3 C_F, with C_F "roughly unity, depending on spatial and temporal growth rates", valid for underdense heating where the microwave frequency exceeds the plasma frequency. Renormalised from 2.4 GHz to 1 GHz the coefficient is 6/2.4^3 = 0.434 W/m2, matching the 0.43 implemented here, and Duncan's 10^6 cm^-3 density normalisation is 10^12 m^-3, matching the term used here.
Scope and limits
Read from an image render, not the text layer, which on this page corrupts 10^6/n to "106/n" and C_F to "3CF". The relation is a theoretical result, not a measurement. Duncan attaches his own caveat to it - see CLM-0694 - which materially qualifies how a single threshold number should be used. Equation (11) prints no units for n (VER-1343 PARTIAL, 2026-09-19): a sweep of the text layer of all ten pages for "cm3", "cm-3" and "electrons/cm" returns nothing, so the reading of Duncan's 10^6 as 10^6 cm^-3, equal to the 10^12 m^-3 term used here, on which the 0.43 W/m2 renormalisation rests, is an inference this record makes and the document does not state; it is the physically sensible reading, since 10^6 per m3 would be six orders too low for the F-region.
What it assumes
that the 1980 conference precursor states the same relation as the 1981 journal paper it precedes.
Where it comes from
Equation (11) verbatim from the rendered image, with its following definitions: "where n is the ambient electron density, T_0 is the ambient electron temperature, f is the microwave frequency, and C_F is roughly unity, depending on spatial and temporal growth rates. This expression is valid for underdense ionospheric heating (f > f_p), which is the case for the SPS ionosphere-microwave interactions." Arithmetic: 6 / 2.4^3 = 6 / 13.824 = 0.4340.
Related records
- Answers question
- QST-001 not published in this release
Cite this
energyaperture.com/c/clm-0693
CLM-0693, Energy Aperture, as of 1980-06.
Connected records
Other published records linked to this one. A list, not a judgement.
- 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-0093The thousand-fold disagreement between the two published versions was a lost micro prefix in the abstract I was working from. The papers...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...