Value chain · CLM-0057
In plain terms
There is a formula for the instability threshold. It depends on electron density cubed, electron temperature to the fourth power, and frequency cubed, and it has no single value because it assumes how far the beam travels while the instability grows.
The claim as recorded
A closed-form threshold for F-region thermal self-focusing instability exists, given as P_th in W/m2 equals 0.43 times (10^12 m^-3 divided by N_e) cubed, times (T_e divided by 1000 K) to the fourth power, times (f divided by 1.0 GHz) cubed, and the source states there is no absolute threshold because the expression embeds an assumed spatial growth length.
Scope and limits
Quoted from a review, not derived, and Duncan (1981) is not held. The expression is not a hard limit and cannot be evaluated to a single number without choosing a growth length, an electron density and an electron temperature. Electron density enters cubed and temperature to the fourth power, so both dominate the answer far more than frequency does, and both vary naturally over wide ranges.
What it assumes
No assumptions are recorded against this claim.
Where it comes from
Quoted from SRC-104: "P_th(W/m^2) = (0.43)(10^12 m^-3/N_e)^3 (T_e/1000K)^4 (f/1.0GHz)^3", with the source's own caveat that "there is no absolute threshold". Underlying heating equation from Gurevich 1978 as quoted in the same review: dT_e/dt = 2e^2 nu_e P/(3m eps0 c omega0^2) - delta nu_e(T_e - T).
Related records
- Answers question
- QST-009 not published in this release
Cite this
energyaperture.com/c/clm-0057
CLM-0057, Energy Aperture, as of 2004.
Connected records
Other published records linked to this one. A list, not a judgement.
- Also from SRC-104
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