CALC-004

Is 23 mW/cm2 a universal constraint or one lineage's figure?

Feeds CLM-0042. Answers the question put on 2026-09-02: are the citations exhausted, and does independent support for the figure exist?

Why it was needed. Every document in the UK citation chain treats 230 W/m2 as a fixed limit. If it is a physical constraint, that is correct. If it is one design lineage's choice at one frequency, then the UK chain has inherited a parameter without asking whether it applies to its own design.

Inputs, all from CLM-0041, Shinohara Table 1.1, column alignment verified:

Conversion, applied throughout: 1 mW/cm2 = 10 W/m2.

Working, ratios against the NASA/DOE figure.

JAXA1     26 / 23 = 1.13 x
JAXA2    100 / 23 = 4.35 x
Old JAXA 180 / 23 = 7.83 x

Result. Three of four designs exceed the 23 mW/cm2 figure, by 1.1 to 7.8 times. All three are at 5.8 GHz. The one design at 23 mW/cm2 is the one at 2.45 GHz, which is the frequency the 1978 threshold was derived for (CLM-0039).

Ground segment consequence, order of magnitude. Received power equals intensity times area, so for a fixed delivered power the required rectenna area scales inversely with permitted peak intensity. Taking the UK reference of 2 GW delivered:

At 230 W/m2   (2.45 GHz, inherited figure)   area index = 1.00
At 260 W/m2   (JAXA1, 5.8 GHz)               area index = 0.88   ~12 pct smaller
At 1,000 W/m2 (JAXA2, 5.8 GHz)               area index = 0.23   ~4.3x smaller
At 1,800 W/m2 (Old JAXA, 5.8 GHz)            area index = 0.13   ~7.8x smaller

This is an inverse-proportionality indication only. A real rectenna area depends on the beam profile, the collection efficiency and the taper, none of which is held constant across these four designs, and their stated rectenna diameters do not scale as this simple relation would predict. So treat these as showing the DIRECTION and rough SIZE of the effect, not as design figures.

What this does and does not establish.

It establishes that 23 mW/cm2 is not a universal physical constraint. Different national programmes specify materially different figures, and the difference correlates with operating frequency in the direction physics would predict, since ionospheric absorption falls with frequency.

It does NOT establish that 5.8 GHz permits a higher ionospheric threshold. The JAXA figures might differ for unrelated reasons - rectenna cost, land availability, or a different risk appetite - and CLM-0034 records that nobody has computed the threshold at 5.8 GHz at all. Establishing the causal link needs the primary JAXA design documentation, which is not held.

Why this matters, and it cuts the other way. Every other finding on QST-001 makes SBSP look worse: an inherited figure, no exposure standard cited since 1980, a citation chain that closes on itself. This one makes it look better. If the constraint is frequency-dependent and the UK design is at the frequency with the tightest limit, then the UK ground segment is larger and more expensive than it needs to be, and nobody in the chain appears to have asked. That is a commercial question with a cheap first answer: what frequency does CASSIOPeiA actually use, and was the choice made against the ionospheric constraint or independently of it?

Next calculation, not yet done. The frequency scaling of the ionospheric absorption term, which would let the 1978 threshold be restated at 5.8 GHz from first principles rather than inferred from JAXA's choices. That needs the Perkins and Roble treatment, SRC-095, which is not held.

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