CALC-141

The UK reference design's beam against the power-beaming tests checked: power bounds, ratios and the area a test beam could cover

REGISTERED 2026-10-15. Drafted for CLM-1452 (lessons records draft P, commit a14c5339), checked by an independent reader (check P: FIX, all applied, round 2 PASS), landed by x-high-1 at coord's request. Script: lessons-beam-scale.py. verified: VER-2414 CONFIRMED 2026-10-15.

Feeds CLM-1452. Basis: watts of microwave beam power, as sent or as received; W/m2; m2. A comparison of total power and beam area to the nearest order of magnitude, not a beam-propagation or local-intensity calculation.

Why it was needed. CLM-1452 gives three results from arithmetic. The UK reference design's beam carries between about 2 GW and about 3.4 GW. That is about six orders of magnitude more than the 2,081 W that Xidian University's paper reports as sent in its 2022 ground test. At the design's centre maximum, that test's beam could cover at most about 9 m2, against 68.4 km2. CALC-001 holds only the footprint. This record holds the rest of the working, with the source and tier of each input.

Inputs. The tier is that of the source each figure comes from. The T5 figures corroborate only: the result is the same without them.

Like for like. The design's beam is made from the electricity generated on the satellite, and the rectenna turns it back into the grid output. So the beam carries less than the 3.4 GW generated and more than the 2 GW delivered, both as sent and as received. The Xidian 2,081 W and the OHISAMA 1 kW are power at the source. A ratio of the design's bounds to them therefore compares power sent with power sent, and does not inflate the gap. Line C also compares the two at the rectenna, and compares the grid output with the test's DC output.

Area bound. A beam that carries a power P cannot hold an intensity I or more over an area larger than P / I, because the power over that area would then exceed P. This holds whatever the beam's shape and wherever it is measured.

Working (python output, transcribed).

A  footprint (CALC-001)   pi x 3.35 km x 6.5 km = 68.41 km2 = 6.84e7 m2
B  design beam            more than 2 GW (grid output), less than 3.4 GW (generated)
   mean over footprint    2.0e9 / 6.84e7 = 29.2 W/m2;  3.4e9 / 6.84e7 = 49.7 W/m2
   centre max / mean      240 / 29.2 = 8.2;  240 / 49.7 = 4.8
   not used               240 x 6.84e7 = 1.64e10 W (16.4 GW), 4.8 x the generated power
                          (230 W/m2: 15.7 GW; 245 W/m2: 16.8 GW)
C  Xidian 2022, sent      2.0e9 / 2,081 = 9.61e5;  3.4e9 / 2,081 = 1.63e6  (log10 5.98 to 6.21)
   at its rectenna        2,081 x 0.873 = 1817 W;  1.10e6 to 1.87e6  (log10 6.04 to 6.27)
   grid against DC out    2.0e9 / 736 = 2.72e6  (log10 6.43)
   consistency            736 / 0.1505 = 4890 W DC in;  x 0.4255 = 2081 W sent;  736 / 1817 = 0.405 at the rectenna
D  reported, T5 only      2.0e9 / 1,180 = 1.69e6;  2.0e9 / 1,000 = 2.00e6;
                          3.4e9 / 1,180 = 2.88e6;  3.4e9 / 1,000 = 3.40e6  (log10 6.23 to 6.53)
E  area at 240 W/m2       2,081 / 240 = 8.67 m2;  1,180 / 240 = 4.92 m2;  1,000 / 240 = 4.17 m2
   sensitivity            2,081 / 230 = 9.05 m2;  2,081 / 245 = 8.49 m2
   footprint / area       6.84e7 / 8.67 = 7.89e6
   at the design's mean   2,081 / 29.2 = 71.2 m2;  2,081 / 49.7 = 41.9 m2;  6.84e7 / 71.2 = 9.61e5;  6.84e7 / 41.9 = 1.63e6
F  Xidian on its rectenna pi x 2.6^2 = 21.24 m2;  1817 / 21.24 = 85.5 W/m2;  / 240 = 0.36
G  Goldstone 1975         DC out: 2.0e9 / 3.0e4 = 6.67e4 (log10 4.82);  3.4e9 / 3.0e4 = 1.13e5 (log10 5.05)
   at its rectenna        30,000 / 0.82 = 36585 W;  5.47e4 to 9.29e4  (log10 4.74 to 4.97)
   mean on its rectenna   36585 / 24.5 = 1493 W/m2;  / 240 = 6.2  (17 x 1.22^2 = 25.3 m2: 1446;  26.8 m2: 1365)
   peak, stated (T2)      1,700 W/m2;  / 240 = 7.1
   sent, T5 account       36585 / 0.12 = 304878 W;  6.56e3 to 1.12e4  (log10 3.82 to 4.05)
   at the 450 kW rating   4.44e3 to 7.56e3  (log10 3.65 to 3.88)
   area at 240 W/m2       30 kW: 125 m2;  36.6 kW: 152 m2;  305 kW: 1270 m2;  450 kW: 1875 m2
   footprint / area       6.84e7 / 1875 = 3.65e4  (at the 450 kW rating)

Result. The design's beam carries between about 2 GW and about 3.4 GW. That is 9.6e5 to 1.6e6 times the 2,081 W that the Xidian paper reports as sent in its 2022 ground test (log10 5.98 to 6.21): about six orders of magnitude, or about a million times. Compared at the rectenna, or as grid output against the test's DC output, the ratio is 1.1e6 to 2.7e6, the same order. At the design's centre maximum of 240 W/m2, the Xidian beam could cover at most 8.7 m2 (8.5 to 9.0 m2 at 245 and 230 W/m2), and the design's footprint is 7.9e6 times larger. The two figures reported in the press in 2026 give 1.7e6 to 3.4e6 times (log10 6.23 to 6.53) and at most 4.2 to 4.9 m2. They agree with the result and do not carry it.

Against CLM-1452. Every figure the record states reproduces: 68.4 km2; 2 to 3.4 GW; 9.6e5 to 1.6e6, about six orders; 1.7e6 to 3.4e6 for the reported figures; 8.7, 4.9 and 4.2 m2; 7.9e6; about 86 W/m2, about a third of 240 W/m2; the 16 GW bound, not used; and for Goldstone, the figures below. The test report gives the DC output, 30 kW, and the beam carried more. About 37 kW reached the rectenna (30 / 0.82). The design's beam is 5.5e4 to 9.3e4 times that, still about five orders, and 37 kW could cover up to 152 m2 at 240 W/m2. A 1975 newspaper report (CLM-1306, T5) says that only about 12 per cent of the transmitter's power was intercepted. On that account the beam as sent was near 0.3 MW, about four orders below the design's beam (6.6e3 to 1.1e4), and could cover at most about 1,300 m2 at 240 W/m2. The same report rates the klystron at 450 kW. If the tube ran at or below that rating, the beam could cover at most 1,875 m2, and the design's footprint is at least 3.6e4 times larger.

Where this fails. - It compares total power and beam area, not local intensity. If the beam collection efficiency is the share of the sent power that reached the rectenna, the 21.2 m2 Xidian rectenna received a mean of about 86 W/m2, 0.36 of the centre maximum of the design. At Goldstone about 37 kW fell on a rectenna of 24.5 m2, a mean of about 1.5 kW/m2, about six times the design's centre maximum, and a 2021 review gives a peak of up to 1.7 kW/m2 on it (SRC-269 PDF p15). So a small test can reach the design's intensity, or more, over tens of square metres. The arithmetic separates the tests from the design on total power and area only. - The area bound sets the test beam at the design's centre maximum against the whole footprint, and most of the footprint receives far less: the beam's mean over it lies between 29 and 50 W/m2 (line B). At that mean, the Xidian beam could cover at most 42 to 71 m2, and the footprint is 9.6e5 to 1.6e6 times larger, the power ratio again (line E). So 7.9e6 is the gap at the centre maximum, not a second gap beside the power ratio. - Neither UK document held states the beam power of the reference design. The bounds come from the generated power and the grid output, and both are rounded figures. The 3.4 GW is from the 2020 Phase 1 report's satellites, applied to the reference design of the 2021 summary, which delivers the same 2 GW and itself gives over 3 GW generated on the satellite. The 2020 report gives 2 GW of microwave power for another of its concepts, SPS-ALPHA (SRC-024 PDF p16), at the lower bound. A beam of 2 GW changes no order of magnitude here. - The UK documents give 230, 240 and 245 W/m2 for the beam intensity. Across them the Xidian area bound moves from 8.5 to 9.0 m2, and no result changes. - The reading of the beam collection efficiency is ours. The paper's own figures agree with it: 736 W of DC output at 15.05 per cent DC-DC means 4,890 W of DC input, which at 42.55 per cent DC-RF gives the 2,081 W sent; the rectenna then turns about 40 per cent of the 1,817 W it receives into DC. - The reported 1,180 W and 1 kW rest on two press reports, and neither report is held. The OHISAMA figure is a plan. Nothing held shows that OHISAMA or Arachne has flown. Arachne's output power is stated in none of the AFRL documents held, so it is not assumed to be at kilowatt scale. - Three demonstrations for 2025-2026 were checked, and no search has set out the full set. Older ground tests carried more power: Goldstone is four to five orders below the design's beam, not six. - The Goldstone power as sent rests on a newspaper report (T5) and on an interception share that a test lead gave the paper. The test report held (CLM-1097) gives the DC output and the efficiency, not the transmitter's operating level. A 2021 review restates the output three ways, 35 kW (PDF p2), 30 kW of DC (PDF p7) and 30.4 kW of DC (PDF p15), and a 2022 paper gives 34 kW (SRC-269; CLM-1097, CLM-1134). Read as DC, 35 kW would put about 43 kW on the rectenna, and no order changes.

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