CALC-097

How small can the beam be made, and the answer is kilometres

Feeds CLM-0889. Answers QST-004. Basis: metres of first-null spot diameter at the ground.

Why it was needed. CLM-0231 was held at review on the objection that a microwave transmission concept cannot be developed into a weapon "because the beam strength cannot exceed something relatively small". The register holds no statement of that bound. SRC-228's own reason is qualitative - larger powers and apertures "would generally distinguish" a weapon from an energy system - and CLM-0231 reproduces that faithfully without converting it into a physical limit. This converts it.

Relationship, standard diffraction, derived rather than quoted. For a circular aperture of diameter D radiating wavelength lambda at range R, the first-null spot diameter is

d = 2.44 lambda R / D

and the peak intensity for transmitted power P therefore scales as

I ~ P / d^2  ~  P D^2 / (lambda R)^2

Inputs. Range is geostationary altitude, 35,786 km, for both.

Working.

1978 reference   d = 2.44 x 0.1224 m x 3.5786e7 m / 1000 m = 10,685 m   (10.7 km)
Caltech CSSPS    d = 2.44 x 0.0300 m x 3.5786e7 m / 1600 m =  1,636 m   (1.64 km)

THE RELATION IS VALIDATED AGAINST THE REGISTER BEFORE IT IS USED. CLM-0869's support quotes SRC-085's own "10 KM RECTENNA DIAMETER" for the 1978 design. The derivation gives 10.68 km against that stated 10 km, 6.8 per cent high, from the aperture and frequency alone. A relation that reproduces a design's own published ground dimension is doing real work.

Result. Spot size is not a design free parameter. At a given aperture and frequency the beam cannot be focused tighter than 10.7 km from geostationary orbit, so peak intensity cannot be raised by concentration. It rises only with transmitted power or with aperture area - both of which are large, visible and expensive, which is exactly the distinction SRC-228 draws qualitatively.

What this does not establish, and the laser case. The relation applies to a laser beam too, and laser designs are now held. Lockheed's 1978 design (CLM-1232) beams 10.6 um light from a 31.5 m relay aperture in GEO, over at least 35,786 km:

d = 2.44 x 10.6 x 10^-6 m x 35,786,000 m / 31.5 m = 29.4 m

which fits its stated 31.5 m receiver. The diffraction floor that keeps a microwave spot at about 10.7 km keeps that laser spot at about 29 m, some 360 times smaller (10,700 / 29.4 = 364). This calculation does not establish what intensity is safe or what harm a small spot could do; the held exposure limits are in CLM-1233 and CLM-1235, and they are 1970s infrared figures.

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