Estimation of Backscattering Cross Section for the Arecibo 430-Mhz

March, 1995 Arecibo Incoherent Times An unofﬁcial quasi-scientiﬁc inquiry at the Arecibo Observatory No. 7 Editor: Qihou Zhou, [email protected], phone:809-878-2612, fax:809-878-1861

Estimation of Backscattering Cross-Section for the Arecibo 430 MHz ISR

Qihou Zhou

One question that has always haunted me is whether the Arecibo ISR can really pick up a pin point at a distance of 300 km. Other people have told me yes. I know also from experience and pride that Arecibo ISR is indeed very very sensitive. But, I am still skeptical, doubtful,... until I have made my own measurements and calculations.

First, the experiment: High voltage=88 kv; Calibration=97 K; RF Pulse width and gate width= 8 us; no coding. fof2 from Ramey digisonde reads 5.5 MHz at the time of experiment; F-region peak appears to be at about 225 km; F-region peak signal temperature is 110 K, slightly higher than the calibration. The experiment was conducted at about 9 pm so that ion temperature can be assumed to be equal to electron temperature.

Second, the number crunching: Electron density at 5.5 MHz = 3.8x105/cm3 = 3.8x1011/m3; Total volume illuminated by radar at one range gate = 1.2π0.332 km3=4x108m3 (assuming an 1/6o 3 dB full beam width); Total number of electrons illuminated at one range gate = 1.5x1020; Effective IS cross-section per electron = 0.5*10-28 m2; Therefore, the total effective scattering cross-section is 7x10-9 m2 to have a signal of 110 K at 225 km.

The effective scattering cross-section for a signal temperature of Ts at range r can be generalized as:

σ × –32 1  4 eff = 2.5 10 ------ T sr m2K

Assuming that the detectable signal temperature is 10 K, at a range of 100 km, the minimum detectable effective cross-section is 2.5x10-11 m2, which is much smaller than the point of the pin my grandma used!

1 A very sensitive IS radar is not necessarily good unless its gain at sidelobes can be effectively sup- pressed. Since the effective scattering cross section of a Stealth is a well guarded secret, it cannot be terribly wrong to assume that a Boeing 747 has a effective scattering cross-section of 1000 m2. For a Boeing ﬂying at a distance of 150 km, the signal temperature would be 7x1013 K if we could point the Arecibo radar sideways. I have never remember seeing an obvious aircraft echo at 150 Km (and trust me, I have seen lots of ISR proﬁles). It seems to be reasonable to assume that a Boeing 150 km away at cruising altitude can only be blamed as a 10 K nuisance. The relative gain at horizon with respect to the beam center is therefore about 10-13, i.e., -130 dB. Experience tells us this is only good enough that we don’t have to worry about interferences generated by passive targets for F-region studies.

--- P.S. Feb. 1997

The effective scattering cross-section is not the physical cross-section of a target. For a target whose size is smaller than the probing wavelength, Reileigh scattering has to be taken into consideration. With this into consideration, the size of the physical target is somewhat smaller than 1 cm at 100 km.