A New Bound on the Radar Cross-section of the Sun Bill Coles, UCSD Mike Sulzer and John Harmon, NAIC Jorge Chau and Ron Woodman, JRO We have not observed a solar echo using the 50 MHz radar at Jicamarca, Peru; and our upper bound on the echo cross section appears to conflict with earlier observations.

History of Solar Radar -proposed by Kerr in 1952 to probe corona around 1.5 R S -detection at 25 MHz at Stanford in SNR marginal -daily observations at 38 MHz at El Campo, 1961 through no detection at 50 MHz at Jicamarca in marginal detection at 40 MHz at Arecibo in unpublished The El Campo observations were never understood. They could not be correlated with any other solar observations, and they showed no sign of the solar rotation period (27 days). Revival of solar radar is interesting because of: (a) proposed Arecibo ionospheric heater; (b) Yohkoh, SOHO, Trace, have greatly increased solar data; (c) radar signal processing has improved greatly; (d) receiving arrays like LOFAR could image the echo.

El Campo Solar Radar Frequency: MHz Main array: 128 x 8 EW Cross-polarized array: 128 x 4 NS Total Area: 18,000 m 2 Beam Size (NS x EW): 1 o x 6 o Total Power: 500 kW Operated by MIT/Lincoln Laboratory

Typical Range-Doppler Spectra from El Campo 50 km/s

Enhanced Range-Doppler Spectra from El Campo

Daily measurements of cross section

Signal to Noise Calculation Reflected transmitter flux (w/m 2 ) P R = P T G T L P  /(4  R 2 ) 2, here L P is the plasma loss and  is the solar cross-section Solar flux (w/m 2 /polarization) P S = k T S  B / 2, here  is the solar solid angle =  / R 2 Signal to Noise Ratio = P R / P S P R / P S = (P T A T L P )/ (4  R 2 k T S B)

Theoretical Comparison on El Campo and Jicamarca Jicamarca:P T A T = 80 kw * (60,000 * 0.66) = 3.17 El Campo:P T A T = 500 kw * (19,500 * 0.75) = 7.31 Jicamarca has ≈ 0.8 more plasma loss and  √2 polarization gain Jicamarca / El Campo  0.48

Signal to Noise Calculation At Jicamarca with B = 10 KHz, P R = P S Radiometer noise (rms) = P S /(B Time) 0.5 = P S Thus SNR  23 in each polarization

Jicamarca Feb. 2004: Total power in 1 MHz band Solar activity was low to very low, but the solar noise doesn’t look time stationary and it’s not white either! Vertical scale is 10 dB per grid line

Time variation requires optimal weighting Optimal weight = 1 / Noise Variance = 1 / P S 2 For typical data SNR OPTIMAL / SNR UNIFORM = 50 and SNR OPTIMAL / SNR MINIMUM = 0.6, i.e. effective time =.6 2 =.36 Optimal weighting makes the code autocorrelation non-ideal, in fact it becomes more like gaussian noise. This increases the sidelobes but does not alter detectability.

Questions: Why might the return have been lower than expected? What did James et al observe at El Campo? The return might be weak because: The doppler broadening is >> 10 KHz. The plasma loss is >> 3 dB. James et al, could have been observing leakage of solar bursts into their decoded output.

Simulation of N E vs Radial Distance near the Reflection Point

Radial Distance (km) Tangential Distance (km) Simulation of N E in 2-D plane. A radio wave incident from the right cannot propagate into the black region.

Doppler broadening due to compressive plasma waves; or Plasma loss > 13dB due to multiple scattering near the turning point; would kill the echo. Either is process is plausible. But either process would have also made the echo at El Campo undetectable!

The Future