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A New Bound on the Radar A New Bound on the Radar
Cross-section of the SunCross-section of the Sun
Bill Coles, UCSDBill Coles, UCSD
Mike Sulzer and John Harmon, NAICMike Sulzer and John Harmon, NAIC
Jorge Chau and Ron Woodman, JROJorge 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.
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History of Solar Radar
-proposed by Kerr in 1952 to probe corona around 1.5 RS
-detection at 25 MHz at Stanford in 1959 - SNR marginal
-daily observations at 38 MHz at El Campo, 1961 through 1969
-no detection at 50 MHz at Jicamarca in 1964
-marginal detection at 40 MHz at Arecibo in 1967 - unpublished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.
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El Campo Solar Radar
Frequency: 38.25 MHzMain array: 128 x 8 EWCross-polarized array: 128 x 4 NSTotal Area: 18,000 m2
Beam Size (NS x EW): 1o x 6o
Total Power: 500 kW
Operated byMIT/Lincoln Laboratory1961-1969
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Typical Range-Doppler Spectra from El Campo
50 km/s
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Enhanced Range-Doppler Spectra from El Campo
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Daily measurements of cross section
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Signal to Noise Calculation
Reflected transmitter flux (w/m2)
PR = PT GT LP /(4 R2)2, here LP is the plasma loss and is the solar cross-section
Solar flux (w/m2/polarization)
PS = k TS B / 2, here is the solar solid angle = / R2
Signal to Noise Ratio = PR / PS
PR / PS = (PT AT LP )/ (4 R2 k TS B)
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Theoretical Comparison on El Campo and Jicamarca
Jicamarca: PT AT = 80 kw * (60,000 * 0.66) = 3.17
El Campo: PT AT = 500 kw * (19,500 * 0.75) = 7.31
Jicamarca has ≈ 0.8 more plasma loss and √2 polarization gain
Jicamarca / El Campo 0.48
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Signal to Noise Calculation
At Jicamarca with B = 10 KHz,
PR = 0.0203 PS
Radiometer noise (rms) = PS/(B Time)0.5 = 0.00063 PS
Thus SNR 23 in each polarization
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QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
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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
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Time variation requires optimal weighting
Optimal weight = 1 / Noise Variance = 1 / PS2
For typical data SNROPTIMAL / SNRUNIFORM = 50 and
SNROPTIMAL / SNRMINIMUM = 0.6, i.e. effective time = .62 = .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.
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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.
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Simulation of NE vs Radial Distance near the Reflection Point
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Radial Distance (km)
Tan
gent
ial D
ista
nce
(km
)Simulation of NE in 2-D plane. A radio wave incident from the right cannot propagate into the black region.
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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!
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The Future