A New Bound on the Radar

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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.
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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  unpublished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 MHz Main
array 128 x 8 EW Cross-polarized array 128 x 4
NS Total Area 18,000 m2 Beam Size (NS x EW) 1o
x 6o Total Power 500 kW Operated by MIT/Lincoln
Laboratory 1961-1969
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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
? v2 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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Jicamarca Feb. 2004 Total power in 1 MHz band
Vertical scale is 10 dB per grid line
Solar activity was low to very low, but the solar
noise doesnt look time stationary and its not
white either!
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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 gtgt 10 KHz.
• The plasma loss is gtgt 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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Simulation of NE in 2-D plane. A radio wave
incident from the right cannot propagate into the
black region.
Tangential Distance (km)
Radial Distance (km)
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• Doppler broadening due to compressive plasma
  waves
• or
• Plasma loss gt 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