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.

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-marginal detection at 40 MHz at Arecibo in 1967 - unpublished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.

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

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/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)

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

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

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

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 / 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.

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 NE vs Radial Distance near the Reflection Point

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.

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