Incoherent Scatter: Theory and Measurable Parameters

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Incoherent Scatter Theory and Measurable
Parameters

• Philip J. Erickson
• Atmospheric Sciences Group
• MIT Haystack Observatory
• CEDAR 2008 Workshop
• AMISR Tutorial
• Saturday June 21, 2008

Special Thanks To Mike Nicolls, Craig Heinselman,
Bill Bristow, Tony van Eyken, Josh
Semeter and Don Farley
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Ionospheric Remote Sensing Timeline (1)

• 1871 Lord Rayleigh theory for scattering of
  light from the atmosphere
• 1902 Oliver Heaviside predicts ionosphere
  specifically, E region
• 1906 Thomson shows electron is an EM wave
  scattering dipole with a very small cross-section
  (1E-28 meters squared!)
• 1928 Fabry shows random electron gas should
  Doppler broaden scattering wave
• 1925-26 Appleton, Barnett, etc. locate
  ionospheric plasma layer
• 1931 Sydney Chapman develops first ionospheric
  models
• 1930s Ionosondes begin to probe ionospheric
  structure by relying on plasma frequency
  resonance at HF frequency (hard reflection)

q qm exp(1 z exp(-z))
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Incoherent Scattering Principle
But what if we use a probing frequency gt plasma
frequency (but not so high that collective plasma
behavior is lost)? now we are employing
Thomson scattering or incoherent
scattering Incident EM wave accelerates each
charged particle, which now becomes a
transmitting antenna itself and re-radiates a
scattered EM wave. For a single electron
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Incoherent Scattering Principle
Ionosphere is a charged plasma, filled with
electrons and ions .. each can become a
scatterer. This could work! If we are even
luckier, the energy extracted from the incident
wave is so small that the Born approximation
holds (i.e. lower altitudes dont absorb the
signal completely). So each electron is an
independent random dipole. But the electron
cross-section is really small so not much energy
comes back. Quite hard to detect. How bad is
it?
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Incoherent Scattering Detectability
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Incoherent Scattering Detectability
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Incoherent Scattering Detectability
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Incoherent Scattering Detectability
Not bad But you need a megawatt class
transmitter and a huge antenna. Fortunately,
technology makes this possible in the mid 1950s.
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First Incoherent Scatter Radar

• W. E. Gordon of Cornell is credited with the idea
  for ISR.
• Gordon (1958) has recently pointed out that
  scattering of radio waves from an ionized gas in
  thermal equilibrium may be detected by a powerful
  radar. (Fejer, 1960)
• Gordon proposed the construction of the Arecibo
  Ionospheric Observatory for this very purpose
  (NOT for radio astronomy as the primary
  application)

40 megawatt-acres

• 1000 Diameter Spherical Reflector
• 62 dB Gain
• 430 MHz line feed 500 above dish
• Gregorian feed
• Steerable by moving feed.

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Proceedings of the IRE, November 1958
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First Incoherent-Scatter Radar

• K.L. Bowles Cornell PhD 1955, Observations of
  vertical incidence scatter from the ionosphere at
  41 Mc/sec. Physical Review Letters 1958
• The possibility that incoherent scattering
  from electrons in the ionosphere, vibrating
  independently, might be observed by radar
  techniques has apparently been considered by many
  workers although seldom seriously because of the
  enormous sensitivity required

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First Incoherent-Scatter Radar

• Gordon (W.E. Gordon from Cornell) recalled this
  possibility to the writer spring 1958 D. T.
  Farley while remarking that he hoped soon to
  have a radar sensitive enough to observe electron
  scatter in addition to various astronomical
  objects
• Bowles executed the idea - hooked up a large
  transmitter to a dipole antenna array in Long
  Branch Ill., took a few measurements.
• Gordon presenting on same day at October 21, 1958
  Penn State URSI meeting
• And then I want to tell you about a telephone
  call that I just had.

Oscilloscope camera 4 sec exposure (10 dB
integration)
6 week setup time
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Incoherent Scattering Detectability
Bowles results found approximately the expected
amount of power scattered from the electrons
(scattering is proportional to charge to mass
ratio - electrons scatter the energy). BUT his
detection with a 20 megawatt-acre system at 41
MHz (high cosmic noise background should be
marginal) implies a spectral width 100x narrower
than expected almost as if the much heavier
(and slower) ions were controlling the scattering
spectral width. In fact, they do.
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Plasma Not free electrons

• Electrons in the ionosphere are not a gas of
  independent particles. They are one of the
  constituents of a plasma.
• When probing a plasma with a wavelength that is
  longer than the Debye length, collective effects
  must be accounted for.

In the ionosphere n 1e10 1e12 Te 300 -
2000 lD 1-30 mm
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Collective Effects

• Results are
• The scattered power is still close to that
  predicted by Thompson scatter.
• Return signal is as if scattered from particles
  with total cross section of electrons but with
  mass of ions!
• Doppler broadening is much smaller.
• Required bandwidth is smaller
• Required antenna gain is smaller

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Collective Effects
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Ionospheric Remote Sensing Timeline (2)

• mid 1950s IS returns observed in BMEWS UHF
  military radar defense network, but dismissed as
  noise
• 1958 1961 IS theory developed and refined
• 1960 V. C. Pineo makes first L band IS
  measurements at Millstone Hill (later UHF)
• 1960-61 Jicamarca Radio Observatory begins
  operations
• 1960-63 Arecibo Observatory constructed based
  on Bill Gordons original idea, begins
  operations. IEEE Milestone largest radio
  telescope on Earth
• 1971 Chatanika radar begins operations in
  Alaska moved to Sondrestrom Greenland in 1983
• 1985 EISCAT European incoherent scatter radars
  begin operation in Norway, Sweden, Finland
  later, EISCAT Svalbard added
• 2005-6 AMISR phased array IS radar begins
  operations

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Arecibo, PR 430 MHz
Poker Flat, AK 440 MHz
Jicamarca, Peru 50 MHz
2.85 megawatt acres
Millstone Hill, MA, USA 440 MHz
Sondrestrom, Greenland 1295 MHz
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Back to ISR Theory
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Reflection at a Discontinuity
ISRs do not measure density directly. Scattering
is from fluctuations in the index of refraction
(i.e. discontinuities in density) matching the
radar wavelength.
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Density Fluctuations

• Random thermal fluctuations are present in any
  system.
• In a plasma, there are thermal fluctuations in
  both the ion gas and the electron gas.
• If the probing wavelength is longer than the
  Debye length, the fluctuations dominate the
  characteristics of the scatter.

In the ionosphere n 1e10 1e12 Te 300 -
2000 lD 1-30 mm
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Density Fluctuations

• Thermal fluctuations in an ordinary collision
  dominated gas can be considered to be made up of
  sound waves.
• In a plasma, the fluctuations are ion-acoustic
  waves and electrostatic plasma (Langmuir) waves.
• The probability distributions for the wave modes
  and their spectrum can be derived by various
  means.

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Ion Acoustic Waves
Ions
Thermal velocity
Electron Gas
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Wave Spectrum
Not to scale
Electron Plasma Waves
Ion Acoustic Waves
Plasma parameters fluctuate with the waves
(density, velocity, etc)
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Damped resonance

• Waves in a plasma are resonances.
• Damped resonances are not sharp
• Example Q of a resonant circuit.
• IS Thermal ions have motions close to
  ion-acoustic speed (Landau damping surfing
  locked to I-A waves)

fr
fr
Resonance
Damped Resonance
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Wave Spectrum (ISR Spectrum)
Why arent the Langmuir (plasma) waves damped?
Electron thermal velocity 125 km/s but plasma
wave frequency several MHz Not much
interaction and not much damping.
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IS Spectrum Dependence Measurable Parameters

• Electron density
• Electron, ion temperature (Te is not Ti
  everywhere)
• Line of sight velocity Doppler shift
• Ion composition more than one species
• Plasma line measurements Ne, Te, velocity
  parallel to B
• More
• Photoelectron heating
• Conductivities, currents
• Non-Maxwellian plasmas
• Ion-neutral collision frequency spectrum
  narrows
• Ion gyro resonance mass spectrometer
• Coulomb collisions

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Measurable Parameters Flow Diagram
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Interactive IS Spectrum Demonstration
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In practice, evaluating IS theoretical
calculations can get complicated. For example,
properly accounting for the presence of a
magnetic field requires evaluation of the
Gordeyev integral But dont worry UAF
staff sweat those details for you. Were full
service. Of course, we can provide full
references to the theory if youre really
interested
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ISR Practicalities Data Reduction
NB Power spectrum (freq domain) lt-gt
Autocorrelation function (time domain)
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ISR Measurement Results Example PFISR
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Other Practical Considerations

• Experiment design resolution, parameter
  accuracy tradeoffs
• Higher order data products vector velocity
  fitting, full profile analysis, etc.
• System characteristics e.g. traditional
  single-antenna radars versus inertialess phased
  arrays (AMISR design)
• But UAF staff are full service and ready to
  assist you.
• Bottom line you dont have to be a radar expert
  to use the power of ISR for your science goals.

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SummaryIncoherent Scatter is the most powerful
ground-based tool for remotely sensing the
ionosphere and thermosphere.
P. J. Erickson (MIT Haystack) pje_at_haystack.mit.edu