The Polarization, Frequency Structure, and Bandwidth of
Auroral Kilometric Radiation
R. J. Strangeway, P. L. Pritchett, R. E. Ergun, C. W. Carlson,
J. P. McFadden, and G. T. Delory
Outline
•
The Cyclotron Maser when k|| = 0
"Horseshoe" distributions can drive instability, but requires
very low cold plasma densities to remove stop-band.
•
Evidence in Support of k|| = 0
Horseshoe distributions observed.
Low plasma densities, with fpe << fce.
Hot electrons are the dominant species.
Wave emissions below the cold electron gyro-frequency.
Wave polarization consistent with perpendicularly propagating
X-mode waves.
Implication: The parallel electric field is the "free energy"
source for AKR.
•
Bandwidth of AKR
Depends of method of analysis.
Inspection of waveform implies ~ few 100 Hz.
Lagged auto-correlation gives narrowest bandwidth.
•
Conclusions
Why the cyclotron Maser?
Gyro-resonance would couple directly into the R-X mode, but for the
classical gyro-resonance
∞
∞
∂f
dv ⊥ = − ∫ fdv ⊥
γ ∝ ∫ v⊥
∂
v
⊥
0
0
which is negative for any distribution.
Wu and Lee [Astrophys. J. , 230, 621-626, 1979] made the critical point: the
relativistic gyro-resonance removes the damping due to the tail of the
distribution – the resonance ellipse –
ω − k || v|| = Ω e (1 − v 2 / c 2 )
Other authors in the 1980's [Pritchett, Strangeway, LeQueau, Louarn, et al.]
noted that relativistic effects on the wave’s dispersion allow f < fce. Then
k|| = 0 and the primary auroral electrons can be the source of AKR.
Instability for k|| = 0 requires very low cold plasma densities – otherwise a
stop-band is present.
Two species dispersion relations with high thermal background temperature
(Strangeway, JGR, 1986)
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Electron Distribution in
Density Cavity
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Loss Cone
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Energy Flow
1. Acceleration by Electric Field
2. Mirroring by Magnetic Mirror
3. Diffusion through Auroral Kilometric Radiation
1•10 5
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-12.0
What Is the Bandwidth of AKR?
Baumback and Calvert [GRL, 1987] reported AKR bandwidths as small as
5 Hz, for a tone varying by 400 Hz/s. 512 point FFT’s of 16 kHz Nyquist
frequency "wave tracker" data give good time resolution, but have 64 Hz
frequency resolution – too broad to resolve 5 Hz.
How do Baumback and Calvert [1987] resolve 5 Hz? For example a tone
varying by 400 Hz/s should not be resolvable to less than 20 Hz
( ∆f / ∆t ≈ 1) .
Baumback and Calvert used filtered auto-correlation:
n
f c (t ,τ ) =
∑ W ( kδt ) f (t − kδt + τ / 2) f (t − kδt − τ / 2)
k =0
n
∑ W ( kδt )
k =0
For 400 Hz/s, tone taking τ up to 85.5 ms, implies ∆f ≈ 40 Hz but W is a
filter of width ≈ 14 ms, implies ∆f ≈ 6 Hz. Does the filter width determine
the bandwidth?
Comparison of different methods:
Wave-form
64 Hz resolution FFT
8 Hz resolution zero-padded FFT
Filtered auto-correlation.
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Auto
Conclusions
AKR in the source region is consistent with X-mode generated by the
primary auroral distribution – loss-cone may be a secondary
source.
The parallel electric field responsible for auroral electrons continually
replenishes the distribution, unlike the loss-cone, which can’t
be replenished (see also Louarn et al., JGR, 1990).
AKR bandwidth is ~ few 100 Hz in the source region (∆f/f ~ 0.1%).
Generally too narrow to be explained solely in terms of intrinsic
bandwidth. The parallel electric field implies AKR is a driven
instability – simulations of driven AKR may help address
source region bandwidth.