12.6 Summary
14.1.3 Discussion
The pulsations in this event show two pulsation frequencies that are observable in the ionosphere. The fact that they are observable in the ionosphere indicates that the Ped- ersen conductivity is sufficiently low for the first order electric fields to be present in the ionosphere and produce theE×B drifts that are observed by the radar.
The two frequencies are roughly three times apart, possibly indicating that the higher frequency pulsation is a higher harmonic of the lower one. In order to test this hypothesis
SANAE FFT Beam 13
0.000 0.005 0.010 0.015 0.020
Freqency/[Hz]
7 8 9 10 11 12 13 14 15 16 17
Range Gate
Period 17:20 - 18:40 UT
Figure 14.7: Spectra for the lower frequency pulsations from 2 September 2004.
data were extracted from ground-based magnetometers and magnetometers on board the geostationary GOES 12 satellite.
The ground-based data from the BAS low power magnetometer M85/002 (figure 14.8) shows pulsations at the same time as the lower frequency pulsations and with the same frequency. There is no evidence of the higher frequency pulsations in the magnetometer data.
The Tsyganenko magnetosphere model [66] was used to trace the magnetic field line that passes through the point 67◦S and 45◦E AACGM (the centre of the green cells in figure 14.3) into the GSMx−y plane. The points during the four hours of interest are shown as the black curve in figure 14.9. Figure 14.9 also shows the GOES 12 position at the same time in red. The GOES 12 data in figure 14.10 show both the lower frequency pulsation and the higher frequency pulsation. The higher frequency pulsation, just below 8 mHz in this plot due to aliasing, occurred from 17:00 UT till just after 18:00 UT. This is the same time as the radar’s lower frequency pulsations. These lower frequency pulsations are also visible in the GOES data.
If the lower frequency is the fundamental (n = 1) and the higher frequency data are indeed the third harmonic (n = 3) then one would expect nodes in b at the equator to mean that the geostationary magnetometer would not observe the pulsations. The fact that the pulsation is being observed by the radar indicates that the conductivity in the ionosphere is sufficient for the first order correction electric and magnetic fields to be present. The event is close to the equinox meaning that the two polar ionospheres would have comparable conductivities needed for first order standing waves.
The box model of figure 3.2 shows that the first order corrections are 90◦ out of phase
CHAPTER 14. SOME EVENTS IN DETAIL 117
BAS LPM M85/002
17:31 17:45 18:00 18:14 18:28
Time/[UT]
-50 0 50
Bx
17:31 17:45 18:00 18:14 18:28
Time/[UT]
-50 0 50
By
17:31 17:45 18:00 18:14 18:28
Time/[UT]
-50 0 50
Bz
Spectra
0.000 0.002 0.004 0.006 0.008 0.010
2 4 6
0.000 0.002 0.004 0.006 0.008 0.010
1 2 3 4 5
0.000 0.002 0.004 0.006 0.008 0.010
Frequency/[Hz]
1 2 3 4
Figure 14.8: BAS LPM data for 2 September 2004. The spectra of the components are shown on the right.
GSMz = 0 (x-y plane)
-20 -10 0 10 20
GSMx/[re]
-20 -10 0 10 20
GSMy/[re]
16 UT 17 UT 18 UT 19 UT
Figure 14.9: GSMx−y plane. The black line is the location of the point 67◦S and45◦E AACGM in the ionosphere traced along a field line into thex−y plane. The red line shows the position of GOES 12.
Spectrogram of GOES12 By for a 64 minute sliding scale
14:00 16:00 18:00 20:00 22:00
Central Time/[UT]
0.000 0.002 0.004 0.006 0.008
Frequency/[Hz]
Figure 14.10: GOES 12 magnetometerBy data for 2 September 2004. The spectra are generated with a 64 minute sliding scale.
with the zero order standing waves and would thus result in observable magnetic fields in the equatorial plane for the fundamental and third harmonic pulsations. A numerical calculation of equations 5.3 and 5.4, using the dipole model of chapter 5, starting with Bφ= 1 +ı1 andEν = 0 +ı1 in the ionosphere and mapped towards the equatorial plane are shown for the fundamental mode standing wave in figure 14.11. This shows that there will be a non-zero value for the imaginary (first order correction) part ofBφ in the equatorial plane which can be measured by GOES.
If the fundamental has a frequency of 3 mHz then one would expect the third harmonic to be 9 mHz. The radar and GOES 12 data are sampled at 60 s intervals giving a Nyquist frequency of 8 mHz. This would mean that the high frequency pulsations would be aliased to 7 mHz. This is the frequency seen strongly in the GOESBy data of figure 14.10. The radar data in figure 14.4 has too low a resolution to accurately resolve the peak as the pulsations were only observable for twenty minutes.
The higher frequency velocity data for 10 minutes in the two blue cells of figure 14.3 is shown in figure 14.12 with the more eastward cell in red. A fit to the unwrapped phase of the analytical signal for the two pulsations gave a phase difference of 73.2◦ giving an m number of 14.6. The red curve leads the black curve indicating that the phase is propagating in a westerly direction. The event is in the afternoon MLT sector indicating that the phase is propagating in a sun-wards direction.
CHAPTER 14. SOME EVENTS IN DETAIL 119
0.0 0.2 0.4 0.6 0.8 1.0 -0.6
-0.4 -0.2 0.0
Re[E ν ]
0.0 0.2 0.4 0.6 0.8 1.0 z = sin(lat) -0.20.0
0.2 0.4 0.6 0.81.0
Im[E ν ]
0.0 0.2 0.4 0.6 0.8 1.0 0.0
0.2 0.4 0.6 0.8 1.0
Re[B φ ]
0.0 0.2 0.4 0.6 0.8 1.0 z = sin(lat) 1.0
1.1 1.2 1.3 1.4 1.5
Im[B φ ]
Figure 14.11: Numerical calculations ofBφandEν starting in the ionosphere and mapping towards the equatorial plane.
Higher frequency Pulsation
16:10:47 16:19:47
Time/[UT]
-300 0 300
Velocity/[m/s]
Phase for Beam 8 Range Gate 10
16:10:00 16:19:59
Time/[UT]
0 500 1000 1500
Phase/[Degrees]
Phase for Beam 15 Range Gate 9
16:10:00 16:11:40 16:13:20 16:15:00 16:16:39 16:18:19 16:19:59 Time/[UT]
500 1000 1500
Phase/[Degrees]
Figure 14.12: The top panel shows the higher frequency pulsation from the two blue cells of figure 14.3.
The red trace is for the cell in beam 15 and the black for beam 8. The bottom two panels show the unwrapped phase of the analytical signal of each pulsation.
2002080508d 2002080508h
Figure 14.13: Percentage clean scatter for SANAE and Halley Bay on 5 August 2002. The brighter the cell, the greater the percentage clean scatter.
Higher order standing waves translate into a higherkz. In section 4.5 it was shown that below the ionosphere the pulsation is actually an evanescent electromagnetic wave of which the attenuation is proportional tokz, explaining why the higher frequency pulsation is not observed in the ground data.