To: | [email protected] |
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Subject: | Re: VLF: Transatlantic success East to West - nonreciprocity |
From: | Markus Vester <[email protected]> |
Date: | Mon, 11 Dec 2017 06:51:57 -0500 |
Cc: | [email protected] |
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I've also been looking for a simple and intuitive explanation, without luck so far. Maybe a plausible approach is thinking of Hall conductivity in the lower ionosphere, which would tilt the current density (i.e. the source of the reflected field, blue) versus the impinging electric field (red). The vertical tilt angle (upwards or downwards) depends on the horizontal component of Earth's magnetic field (green). So for a west-to-east path, I speculate that the source dipoles may be tilted downwards, and better radiate in the direction of the outgoing wave. 73, Markus (DF6NM) -----Ursprüngliche Mitteilung----- Von: Paul Nicholson <[email protected]> An: rsgb_lf_group <[email protected]> Cc: Michael Smith <[email protected]> Verschickt: Mo, 11. Dez 2017 11:43 Betreff: Re: VLF: Transatlantic success East to West Jacek wrote: > could you give a short explanation? i don't really understand > nonreciprocal propagation I don't either, really. The ionospheric reflection coefficient depends on the direction of the radio wave relative to the Earth's magnetic field. The wave accelerates free electrons in the plasma, and they're pulled into circular or helical paths by the magnetic field. This alters the phase of the reflection and the attenuation of the wave through energy loss by collisions. The consequence is the reflection coefficient isn't a nice simple number, it's a 2x2 matrix with each component a (frequency dependent) complex number. It's all the in Appleton-Hartree equations https://en.wikipedia.org/wiki/Appleton%E2%80%93Hartree_equation which are quite easy to calculate and program (easier than they look at first glance) but few people would admit to understanding them. Spent some time with LWPC measuring the T/A path at some different frequencies. The figures below are the extra loss on the east-to-west, compared with west-to-east. The results don't depend much on which end points I choose, but are quite frequency dependent: Midnight UTC: 18.0 kHz: 2 dB 17.4 kHz: 3 dB 16.5 kHz: 6 dB 16.0 kHz: 9 dB 15.0 kHz: 14 dB 14.0 kHz: 18 dB 13.0 kHz: 16 dB 12.0 kHz: 13 dB 11.0 kHz: 11 dB 10.0 kHz: 10 dB 9.0 kHz: 10 dB 8.2 kHz: 12 dB 5.2 kHz: 27 dB 4.2 kHz: 44 dB 2.9 kHz: LWPC doesn't run Generally a lot more anisotropy as the frequency drops, but there's a funny peak around 14 kHz. Midday UTC: 18.0 kHz: 4 dB 17.4 kHz: 4 dB 16.0 kHz: 5 dB 15.0 kHz: 5 dB 14.0 kHz: 6 dB 13.0 kHz: 7 dB 12.0 kHz: 8 dB 11.0 kHz: 9 dB 10.0 kHz: 10 dB 9.0 kHz: 12 dB 8.2 kHz: 14 dB 5.2 kHz: 35 dB 4.2 kHz: no output from LWPC The funny peak vanishes during the day. So, nowhere near as much anisotropy as I thought at 17.4 kHz. I don't fancy our chances at the lower VLF bands - it might be easier to take the long path! -- Paul Nicholson --
Hall_angle.jpg |
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