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
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