Calculation of Ionospheric
Turbulence
Robert Lomas
If I work out what happens to a single electron then I can estimate the total
currents by substituting my calculation of the movement vector into the
current density equation, derived from critical frequency observations.
I have imagined my model showing two gravitational attractors revolving round
the Earth and pulling my representative floating electron in different
directions as they traverse the sky.
My electron will be subject to similar forces to those which move the sea in
and out with the pattern of the tides, but tides are damped movements because of
the viscosity of the liquid in the sea. My representative electron was free to
move in any direction as quickly or as slowly as it wanted, without any friction
of water flow to slow it down. (Although if I come to refine the model I will
need to take account of such effect as the Colomb backscattering, caused by the
electrons repelling each other if they get too close. But for the sake of this
order of magnitude calculation I will ignore that complication.)
Here is a diagram of the model I used. The three small arrows show the
direction of the gravitational forces on the electron.
To work out how the electron moves I need to work out the strength and
direction of each of those forces. To do this I simply apply Newton's Law of
Gravitational Attraction. The detail of this calculation it is shown below.
Now these three forces pulling at this individual free electron are not
static, both the gravitational pull of the Sun and of the planet are rotating
about the centre of mass of the Earth, which for ease of calculation I defined
as my fixed reference point. The little electron is in the middle of a three way
triangle of gravitational attractors all trying to pull it towards them and two
of them moving rapidly across the sky, in a complex dance which some times
brings them together but often moves them apart.
Calculating the Movement of a Free
Electron subject to Three Moving Gravitational Fields.
First I have to define some variables to use. Here they are:
Let m_{e} = the mass of the Earth
Let m_{p }= the mass of the planet
Let m_{s} = the mass of the Sun
Let m_{0 }= the mass of the free electron
Let d_{1} = the distance between the free electron and
the planet
Let d_{2} = the distance between the free electron and
the Sun
Let h = the height of the ionised layer which contains the
free electron
Let f_{1} = the gravitational force of the Earth on
the electron
Let f_{2} = the gravitational force of the Sun on the
electron
Let f_{3 }= the gravitational force of the planet on
the electron
Let G = Newton's general gravitational constant
The first step is to calculate these three forces in terms of
the known parameters.
First the gravitational pull of the Earth on the electron:
Next the pull of the Sun on the same electron.
Finally the pull of the planet on that poor much tugged
electron.
If I am to discover anything about how these forces tug at the
electron I must know how they main players are moving and to do that I have to
have some line to measure from. I decided to define a line between the centres
of mass of the Sun and the Earth at midnight GMT as my reference line. The angle
that the Sun makes with this line is represented by Theta. The angle the planet makes with this same reference line is Phi. Both these angles change continuously but both the angles and their rates of change can easily be
measured by standard astronomical techniques.
Using these time varying angles and their relationship to the
previously calculated gravitational forces I can now work out the cumulative
force on the electron along the line between the centres of mass of the Sun and the Earth (f_{v})and also at right angles to this line(f_{h}),
which is, the force parallel to the surface of the Earth. These two forces
turned out to be a very interesting function of the Theta and Phi, as I have shown below.
The combination of these perpendicular and vertical forces is
found by adding the two vectors thus to find the resultant or combined forces
which I've called f_{r}
_{ }
At first sight this function looks a
little complicated but it has some very clear features which indicate that it is
going to cause turbulent behaviour. The interaction between the Sin and Cos
functions is going to be very unstable around the points when either angle
approaches 0, 90, 180, or 270 degrees. At this point one of the functions is
rapidly approaching 1 whilst the other is approaching 0. When the number one is
divided by zero, the function tries to become infinitely large. This means that
when the gravitation fields of the Sun and planet occupy approximately the same
angle in the sky; are opposite each other; or when they are at right angles to
each other, the crisscrossing forces are really going to churn up the electron
cloud and seriously rattle individual electrons about.
