OK, lets try to model the fundamental phenomena we're talking about and
try to understand them in terms of simple electrostatic principles.
We start with these assumptions:
1. Vertical antenna of length l
2. Antenna grounded at base
3. Ideal RF current sensor at base (i.e., receiver)
4. Complete absence of electrostatic fields except from #5 below
5. A single negative charge Q that can be moved from infinity to actual
contact with the antenna.
6. Electromagnetic effects of a moving charge are not considered; they
do exist, of course, so reader beware.
We start by placing the charge Q at infinity so that there is no net
charge on the antenna.
As Q is brought near the antenna, its field will cause a redistribution
of charges on the antenna. Because the antenna is connected to the earth
at its base, a negative charge will flow into the earth from the
antenna. This will result in the antenna having a net positive charge Q'
such that |Q'||Q| (i.e., the closer the charge is to the antenna, the
smaller the difference between Q' and Q, and in the limit, they are
equal). The negative charge flowing to earth causes a current to be
detected by the RF current sensor at the base of the antenna.
As the charge moves closer and ultimately touches the antenna,
a movement of exactly -Q into the earth is completed, with the result
that the antenna once again has a net charge of zero and from the moment
of impact, no further charge redistributions or currents take place.
Note that in this model, the signal we hear is actually generated by the
approach of the charge, rather than by its actual physical presence on
the antenna. (Consider the effect of insulated wire with this model.)
This is the specific mechanism in the model by which a charge colliding
with the antenna causes a quantifiable current in the receiver. Our
objective is to get a handle on the waveshape (risetime, peak, etc.) of
this current; i.e., can it be detected by a receiver as a noise impulse?
The waveshape of the current pulse will be determined mainly by 1) the
magnitude of the charge; 2) the time required for the charge
redistribution to propagate through the antenna; and 3) the velocity
with which the charge approaches the antenna. We know the magnitude of
the charge by construction and assume propagation of the charge
redistribution (i.e., we are not talking about charge carrier drift) at
the speed of light.
The critical element, of course, is the velocity of the charge as it
approaches the antenna. The lower its velocity, the longer the risetime
of the induced current pulse. If Q is attached to a snowflake with a
velocity of one mile per hour, the current peak will be quite low
because the charge redistribution will occur over a relatively long time
period.
But if we assume the charge velocity is so high that the other factors
establish risetime, we can estimate some of the interesting pulse
parameters.
For example, if the antenna is conveniently 1/100 mile long and Q = 1
pC, we get a peak current on the order of 20 uA. If our receiver front
end is 50 ohms, that peak current would generate a 1 mV peak voltage
pulse with a negligible risetime. (Please check my arithmetic) I think
the model shows this to be the highest peak current attainable (under
quite unrealistic assumptions).
If the rise-time of the current pulse depends on the particle's
velocity, then it is not clear how that pulse's peak amplitude can be
increased. I'm not persuaded that resonance is relevant, particularly
since so much of the noise we are discussing is very broadband.
We can explore the number of charges that must arrive in some time
window to achieve a given combined pulse magnitude at the receiver.
First, however, someone who has not forgotten his math and physics
should algebraically relate pulse risetime and peak value to charge
velocity. Then we would have an indication of the detectability of a
single charge striking an antenna. We could predict the magnitude of the
charge and/or the velocity needed to achieve some specified signal level
at the input of the receiver. This relationship has not yet been
presented and without it, understanding of the possibility of
non-coronal precipitation static remains elusive.
Are there other approaches to quantitative demonstrations out there?
Does someone have an alternative model of how a charge striking an
antenna is translated into a detectable signal?
Have fun!
73,
Chuck
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