[TowerTalk] Voltage at Wire’s End

[Lux, Jim]

On 10/4/22 10:44 AM, Edward McCann wrote:
>
> You might look at this approach.
> While a bit theoretical, the concept seems sound.
>
>  https://www.witpress.com/Secure/elibrary/papers/BE99/BE99016FU.pd 
> <https://www.witpress.com/Secure/elibrary/papers/BE99/BE99016FU.pdf>
>
This is essentially what NEC is doing - it's a development of an 
expression suitable for numerical evaluation (i.e. solving a system of 
linear equations) - for the special case of an ideal thin wire over a 
dielectric ground.  And, you can see by the references to works by 
Miller, Poggio, Burke, RWP King, and so forth that he's extending the 
analyses that underlie NEC.  There are thousands of papers like this 
providing partial solutions for a variety of "useful" configurations - 
J.R. Wait is famous for all of his "wire on a dielectric boundary" 
papers. There's a whole raft of papers providing approximations, 
especially for parallel wires (those form the basis for many of the 
early Yagi-Uda design methods)

Back in the 40s, 50s, and 60s, we didn't have fast computers, so 
numerical methods that could solve a case of interest on a hand 
calculator or a slow computer were of much interest.

Pocklington's Integro-differential Equation (see ref 13)  from the late 
1800s forms the basis for all of this stuff.


Orfanidis's on-line electromagnetics/antennas text book is a great place 
to look for the formal derivations and the numerical approximations used 
to solve it.

https://www.ece.rutgers.edu/~orfanidi/ewa/ch24.pdf

(even nicer, he has a whole library of matlab codes to run the 
calculations which you can download.  I use them all the time, 
translated to python, these days)

This is a nice lecture on this stuff and how it develops into what we do 
with NEC.  So if you were wondering about Green's function, and such, 
this is not a bad start

https://empossible.net/wp-content/uploads/2019/08/Lecture-9c-Method-of-Moments-for-Thin-Wire-Antennas.pdf

What's important to remember is that Pocklington provides a generalized 
integral equation for the currents along a wire (and by extension, the 
voltages, Maxwell, and all).  It's up to you to solve it, and "method of 
moments" is one way to do that.


I suspect that to answer the question, semi empirically - we could set 
up a NEC model, run it for a variety of cases, with the right internal 
"instrumentation" (NT cards or whatever) and then make some graphs to 
show "approximate voltage at the end" with some error bars.

It's unclear how useful this would be.  For most folks, that the voltage 
is "high" is sufficient.  For detailed cases, one tends to either model 
the specific geometry, or do tests.  I was involved in making 
measurements on high power tesla coils (everyone wants to know "how many 
hundred kV is it?) about 25 years ago.  More recently, in my work, we 
aren't so interested about the exact voltage, but that it does or 
doesn't break down.

For Mars missions, and for airborne experiments at high altitude, JPL 
has a big vacuum chamber with a large clear "bell jar" in a anechoic 
chamber where we can run high power into an antenna under test in an 
atmosphere of Mars gas or just low pressure air and see if we get corona 
or breakdown.  The DS-2 probes to Mars had a "1/4 wave spike" antenna 
for their UHF transmitter, and in the original design, it would break 
down with the few watts being fed to it (Mars is sort of the ideal 
atmosphere for HV breakdown - low pressure and CO2 and Argon)

https://mesa.jpl.nasa.gov/facilities/high-power-test-facility

(I helped set up the smaller test chamber, when I worked in that section 
at JPL)