Re: Jonathon's 6" Coil (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

---------- Forwarded message ----------
Date: Tue, 26 Jun 2007 21:05:24 -0700
From: Barton B. Anderson <bartb@xxxxxxxxxxxxxxxx>
To: Tesla list <tesla@xxxxxxxxxx>
Subject: Re: Jonathon's 6" Coil (fwd)

Hi DC,

I didn't read any of these emails until now. Guess I came in on the tail 
end of things (man, you guys are quick)!

>To test the true peak output of a resonance transformer, it must be operated 
>in a "single-shot" mode.  I use 1 pulse every 120 seconds which gives any 
>residual ions time to clear the previous spark channel.
>
>The peak potential is then a function of the spark's distance between two 
>standard 1/2 inch dia. rod gaps.  I think chip has posted this information 
>in the archives for reference.
>
>In short summary:
>
>60 cm = 332 kV     70 cm = 382 kV     80 cm = 435 kV     90 cm = 488 kV 
>100 cm = 537 kV
>
>40 cm = 225 kV     30 cm = 172 kV     20 cm = 124 kV     15 cm = 102 kV
>
>  
>
Rod Gaps? Then these numbers look very good. Javatc uses sphere gap 
geometry where the voltage between spheres required for surface corona 
is twice as great as rod gaps with planar geometry. When sphere 
electrodes are close, they act like planar electrodes, but as they are 
separated, their spherical geometry becomes a factor and increases the 
voltage required for surface corona (up to a self-limiting max where 
further separation will no longer increase this value). The gap 
separation above is great compared to the gap to curvature ratio.

In Javatc (static gap section), I looked at 1/2" spheres at same 
distances as above:
10 cm = 129 kV / 2 =  64.5 kV
15 cm = 187 kV / 2 =  93.5 kV
20 cm = 243 kV / 2 = 121.5 kV
30 cm = 352 kV / 2 = 176.0 kV
40 cm = 458 kV / 2 = 229.0 kV
50 cm = 562 kV / 2 = 281.0 kV
60 cm = 665 kV / 2 = 332.5 kV
70 cm = 766 kV / 2 = 383.0 kV
80 cm = 867 kV / 2 = 433.5 kV
90 cm = 966 kV / 2 = 483.0 kV
100 cm = 106.5 kV / 2 = 532.5 kV

So, your measurements look great from my calculated view of the world. 
Looks like I need to update Javatc's spark length predictions in the 
static gap table to include planar gaps. I list quite clearly in the 
help files that Javatc is looking at sphere electrodes only. But, it 
would be easy enough to equate the planar geometry (not as I've done 
above, there is actually equations for planar electrodes). Javatc uses 
derivations from Electrode geometry equations of the L.A.N.L. report 
"High-Power Microwave-Tube Transmitters, chapter 7, by William North" 
(the North Report). It's an enlightening readers who haven't yet studied 
this chapter:
http://www.classictesla.com/download/north7.pdf

BTW, Field Strength used in Javatc is from the web site of our 
illustrious member Jim Lux.
Field Strength = p * ( B / ( C + ln ( p * d)))

where

p = pressure in Torr (mm Hg). For air, this value is 760
B = 365 Vcm-1 Torr-1
C = ln( A / ln ( 1 + 1 / gamma))
d = gap width

where
gamma = 0.095 (secondary ionization coefficient)
A = 14.6 cm-1 Torr -1

I set the gamma value at 0.095 myself as I compared Jim's equations to 
other equations. After a complex time consuming study, I realized Jim's 
equation was right on the mark. I then compared the gamma factor through 
several exercises and found my way to 0.095 (this occurred a long time 
ago and I don't remember all the details at how I ended up there, but I 
do remember I spent a lot of time deciphering a "real" gamma factor.

>Actually, you were around 560 kV output.  You can also check this value by 
>using the equation:
>
>Vsec = Vpri x 80% x SQR(Lsec/Lpri).  This equation is very close, usually 
>within a few percent.
>  
>
When discussing output voltage, we should remember that we are talking 
about the top terminal maximum voltage (not a spark voltage as it can 
confuse when coilers don't consider spark impedance). The max voltage 
occurs for a quick moment in the cycle and the capacitance storing that 
energy at that moment is denoted as Cee in Javatc (secondary outputs). I 
use this value to define the "peak" (not rms) top terminal voltage in 
both the RSG and Static Gap tables where Vtop = Vpri x sqrt(Cpri/Cee) 
and is therefore a decent top voltage prediction for that moment in the 
cycle where it is maximum. Spark length is not related to this value.

Note that in the Transformer table I show a spark length based on John 
Freau's empirical (tried and tested) equation. This value will always be 
less than my equation shown in the RSG and Static Gap tables. The reason 
other than different but similar equations, is that in the Transformer 
section, there is an efficiency factor included based on Dr. R's posted 
secondary diameter efficiency. All of these spark length equations are 
empirical and derived from helical solenoid secondary coils only. Most 
coilers would fall into an 85% efficiency factor due to diameter of 
coil. Here is a write up by Dr. Resonance showing the factors used.
http://www.classictesla.com/download/resonance_tips.pdf

Take care,
Bart