Re: Wire Length (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

Moderated and approved by: Gerry Reynolds <greynolds@xxxxxxxxxx>



---------- Forwarded message ----------
Date: Tue, 26 Dec 2006 07:49:55 GMT
From: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>
To: tesla@xxxxxxxxxx
Subject: Re: Wire Length (fwd)

Bart, All,

With the primary and center load added, the rim-grounded planar
spiral model gives:-

f1          461 kHz
f3         1228 kHz  
f5         1960 kHz

Les @ f1    4.61 mH
Lee @ f1    5.35 mH

Cdc        92.3 pF
Ces @ f1   26.3 pF

Lpri     16.5 uH

Addition of the center load has pulled the frequency down by
only about 4 or 5 percent.  But it does seem to stabilise the
calculations quite a bit - the variation of f1 with different
segmentation plans is about +/- 5 kHz.

Highest surface field gradient on the topload is about 0.11
kV/cm per kV of center voltage, occuring on the top of the
sphere.  So if breakout occurs at 24kV/cm, that's a center
voltage of 24/0.11 ~= 220kV.  

I ran a time domain model using a primary cap of 7.22nF and
a firing voltage of 10kV.    The 'split' frequencies come out
at 382 kHz and 613 khz, giving an effective k of 0.44.

Here is an animation spanning about 3.5 full beats (pri-sec
transfer in about 2.1uS).

 http://www.abelian.demon.co.uk/tmp/baps-rg3.anim.gif

There is incomplete energy transfer (not surprising - no
attempt is made to fine-tune the model), but the primary energy
residue doesn't look too bad at all.  Not too much should be
read into the fine detail of these waveforms: small changes
in the modelling produce relative phase and frequency shifts
of the various components, altering the detail significantly.

But the voltage gradient looks ok, doesn't it? No nasty steps
or spikes. There is an HF transient rolling back and forth,
but this shows up mainly in the current waveform, indicating
it is of quite low impedance.

Peak center volts for a 10kV firing is around 145kV, so no
breakout predicted if a simple 24kV/cm surface threshold
applies.

BTW, I had a play for the first time with the IE browser on
windows.   It didn't make a very good job of playing these
animated gifs - very slow and jerky.   I hope that's not
generally the case with IE.

--
Paul Nicholson
--