TSSP: List Archives

From: Paul
Date: Thu, 09 May 2002 19:02:33 +0100
Subject: Re: [TSSP] Secondary voltage stress factor

Hi All,

Thanks John and Kurt for gathering the data on TT-42.  I modeled
the coil to obtain 590 kV at the top for a 4J bang.  For some reason
I had to set the tap to 12 turns rather than 14.5 in order to tune
the thing, so the model is not quite set up right.  The coupling is
modest, and the waveforms are pretty much the same as the k=0.1
example in pn040502.

The secondary has length 48 cm, so the 590 kV gives 12.3 kV/cm.

The h/d ratio is 4.5, and quite high off the ground, so from the
base = 2 * d table in 

 http://hot-streamer.com/bob/sfac/index.html

we get a stress factor of around 1.4, thus giving a maximum gradient
of around 12.3 * 1.4 = 17.2 kV/cm due to non-uniformity of the 
resonant voltage distribution.

So if this gradient represents the point at which the coil is almost
giving racing arcs, then we have an additional factor of
26/17.2 = 1.51 necessary to account for surface effects and non-
uniformities of the field along the coil.

Now I'm thinking in terms of Boris's dielectric non-uniformity, and
we have pairs of parallel conductors immersed in the coating 
dielectrics.  It occurs to me that we have another 'geometric' 
factor involved here.  

Consider

 http://www.abelian.demon.co.uk/tssp/tmp/bp080502.gif

showing a cross section of turns with some sort of coating.
The full turn-turn potential appears across the gap C, so the
stress at this point is our 17.2kV/cm divided by (1-spacing_ratio).
The spacing ratio for John's coil is 0.88 so in the gap C we have
17.2/(1-0.88) = 143 kV/cm.  

Now if the coating/air interface follows the contours of the wires
slightly,  the troughs B will see a higher field than the average
17.2kV/cm, although not as high as that at C.  The field at B will
exceed the average by some factor which depends of the permittivity
of the coating, the depth of the troughs, and the spacing ratio.

It seems to me that we could account for a significant extra factor
by this line of reasoning.  Perhaps we should contemplate solving the
laplace equation for a range of geometries to tabulate an additional 
'corrugation factor' to be applied over and above the stress factor
due to voltage distribution?

Boris wrote:
> real coils discharge  in that case for a mere
> fraction of resonant TC semicycle (microsecond or so
> and 95% of energy "gone with a wind").

Well certainly the topload energy is lost quickly, but the coil
energy will take several cycles to dissipate. The coil *charge* will
need a quarter-cycle to drain from the coil, but in doing so most of
its energy will be transferred to the coil's B field, and the coil 
will continue to oscillate like this (with both ends grounded, ie in
the half wave mode) for a few cycles until all the coil energy is
dissipated in the arc of the topload discharge. So I think the
arc discharge will remain for a few cycles.  Thus the impulse I
simulated the other day, which just empties the topload of charge,
is not a good model.  I need to clamp the topload to ground, and
switch to a set of grounded-top normal modes,  until the load
current has dropped below some value too low to maintain the arc, 
at which point the model would switch back to the open-top mode set.
There will still be some sort of transient sloshing back and forth,
and it will be interesting to see how big that is.

>From an energy point of view, the short impulse simulated the 
other day takes the topload energy out of the 1/4 wave mode and
scatters it across a wide range of modes.  By clamping the
coil top to ground by a longer discharge, I think most of 
combined topload and coil energy will be switched to the 1/2
wave mode and the sharp transient will not be so big, although
we may get some interesting voltages just above the middle of
the coil.  I'll try to run some simulations of this at the
weekend.

As regards dielectric polarisation - I seem to recall coils that
give racing arcs being associated with static shocks during handling
of the secondary, and that discussions have revolved around how
the racing arcs caused the static - but perhaps it is the static
causing the racing arcs?  I suppose that if a charge displacement is
trapped in the dielectric, it can only act to worsen the non-
uniformity of the field.  Therefore any stress factor that we deal
with here must be considered a lower limit valid in the absence of
static polarisation.

The stress factor tables calculations have come to a halt. The model
has failed to compute for the sharpest of the pointed cones, so 
there are some holes in the corners that I need to look at.  The
problem is that the small turns near the tip have such a small
capacitance to the far turns of the wide end that the potential
matrix becomes non-invertible at the numerical precision used.
Perhaps I'll just cheat and use +/- 0.99 for B to avoid the
singularity.

You can see why cylinder coils are used in preference to all the
other shapes - they have consistently the smoothest voltage
profiles.
--
Paul Nicholson,
--


Maintainer Paul Nicholson, paul@abelian.demon.co.uk.