From: "Malcolm Watts"
Date: Fri, 10 May 2002 10:46:07 +1200
Subject: Re: [TSSP] Secondary voltage stress factor
Hi Paul, all,
Just a quick one regarding the accumulated static in
the secondary insulation:
On 9 May 2002, at 19:02, Paul wrote:
> 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.
I have a (spacewound 1:1) coil that exhibits this phenomenon but has
never flashed over in its life.
Regards,
malcolm
> 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.