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.