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*To*: tesla-at-pupman-dot-com*Subject*: Re: Big top loads*From*: "Jim Lux" <jimlux-at-jpl.nasa.gov> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)*Date*: Wed, 07 Jun 2000 11:59:08 -0600*Approved*: twftesla-at-uswest-dot-net*Delivered-To*: fixup-tesla-at-pupman-dot-com-at-fixme

While the capacitance of the toroid may not be all that dependent on the chord (diameter of the "tube"), the diameter of that IS important for another reason. If you make it too small, the max voltage you'll get on the topload will be limited by corona or breakdown to air due to the small radius of curvature. Limiting the voltage will limit the amount of energy you can store in the top load, which has a very real and direct influence on the spark length. Consider some limiting cases: a knife edged disk which will have a very low breakdown voltage, but a capacitance that is not that different from a sphere of the same diameter, which will have a high breakdown voltage. Unfortunately, there isn't an easy formula for the breakdown voltage (i.e. the max field) from a toroid, although there are some empirical data from various HV mfrs, etc. Typically, one uses a finite element program (like Terry's) to actually model the field. Clearly, it is bounded somewhere between the radius of curvature of the outside (i.e. the total od of the toroid) and the radius of the tube.

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