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Re: Big top loads
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.