Re: Breakdown voltages of toroids

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Original poster: "Jim Lux" <jimlux-at-earthlink-dot-net> 

I assume you're figuring breakdown for when the Efield at any point on the
surface exceeds 31 kV/cm (or whatever number you used for the sphere)...
How do your sphere gap numbers compare to the tables?

----- Original Message -----
From: "Tesla list" <tesla-at-pupman-dot-com>
To: <tesla-at-pupman-dot-com>
Sent: Thursday, December 11, 2003 5:07 PM
Subject: Breakdown voltages of toroids


 > Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
 >
 > Hi all:
 >
 > I have run some simulations of toroid breakdown voltages to see how
 > they compare with a sphere.
 > I started with a sphere with 2 cm of diameter, that has a
 > breakdown voltage of about 30 kV.
 > I kept the 2 cm as the minor diameter of the toroid and increased
 > the major diameter in 2 cm increments.
 > I calculated also the capacitances. The results were:
 >
 > 2 cm    sphere:    30.0 kV  1.11 pF 1.00
 > 4x2 cm  toroid:    45.2 kV  1.94 pF 1.51
 > 6x2 cm  toroid:    56.6 kV  2.71 pF 1.89
 > 8x2 cm  toroid:    65.8 kV  3.44 pF 2.19
 > 10x2 cm toroid:    73.5 kV  4.15 pF 2.45
 > 12x2 cm toroid:    80.1 kV  4.83 pF 2.67
 > 14x2 cm toroid:    85.6 kV  5.50 pF 2.85
 > 16x2 cm toroid:    91.1 kV  6.15 pF 3.04
 > 18x2 cm toroid:    95.7 kV  6.79 pF 3.19
 > 20x2 cm toroid:    99.9 kV  7.41 pF 3.33
 >
 > 6.697x2 cm toroid: 60.0 kV  3.07 pF 2.00
 > 15.56x2 cm toroid: 90.0 kV  6.01 pF 3.00
 >
 > The last column is the ratio to 30 kV, the breakdown voltage due to
 > the minor diameter alone.
 > It's easy to scale these results for toroids of other dimensions.
 > For example, a 30x10 cm toroid would have 5 times the breakdown
 > voltage of the 6x2 cm toroid, or 283 kV, and 25 times (5x5) the
 > free-space capacitance, or 13.5 pF.
 > It's not difficult to interpolate an approximate curve in the
 > breakdown voltage data and derive an approximate formula.
 >
 > I have also updated the Inca program to plot potential and
 > electric field graphs. An example of electric field plot,
 > for the 6x2 cm toroid in free space charged to 56.6 kV:
 > http://www.coe.ufrj.br/~acmq/programs/toroid.jpg
 >
 > Antonio Carlos M. de Queiroz
 >
 >