Re: Breakdown voltages of toroids

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: Finn Hammer <f-h-at-c.dk> 

Antonio,

I have the tooling for a 160mm by 600mm toroid, and consider having made 
the accompanying half sphere, for a Van der Graff terminal.
I now know that it will be able to supress breakdown at voltages below 
31*8*2.19=543kV. That is pretty nice to know.

You earned your laurels a long time ago, and you add guilding to them by 
your work. I feel honoured to be on this list with you.

Cheers, Finn Hammer

Tesla list wrote:
>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
>