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Subject: Re: Breakdown voltages in Spherical Fusors
Date: Nov 29, 11:07 am
Poster: Pat

On Nov 29, 11:07 am, Pat wrote:

> Miley, et.al. wrote a paper where they looked at the voltage/current characteristics of spherical fusors. ("Discharge Characteristics of the Spherical Inertial Electrostatic Confinement Device", IEEE Trans Plas. Sci. V25,#4, Aug 97).

>In the paper they go through many gyrations to compare the breakdown characteristics of the spherical fusor against a theoretical glow discharge, etc. In it, they note that that the pd term (pressure * distance) for a given voltage is about 1/3 of what would be expected for a plane electrode case, etc. They claim that this is due to the transparency of the grid, etc. Further, they go through some real handwaving to explain why the curve matches the simulation of 99% transparency, when the real device is only 80-90% transparent, invoking microchannels, and all manner of charge exchange collisions, etc.
>I have no doubt that these effects exist, given the observed difference in voltage between solid and grid electrodes.
>However, I have a simpler explanation for the lower operating voltage at a given pressure an distance. They calculated based upon the distance between the inner grid and shell. However, for concentric spheres, the E field isn't uniform. In


fact, for the relative sizes that they used (30 cm diam, 7.5 cm diam grid) the magnitude is about 3 times higher at the inner grid than would be calculated using voltage/spacing.
>In any case, their empirical expression for the striking voltage is probably correct:
>V = 0.118 * A / (pd)^2 kV *(torr-cm)^2/amu
>Where A is the atomic mass, pd in torr-cm
>Does anyone have any other empirical data to add to confirm or revise the above expression?

Well, there are some linear hollow cathode
discharge devices that have the following
variation between the pressure and the
operating voltage and current:

P ~ I^0.5 / V

This is for a fixed distance d (in your Pd)


V ~ I^0.5/(Pd)

If you increase the distance d, you increase
the pathlength for ionization. Now, in
the spherical IEC device, which distance do
you use as d? If the inner cathode was solid,
then yes, it would make sense to use the distance
between the outer and inner electrodes as an
empirical parameter. However, since ions and
electrons can circulate through the transparent
inner electrode, one may have to consider the
diameter of the inner grid as an empirical
parameter to test as well.

The Pd parameter is one that was developed
specifically for solid electrodes and ones
that were usually planar. Experiments
were also performed with concentric
cylindrical and spherical electrodes, and also
round electrodes immersed in a gas and separated
by a distance d. You may want to consult
some references by Von Engel, who was an
early pioneer in gaseous electronics.

Here's a good reference:

Ionized Gases, by A. von Engel, Oxford at
the Clarendon Press, 1955. See Chapter 7,
Ionization in an Electric Field.