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Re: Spheres vs Toriods

At 08:04 PM 4/3/96 +0700, Jack wrote:

>To all,
>
>        I have been trying to figure out the magic behind the toriodal
>shape. I was under the impression that the dominant factor in a high voltage
>collector was the radius of curvature.  This would make a sphere or an
>oblate spheriod the best choice.  
>        Could someone enlighten me as to why the toriod is the shape of
>choice?  Wouldn't the sphere be better?  Is the toriod such a success
>primarily because of the lower cost of fabrication, or is there a technical
>reason for it's popularity?
>
>        On an unrelated issue, are there any coilers in Tucson or it's
>environs?
>
>Thanks,
>Jack
>

Hi Jack,

Actually a more dominant factor for a voltage collector would be the field
symmetry of the electric field.  The symmetry of the electric field for
sphere is simply spherical.  But the symmetry of the electric field
generated by a toroidal geometry is quite different.  The E field within a
toroid also changes slightly as certain conditions arise, where as with a
spherical geometry they remain pretty much constant.  

When using a spherical discharge terminal, you will generally get discharges
all over the surface area of the sphere, due in part to its uniform
spherical electric field symmetry.  Now with a tororid, the field symmetry
is not as uniform, thus you will generally get a discharge along some
circle, with its center at the radial (or center) of the toroid.  This
hypothetical circle sits uniformly somewhere on the outer surface area of
the toroid.  Thus one can conclude that the surface area, from which the
discharge originates form a toroidal geometery, is not as large as the
discharging surface area in or on a spherical geometry.  Put in simpilier
terms, the magnitude of discharge is less dispersed in a toroid, thus it is
much more suited for use in discharge applications, especially TCs. (NOTE:
The charge in a toroidal discharge terminal also has a higher tendency to
accumulate on the outermost rim (outer diameter) of the toroid, thus further
reinforcing the above explaination.)

Note, in the above I used the term "generally".  For clarity, it simply
means that usually it happens that way, but not always.  Sometimes there are
conditions and other variables which arise, that we cannot necessarily
control, which can and usually do change the overall outcome and performance
of the situation at hand.

I hope that was not to hard to follow.  I could have explained the physics
behind it all, but that really would not be very useful to everyone.  If by
chance I have missed something or left something out, someone please let me
know...

Tim

o------------------------------------oo---------------------------------o
| Timothy A. Chandler                ||   M.S.Physics/B.S.Chemistry     |
o------------------------------------oo---------------------------------o
| NASA-Langley Research Center       ||   George Mason University       |
| Department of Energy               ||   Department of Physics         |
| FRT/Alpha - NASALaRC/DOE JRD/OPM   ||   Department of Chemistry       |
| CHOCT FR Designation #82749156/MG09||   OPC-EFC                       |
o------------------------------------oo---------------------------------o
|                 Private Email Address:  tchand-at-slip-dot-net               |
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