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Re: Spheres vs Toriods

At 09:04 AM 4/4/96 +0700, you wrote:
>>From tchand-at-slip-dot-net Thu Apr  4 01:16 MST 1996
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>Date: Wed, 03 Apr 1996 23:32:44 -0500
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>From: Tim Chandler <tchand-at-slip-dot-net>
>Subject: 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

Tim,
        Thanks for a well presented explanation.  I had simply lumped TC
terminals into general catagory -high voltage terminals- and had not given
thought to the different parameters.  Thanks again for your time!
Jack