Re: Primary Heating

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

Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

David Rieben wrote:
> most of the heating is confined to the 2 innermost turns

Gary Lau wrote:
> I've observed the inner-turn-only heating both on my
> "normal" flat primary, and also on my two-layer primary

Antonio Carlos M. de Queiroz wrote:
> Eddy currents in the thick continuous conductor used in the
> primary where the magnetic field is more intense.

Bert Hickman wrote:
> If power losses scale as the square of the B field, then a B field
> that's 5X as great implies losses that are 25X as great... and this
> may indeed be the root cause of preferential inner turn heating.

Hi All, 

I integrated the Biot Savart equation in the space around a flat
spiral primary to produce some plots of relative B field strength,

 http://www.abelian.demon.co.uk/tmp/primary-field1.gif

for a uniform current in the primary.  The arrows show the direction
of the field and their length is proportional to the flux density B.

Notice that the lines are very much longer across the inner few
turns, compared with the rest of the primary.  A closer look is in

 http://www.abelian.demon.co.uk/tmp/primary-field2.gif

suggesting that the inner-turn field is significantly stronger than
elsewhere on the primary.  A factor of 5 might be a suitable figure
for the back of an envelope.  As Bert says, those inner-most few turns
are getting 25 times the proximity loss of the other turns.  So
proximity loss could be the culprit.  

But is this high proximity loss sufficient in size to cause the
observed heating effect?  I don't know how to calculate the proximity
loss for conductors with radius greater than the skin depth.  The best
I can do is apply

 http://thayer.dartmouth.edu/inductor/sfdj.pdf

which is quite easy and I might put into acmi, but only applies to
thin wires, not primary tubes.
--
Paul Nicholson
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