Re: flat coil ?

["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>


> Outer Diam. = 45"
> Inner Diam. = 2"
> Wire Diam. = 0.063"
> Turns = 316
> Inductance = 44mH

Now with the 2" hole in the center, we get 

Ldc = 43 mH
Les = 55 mH
Ces = 19 pF

Fres = 155 kHz
Rdc = 5.2 ohms

So I think we have a decent model now of Chris's flat secondary.

Now what about a primary?  You could consider:

  Geometry = flat spiral
  Active turns = 3
  Pitch = 0.75"
  Material = 0.25" diam tube
  OD = 45"
  ID = 40.5"
  Height = 12" below the plane of the secondary.
  
to give
  
  Lp = 23.4 uH
  k = 0.22

and the extra capacitance which this applies to the secondary drops
the Fres down to 151 kHz, so would need 48nF to resonate with the
secondary.  But this design leaves the inner primary turns a mere 15"
from the part of the secondary where the voltage is 80% of vtop,
which is asking for trouble.  An alternative might be a flat primary
in the same plane as the secondary, eg

  Geometry = flat spiral
  Active turns = 2
  Pitch = 0.75"
  Material = 0.25" diam tube
  OD = 68"
  ID = 65"
  Height = level with secondary

if you have the space!  This gives

  Lp = 19.6 uH
  k = 0.21

This arrangement only lowers the Fres to 154 kHz, and the entire
primary is in a cold region of the secondary's E-field. Cpri = 55nF.

But you wouldn't be advised to build a primary yet, not until you've
decided what sort of a center terminal you'll use, and what the
primary charging supply will be.  If you have a favourite primary cap
that you want to use, let us know the value so that we can have fun
inventing a primary to match.

As for top terminals, if you were to fix a small sphere on top of
your center core, say 2" diam with center 3" above the plane, the
Fres would only drop a little, to 153 kHz.  In this case, the coil
is shielding the topload sphere, rather than the other way around.

The energy storage capacitance of the secondary (with sphere) is
around 27 pF, so if you had say a 9kV primary voltage, the peak top
volts could be up to

   Vpri * sqrt( Cpri/Cee) = 9kV * sqrt( 55nF/27pF) 

which comes out at around 400kV.  That gives an average radial
field of 400kV/22 kV/inch = 18 kV/inch.  Remembering that 80% of
the voltage is impressed across the outer 50% of the winding, the
actual value would be nearer 30kV/inch.  Added to this would be the
additional induction from the primary, and the tssp model reports a
worst case radial gradient of 2kV/turn, or 29kV/inch at 11% in from
the rim.  I don't know whether that's enough to cause racing arcs.

Can't give more accurate predictions without knowing how the coil is
supported, but I hope these figures help to give some sort of feel
for the territory you are entering.
--
Paul Nicholson
--