RE: Quarter Wavelength Frequency

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

Original poster: Jan Wagner <jwagner-at-cc.hut.fi> 

Hi,

On Mon, 12 Jul 2004, Tesla list wrote:
 > Original poster: "David Thomson" <dwt-at-volantis-dot-org>
 > Original poster: Shaun Epp <scepp-at-shaw.ca>
 >  > Where did you get the idea that photons are flowing???
 >
 > Terry stated:
 > The only way to magnetically link the coils is via photons, the carrier of
 > electromagnetism*.
 >
 > Of course I don't mean the photons are flowing as in DC, they are following
 > the AC current of the electrons that generate them.  And "flowing" isn't
 > even correct as we all know electrons don't actually flow.  Don't get hung
 > up on the poetic license.

I suppose photons do flow as in "DC", e.g. output of DC coil. They
just wiggle ("AC") while they flow in "DC". But, this isn't really
relevant...

 >  > A large amount of induced current close to the base,
 > because that is where the primary coil is.
 >
 > I doubt seriously that the current is determined by the location of the
 > primary coil, although the two conditions do coincide.  It would appear
 > there must be a quantum explanation involving electrons and photons for the
 > higher current being stronger nearer the primary coil and the higher
 > potential being stronger nearer the top capacitance.  As far as I know, the
 > position of a primary coil is not a quantum cause.

The position can be chosen, and there's an optimal position.

E.g., the low impedance at the grounded base is the best place to drive
the coil with an external non-homogenous magnetic field. In an impedance
matching sense, the location of the primary coil really matters. The
driving current loop creates a strong magnetic field in the near-field,
with very small electric field component, e.g. is very low impedance.
This matches very well with the low impedance of the TC base. At the top,
you would be pumping a high impedance (large electric field, small mag
field) with a low impedance source - not optimal at all.

Things aren't very different when you suddenly disconnect the base from
ground. The EM field distribution then just rearranges itself, according
to the geometry, and the TCsecondary field will now have its lowest
impedance at the center (axially), so having the pri at the bottom isn't
optimal any more. How the field goes on about rearranging itself you can
simulate and watch with discretized Maxwell equations, for example with
some 3D FDTD method. (looks like there's at least one XFDTD prog version
on share via www.emule-project-dot-net, but OTOH there are also many freeware
tools and source code on the internet, and there's www.aplac-dot-com circuit
sim demo version which can handle FDTD, albeit it's more like for smaller
VHF/UHF helix antennas...)

Also, Shauns explanation with magnetic flux is IMHO correct as well,
because the field isn't homogenous. This isn't a solenoid at DC.
If the cross section area A at the TC bottom is the same as at the top,
and the TC bottom is excited with whatever means (mag field, or low
impedance signal generator), B is stronger at the bottom than at the top,
so the flux through A is also higher at the bottom than at the top.

 > So I'm back to my original question, is there an equation that quantifies
 > the resonant frequency in terms of the actions of the electrons and photons?

Maxwell equations, over time. Given the large dimensions of TCs, those
equations are suited best. Maybe as FDTD. You could attempt to apply
QFT/QED (http://en.wikipedia-dot-org/wiki/Quantum_electrodynamics etc) but I
really doubt the result is anything comprehensible...

 > And I'll state again, if the quarterwave is not the sole determinant of the
 > resonant frequency because photons are carrying magnetic flux to the other
 > end of the coil before the primary coil induced electrons get there, then
 > photons must be influencing the resonant frequency of the coil via RF.

Does moving from the vicinity of one radio station to some other,
noticeably change the resonant frequency of the coil?
Though so... ;-)

OTOH you're right that the electrons at both ends constantly interact with
each other via the field / photons, and the interaction is almost
immediate. Though this doesn't mean the electrons would be moving anywhere
far. Definitely they won't be reaching one end from the other in many
thousand cycles -at- f_res, meaning it's maybe better to think about the
electrons wiggling back and forth in a small restricted area, while the
amount of wiggling and general direction of movement is determined by the
local EM field (superposition of self-generated and from all other
electrons)
Anyways, the overall electron interaction you can however model with the
standard Maxwell eqs, once again. Along the same lines as Paul Nicholson &
co's in their paper/website.

Oook... I hope I didn't write too much garbage... ;-)

 > There must be a way to quantify this and get a perfectly accurate resonant
 > frequency formula for a Tesla coil.

Yup. Would at least be of academic interest, if no other use. ;-)

cheers,
  - Jan

--
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  Helsinki University of Technology
  Dept. of Electrical and Communications Engineering
  http://www.hut.fi/~jwagner/ -