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TC dynamics [was Magnifier system]

Malcolm wrote:

[snip]

>      The bottom turn in each has the highest current of all turns
> since it subjected to the greatest capacitive loading of all turns.
> As you travel up the winding, the loading becomes progressively less
> and if you have no terminal, the top turns pass virtually no current
> at all (under no spark conditions). Each turn is inducing a current in
> its neighbours and hence voltage across its neighbours. IMO the
> volts/turn should be rather high at the base and virtually nil at the
> top, but the sum of the voltages is great, and there is a volt/turn
> gradient that tapers off as one reaches the top of the winding i.e.
> the top turn barely contributes. I should note here that an analysis
> by Greg Leyh suggests that mutual inductance between the turns does
> not greatly contribute though and I'd be very interested to hear what
> he has to say about this.


  I've asked physicists and pulsed-magnet designers at work to describe
how a TC works, and after a bit of thought they are usually amazed at
how complex the operation of 'a simple two-coil system' can be.
  Diffuse properties of the TC, such as coupling between turns and 
distributed capacitance, prevent the designer from treating the TC 
in a simple way, such as either purely a resonant quarter-wave stub, 
or as a lumped-element resonant transformer.
  The effect that coupling between turns has on coil performance seems to
depend strongly on the type of coil, and how it's built.  Let me define 
here what I mean by coil type. It appears that all TC's and magnifiers 
fall somewhere on a continuous scale that extends between two extreme cases:
  
  Extreme #1 -- The quarter-wave resonant xmsn line transformer.  An old
favorite used to match antennas to feed lines, this device works by 
inducing a standing wave onto a fixed length of xmsn line, and then by
tapping into it at the right place in order to extract the power at the
correct impedance.  A tube-type CW tesla coil is probably the closest
member of the TC family to this model, since it has fewer windings and 
little or no top electrode.  It's capacitance to ground is finely 
distributed along the outer surface of the secondary like an xmsn line,
and not lumped at the end of the coil to any extent.

  Extreme #2 -- The lumped-element resonant transformer.  This device
consists of discrete L's and C's, arranged to form tuned tank circuits
that have some degree of coupling with each other.  Tuned xfmrs in
radio circuits are a good example.  A TC with many turns and a very large 
toroid would be more accurately described in this way, since the C of
the big top electrode dominates [and even partially shields] the distributed 
C along the outer surface of the secondary.

  In the first extreme, coupling between adjacent sections of the xmsn line
increases the dispersion, which if allowed to increase too far will start 
to noticably affect the Q of the system.  In PSPICE models of TC's with no
top electrode, the performance starts to degrade if the coupling between 
adjacent sections [section in this case = 1/12 of the sec] is made larger 
than about 0.1. 
  In the second extreme, coupling between adjacent sections of the secondary
winding does not directly affect performance, but rather only increases the
effective inductance of the secondary.  Perhaps one way that a larger
toroid helps is by making the TC act less like a 1/4 wave transformer, 
thus masking the negative effects of coupling between turns.
  Although the voltage profile in a 1/4 wave xfmr looks like a quarter-sine
from bottom to top, the voltage profile in a lumped-element xfmr should be
linear, with each winding contributing the same amount of voltage.  A TC 
should be somewhere between linear and sine, depending on the size of the
top electrode and the distributed capacitance.  

Has anyone out there succeeded in taking a voltage [or current] profile
of their coil under no-spark conditions?

-GL