Secondary current vs voltage

["Tesla list" <tesla-at-xxxxxxxxxx>]

Original poster: paul-at-abelian.demon.co.uk 

Dan Kunkel <dankunkel-at-hotmail-dot-com>  asked:
 
> Why is it that it is accepted that there is a large amount of
> current at the base (near the ground) of a the secondary coil
> and not at the top?

Picture a number of amps of AC going into the base from the ground
plane. Remember that 'current' is a rate of flow of charge - so many
coulombs per second. As this current moves up the coil, charge is
deposited along the way in order to build up the voltage across
the coil's capacitance, so as you go higher up the coil there is
less moving charge remaining - a lower current. 

If you're reading this on a fixed width font, the following diagram
might help to picture this,

   BASE                                             TOP

    10A->     9A->      8A->      7A->      5A->    0A
   /\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
   |      |         |         |         |         |         
   |      |         |         |         |         |
   |      |         |         |         |         |
   |      = 10pF    = 5pF     = 1pF     = 1pF     = 2pF
   |      |         |         |         |         |
   |      |1A       |1A       |1A       |2A       |5A
   |      |         |         |         |         |
   ------------------------------------------------
             G R O U N D   P L A N E

I've shown the coil capacitance as a number of lumped C joining
the coil to ground, the values getting smaller as you go up. 
Of course, you should imagine these capacitance lumps to be
'smeared out' into a continuous distribution of capacitance.

The currents flowing downwards through the capacitances are called
displacement currents, since they don't involve an actual carrying
of charge - the charge is 'sticking' to surface of the coil and
inducing an equal and opposite charge in the ground plane, so it
looks as if a current is passing between the coil surface and ground.

The coil current is forced to be zero right at the top, since it's
go nowhere else to go, unless a toroid is fitted, in which
case the remaining current at the top is 2.pi.F.Ctop.Vtop.

> I thought the key to Tesla coils was that the current and voltage
> were in phase.

Yes, all the voltages are in phase with each other at resonance, and
likewise so are all the currents. The voltages are all 90 degrees
out of phase with the currents. This uniform-phase current does not
imply that the current amplitude must be the same all the way
along.

For a more detailed look at voltage and current profiles along
the tesla secondary, see the graphs in

 http://www.abelian.demon.co.uk/tssp/pn1710/

Hope that helps!

Regards,
--
Paul Nicholson,
Manchester, UK.
--