Re: Resonance, and now magnifiers

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

Original poster: "Paul Nicholson" <paul-at-abelian.demon.co.uk> 

It might be worth listing again some of the other possible
advantages of the magnifier configuration.  Items in this list
don't depend on any of the 'exploitation of overtones' that
we've been discussing, but stand on their own as independent
justifications.  Some of these were mentioned recently in
another thread.

* It allows the hot end of the resonator to be located further
away from the primary stuff, eg several metres to one side.

* A large resonator may be more manageable in two pieces.

* Each coil can be replaced independently after damage, or
redesigned, etc.

* Flexibility. The owner of N secondaries and M tertiaries has
N*M possible magnifiers in his possession.  Or if you don't care
which are secondary and which are tertiary and just call them N
assorted coils, you have N*(N-1) magnifier combinations to play
with.

Arguably then, there are some reasons for splitting up the resonator
in this way, whether or not there is any fancy tuning in mind.

Steve Conner wrote:
 > If this is true, would a forced response magnifier that only
 > excites the 1/4 wave mode be practical?

I'm sure it would be practical, and for the above reasons perhaps
beneficial in some cases.   Indeed, doesn't the traditional CW
coil, base fed via a ferrite cored coupling transformer, fit this
description?   The initial normal mode transient dies away as the
forced response builds up.  To exploit higher overtones in this type
of operation, you would have to tune them to match a harmonic of
the drive.  Then a square wave low Z (constant V) drive would cause
current flow at the harmonic frequency as well as the fundamental.
Thus the overall input 'Z' would seem lower and the coil would
draw more total power from the driver.  The overtones would be tuned
to the drive harmonics by hooking capacitance to the coil in
various places.

 > Does a successful magnifier tuning manipulate the 3/4 wave
 > mode to cause a voltage _minimum_ around the top of the
 > driver coil and bottom of the extra coil?

The 3/4 wave mode would have its voltage maxima somewhere
in the vicinity of the junction of the two coils.  But does
it have to sit on the transmission line?  I'll try to discuss
that.

If you just pick two coils at random and string them in series,
there's only a slim chance that the 3/4 wave maxima will be at
the junction.  Odds are more likely it will reside inside one
coil or the other.  (Wherever it is, it'll move upwards as
tertiary top-C is applied.)

I'm pretty sure (but haven't actually checked) that as you
go about loading the transmission line with extra capacitance,
the effect on the 3/4 wave voltage distribution is to draw
the maxima towards the junction from whichever coil it started
out in.  That'll have to be checked to make sure.

Similar comments apply to the voltage node (minima) of the
middle resonance.  Now I referred to this as a 1/2 wave in a
previous post, but then I remembered that Antonio had shown
us it was really another 3/4 wave...

Antonio wrote (on 18th Nov 2003):

 > The low-frequency component rises continuously along the
 > coils (1/4 wave).

 > The middle-frequency component is zero at the transmission
 > line and accounts always for one half of the output voltage
 > (3/4 wave with zero at the transmission line, or a degenerate
 > 1/4 wave mode that starts at the transmission line).

 > The high-frequency component is always negative at the
 > transmission line, to cancel the first component there,
 > and positive at the top.  (3/4 wave too, with a zero
 > somewhere at the third coil).

which sums things up very nicely.  Since we appear to have
two modes that look like a 3/4 wave (one of which, the middle,
would like to be 1/4 wave or maybe 1/2 wave but for its interaction
with the primary),  it might be better just to number the modes,
in order of frequency, as say

mode 1: secondary and tertiary combined is 1/4 wave;
mode 2: secondary is 1/2 wave, tertiary is 1/4 wave, total 3/4 wave;
mode 3: secondary is 1/4 wave, tertiary is 1/2 wave, total 3/4 wave;

A while ago I made up animations of these three modes for a
hypothetical magnifier, to illustrate what they look like.

   http://hot-streamer-dot-com/tssp/tmp/mag1.mode1.anim.gif
   http://hot-streamer-dot-com/tssp/tmp/mag1.mode2.anim.gif
   http://hot-streamer-dot-com/tssp/tmp/mag1.mode3.anim.gif

In these animations the secondary spans 0-30% of the graph,
the tertiary 30% to 100%, so you can see the little discontinuity
in the graphs at that boundary.  The modelled primary is a
helical around the lower half of the secondary (0 to 15%) so the
pri-sec coupling is high.

These modelled coils where picked at random, and lo and behold
we got the mode 3 maxima at 50%, ie 20% above the transmission
line/junction.  The mode 2 minima is about 10% above the junction.

The combined motion of all three resonances looks like

   http://hot-streamer-dot-com/tssp/tmp/mag1.anim.gif

The tuning target is to get all three modes to coincide at a joint
top volts peak at the same instant.  This in itself doesn't require
the mode 3 voltage maxima to be on the transmission line, nor the
mode 2 voltage zero.  But if we also want to obtain the maximum
energy transfer to the top end of the tertiary, there is another
condition to maintain...

Bert Pool has given an example of the large transmission line
capacitance which can be favourably used:-

 > I use a 12 inch wide, fifteen foot long strip of
 > aluminum flashing as a transmission line.

This can store a lot of energy per volt and we would like as an
additional requirement to arrange things so that at the instant
the 3 modes meet their simultaneous topvolts peak, the 3 modes also
combine momentarily to give zero volts at the transmission line.

This additional requirement ensures that all the energy is removed
from that intermediate storage and passed on. Ideally, mode 2 is
identically zero because we put its voltage node on the t-line.
So we just need mode 1 and mode 3 to be momentarily equal in
amplitude but opposite in polarity so they add to zero, also at
the t-line.

(This certainly isn't happening in the modelled system above,
which is just at a random tuning.  Nor is it likely to happen
in a real magnifier, except either by accident or by some very
careful planing.)

Now I target the t-line for the scene of this momentary zeroing
of stored energy because this is likely where there greatest
capacitance is located, and therefore is the best place to remove
all the energy from.  But wherever we choose to take advantage of
this momentary zero, we'll still have non-zero volts elsewhere in
the coils and inevitably some energy must remain in the E-field
of the coils rather than the E-field of the top C.

Note that with this tuning, the entire peak topvolts is momentarily
expressed across the tertiary.

Suppose we now rope in further overtones. The effect is to introduce
additional points along the coils where the voltage can be made
momentarily zero at the appropriate instant.  As we add more and
more carefully timed overtones into the mix, we see that we can
achieve more and more cancellations coincident with the joint
topvolts peak.

In this way we tend towards a system portrayed by a single pulse
travelling up the coils, building in amplitude to wash against
the topload leaving the coils momentarily largely bereft of voltage.

Perhaps Antonio can confirm that description accords with his models
of higher order networks.  The result I think tends towards a
broadband pulse TC, perhaps not dissimilar to pulse forming networks
in radar magnetron supplies and that sort of thing.

But unfortunately again, the entire topvolts is momentarily set
across the top-most coil, which must set a limit to how far we can
go with cramming all the stored E-field energy into the top end of
the resonator in this manner.

It's a daunting prospect to face designing and tuning to this
overtone harnessing recipe.  Perhaps only Antonio has ever managed
to do that.  Not only do we have to tune the frequencies of the
modes to achieve that joint topvolts peak, we also have to tailor
their voltage distributions and relative amplitudes in order to
achieve that momentary zero on the t-line necessary for max energy
transfer to the topload.  Quite a tall order.

More realistically, it might be better to ask what the proud owner
of an existing magnifier might do to check out and exploit some of
these ideas.  It ought to be possible to examine an existing system
that already works quite well with a view to determining where the
maxima and minima of each mode sit, and to what extent the three
modes are in the correct tuning for a joint topvolts peak.  On the
basis of such an examination, it might to be possible to determine
some (perhaps small) adjustment which will in principle improve
things.  One thing working for us is that we have software that can
model all this for any particular installation. Perhaps some of this
will be a tempting line of research for an advanced coiler.
--
Paul Nicholson
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