TSSP: List Archives

From: "Malcolm Watts"
Date: Wed, 2 May 2001 16:49:23 +1200
Subject: Re: [TSSP] Time domain modeling

Hi Paul,
         Some questions, some information and some comments:

     Firstly, I have enjoyed immensely reading through the notes you 
have been producing and it has been a great little exercise to 
stretch myself to follow them (which I am mostly doing although it 
has been some years since I actively applied calculus to electronic 
modelling). I am getting up to speed once more :)

On 2 May 01, at 4:33, Paul wrote:

> boris petkovic wrote:
> 
> > This seems to me to be a secondary current waveform
> > graph display,and not primary one at first sight?
> 
> Yes!  Why didn't I see that?  Guess I was just glad to 
> see a beat appear.  Somewhere I've inverted the phase of
> one of the modes,  there'll be a - sign dropped somewhere,
> but just one of the modes and not all... hmm how did I
> manage that!!
> 
> > never heard for "Fredholm" equation ..
> > Seems,extra study have to do.
> 
> 'Mathematics of Classical and Quantum Physics'
> Byron and Fuller, Dover 1992,
> Vols 1 and 2 in ISBN 0-486-67164
> 
> The above is an outstandingly good book - IMO the all-time best 
> math/phys book every put together. Amazingly it is low cost
> too! 
> 
> Also,
> 
> 'Numerical Mathematics'
> Froberg, 1985,
> ISBN 0-8053-2530-1
> 
> has a chapter on this subject - mainly concerned with the
> computational aspects.
> 
> And also the well known 'Numerical Recipes in C', chapter
> 18.
> 
> Malcolm Watts wrote:
> 
> > I was looking at the large number of oscillations within the
> > beats. Are we talking about the same beat envelope whose url you
> > posted (Thor primary current waveform)?
> 
> Yes, same url. The frequency difference 68.129 - 65.908 = 2.221kHz of
> the waveform as plotted gives a notch every 450uS. With the revised
> frequencies of 69.144 and 65.018 there are only around half as many RF
> cycles per beat. I just found another error in the coupling operator
> u, so I expect the coupling is now different again.

I wondered.
 
> A long weekend coming up, so I'll try to get some more done
> then. I'm keen to answer the question - 'How much of the bang
> energy goes into the first two modes?' which translated means
> 'How well do the spatial distributions of the first two modes
> cancel out along the solenoid?', with the corollary 'How does
> the answer vary with k'. 
> 
> My guess is the answer will be 'not much energy at low-ish k',
> but with more of a spread at higher k.
> 
> When voltages reach a point where the load becomes non-linear,
> the opportunity for energy transfer between modes arises.

Are you meaning spurious and transient loads of various kinds caused 
by sparks being formed at the terminal?

> If a significant fraction of the energy of the main two modes
> spills over into the higher resonances, that could spell trouble
> for the secondary. This higher-mode energy is largely trapped
> in the secondary, so maybe if conditions are right it gets
> 'topped up' on each cycle of the main RF waveform.

Which suggests a link with "racing sparks" although breakout is not a 
pre-requisite for them to occur. 

> A question to those who have looked at secondary voltage
> waveforms on the scope: When arc discharge occurs from the
> topload to ground, does the breakdown path continue to
> exist into the next half cycle and beyond, or does the conducting path
> extinguish at the first zero crossing and have to re-form if it can,
> on the next half-cycle?  Maybe the answer is 'partly', ie some of the
> ionisation is left over and a temporary lower breakdown voltage is
> available to the next half-cycle. Can anybody advise?

The answer is highly dependent on the loading conditions. There is no 
fixed in concrete impedance for an attached spark. Even the crudest 
observations of gap behaviour show this. For a particular system you 
can see the gap dim as the discharge distance is reduced only to have 
the gap brighten again as the terminating impedance drops further 
with a further reduction in distance and other resonant modes begin 
to become dominant (as outlined in your excellent notes!). There is 
an optimum terminating spark which can drain the secondary in just a 
couple of cycles. Trying to define it is not simple as the impedance 
is time-varying with current which is constantly changing (OK - that 
sounds like a tautology of sorts). You might consider that there is 
an optimum rate of energy drain which could be equated to some 
equivalent purely resistive termination (at a guess matching Zft).

      The points you made in the earlier notes about Z match 
difficulties at the base are well taken. 

> The reason I ask is that, depending on just how long the arc
> discharge path can be considered to be grounding the top of the 
> coil, it looks like quite a substantial amount of energy can be
> transfered into one of the higher modes, to be trapped there.
> Anyone reporting arcs along their secondary - but only when the
> top is actually discharging?

I have seen them occurring both with and without breakout. I suspect 
not allowing the secondary to breakout with high voltage production 
is as responsible in some cases as "incorrectly" terminating the 
resonator.
 
> Just some of many question a non-linear time domain model 
> should be able to answer.

I applaud your goals. To my knowlege, this is the first serious 
attempt to throw the book at the problem in a qualitative way.
 
Regards,
malcolm


Maintainer Paul Nicholson, paul@abelian.demon.co.uk.