Re: Wire Length (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

Moderated and approved by: Gerry Reynolds <greynolds@xxxxxxxxxx>



---------- Forwarded message ----------
Date: Sat, 23 Dec 2006 06:57:46 GMT
From: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>
To: tesla@xxxxxxxxxx
Subject: Re: Wire Length (fwd)

Bart, All,

Ok on the topload,  hmm, I should say centerload?  This is
going to be an interesting coil and already is a productive
exercise from the modelling point of view.

That discrepancy between tssp and geotc is occuring in the
internal capacitance calculation.  I haven't located the actual
fault yet, but if I switch off Cint in both models, the results
agree.  Something in here is all messed up, so dont 'cut any
metal' based on these calculations till I sort out the error.

For anyone who might be interested, the 'internal capacitance'
is a 2-D matrix giving the capacitance between each turn and
every other turn.  For example, with Bart's coil of 91 turns,
the matrix would be an array Cint[91][91] and an element, say,
Cint[12][45], gives the capacitance between turn 12 and turn 45.

Actually, if only it were that simple!   In practice it would
take too long to calculate the C between every pair of turns.
So what we do is bunch the turns together into, say, a dozen or
so groups, eg turns 1-8 into group 1, 9-16 into group 2, and
so on.   Then we calculate Cint between each group which is a
much shorter calculation although we sacrifice some accuracy,
of course.  In practice we vary the number of turns in each
group, so as to have smaller groups near the edges of the coil -
where it counts more for accuracy.   All very good, but then
it's a bit fiddly to extract an estimate of a turn-to-turn C
from this reduced Cint array - one has to interpolate - which
would be easy if the Cint function was a nice friendly shape.
Unfortunately, it rises to a sharp cusp for neighbouring turns,
in the manner of the last graph in

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

and that kind of shape is a pig to interpolate across!

In these planar spirals, Cint is quite a bit larger than in
a solenoid - this is the reason for the prominent current
max, the raised Les, and the very raised Lee.   It's also
the reason why a defect in the calculation is showing up.
Normally Cint is just a small (less than 20%) contribution to
the coil's overall capacitance, so a 10% error in Cint would
only make a 1% error in the Fres solution for a solenoid.

Here, with Bart's flat coil, switching off Cint (setting it
to zero) raises the Fres from 464 kHz to 717 kHz, so you can
see that it makes a big contribution.   For those who like to
visualise things, it means that many of the 'lines' of E-field
leaving the coil terminate somewhere else on the coil rather
than on the ground plane.

Ah well, enough writing, I'll go look at some code. First step
will be to remove that nasty interpolation and see what we get.
I've just got a 3 gig quad xeon workstation (man, I don't need a
heater in the office now!) so brute force calcs are on the menu.
--
Paul Nicholson
--