# Re: Primary Heating

```Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

Mark Fergerson wrote:
> ...due to the solenoidal secondary influencing the final field
> shape?

The secondary is not contributing to, or disturbing the field.  It's
there in the plot for illustration only.  A real secondary would
disturb the field by virtue of the resonating current induced in it,
which would make its own contribution to the field (in a direction
tending to partially cancel the flux from the primary - Lenz's law).

> Both these images show some asymmetry in the vertical direction
> particularly some kinks (apparent discontinuities)

Yes, these are artifacts of the cheap and cheerful code, I'm afraid.
The field should be symmetric about the plane through the primary,
and for some reason some of the points below the primary are
going haywire.  I think it's something to do with the location of the
grid points wrt the position of the turns - an aliasing of some sort.
I'll find the mistake and remove it.

I'm afraid as it stands it's only good for demonstrating the overall
shape of the field and to give a rough idea of the relative strengths
across the width of the primary.

> Also of interest is that the field takes one direction at the
> outer edge of the coil, goes through a minimum not quite
> one-fourth of the width in

Indeed and that's a real minima of the field.  Field contributions
from turns outward of this point are in a direction which cancels the
total contribution from the inward turns.  As we move inwards from
this minima, the field becomes dominated by the combined effect of all
the outermost turns. As we move outwards from the minima, the field
becomes dominated by the total contribution from the inner turns, and
these are in the opposite direction. Hence there must be a radius
in between at which the field reverses and therefore the z
component is exactly zero in the plane of the coil at that radius.

The plots assume a uniform current as in a normal primary.  If the
coil were a lightly loaded resonating flat spiral secondary, the
current would be quite non-uniform and this picture would alter a
little, but I think would be qualitatively the same.

> and then shows four increasingly stronger maxima (and increasingly
> stronger "sub-minima") as you go inward. Is that (also) an
> artifact of the program,

Yes, these are program artifacts.  I've allowed the grid points to
go too close to the coil.  Each turn is integrated in only 20 steps,
so it's quite a coarse discretization.

> I'm finally assembling my magnifier system, and if your calculations
> are correct, I'll have to tear it apart and rebuild.

Hey, that sounds a bit drastic!  We can model quite accurately the
coupling between your coils in the various configurations, just by
using acmi to get the low frequency k factors.  When you've found
a geometry that gives a desired k, then we can use another program
to compute the capacitances and from this the detailed AC response.
No need to tear your coil apart, yet :)).

> I'm considering splitting the secondary into identical windings
> above and below the primary to grab both "sides" of the field.

Acmi can model these arrangements, and it may save you some trial and
error.  Send me details of your driver coils off-list.

> I'm not even a newbie when it comes to this kind of programming, so
> all I can say is thanks for what you've done so far,

I admit only two hours was spent on the program, and most of that
was getting the postscript output right, hence the shoddy results.
However, I did do a 3D integration in (x,y,z) rather than (r,z)
cylindrical, just to make sure that the azimuthal (ie the y) component
was small.  It was at most circa 1/100th the r and z components, which
cross-checks that I got the Biot Savart integration right.  Then I
took out the y components from the calculation, to save CPU. Just need
to sort out the grid artifacts and package the plot into acmi.
--
Paul Nicholson
--

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