I am planning to build a special coil of my own design, one that I believe will have some remarkable properties. I am calling on the community here to come along for the ride, and I would welcome your participation at any level.
This work is a spin-off of my theoretical work regarding the structure of the electron.
In my model, the electron is a tiny black hole, with a toroidal event horizon. It has two distinct angular momenta, which combine to impart a helical frame-drag on the surrounding space. For you relativity buffs out there who say that a toroidal event horizon is forbidden, I can assure you that this is a special case which elegantly evades this restriction. The electromagnetic field is identified with the helical frame-drag. Lightlike geodesics on the horizon twist once around, once through the torus, closing on themselves to form perfect circles.
It occurred to me that a conducting coil whose turns match the lightlike geodesics on the electron event horizon might have some interesting properties. It turns out that there is a fascinating mathematical object which embodies this geometry: The Hopf fibration.
I decided it might be helpful to model the magnetostatic field of my theoretical coil before beginning construction. Using the software package Radia, which was used to design magnets at the European Synchrotron Radiation Facility, I have accomplished this and done some basic R&D regarding the coil parameters. I found that when the ratio of (the distance from the center of the torus to the center of the circular loops) to (the radius of the loops) is exactly pi (!), the magnetic field inside the tube of the resulting toroid has nearly equal components in the axial and the toroidal directions. The magnetic field inside the "donut hole" is purely axial at the midplane, and forms a potential well at the center.
Attached are some images. The first is a basic visualization of the coil surface. The second is a plot of surfaces of constant magnetic vector potential; the intersecting contours represent the toroidal and axial components of the field. The third is a plot of the axial and toroidal field components taken along the x-axis, notice the conjunction of the axial and toroidal components within the tube.
Good work ZT.
Here are some of my first thoughts.
I would be interested in seeing graphic outputs of your simulation involving the golden mean, phi and Phi, in addition to PI.
A very interesting site with many amazing photos is:
http://www.goldenmeangauge.co.uk/
http://www.goldenmeangauge.co.uk/cropcircles.htm
http://www.goldenmeangauge.co.uk/nature.htm
As the coil makes one revolution around the circumference of the toroid, it could make one turn around the torus - or two - or three.
If there was a two strand winding around the torus, whereby one strand completed one turn during one circumference while the second strand completed two turns during one circumference, then
one of these windings could be excited with sine wave of frequency f1 and
the other winding could be excited with sine wave of frequency f2
whereby f1 and f2 could be exact multiples/sub-multiples of each other.
OR
one of these windings could be excited with pulses of duration t1 and
the other winding could be excited with pulses of duration t2
whereby it is understood that the pulses have durations in the nanoseconds
and transitions in the pico- to nano-second range. t1 and t2 could be
related such that they are exact multiples/sub-multiples of each other.
OR
one of these windings could be excited with pulses of duration t1 and
repetition rate of pps1 and
the other winding could be excited with pulses of duration t1 and
repetition rate of pps2
pps1 and pps2 could be related such that they are exact multiples/
sub-multiples of each other.
Another question is where to locate the electronics? It looks like for
the simulated case as shown, maybe the middle of the torus,
inside the winding? Your simulation shows a B field minimum there,
however there is an artifact which I do not understand.
As far as the A field is concerned, the center of the toroid appears
to have the minimum A field.
Earl
Quote
I would be interested in seeing graphic outputs of your simulation involving the golden mean, phi and Phi, in addition to PI.
The pi ratio was discovered by accident, while attempting to find some limiting behavior of the magnetic field for different tori. I have done some simulations in which the golden mean enters as an underlying ratio; I'll try to generate a few graphics from these for you.
QuoteAs the coil makes one revolution around the circumference of the toroid, it could make one turn around the torus - or two - or three.
Different winding ratios are intriguing, but for the purposes of this project, I am sticking to a 1:1 winding ratio. In the far limits, other ratios will degenerate into the common toroidal solenoid, or the common current loop. I am splitting the difference, half-way in between these two extremes. This ensures that the windings are perfect circles, and the current will emulate the spin structure of the electron, with each winding threading all the other windings.
There are, however, two ways to combine the rotations, producing a right-handed or left-handed twist. Coils with opposite handedness could be wound on the same core, producing (or reacting to) added dipole fields and canceled toroidal fields, or vice-versa. Also, multiple coils of varying toroidal parameter could be nested one inside the other, while preserving the winding ratio. Differently scaled versions of the same coil could be brought into close proximity (e.g. stacked atop one another), to create a venturi-like effect.
Also, it occurs to me that there might be some benefit to situating an untwisted circular coil inside the tube. So many possibilities!
Quote...one of these windings could be excited with sine wave of frequency f1 and
the other winding could be excited with sine wave of frequency f2
whereby f1 and f2 could be exact multiples/sub-multiples of each other....
Yes, the coils will be pulsed. When I get to the experimental phase of the project, I'll try out a whole range of pulsing methods. I agree that pulses with short duration and even shorter rise-time are the most likely to produce interesting effects, especially with a multi-stranded coil.
QuoteAnother question is where to locate the electronics? It looks like for
the simulated case as shown, maybe the middle of the torus,
inside the winding?
Good question. I imagine that a parallel-plate capacitor in the dipole field might display some interesting behavior. I've got a long way to go before I can start to answer that question.
Quotethere is an artifact which I do not understand.
The B-field graph is a plot of the z-component (axial), and the y-component of the field, taken along the x-axis. The y- component is positive on one side and negative on the other, because the B-field circulates inside the tube. I'll post some vector field plots to illustrate this.
The second plot is in the x-z plane, and the first one is in a plane slightly above the equator, parallel to the the x-y plane. We find that the field has a dipole characteristic outside the tube, and a mixed toroidal and dipole field inside the tube.
ZT,
here is another image concerning an artifact.
Is the blue trace or the red trace an extraneous artifact,
which should not be there?
It disturbs me to not see perfect symmetry when everything else
is perfectly symmetrical.
Which should be removed, the red trace or the blue trace?
Earl
Quote from: Earl on January 29, 2008, 08:02:49 AM
ZT,
here is another image concerning an artifact.
Is the blue trace or the red trace an extraneous artifact,
which should not be there?
It disturbs me to not see perfect symmetry when everything else
is perfectly symmetrical.
Which should be removed, the red trace or the blue trace?
Earl
Earl,
Both traces should be there. The field is sampled along the x-axis, which is the abscissa in this graph.
In your markup, you colored the red trace blue and the blue trace red, which is a bit confusing, but no matter, just follow along closely: In my original graph, the red trace is the y-component of the magnetic field. The blue trace is the z-component. You can think about it like this; on the right, the y-component of the field inside the tube is coming toward you, out of the screen, and on the left, it is going away, into the screen. The z- and y- components have nearly the same magnitude inside the tube, so on the left in this graph their individual traces appear to merge. Here's a close-up of the field on the left, showing the individual traces.
It is precisely this (near) convergence of the field intensity profile within the tube that led me to believe that this particular "pi-ratio" geometry is "special". Other tori do not display this close agreement of the field intensities, instead either the axial or the toroidal field begins to dominate within the tube. The slight non-uniformity within the tube I think is due to the asymmetry of the fringe fields, which can exit the coil more easily on the outer perimeter of the torus, where the windings are farther apart. When the ratio of the radius of the individual rings to the displacement of their individual centers from the origin is 3.141592653589793..., we get the closest agreement of the two traces. This was discovered empirically, and it still baffles me as to "why pi?".
Here is a blown-up version of the graph, in which it should be easier to distinguish the two components. Blue is the z-component (up-down) and red is the y-component (into and out of the page).
May I also enjoy the ride?
Hopf fibration is beyond my skills but maybe I can follow it. For now, I however fail to see a potential practical connection (ref 'interesting properties') between electron model and toroidal coil. Is it the potential well you envisage as giving hope or something else (i.e. singularities)? Can you detail on it in the available time? Also, it is not clear for me if you aim toward a superconducting coil or a regular one.
The topics look very promising.
Thanks for sharing it with us,
Tinu
Quote from: zerotensor on January 29, 2008, 04:23:42 AM
I am planning to build a special coil of my own design, one that I believe will have some remarkable properties.
Hi zerotensor,
Can you please give a descriptive of the size, and configuration of the coil discussed ?
Thank you,
- Schpankme
Quote from: tinu on January 30, 2008, 09:40:36 AM
May I also enjoy the ride?
Hopf fibration is beyond my skills but maybe I can follow it. For now, I however fail to see a potential practical connection (ref 'interesting properties') between electron model and toroidal coil. Is it the potential well you envisage as giving hope or something else (i.e. singularities)? Can you detail on it in the available time? Also, it is not clear for me if you aim toward a superconducting coil or a regular one.
The topics look very promising.
Thanks for sharing it with us,
Tinu
As to why I think that this coil geometry might produce something unusual, in the end, it's just a hunch. But a good, educated hunch, I think. I like the idea of taking a whole bunch of electrons and making them dance together as one giant electron. That's what happens inside a superconductor, as the wavefunctions of the electrons cohere and spread out across the entire material. Magnetic flux is quantized inside a superconductor, and manifests itself as toroidal vortices of supercurrent within the material. What would happen if we confined the flow of electrons to this primal, underlying geometry with a specially-designed coil? I want to find out.
I would love to work with superconductors, but I think I'll try copper at room temperature first (unless some superconducting wire should happen to fall off a truck) ...
@zero,
if that is your'e question then steven mark has already answered it. it is eltecro magnetics of the earth. what part of that do you not understand?
lol
sam
Quote from: Schpankme on January 30, 2008, 06:17:27 PM
Can you please give a descriptive of the size, and configuration of the coil discussed ?
- Schpankme
For the prototype, I will wind copper on a torus with an outer diameter of about 250mm.
I will choose the toroid described above, whose windings thread the torus once for every revolution around.
I misrepresented the ratio of the individual rings' radii to the displacement of the rings' centers from the origin. It is 1+Pi, not Pi as I stated earlier (I was using a differential ratio in my calculations). The conjunction of the toroidal and poloidal B-field intensities within the tube motivates my choice of this particular torus for study.
64 rings, each composed of an as-yet undetermined number of copper windings, will be inclined at an angle of 13.972 degrees relative to the equatorial plane. They will be spaced equally around the torus.
Appealing to the toroidal coordinate system, I am choosing the torus of constant v = Log(1 + Pi + Sqrt(2 Pi + Pi ^2)), with scale factor a = 100mm. The Hopf-rings on this torus have a radius of 103.049 mm. Their centers are situated on a circle in the equatorial plane with radius 24.8815 mm.
I will use an air core. The form for the windings will fashioned from of rings of non-magnetic material, probably wood, brass, or teflon. They will have grooves to seat the windings. There will be 64 grooves on each support, each accommodating a multi-turn ring of copper wire.
Quote from: supersam on January 30, 2008, 10:49:55 PM
@zero,
if that is your'e question then steven mark has already answered it. it is eltecro magnetics of the earth. what part of that do you not understand?
Of course! It is all so clear to me now. wha? huh? ???
Here's a graphic of the prototype coil configuration.
Looks good.
The pressure is on.
You got design, sims, 3dmodels, time to crank it out.
It can be a real meatfest if there is no physical production.
Any builds are good. Results vary as always. Any high speed current freqs produce.
Your model looks like a full winding of the Rodin coil too.
--giantkiller. Build it and they will come. I've always liked that saying. :D
@zero
A very interesting project, I think the more non-conventionally wound coil configurations that are tested the better, your simulations are great, I wish you luck...
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So how is it going ZT?
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I've had a few setbacks obtaining materials for the prototype; It may be a while before I can begin construction.
In the meantime, I am keeping myself busy with some visualizations.
Check out this animation I made:
http://video.google.com/videoplay?docid=-8711002588473203448&hl=en (http://video.google.com/videoplay?docid=-8711002588473203448&hl=en)
Thats a great visualisation, it really shows the similarity with the Rodin Coil, I hope you get what you need to build your coil, keep up the good work :)
A
@zero
This is a bit old now but you may be interested in this coil and test I proposed some time ago ...http://marksnoswell.cgsociety.org/gallery/329928/
I have attached the image of the coil here. I have not done this test yet but did work out how to physically make the spin 1/2 coil.
below is the rough explanation that went with the proposal... but before that I wanted to say that I like your thinking although I dont agree with the model of the electron you propose. It also turns out that a toroidal manifold can not support a spinor -- which could also be used as an argument that a toroidal manifold would separate (filter if you will) regions of dictinctly different spin resonance properties... which can be usefull in designing novel devices.
cheers
mark.
---- explanation that goes with proposed coil and test ----
AH-- I do conceptual physics theory development to "relax" ... anyway. Sometimes I also take the opportunity to test renders and really go over the top on the scientific renderings. This is one of those times.
For those of you interested here is my discussion on this device...
I have been pondering the first chapter of Carver Mead?s book ?Collective Electrodynamics?. You can find the first chapter on line here -- http://www.pnas.org/cgi/content/full/94/12/6013.
He considers a superconducting loop? In a closed superconducting loop the current (and magnetic flux) can ONLY take on discreet levels. The explanation is that the electron wave must be in phase around the loop. OK ? but there is a really big difference between the inside and outside diameters of the wire loop ? compared to the wavelength of the electrons that is. So how can all the electrons in the superconductor be in phase? ? in a collective system they *all* are, the question is how?
There are several interesting ideas that suggest themselves. The first is that there is a voltage (and frequency) gradient across the wire ? with a lower frequency on the outer perimeter. This would keep everything in phase. This is possible and arises from the natural self repulsion of opposite currents (repulsion from the centre of the coil due to current repulsion from the opposing current in the opposite side of the coil).
The second idea is rather appealing? First I should point out that the skin depth in a superconductor is only about 50 nm (0.00005 mm). So even in a 0.1 mm wire the current is flowing in a very thin tube on the surface. Now if the current spiralled around the outside of the tube by 180 deg (or (2n+1)pi times) per loop then this would make all paths around the loop almost the same length. It is noteworthy that it would now take two times around the loop for a wave to return to it?s start ? and electrons are spin ? (which means that you have to rotate them 720 deg before they return to the same configuration). To say the least -- wow! The render here is of a coil to demonstrates this spin ? current flow on the surface of a toroid. Over this are wound two identical probe coils with opposite spins ? the question is would you detect different mutual coupling in the probe coils with a signal injected into the toroidal spin soil? ... if you do then this method could be used to test if this surface spin of current flow occurs in superconducting loops.
Hmmm... here is a third possibility that is a little more out there. This could work with the first two ideas. That is that ?current? is related predominantly to rotation frequency of the electrons. We know as the voltage goes up that the frequency goes up (as does the mass ? but not by 9 or more orders of magnitude sufficient to account for the electrodynamic inertia). Perhaps it?s the rotational torque between the large scale 4 dimensions and the internal 4 dimensions (string theory and Tony Smiths D4-D5-E6-E7-E8 VoDou physics model) that we interpret as electrodynamic inertia. This would explain why this electrodynamic inertia is uncoupled from ?classical? inertial mass of the current carrying electrons.
(OH ? oh ? oh ? this just gave me an idea to explain how a current flowing in one conductor induces a current flowing in the opposite direction in a neighbouring conductor? but that will have to wait for next month)
The next interesting things to note is that the total electrodynamic mass calculated from the inertia of the current carrying electrons can exceed the total mass of a typical coil ! ? and yet this is not felt as ?normal? inertial mass. It?s not as if the coil gets a lot heavier (it does get a very little heavier due to the stored energy) as the electrons accumulate a massive inertial mass. And you can rotate a coil carrying a massive current without it resisting rotation ? although I can?t find experiments to verify this.
This leads me to wonder if anyone has ever measured the ESR (electron spin resonance) of the electrons in a superconducting coil as it is turned ? do the electrons precess and give rise to an ESR signal as they resist rotation by their own magnetic field? Has anyone even measured the resistance of a superconducting coil to rotation? These may seem stupidly trivial things to measure but I can?t find any record anywhere of experiments like this.
... anyway. Read Carver Meads first chapter. It?s very simple and it shows just how we would have formulated our understanding of electromagnetism with the hindsight of superconductors.
@Mark
Love that coil rendering, rendering a coil at that quality, wow thats dedication! A nice piece of work...
More Importantly I like the premise of that paper you referenced...
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