As I dimly recall, the graphs on that paper showed very low magnitude effects and odd shapes to the response. I think it likely that one could do a lot better than the coiled-coil approach, which has very long magnetic circuit, by using many small soft ferrite toroids arranged into a larger A-field loop. This maximizes B field and its curl. Using fewer turns and more current in the toroid windings not only helps frequency response and rate of change of B and its curl, A, but helps minimize the voltage gradient across the windings, which gave Lodge and Davies so much trouble. (Also use a second layer of winding going back over the first and ending at the starting place to avoid an implicit 1-turn winding around the larger circumference of the toroid.) All the toroids can be wired in parallel to further decrease inductance at a given B and thus maximize the rate of change of B.
Spinning a toroid or toroids so that their axes sweep around a circle shoud allow creating a sinusoidally varying A field; A pair of toroids with perpendicular axes driven in quadrature should produce the same effect.
[Edit: For your monopole receiver, the electric field should be detectible despite shielding, so try a TI OPA928, non-inverting impedance-converter setup (output to - input, + input floating or with an electrode with larger area to increase capacitive coupling) with a +/- 6-8V split battery power supply (12-16V total). With 10% humidity at 15-20C it should have a detection limit close to 1e-17A at up to 2.5MHz, with about 1uV noise. These can detect deep sub-electron charges, even sub-pico electron/s charges so they're just ridiculously sensitive to all sorts of things. They pick up 120V AC wiring from several meters away. Crossing your legs will peg them from the capactance change of your shoe. Don't breathe near them. Don't even move your eyes too near them. Less than $20 qty. 1, or about $400 for a dev board.]
Also check out my one-page "Physical Units Factor Tables", which shows the relationships between 50 types of physical quantities, including 22 EM quantities, by factoring them into space, time, mass and charge: https://enonh.substack.com/p/the-periodic-table-of-physics
The calculator / physically-typed language, Frink, that PUFT documents I have found very useful for over 20 years. All documentation is on the main frinklang.org page, as well as a link to a web interface. The .jar file has no dependencies except a JRE, it will run in a Chat GPT sandbox. The units.txt file is also worth browsing to see what's already built-in, of course you can easily add new named unit types and derived units to it.
Are you talking about orienting the holes of magnetized tori against a surface so the vector potential is normal to that surface?
Note that you could ALSO arrange the tori along a closed string, and that string would be the vector potential, the curl of this would be a B-field through that ring. You wouldv'e basically made an artificial E-field, which is the –d/dt of A.
First I was thinking of a loop of tori as a replacement for the coiled-coil around a loop geometry.
Since there may be no need to make a circuit of the A-field, perhaps a simple stack of axially-aligned tori, half of them above and half below the detector would be better, or a planar array as you suggested, or add to the stack a pair of spherical caps around the stacks above and below so that their axes all point toward the detector and all have a vector component reinforcing the central stack as much as possible within the limited conical volumes above and below the detector. Or as many tori as you can pack in those volumes with their axes pointed at the detector.
The key to getting max A is maximizing the circulation of B within the volume, especially close to the detector, so the toroids' core material should be selected for max field saturation level first, then secondarily for permeability to reduce amp-turns needed, then probably high-frequency response if you're testing creating E-field from changing A, and perhaps resistivity, but I don't think efficiency or loss is as much of a concern as simply packing as much ferrite per volume in, thus as much B-field per volume. The toroids should be small in volume with short effective loop lengths to maximize curl of B per volume.
Very high inductance per cc core material, high permeability and decent saturation with a pretty short field path and as small as you can get with a reasonably-sized hole. For the individual toroids you want high induction to make B with minimum amp-turns, but for the system as a whole you want minimum induction to get high-frequency operation-- so wire the toroids in parallel and use a high-current, low voltage source. I'd double shield the detector with mu-metal to do both electric and magnetic shielding. You could shield the tori, but it would be expensive and wouldn't work as well.
Enon, I just love this. This intersects strongly with what I've been thinking about before. I'll get back to you once those ideas advance. Feel free to shoot me an email if you want to talk about this in more depth.
Enon, thank you for bringing Hestenes' Dirac reinterpretation in geometrical terms to my attention! This is cutting edge stuff. I need to dig deeper. Your reply is much appreciated.
As I dimly recall, the graphs on that paper showed very low magnitude effects and odd shapes to the response. I think it likely that one could do a lot better than the coiled-coil approach, which has very long magnetic circuit, by using many small soft ferrite toroids arranged into a larger A-field loop. This maximizes B field and its curl. Using fewer turns and more current in the toroid windings not only helps frequency response and rate of change of B and its curl, A, but helps minimize the voltage gradient across the windings, which gave Lodge and Davies so much trouble. (Also use a second layer of winding going back over the first and ending at the starting place to avoid an implicit 1-turn winding around the larger circumference of the toroid.) All the toroids can be wired in parallel to further decrease inductance at a given B and thus maximize the rate of change of B.
Spinning a toroid or toroids so that their axes sweep around a circle shoud allow creating a sinusoidally varying A field; A pair of toroids with perpendicular axes driven in quadrature should produce the same effect.
[Edit: For your monopole receiver, the electric field should be detectible despite shielding, so try a TI OPA928, non-inverting impedance-converter setup (output to - input, + input floating or with an electrode with larger area to increase capacitive coupling) with a +/- 6-8V split battery power supply (12-16V total). With 10% humidity at 15-20C it should have a detection limit close to 1e-17A at up to 2.5MHz, with about 1uV noise. These can detect deep sub-electron charges, even sub-pico electron/s charges so they're just ridiculously sensitive to all sorts of things. They pick up 120V AC wiring from several meters away. Crossing your legs will peg them from the capactance change of your shoe. Don't breathe near them. Don't even move your eyes too near them. Less than $20 qty. 1, or about $400 for a dev board.]
Since so many physics mysteries are connected to the potentials and the scalar field, you might try to relate the Geometric Algebra Dirac wave equation scalar phase field, beta, as well: https://enonh.substack.com/p/x-the-dirac-equations-lorentz-invariant
Also check out my one-page "Physical Units Factor Tables", which shows the relationships between 50 types of physical quantities, including 22 EM quantities, by factoring them into space, time, mass and charge: https://enonh.substack.com/p/the-periodic-table-of-physics
The calculator / physically-typed language, Frink, that PUFT documents I have found very useful for over 20 years. All documentation is on the main frinklang.org page, as well as a link to a web interface. The .jar file has no dependencies except a JRE, it will run in a Chat GPT sandbox. The units.txt file is also worth browsing to see what's already built-in, of course you can easily add new named unit types and derived units to it.
Are you talking about orienting the holes of magnetized tori against a surface so the vector potential is normal to that surface?
Note that you could ALSO arrange the tori along a closed string, and that string would be the vector potential, the curl of this would be a B-field through that ring. You wouldv'e basically made an artificial E-field, which is the –d/dt of A.
First I was thinking of a loop of tori as a replacement for the coiled-coil around a loop geometry.
Since there may be no need to make a circuit of the A-field, perhaps a simple stack of axially-aligned tori, half of them above and half below the detector would be better, or a planar array as you suggested, or add to the stack a pair of spherical caps around the stacks above and below so that their axes all point toward the detector and all have a vector component reinforcing the central stack as much as possible within the limited conical volumes above and below the detector. Or as many tori as you can pack in those volumes with their axes pointed at the detector.
The key to getting max A is maximizing the circulation of B within the volume, especially close to the detector, so the toroids' core material should be selected for max field saturation level first, then secondarily for permeability to reduce amp-turns needed, then probably high-frequency response if you're testing creating E-field from changing A, and perhaps resistivity, but I don't think efficiency or loss is as much of a concern as simply packing as much ferrite per volume in, thus as much B-field per volume. The toroids should be small in volume with short effective loop lengths to maximize curl of B per volume.
Here's one that looks like it would be good, though doubtless there are better: https://www.mag-inc.com/Media/Magnetics/Datasheets/C058378A2.pdf
Very high inductance per cc core material, high permeability and decent saturation with a pretty short field path and as small as you can get with a reasonably-sized hole. For the individual toroids you want high induction to make B with minimum amp-turns, but for the system as a whole you want minimum induction to get high-frequency operation-- so wire the toroids in parallel and use a high-current, low voltage source. I'd double shield the detector with mu-metal to do both electric and magnetic shielding. You could shield the tori, but it would be expensive and wouldn't work as well.
Enon, I just love this. This intersects strongly with what I've been thinking about before. I'll get back to you once those ideas advance. Feel free to shoot me an email if you want to talk about this in more depth.
Enon, thank you for bringing Hestenes' Dirac reinterpretation in geometrical terms to my attention! This is cutting edge stuff. I need to dig deeper. Your reply is much appreciated.
*Masahiro Daibo ✨ https://ieeexplore.ieee.org/document/8304422
The field is never zero. The container is zero.