Q: I'm exploring magnetic energy storage, and one point I haven't been able to find is a formula for the inductance of a current loop. What I'm after is a relation between the energy stored and the stress on the loop. From that, and resonable figures on material strengths, I hope to figure energy/mass for such a system.
A: You could also consider energy storage in a loop of magnetic material using spin waves that propagate around the loop rather than energy storage using current flowing around a loop of wire.
Q: How would that work?
A: Spin waves have momentum. You give a little push to them over and over creating a series of coherent spin waves that get larger and larger in amplitude.
First you make a ring of magnetic material. Visualizing the ring in a horizontal plane, you make the magnetic material of anisotropic magnetic particles such that they have a well defined easy axis in a particular direction. Acicular magnetic particles like those used in credit cards or recording tape may work but the particles can't be randomly oriented on the ring. They must be oriented such that the easy axis of all the acicular particles are up and down such that the only 2 possible directions of magnetization are either up or down.
Then magnetize the particles, let's say so North is up to begin with. Then apply a homogeneous (uniform) static magnetic field in the opposing direction but one that is not strong enough to remagnetize it in the opposite direction. Now the aligned spins that create the materials North magnetic field will be susceptible to precession at the frequency established by the static magnetic field.
Now excite precession of the spins with a signal source tuned to the precession frequency and excite with a signal with EM waves that shift in phase around the ring so as to enhance the desired spin wave frequency. This reinforcing signal will stimulate larger and larger spin waves to develop.
But the key to getting a useful amount of energy back out of the system lies in understanding some other related stuff. It has to, due with what happens when trying to apply Lenz's law at microwave frequencies when the reflected load does not reach back to the generator rotor (in this case, replaced with rotating magnetic fields of precessing electrons) until it is no longer opposing the motion of the source but rather aiding it.
To understand all that will happen it may be simpler to start with a simple computer simulation using a single acicular magnetic particle in the center of a circular resonant cavity. Set the static magnetic field strength such that the precession frequency of the spins of the single magnetic particle are at the correct frequency such that the phase delay of radiated EM waves from the precessions are 1/4 wave to the cavity wall and another 1/4 wave back to the particle. Some interesting things will happen. Actually it may be better if in the computer simulation you first try adjusting this delay by adjusting the precession frequency such that it starts out at much less than 1 time period of precession before the back EMF reaches the center and then start making more and more of a delay until the back EMF starts to aid the rotation of the magnetic field.
The computer simulation assumes that the precessing spins within a single particle can be made to precess all more or less in phase with each other. This doesn't always happen in all magnetic materials. A ceramic nanocrystal doped with just a small amount of magnetic material can make it easier. It's a trade off between how easy it is to excite coherent precessions and how much overall coercivity is desired for the magnetic particle. Very weak doping makes the material remagnetize too easily to align with the external static field that is setting the precession frequency. Too strong of magnetic doping causes too strong of coupling between precessing spins to be able to create coherent precession via excitation from an external source.
NOTE: The above is merely a small part of the thread that covers George Bugh's input to the sci.physics.electromag newsgroup. Visit dejanews.com which is now at http://groups.google.com and search for the thread "inductance of current loop" to view some, but not all, of the postings to various threads under this topic. Many posted articles and comments are deleted from the local newsgroup server before they are added to the archives. Still others do make it into the archives but are deleted from the newsgroups shortly thereafter.
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Spinwaves and Power Generation