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Concentrating the Earth’s Magnetic Field for Harvesting

09/27/2009 8:30 AM

In review of Internet literature wherein public interest in energy harvesting from the earth's magnetic field has been expressed, two main objections to such successful harvesting have been encountered. While most objecting parties concede that the total energy stored in the earth's magnetic field at any moment in time is massive compared even to projected world energy consumption over upcoming decades, if not centuries, a number of them have also indicated that the relative "local" weakness of the earth's magnetic field as measured at any given point on the planet's surface makes such harvesting operations impractical. The online encyclopedia Wikipedia documents the surface magnetic flux density (B) as varying between 30 and 60 micro-Tesla over most of the planet's surface, with corresponding values for magnetic field strength (H) of 25 to 50 Amps/Meter.

The second objection has centered around uncertainty about how to convert such static magnetic energy into useable electrical power, as typically a time-varying magnetic flux has been needed to induce a voltage or current in a conventional inductive coil. However, with the advent of superconductive materials, in which DC surface currents are induced by a static magnetic fields' spontaneous rejection from the interior of a superconductive medium, the second objection seems unfounded, as will be discussed below.

I recently investigated the questionable validity of the first objection by determining, through static magnetic simulation using FlexPDE 5.0 software, the degree to which a two-piece ferromagnetic antenna made from a relatively inexpensive substance (like iron) can serve as a magnetic flux concentrator, with the anticipated result being that a given length antenna would effectively capture and concentrate within an air-gap the naturally occurring flux passing through an adjacent volume of space much larger than the volume of the antenna itself. In fact, the amplification gain returned on an investment in a given length antenna was anticipated to vary as a scaled value of the square of antenna length. Although I now only have a version of the software capable of a 2D simulation, I tried to generalize initial explorations in 2D to a third dimension, with harvestable peak magnetic flux densities in the air-gap (of 1 Tesla or so) anticipated for antenna lengths on the order of 100 meters.

The antenna looked simply like this:

|''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''| |''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''|

As discussed above, the second major objection to magnetic field harvesting, that a static magnetic field cannot be utilized for electrical power generation, may have had some credence before the refinement of superconductive physics. However, if my understanding is not too far off, physicists now recognize that a static magnetic field can produce a DC current in a short-circuited superconductive coil, and, should such a circuit be "opened" while providing an alternative path for the coils' inductive current (either into a charged capacitor or DC-battery), that stored "static" magnetic energy can indeed be converted into electrical power. A variant of such technology already exists in SMES (superconductive magnetic energy storage) systems, which are used to transfer electrical energy into the magnetic field of a superconductive coil (and back again) on a repeatable basis.

The presence of a continuously refilling reservoir of magnetic energy within the antenna's air-gap (which ultimately derives power, I think, from the sun's magnetic "solar wind" – as manifests locally in the relatively constant terrestrial magnetic field) may be later demonstrated as capable of providing relatively massive power output via the coupling of a concentrating antenna design with a superconductive coil and power electronics capable of enabling a rapidly repeatable cycle of superconductive short-circuiting - followed by inductive energy off-loading into a DC capacitor and subsequent DC to AC conversion.

Even 0.5 Tesla in a 0.01 cubic meter volume would store a magnetic energy of 100,000 Joules, which, if a 100Hz energy off-loading and "current refresh" cycle were realizable, would yield a 10MW power output capacity. I admit however, that with system complexities being what they are, things are probably not quite as simple as that... does anyone who has access to FlexPDE 5.0 Professional version (unlimited nodes) have interest in extending this simulation, or even going as far as developing code for simulating a superconductive coil placed in conjunction with the antenna?

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#1

Re: Concentrating the Earth’s Magnetic Field for Harvesting

09/27/2009 2:57 PM

Well you certainly aren't the first to think of this (there is quite a bit on the subject on the internet).

a number of them have also indicated that the relative "local" weakness of the earth's magnetic field as measured at any given point on the planet's surface makes such harvesting operations impractical.

Correct. This is THE main problem as the magnetic field of the earth is so small. A refrigerator magnet produces a magnetic field of about 0.1T, that's 100,000uT compared to the mean magnetic field of the earth at 45uT (2200 times smaller). This means you need an enormous area to get any useful power out. 100m long 'antenna' are not going to be enough even for small amounts of power.

How did You calculate your magnetic field strength and antenna magnet field figures as they seem unrealistically high (leading to your false conclusion of a potential 10MW generation).

Lets get some perspective. Here is a good real world example for you - the height of the support tower alone of a 2.5MW wind turbine is about 100m. Do you think two lengths of 100m iron are going to produce the same power as 4 of these wind turbines?

http://www.wind-energy-the-facts.org/index-18.html

Sorry, no free lunch here.

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#2

Re: Concentrating the Earth’s Magnetic Field for Harvesting

09/27/2009 9:59 PM

Something doesn't seem right with the basic math...

"Even 0.5 Tesla in a 0.01 cubic meter volume would store a magnetic energy of 100,000 Joules"

(For those stuck on English units, this volume is a cube ~8.5 inches per side ;-)

I can only get ~1000 Joules from these numbers.

U = energy density [Joules/meter^3]
mu0 = 4*pi*10^-7 [Henry/meter]
B = flux density [Tesla] or [Wb/meter^2]
V = volume [meters^3]
E = energy [Joules]

Energy density in a magnetic field is given by

U = 1/(2*mu0) * B^2

units check

[Joules/meter^3] = [meter/Henry] * [Wb^2/meter^4]
[Joules/meter^3] = [Wb^2/Henry] / [meter^3]
[Joules/meter^3] = [Joules/meter^3]

OK!

U = 1/(2*4*pi*10^-7) * 0.5^2
U = 99472 [Joules/meter^3]
E = U * V = 99472 [Joules/meter^3] * 0.01 [meter^3]
E = 994.7 [Joules]

Keep digging. You will eventually find and fix the errors in the calculations and hopefully the flaw in the magnetic antenna concept as well. Hint: Study a text on EM theory and don't blindly trust the output of a computer simulation.

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#3
In reply to #2

Re: Concentrating the Earth’s Magnetic Field for Harvesting

09/27/2009 11:30 PM

G.A.

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#4
In reply to #2

Re: Concentrating the Earth’s Magnetic Field for Harvesting

09/28/2009 4:00 AM

Yeah, I forgot the 0.01 m^3 multiplier, and was trying to make a big impression of how much energy was stored in a small volume. Actually, I was initially drawing my optimism from the size of the H field in the gap, and the corresponding large currents that could be induced in a superconductive coil. These inductive currents, then, could flow through a diode into a capacitor where the upper ceiling on power output would be limited only by whatever upper limit on "refresh frequency" the superconductor naturally imposed.

Rather than say all this, I did a much too hasty calculation of magnetic energy just before making my first post, and made a glaring error which may prejudice readers against the general idea. This error, however, does not obviate the idea. The maximum possible power output would still seem to be Energy*Frequency. I arbitrarily chose 100Hz to yield 10MW, which sounded impressive, but I could just have just as easily [though perhaps not ;)] had the Energy figure correct (1000J) and chosen 10,000Hz as my refresh frequency, yielding, again 10MW.

What upper limits on refresh frequency there may actually be I can't begin to say with any assurance, although with different direction surface currents flowing on the inside and outside of a superconductive coil (at least in the open circuit condition) I suspect they have to do with AC field penetration into the interior of the coil which at some point, breaks down the effective separation between the inside and outside surface currents flowing in a magnetically immersed superconductive coil.

What seems clear to me is that I am not positioned to bring this idea any further myself. I have no academic contacts, and my history of mental illness and corresponding lack of work history makes me easy to disregard (even though I graduated cum laude in EE) ...and perhaps justify-ably so.

As for the simulation, not only do I not trust a "proper" simulation's match with "the World," I also mistrust my ability to do a proper simulation! Hence my request for help in verification. One thing is, as a given antenna length with gap width gathers a fixed amount of flux from the surrounding volume, I chose an antenna cross-sectional area of 0.01 m^2 (11 cm circular diameter), which bumps up the B and H field magnitudes by a factor of 100. This (11cm diameter) seemed like a decent size (to me) for a matching superconductive coil.

Anyway, you corrected a glaring error in my post, and did it with a kind tone which I deeply appreciate.

Godspeed.

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#5
In reply to #4

Re: Concentrating the Earth’s Magnetic Field for Harvesting

09/28/2009 8:31 AM

I have known many superb educators and envy their gift to enlighten others. I wish I had their gift and their patience.

I don't want to suppress thought processes, development of new concepts, and possibly new and revolutionary technologies. However, the idea of harvesting significant energy from the Earth's magnetic field is flawed. It is just another item to add to the long list of "free" energy misconceptions. Through study and/or experimentation, I believe you will eventually come to an understanding of the truth. Hopefully you will maintain your creative energy and direct it towards concepts which have a real chance of making a positive change. Best wishes.

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#6
In reply to #4

Re: Concentrating the Earth’s Magnetic Field for Harvesting

09/28/2009 10:05 AM

Welcome to CR4

Enjoy!!

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#7
In reply to #4

Re: Concentrating the Earth’s Magnetic Field for Harvesting

09/28/2009 10:31 AM

What happens to your antennae when you discharge the energy? Shouldn't you get a reaction similar but opposed to what happened when it got charged?

It looks like you would end up with a large EM transmitter!

Even if you use superconductors to obtain large currents, they have a very low voltage capacity. This makes them very difficult to pump up to a usable voltage. We don't have yet a powerful and efficient uV to V up converter. Maybe one day but not in the next 10 years.

You will have more chances success with solar winds and very large (100 Km) antennas.

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#8
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Re: Concentrating the Earth’s Magnetic Field for Harvesting

09/28/2009 9:09 PM

marcot wrote: "Even if you use superconductors to obtain large currents, they have a very low voltage capacity."

I'm going into a somewhat winded discussion of this, as I am in part hammering out the reasoning for myself. Thanks for bearing with my wordiness... I believe the low voltages you refer to are covered in the book:

Bernoulli potential in superconductors: how the electrostatic field helps to Understand Superconductivity

As I browsed this book, whenever a steady-state superconductive current diverges from a straight path, patches of extra charge concentrations (or charge deficits) build up voltages, which exist external to the superconductor, and which internally, apply themselves only to the accelerations of charge which accompany the divergence from a straight path. Flux linkages are not changing in steady-state, so no conventionally inductive voltages are present.

These steady-state voltages are likely indeed small, and our design template being discussed does make use of them in the transition from the energetically "spent" open circuit condition to the short circuit condition, or the "current refresh" portion of the repeatable energy off-loading cycle. These small voltages, when applied across the near negligible resistance and inductance of the external circuit's short circuit, quickly refresh the original short circuit current.

Under transient coil conditions, however, (like when the short-circuit current is suddenly interrupted and directed into a charged capacitor) the actual magnitudes of currents and associated flux linkages are changing, so more conventionally large inductive voltages are capable of being supported by the superconductor.

As I see it, the superconductive coil in this configuration may properly be thought of as two inductive coils - one for the inner surface and one for the outer surface. In "spent" open circuit conditions (external circuit current reduced to zero), the magnitude of the inner surface current and the (opposed in direction) outer surface current is equal, with small Bernoulli's voltages built up at the ends of the coil where the outer surface current suddenly reverses direction to "become" the inner surface current.

In the short circuit condition, the inner surface current is zero, and all the external surface current flows in the external circuit as "short-circuit" current. Then as the circuit is opened through a diode to the voltage of a charge capacitor, the external surface current begins decreasing and the internal surface current begins increasing (in the opposite direction) -and as they do, the external circuit current being dumped into the capacitor heads toward zero as energy is off-loaded into the cap - finally reaching zero as the internal surface current magnitude matches the external surface current magnitude. Basically just Kirchoff's (sp?) current law as applied at the termination point of the superconducting coil.

On the questions relating to this amounting to a large EM transmitting antenna - I think all receiving and transmitting antennas are actually in dialog, both with each other and with the surrounding environment, should that environment change. And while the power for this antenna coil comes from elsewhere, its operation may have both local environmental effects, while also being in dialog with whatever far-away magnetic current loops (in the earth, sun, or intervening space) are providing power for its operation.

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#9

Re: Concentrating the Earth’s Magnetic Field for Harvesting

08/15/2010 4:11 PM

what if you used the moon as your anntenas ancore point? Tuned the antenna to the frequency of the moons orbit and the earths rotation as to attenuates most inductive noise do to stray magnetic fields and solar flare magnetic interfearence. As to the problem of power transmission at the end of the arrey useing a (tesla coil) modulate that frequecy into a HF carrier wave, Then useing tuned receivers tethered to hub points across the globe where it could be harnessed and filterd with super conductor RCL tank cercuits.

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