As described in this report, the limits on the strength of stable magnetic fields are(adsbygoogle = window.adsbygoogle || []).push({});

due to the magnetic forces on the conducting elements that tend to tear them apart:

Magnetic Radiation Shielding: An Idea Whose Time Has Returned?

Geoffrey A. Landis

"The limit to the mass required to produce a magnetic field is set by

the tensile strength of materials required to withstand the magnetic

self-force on the conductors [8]. For the min-imum structure, all the

structural elements are in tension, and from the virial theorem, the

mass required to withstand magnetic force can be estimated as [9]:

M = (rho/S) (B^2 V)/(2 mu) (1)

where rho is the density of the structural material, S is the tensile

strength, B the magnetic field, V the characteristic volume of the

field, and mu the permeability of vacuum."

http://www.islandone.org/Settlements/MagShield.html

You see the strength/density ratio of the material goes by the square

of the magnetic field strength. The conducting wire commonly used for

producing the electromagnets is made of copper because of its high

conductivity and current carrying capacity. The tensile strength of copper

is 220 MPa at a density of 8.92 g/cm³.

The highest measured strength of carbon nanotubes has been 160 GPa at

a density of 1.3 g/cm³. This is an increase of the strength to density ratio

over copper of about 5,000.

Then conceivably with this stronger material we could get higher

magnetic fields strengths by a factor of the square root of this, 70;

so to a magnetic field strength of 70 x 30 T = 2100 T.

However, I have seen some reports that the square of the magnetic field

intensity goes only as the tensile strength itself of the conducting material.

In that case B^2 would only be larger by 800, so B itself larger by a factor

of 28, so to 28 x 30 T = 840 T. Still this would be a major increase in the stable

magnetic fields attainable. Anyone have a reference that says whether it's

the strength to density ratio or just the tensile strength itself that determines

the intensity of the field that can be maintained?

The nanotubes are only available so far at centimeter lengths. Still it would

be interesting to find out on tests with small fields if their use would allow

magnetic field strengths in the thousand tesla range.

For the nanotubes to be used for this purpose they would have to

carry large amounts of current to generate the electromagnets. It has

been shown experimentally that they can carry thousands of times the

current of copper:

Reliability and current carrying capacity of carbon nanotubes.

APPLIED PHYSICS LETTERS, VOLUME 79, NUMBER 8, 20 AUGUST 2001.

"From the experimental results described in this letter we

can conclude that multiwalled carbon nanotubes can carry

high current densities up to 10^9-10^10 A/cm2 and remain

stable for extended periods of time at higher temperature in

air. Furthermore, they conduct current without any measurable

change in their resistance or morphology, indicating that

the sp2 bonds that are dominant in carbon nanotubes provide

much higher stability against electromigration than small

metallic structures."

http://www.rpi.edu/~ajayan/locker/pdfs/reliability.pdf [Broken]

We can estimate the strength of the magnetic field we can obtain from

a given current flow and wire size from the formula B = 2(10^-7)I/r,

for B the magnetic field in Tesla, I the current in amps, and r the

distance from the center of the wire in meters, as described here:

Magnetic Field of Current.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html#c2

For a 100 micron thick wire composed of carbon nanotube material,

using a 10^10 A/cm2 current capacity, we could get 10^6 A of current

through. Then 100 microns away from the center the magnetic field

would be 2,000 T.

One million amps is *quite* a large current. There are gas turbine electrical

generating stations that put out 100 megawatts, enough to power a

small town, that at a voltage of 120 volts would put out about a million

amps. Imagine a generating station with enough power to run a town with

all that power going into a single wire the width of a human hair!

However, I'm wondering if these ultra high fields could be something that can

be reached by amateurs, if not as sustained fields then at least in pulsed

fashion. Perhaps not as much current would be needed if a different arrangement

was made to create the magnetic field, such as a solenoid for example.

This page gives the formula for the magnetic field of a solenoid:

Solenoid Magnetic Field Calculation.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html#c3

You see that for a solenoid using an air core, there is a 4Pi factor in front

instead of 2 as for the long wire case. So it's larger by a factor of about 6

and you would therefore need this smaller amount of current.

You could get a higher field with the same current by using a metal core:

Magnetic Properties of Ferromagnetic Materials.

http://hyperphysics.phy-astr.gsu.edu/hbase/tables/magprop.html#c2

The problem with this is that we are attempting to get the highest field

possible while sustaining the stresses. Using other metals for the core, then

they have less strength than the carbon nanotubes and will fall apart at

lower magnetic field strengths. We could use the nanotubes also for the core

but they give little in the way of higher permeability.

For creating a short pulse of high current, this amateurs page describes getting

25,000 amp pulse from a silicone controlled rectifier (SCR):

The PowerLabs Solid State Can Crusher.

http://www.powerlabs.org/pssecc.htm

And this page claims 70,000 to 100,000 amps can be reached in a short pulse:

Coin Crusher.

http://webpages.charter.net/tesla/crushed_coin.htm [Broken]

Experiments at very high magnetic fields are very important for

theoretical studies. It is likely the nanotubes could withstand the

high stresses induced by the magnetic fields at even higher strengths

than 2100 T for short times, especially for nanotubes chosen to be low

in defects to have the highest strength. Then carbon nanotubes may be

the ideal material to use for producing ultra high magnetic fields for

theoretical work.

Bob Clark

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# Ultra high magnetic fields using carbon nanotubes.

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