Ultra high magnetic fields using carbon nanotubes

[RGClark]

As described in this report, the limits on the strength of stable magnetic fields are
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

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

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

 

[mfb]

You can always make the structure more robust by putting the coil into an external container. What you can't avoid that way (and only make worse) is heating. That's the limit for long-term magnetic fields. Pulsed magnets reach higher fields, with the time given by how long the system needs to melt (or blow apart, if you are okay with some destruction).