Saturday, February 2, 2008

WB-100 Superconductor Magnet Cooling

I have been working on some of the cooling issues for WB-100 - the 100 MW test reactor using superconducting magnets.

The magnet will consist of a series of concentric pipes. The innermost will contain the superconductor and its coolant at 20K. Next will come a vacuum space and next will come LN coolant. In the vacuum space between the superconductor coolant and the LN coolant the walls will be silvered (or some such) to minimize the radiative heat flow between the superconductor coolant and the LN. Think thermos bottle.

Next space after LN coolant will be another vacuum space. It too will be silvered. Then H2O coolant at around 300K. Another silvered vacuum space. And finally H2O coolant at around 600K.

What we are going to have is a series of concentric vacuum bottles with LHe at 20K at the center and H2O at 600K at the outside. All this plumbed to allow enough flow to keep everything at the proper temperature.

Let me add that any electrons ejected from the surface of this contraption will carry away minimal energy. The alphas will be hitting with 2MeV+. The electrons (those that are not lost due to high energy) will be at 50KeV.

My current plan is to coat the outer surface of the coils with Boron which melts at 2349 K. The purpose is to prevent sputtering of the metallic pipes holding the coolant so the only material sputtered into the reactant space will be a reactant - B11. It has been suggested at Coulter Smithing that an outer sheath for the coil of Titanium might work well since any sputtered atoms would act as a getter. OTOH it might poison the reaction. Lots of unknowns here. We may just have to build one and see what happens.

If we use Boron, we will have to figure out how to balance Boron condensation on the outer magnet structure with Boron sputtering from the reaction.

Below is a picture of a cross section of the superconducting coil.

Update: 06 Feb 008 2046z

I was thinking. Since for a power reactor we will need to water cool the coils. Suppose we made the water jacket thick enough to thermalize neutrons. And then had a B10 layer to absorb them.

It should be possible to cut way down on coil damage and still run superconductors in a D-D machine.

MgB is interesting in that it becomes a better superconductor with some neutron damage

With MgB the resistivity goes up. Critical Field goes up. And critical temperature declines slightly.

The main problem seems to be defects caused by B10 absorbing neutrons.

If B10 was used in shielding and B11 used to make the superconducting wire much longer lifetimes in neutron fluxes should be possible.

The the cross section difference is six orders of magnitude B10 to B11. With B10 @ 10,000 barns at .025 eV and B11 @ .01 barns.

Magnesium has a cross section of about .75 for 2.5 MeV neutrons

Mg is .063 Barns for Thermal Neutrons.

Which says that if we can get an operational life of the superconductors at 10 hours with ordinary Boron, a year should be possible with five to six nines pure B11.

Reduce the Flux another factor of 10 with water moderation and a B10 absorption layer and you are up to 10 years operation. Double that Boron 10 thickness and you are up to 100 years. Which should allow for various inaccuracies and production variations.

10 B has a Maxwellian thermal neutron flux cross section of almost 4,000 barns.

11 B is around .1 barn.

At room temperature Borax B(OH)3 is soluble at about 57 g/ liter. Which is about 9.3 g/ liter of B10.

Maximum properties of MgB occur at 2E18/cm^2 total neutron flux. Let us say 1E18 and have some safety margin.

Typical fission reactor neutron flux is 1E12/second. Let us say because of the lower energy per reaction a D-D reactor would have 50X that flux.

So that is 20,000 seconds at full power with natural boron. Say 4 1/2 hours. If we go to B11 superconductors assume a 1,000 time improvement. That is 4,500 hours. Say 6 months roughly. So we need a B10 shield that can reduce the neutron flux at the coils by a factor of 10. Giving a life of 5 to 7 years continuous operation.

Since MgB is cheap, replacing the coils every 5 to 10 years should not be a big burden. In addition preconditioned coils capable of sustaining 30 T might get a premium.

Update: 07 Feb 008 0414z

revised thicknesses
I think it is worthwhile to look at the B10 thickness required to absorb 1/10th of the incident thermal neutrons. I calculated it and came up with .005 cm. That is right 5 thousandths of a cm. To slow the neutrons from an average of 2 MeV to .025 eV (thermal energy) requires a thickness of water of about 2 1/4 inches (5.7 cm). About what I would expect to need on the basis of heat transfer and pumping considerations alone. It might be possible to include that B10 thickness (or even 3X that) in the construction of the 300K coolant channel. Just deposit it on the interior since there is no heat transfer consideration (except pumping losses from wall roughness) involved.

At a flux of 1E12 neutrons a second per sq cm., 1 sq cm will have a total flux of 3.16E20 in 10 years. To handle that number of disintegrations would require a thickness of .003 cm. Not too tough. Since the actual density required could be cut in half without seriously affecting the required volume of absorber, it might work out to fill an extra layer with boron powder. That way any break up of "structure" from radiation damage would have little effect on the absorbing properties compared to initial conditions. A layer .1 cm thick could be adequate if you recompressed it from time to time. Certainly a cm or two would be overkill.

I forgot that a D-D reactor with the same thermal power out as a fission nuke will produce about 50X as many neutrons. The 1E12 factor is based on a fission nuke. Still not a show stopper.

Update:

I have a show stopper. Each neutron absorbed produces 2.8 MeV. In a D-D reactor there is no way to carry the heat away without adding more water layers. At best a very thin layer might buy us some operational time for a test reactor. The advantage may go to using a B11 superconductor even with its lower Tc. That still only gets us months of operation. Probably good enough for experimental work.

BTW the neutron flux in a D-D reactor with a coil radius of 2 m at the coil radius is on the order of 3E14 neutrons a second at 100 MW fusion output.

Further Update:

With an intermediate layer filled with borated water to absorb 99% of the neutron energy, or 99.9%, you might get the flux down to where powdered boron could handle the rest. Great idea. At 9.3 g/l that is 9.3E-4 g/cc. Compared to 2 g/cc that would require about 10 cm - vs .005 cm for a factor of 10 reduction. Not going to work. So it still looks like MgB11 superconductors with B11 at 4 nines or better. That still only buys you a total of 1,000 hours - probably enough for initial experimental work at 100 MW.

If you could maintain a slurry of boron particles and still keep the whole contraption cool - it might work.

The trouble is that it almost doubles the neutron thermal load (1.75X). The neutrons lose 3.65 MeV thermalizing and then the B10 adds a 2.8MeV alpha. Which increases the total heat load by about 40% in what was already a marginal situation.

10 comments:

layoung said...

I like the cross sectional detail drawing. Is there an engineering reason to make the magnet at the center square instead of round? I thought the big lesson from WB-6 was to make everything round. Or does that only apply to the outer charged surface?

M. Simon said...

Indrek did some simulations with round vs. square and found that by the time the field meets the surface of the grid there was no significant difference.

The added "empty" volume gives a place for coolant flow.

Martin C said...

With reference to Dr Bussard's notes on wiffle-ball confinement and the magrid: the optimum shape for the coil casing of a magrid is one that is conformal to the magnatic field lines that set up around it; with wiffle-ball confilement this shape is approximately an ellipse with one flattened end, i.e. a kind of elongated 'D' shape. The flat part of the D faces inward toward the center of the polywell. It should be noted that the cause of both heating and sputtering on the coil canister is high-energy Helium ions coming from the fusion in the center of the polywell, and this will hit the coil canister from one direction only - impacting on the flat face of our elongated 'D' shape. Therefore only this face needs high-temperature cooling (600k water or sodium), and only this face needs anti-sputter coatings (boron or titanium) the rest can be polished stainless-steel. Additionally, there is room in the rounded part of the 'D' for a more massive stainless steel supporting structure, and ducting to carry liquid He and N2 coolants. Hope this helps.

M. Simon said...

There are reasons for making the H2O fluid surround the whole coil.

One is that you will get some mixing from the "cold" to the "hot" side improving heat transfer which I expect will be marginal to begin with.

Near the coils themselves the magnetic field will be roughly circular. So it may not be necessary to construct a special shape for the outer cooling loop.

I'm going to add a bit about neutron shielding to the main text.

Tom Cuddihy said...

How do all those steel / inconel / water layers affect permittivity?

Aren't you going to get eddy currents where the inlets/outlets through various layers connect?

M. Simon said...

Water will not be much of a problem. It has to be pH 7 to keep the high voltage isolated.

I was thinking that copper might be good for the various "tubes" of the grid. Of course it might have to be some low activation steel to support the magnetic forces.

Eddy currents will not be a problem because other than a slow charge up the magnetic field is fixed.

Magnetically saturated steel will not be an issue because I wasn't expecting any help from the steel re: the magnetic fields.

Colin said...

Most superconducting magnet designs I've seen incorporate a Cu or Al stabilizer around the superconductor. Is this something that's included in the superconductor in your cross section?

It seems like the thermal and field stresses on the the standoffs will be large. Have you considered standoffs robust enough to take this without conducting to much heat to the cryogenics? I think the efficiency of cryogenic systems is about 1/400.

M. Simon said...

colin,

This is strictly back of the envelope stuff to suggest an approach.

The engineering details will have to be worked out in conjunction with an MRI magnet supplier in conjunction with the reactor requirement physicists.

The forces involved are in the ton range. Manageable.

Colin said...

The current density,J, will be effected by by the conductor stablizer/semiconductor design. You may want to through a factor of 1/10 into your estimates.

I don't think MRI guys will be able to help much on the cryogenics. Any amount of heat transfer to the LHe equates to a big $. MRIs require LHe servicing, they don't work with the enormously expensive systems to cool LHe. The heating issues with MRI cryogenics is also on a much lower order of magnitude.

To handle the cryogenics for this you're looking at a several $100M facility, like ITER has. And ITER has much more thermal shielding between the plasma and coil.

My naive impression is that it would be more economical to have much lower power systems at higher Sc operating temperatures.

Also the structural considerations are not insignificant, and most experienced physicists would defer to an experienced ME on the matter. That would be one lesson from WB6.

M. Simon said...

Colin,

That is the purpose of the water jackets. To get the thermal load on the MRI magnets down to a level similar to what the MRI guys deal with normally.

The J factor is assumed based on what the MRI guys do every day.

I'm also assuming that the power conversion plant will not be a thermal one but electrostatic.