Off the wall question:

OrionCA · Post by **OrionCA** » Sat Jul 18, 2009 7:55 am

All the discussion about polywell is how much it can be ramped up if the current experiments pan out. I'm curious about the opposite: What is the smallest polywell fusion reactor that could theoretically be built, and is there a guess how much power could be extracted from it?

Could you say...build one small enough to fit in a closet? Could it be miniaturized enough to fit in a fanny pack? If I could build one small enough to fit in the palm of my hand (probably not a good idea, I know) how much power could it generate? Enough to run a coffee maker, or an entire house?

Skipjack · Post by **Skipjack** » Sat Jul 18, 2009 9:01 am

I think this has been discussed before. If I recall correctly, the size of the Polywell depends on the fuel. I might be wrong, but I think it was 1m^3 for TD and 3m^3 for PB. Depending on the actual data they will get from further experiments, these numbers might go up (provided this thing will ever work).
The Polywell allone does not make the reactor facility though. Dont forget that you will also need a sufficiently sized vacuum chamber arround it and then some shielding, powersupplies, energyconversion, cooling and so on. Dr Bussard seemed to believe that you could power an airplane with a polywell. So I guess that it could theoretically be built sufficiently small to be put into a larger airplane, or spaceplane.

kunkmiester · Post by **kunkmiester** » Sat Jul 18, 2009 12:40 pm

I believe there was also some hope that with work, the system could be shrunk after they get it to work, and eventually get small enough to put in a truck.

Out the starting gate though, a 35 foot room or so would be needed just for the reactor.

KitemanSA · Post by **KitemanSA** » Sat Jul 18, 2009 2:37 pm

Remember folks that net power is power out minus power in, and producing 0.1 MILLIwatts out in WB6 required megawatts in. So even something big enough to produce enough power to run a toaster will be a multi-megawatt machine. Probably not something you will want in your closet.

TallDave · Post by **TallDave** » Sun Jul 19, 2009 2:41 am

Well, B^4*r^3 power scaling, so the limit depends on how powerful a magnet you can get into how small a space, but you get to grow the magnet strength a bit slower than you reduce the radius.

So, let's see, 100MW at 1.5 M with (I think) 5T. My rough calc says that means a .15 radius machine (WB-6/7 sized) could make 100MW at about 28T. Of course, we're nowhere close to being able to sustain that today at anything close to that size, but I'm not sure what the thereotical limits are.

For a truly tiny reactor, palm-sized, say 10 cm radius, I think we're looking at about 215T. Which seems likely to also crumple your car into a tiny ball around you.

Here's a link from last year: this giant contraption was supposed to be the most powerful magnet in the world at 100T, and of course it only runs pulsed.

OK, that was fun, but I'd better go study now.

Art Carlson · Post by **Art Carlson** » Mon Jul 20, 2009 6:57 pm

I don't think I take the question seriously enough to actually calculate any numbers. If I did, I would probably provisionally accept Bussard's claim that the field you can produce scales with the radius, so the fusion power scales with R^5. We are assuming the miracle that fusion power is roughly net power at all sizes. What puts a lower limit on the size? One thing is stopping the neutrons, but you might still be able to do that in your closet. More fundamental is the electron gyroradius. Even in the fantasy machine, we need some magnetic confinement, so we would require rho_e < R. This would put a lower limit on the size and power of even a perfect polywell.

TallDave · Post by **TallDave** » Mon Jul 20, 2009 10:59 pm

so the fusion power scales with R^5.

I think gain scales as R^5, power as R^7 (B^4*R^3), according to Bussard, but I'm not anyone agrees how the R^5 gain breaks down in terms of B and R. So I decided to ignore losses (or at least assume they're constant with power despite my wildly fluctuating B and R).

The required B power at small sizes was the first thing that popped into my head, but the other necessary miracles are fun to look at too, esp. now that my exam is over and I have more time for these things. I hadn't thought of the gyroradius issue. Does this mean the holes would be large as compared to the size of the machine? That does seem like a problem.

tombo · Post by **tombo** » Tue Jul 21, 2009 5:29 am

From calc's I posted recently for a 3m dia Polywell, w/ 100 mm thick conductors, w/ a rectangular planform truncube configuration:
For 1 T in the center of the square turn your superconductor sees 17 T at its surface.
So, even at 1 T you are pushing your superconductors very hard.
Scaling that to the highest SC critical current I have heard of being 49 T, you only get ~3 T in the center of the largest coil.
Getting multi-Tesla fields where it counts is going to require much better superconductors than we have now.
Or it will require more smaller coils, say a truncated dodecahedron or other high period shape.

That image of the fields crumpling up the little car is going to be hard to get out of my mind. Ouch!

MSimon · Post by **MSimon** » Tue Jul 21, 2009 6:49 am

tombo wrote:From calc's I posted recently for a 3m dia Polywell, w/ 100 mm thick conductors, w/ a rectangular planform truncube configuration:
For 1 T in the center of the square turn your superconductor sees 17 T at its surface.
So, even at 1 T you are pushing your superconductors very hard.
Scaling that to the highest SC critical current I have heard of being 49 T, you only get ~3 T in the center of the largest coil.
Getting multi-Tesla fields where it counts is going to require much better superconductors than we have now.
Or it will require more smaller coils, say a truncated dodecahedron or other high period shape.

That image of the fields crumpling up the little car is going to be hard to get out of my mind. Ouch! :shock:

You need to get more up to date. 3T MRI coils are in serial production. 7T and 9T MRI coils are being built for experimental purposes.

I have been quoted a rough price for a 3T coil with a 1 m bore. The seller wanted to know how soon I would be ordering.

Art Carlson · Post by **Art Carlson** » Tue Jul 21, 2009 7:47 am

TallDave wrote:
so the fusion power scales with R^5.
I think gain scales as R^5, power as R^7 (B^4*R^3), according to Bussard, but I'm not anyone agrees how the R^5 gain breaks down in terms of B and R. So I decided to ignore losses (or at least assume they're constant with power despite my wildly fluctuating B and R).

Of course. Careless of me. I think that was the spirit of the question, to ignore losses completely and ask what else could go wrong. Even using Rick's scaling of losses, of which I will remain skeptical until I see the data, a polywell reactor will not be small enough to run a coffeemaker. My point was that for some as yet undreamed of magnetic configuration that has confinement orders of magnitude better than cusp confinement in any form, you still have a gyroradius issue.

TallDave · Post by **TallDave** » Tue Jul 21, 2009 7:33 pm

1T is actually pretty close to the .8T WB-8 will be operating at.

That reminds me: I wonder how big WB-8 is going to be? Maybe Rick will let us know, or perhaps Simon can tell us the practical lower limit for that power of magnet. Could it be WB-7 sized, or would it have to be bigger?

I'm also guessing you get fewer pulses as magnets get bigger, since it's going to take longer to cool.

MSimon · Post by **MSimon** » Tue Jul 21, 2009 10:16 pm

TallDave wrote:1T is actually pretty close to the .8T WB-8 will be operating at.

That reminds me: I wonder how big WB-8 is going to be? Maybe Rick will let us know, or perhaps Simon can tell us the practical lower limit for that power of magnet. Could it be WB-7 sized, or would it have to be bigger?

I'm also guessing you get fewer pulses as magnets get bigger, since it's going to take longer to cool.

Barring using Super Conductors it will probably be a pulsed machine. I worked out a while back that a machine that size (coils .3 m dia) tops out at around .5 T for continuous operation (LN2 cooled). Pulsed I figured 1 to 1.5 T. That was for coils of a Bitter design.

My guess is that they are doing conduction cooled magnet wire coils. But who knows?

If they are still doing the nubs type construction it will take a while to cool the machine after each shot. Unless their pumping system is very good. Then they could bring the pressure up to a few torr for cooling and then pump down for a shot.

tombo · Post by **tombo** » Tue Jul 21, 2009 10:50 pm

You need to get more up to date. 3T MRI coils are in serial production. 7T and 9T MRI coils are being built for experimental purposes.

I have been quoted a rough price for a 3T coil with a 1 m bore. The seller wanted to know how soon I would be ordering.

The ones in production are no where near 3 meters in diameter.
1/r^2 scales amazingly fast.
3T/(3^2)=0.11 T at 3 m dia with his technology.
Multiply that by the 17:1 ratio from center of coil to surface of SC that would give 1.9 T at the surface of the SC.
That is quite doable.

Assuming he can pull off the 1 m dia job:
What is his calculated field at the surface of the superconductor?
What is his thickness of the superconductor coil?
And what is the SC material?
I would like to check my model if he gave any details.

As for 9 T at, say, half a meter diameter that would scale to .25 T at 3 m dia and give 4.25 T at the SC surface.
OK I'll buy that too.

But, ask him quote you 3 T at 3m dia.
And then get him to tell you how he plans to do it.
I'd like to hear any answers you get.

MSimon · Post by **MSimon** » Wed Jul 22, 2009 9:20 am

Tom,

It doesn't scale as 1/r^2. It scales as 1/r for constant amp-turns.

http://hyperphysics.phy-astr.gsu.edu/hb ... urloo.html

So 3T @ 1 m = 1T @ 3m. (diameters).

So far the best SCs @ near 0K can support a field in the wire of 100T. Revise your scaling and tell me what the bore field is. This might help:

http://hyperphysics.phy-astr.gsu.edu/hb ... ur.html#c1

tombo · Post by **tombo** » Wed Jul 22, 2009 8:16 pm

OK, I was shooting from the hip on the scaling comments above.
I’ve been looking a 1/r^2 for each dl in the numerical integration for too long.
Yes it does simplify to 1/R at the coil center which is the most important point.

But I stand by my model because it agreed with the analytical solution for a square turn to better than 1% when I turned the current off to the other 5 turns. (I must say I was very pleased to see that result.) I also stand by it because I’ve been much more careful with it than I was with my above comment.

Starting with a current that gives 1.00 T at the center of the square coil then turning off the other 5 coils I get 1.86 T. I.e. the other 5 coils decrease the field at the center of each of the coils by 46% from what they would each create alone. (See table on the thread Optimal Size for Magrid Casings)
Most of the effect is from the adjacent coils not from the opposite coil.
The other coils increase the field at the highest field point by 5.6%.
So we have to push the materials roughly twice as hard as you would think by naïvely assuming no effect from the other coils.

Which SC can do 100 T? I see MgB2 listed at 74 T.

Running the numbers through the model: (3 m dia truncube square plan form coils, 100mm diameter conductors)
For 100 T (per MSimon above) at the highest field point on the conductor surface, the field at the center of the square turn is 5.74 T at 1.99e7 amp-turns. (The field at the center of the square turn is weaker than at the center of the triangular virtual turn.)
For 74 T (MgB2 thin films per Wikipedia) at the highest field point on the conductor surface, the field at the center of the square turn is 4.24 T at 1.47e7 amp-turns.
For 55 T (MgB2 fibers per Wikipedia) at the highest field point on the conductor surface, the field at the center of the square turn is 3.16 T at 1.10e7 amp-turns.

So, if we can get up to those fields & currents then we are still in the running.