Dodec Magnetic field?

KitemanSA · Post by **KitemanSA** » Wed Mar 25, 2009 1:21 am

MSimon wrote:Let us look at the scaling. From .15 m radius to 2 m radius gives a volume multiplication of around 2,500.
An increase in the field from .1T to 10T gives 100,000,000 multiplication.
If you assume a 1 mW starting point that gets you to 100 MW. Roughly.

Scaling the .15m WB6 DD machine to a 1.5mDD machine gives a volume increase of 1000. Scaling the 0.13T WB6 to 1.3 (the same 10x scaling) gives an increas of 10,000. Starting at 0.1mW (if the 1.3e4 neutrons per neutron counted ratio is true) or 0.6mW (if the 1e9 fusions per second number is true) then the result is 1 to 6 kW. So scaling per DrB's numbers is not enough. He HAD to have had other things on his mind, even though he repested the 10x scaling scenario several times in several places. As you point out, going to 10T vice the staight scale 1.3T would give us about 3500 times the output, or ~3 to 20 MW. However, 10T ain't easy even with superconductors. Perhaps he was including the improvement from the reduced losses from a true polywell and the ~3-5x improvement from the better sphericity of the icosedodec.

{"repested" is a partially successful edit from repeated to suggested.}

KitemanSA · Post by **KitemanSA** » Wed Mar 25, 2009 1:35 am

Aero wrote:The question of this thread now becomes, given 3-5x better confinement of the dodec, what is the reduction in radius of a break-even dodec compared to the radius of a break-even truncube?

Folks, DrB didn't want a truncube. He wanted either a cuboctohedron (a rect-cube? recticube?) or an icosedodecahedron (a rectidodec?). His $200M project included as it's first step, the building and testing of a WB6 scale "square" coil recticube and a pentagonal coil rectidodec. Both should reduce the losses from the quasi-line cusps by shortening them a lot (IIUIC) and the rectidodec would improve sphericity too.

KitemanSA · Post by **KitemanSA** » Wed Mar 25, 2009 1:43 am

Aero wrote:I agree that gross scaling = B^4 * R^3 and is solidly founded in physics, most do. WB-100 sized as quoted above targets break-even.

Now here is a good point. Was it ever determined whether this was 100MW net power or 100MW power at 1+W net? I seem to recall a drive power requirement of ~40MW mentioned for the WB100. Does that mean a total 140MW output - 40MW input = 100MW net?

KitemanSA · Post by **KitemanSA** » Wed Mar 25, 2009 2:02 am

MSimon wrote:
KitemanSA wrote:Please note that we can't just scale the WB6 machine and reach 100MW. If my calcs were right, R^7 scaling on the WB6 > WB100 yields about one kW power. One NEEDS to go higher B, better sphericity, etc to get to 100MW. The question should be, how best to do it at the lowest cost.
Well yeah. But that is not the immediate problem. The immediate problem is finding out the rules. And for that a continuation along the cube lines is probably best. We don't even know if offsetting the coils will improve results. For experiments like that it is best for apples to apples comparisons for one and the minimum number of coils to minimize the effort in moving them around for another.
Break even is good. Knowing the scaling laws is better. (for now)

Fine, but the rules include the effects of better geometries too. Until we find out those effects, it makes no real sense to go big. If the 5x improvement is also subject to the scaling discussed, that would be a difference of 5x the size. Don't we want to know that?

TallDave · Post by **TallDave** » Wed Mar 25, 2009 2:30 am

Well, I did this calc at the Polywell wiki a while back:

OK I get 1E+9 neutrons * .5 fusions per neutron x 17.6 MeV per fusion x 1.6E-19 eV per joule = .00141 joules/second = .00141 watts

Doing the math, an increase in r of 10 gives us 10^7 times more fusions, or 5E15, which works out to about 14kW. You get to 100MW at about r*36.

Of course it's not really r^7 though, it's r^3 * B^4. It's pretty easy to see you can increase B faster than R and get to 100MW at r=10 at some value of B. Now, let's see, to get to 100MW...

...it works out to requiring B 92 times greater if r is increased by 10 (this is roughly the .1T to 10T Simon mentioned)

.00141 * 10^3 * 92^4 = 101,011,407 watts.

I seem to recall a drive power requirement of ~40MW mentioned for the WB100

I think Rick said they were calculating around 5-10MW.

TallDave · Post by **TallDave** » Wed Mar 25, 2009 2:40 am

Ah, this is interesting:

This demonstration will require about $ 200 M (USD) over 5 years,
with an IEF machine of 2.5-3 m in diameter, operated at over 100 MW.

OK, let's do that again for r*20... and now we're looking at about B*55, or around 5T.

Of course, this all changes for p-11B. The above is a fairly optimistic D-T calculation... but then the D-T rate is 68x higher than the D-D from WB-6, isn't it? Hrm. And then you have the D-Ts that result from one path of the D-D...

Well, it's all pretty rough anyways.

Rick probably has much better calculations bouncing around over at EMC2.

TallDave · Post by **TallDave** » Wed Mar 25, 2009 2:54 am

Aha. If you plug in the 68x better D-T rate, you get to 100MW right at r * 20, assuming you scale B with R. I'm guessing that's the rough calc Bussard was doing. Then he later realized "Hey, I can scale B to 3T (doable) and still get to 100MW at only r*10!" and so we started talking about 1.5M.

MSimon · Post by **MSimon** » Wed Mar 25, 2009 6:58 am

Aero wrote:I agree that gross scaling = B^4 * R^3 and is solidly founded in physics, most do. WB-100 sized as quoted above targets break-even.

We hope that loss scales at R^2 or lower, but that is in dispute. Using R^2 losses gives B^4 * R, and your numbers, gives net power = 1 mW * 100,000,000 * (2/.15) = 1.3 MW That is to close to hang my hat on. Using a dodec configuration with the same parameters gives 3-5x 1.3 MW, = 4 MW - 6.7 MW. That is still not a very comfortable margin. there are a bunch of limitations in our knowledge of loss scaling, and then there is the potential of heat overload on the coils. (Not to mention that it is all based on 3 neutrons.)

I argued on another thread that we were not planning on a large enough machine, and I am still of that opinion. If we are not careful, we will have a "Jet" on our hands if we are so lucky. Then the net power BFR will be designed by committee, if the program survives.

I'm not sure it matters. If it proves the scaling laws, no insurmountable instabilities show up, and it is any where near close to net power the follow on unit will get built in 6 months.

In any case you left out the increase in collision cross section with increased drive. That should give a 10X to 30X power increase.

TallDave · Post by **TallDave** » Wed Mar 25, 2009 3:03 pm

Oops, no he says 3M diameter up there, which would of course be twice the radius. So it was always 1.5M radius.

MSimon, you're talking about a deeper well (in terms of eV) there, correct? Can you explain how we arrive at the 10-30x power gain there? The cross-section math is still a bit of a gray area for me.

I have to agree, understanding the scaling, esp. loss scaling, is the most important thing right now. Art has pointed out some ways a large machine will be considerably different. I would not be at all surprised if the first large attempt runs into problems and requires a follow on to reach net power, and I wouldn't really regard that as a failure. Just remember, this is still all orders of magnitude cheaper than ITER.

KitemanSA · Post by **KitemanSA** » Wed Mar 25, 2009 3:08 pm

TallDave wrote:Aha. If you plug in the 68x better D-T rate, you get to 100MW right at r * 20, assuming you scale B with R. I'm guessing that's the rough calc Bussard was doing. Then he later realized "Hey, I can scale B to 3T (doable) and still get to 100MW at only r*10!" and so we started talking about 1.5M.

Now here is another good question. Did DrB assume DT for the WB100? He used DD for WB6 and that yields about 7.5MeV per neutron produced. And we know he suggested a 2m radius for pB.
DT produces twice as many neutrons per fusion than DD, (1 vs 1/2) but produces 17.5MeV for that neutron. And as pointed out, the cross section is higher. I have been scaling WB6 to WB100, all else equal.

TallDave · Post by **TallDave** » Wed Mar 25, 2009 3:15 pm

Kite,

I'm guessing when pitching WB-100, he generally made optimistic assumptions. And of course every other D-D gives you a D-T anyway.

http://en.wikipedia.org/wiki/Nuclear_fusion

But that would have happened in WB-6 too, now that I think about it. Hrm.

KitemanSA · Post by **KitemanSA** » Wed Mar 25, 2009 3:17 pm

MSimon wrote: In any case you left out the increase in collision cross section with increased drive. That should give a 10X to 30X power increase.

I was under the impression that the B^4 scaling either increased the n density or the drive velocity, not both. A stronger B allows more electrons (higher n) or higher velocity electrons (deeper well, higher velocity) or a combination of both, but not both at full scaling together. Your statement seems to imply that DrB's scaling rules were significantly off. What am I missing?
The need to go to 2m radius to counter the extra drive needed for pB seems to suggest that we wouldn't get "extra drive" with the scaling rules. We could trade "extra drive" for extra density and the results would come out about even.

TallDave · Post by **TallDave** » Wed Mar 25, 2009 3:21 pm

TallDave wrote:MSimon, you're talking about a deeper well (in terms of eV) there, correct? Can you explain how we arrive at the 10-30x power gain there? The cross-section math is still a bit of a gray area for me.

Ah here we go.

KitemanSA · Post by **KitemanSA** » Wed Mar 25, 2009 3:21 pm

TallDave wrote:I'm guessing when pitching WB-100, he generally made optimistic assumptions. And of course every other D-D gives you a D-T anyway.
But that would have happened in WB-6 too, now that I think about it. Hrm.

We know he went DD for WB6 to avoid the legal entanglements with using Tritium, permits and stuff. He wrote that somewhere, I don't remember where. (Or maybe said it on the Google tape?) Thus he could VERY well have been assuming DT for WB100. It gives ~twice the energy PER NEUTRON than DD. As you say... hrm.

TallDave · Post by **TallDave** » Wed Mar 25, 2009 3:36 pm

TallDave wrote:
TallDave wrote:MSimon, you're talking about a deeper well (in terms of eV) there, correct? Can you explain how we arrive at the 10-30x power gain there? The cross-section math is still a bit of a gray area for me.
Ah here we go.

So, WB-6 operated at 12.5kV. Does anyone know what well depth we were looking at for WB-100? It looks like at about 70kV we gain around an order of magnitude for D-D/D-T reactions, and closer to two for D-He3.