Maximum size allowed by energy flux constraints

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Art Carlson
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Maximum size allowed by energy flux constraints

Post by Art Carlson »

In face of the prospect that the confinement time of a polywell might not be as good as some hope, it is tempting to take solace in the thought that it would only need to be made a bit bigger, especially if one accepts the favorable scaling of Q with a high power of R as propagated by Bussard. This is how I used to think about tokamaks until I realized that, if the particle confinement time is more than about 10 times the energy confinement time, then bremstrahlung from the helium ash will detsroy any prospect of breakeven operation, now matter how good the cross-field transport is (i.e. no matter how big the tokamak is).

In this spirit, I would like to consider a limit on the maximum size of a polywell reactor, irrespective of confinement behavior. The most serious engineering work that has ever been done on a machine to magnetically confine a plasma near reactor conditions is ITER, so I would like to take that as my baseline. I think we all are thinking that within technical limits a stronger field is always advantageous for a polywell, just as it is for a tokamak, so I assume we find a way to produce ITER-like fields in a polywell, but not much stronger. Second, I think I can claim without risk of contradiction that there is a limit on the energy flux through the wall of a reactor. This is certainly a major consideration in any tokamak reactor design, although perhaps not the most important factor. It is also conceivable that the simple topology of a polywell allows a higher wall load, e.g. because the first wall can be exchanged once a month instead of once very ten years. But this gives us a point of reference.

A major difference between a tokamak reactor and a polywell reactor is the plasma beta: 10% vs. 100%. This translates into 100 times the fusion power density. for a given field. To get the same energy flux at the wall, the 2 m minor radius of ITER would have to be scaled down to 2 cm, or somewhat less than 10 cm for the length of the side of the magrid cube. (The energy flux scales linearly with R because the total power goes as R^3, and the area it is spread over goes as R^2.) That would be a handy, pocket-sized reactor with an output of a couple MW. Everyone's dream.

I think even the most optimistic among us do not expect that a break-even reactor could have sides of less than 1 m, which would bring us back to the GW range, but only if we can design a first wall that can take 10 times the design value for the energy flux of ITER. That is a tough engineering order, but maybe it is possible. If we have to even double that, then we double the required wall loading and have something like a 10 GW monster. Now, I think our utility system could deal with 10 GW power plants, but they are on the chubby side. My point is, if the scaling isn't good enough for WB-100 (or at most WB-200) to reach breakeven, then we have lost the game. We won't have the option of simply making it a bit bigger. Bussard doesn't have to be very far wrong for his concept to fail in a practical, if not a scientific sense.

TallDave
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Post by TallDave »

If we have to even double that, then we double the required wall loading and have something like a 10 GW monster....We won't have the option of simply making it a bit bigger.
Sure you do. You can just decrease the B field strength. Or am I missing something there? (This might be counter-intuitive because normally you don't deal with situations where you want to decrease power density -- especially in a tokamak, I imagine. But this is less the case in a Polywell, where temperature is easy and there are no gains from ignition.)

In a Polywell, the "first wall" is the Magrid. If you're at the limit of Magrid loading costs grow as r^3 while power now grows at only r^2 (moving B down to compensate, thus scaling power at the same rate as the radiative inverse square law and so keeping flux constant), so there's an economic consequence.

M Simon did some calcs on this a while back in the Design forum. With currently available materials, the sweet spot is probably around 100MW at 1.5M. There are other less sweet options.

But there's another problem...
Now, I think our utility system could deal with 10 GW power plants
Maybe, in some highly dense power-consumption areas. Western Europe and the U.S. coasts might be able to absorb that, albeit with some hefty distribution costs. But if you can only build 10GW plants that severely limits the practical applications.

D Tibbets
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Re: Maximum size allowed by energy flux constraints

Post by D Tibbets »

Art Carlson wrote:In face of the prospect that the confinement time of a polywell might not be as good as some hope, it is tempting to take solace in the thought that it would only need to be made a bit bigger, especially if one accepts the favorable scaling of Q with a high power of R as propagated by Bussard. This is how I used to think about tokamaks until I realized that, if the particle confinement time is more than about 10 times the energy confinement time, then bremstrahlung from the helium ash will detsroy any prospect of breakeven operation, now matter how good the cross-field transport is (i.e. no matter how big the tokamak is)....
Is the helium ash a potential problem in the Polywell from a bremstrahlung standpoint? In the polywell, most of the alpha particles produced have enough kinetic energy to leave the core/ magrid interior and hit the walls (perhaps after being slowed down with energy collecting grids)and need to be be removed from the outer area of the vacuum vessel by pumping. This as opposed to the Tokamak in which I understand the ash is contained in the confined reaction plasma so long as it can be maintained.

[edit] My question was partially answered by A. Carlson in another thread-near the bottom of page 4, thanks.
viewtopic.php?t=1204&start=45

Dan Tibbets
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Art Carlson
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Q scaling when energy flux is limiting

Post by Art Carlson »

TallDave wrote:
If we have to even double that, then we double the required wall loading and have something like a 10 GW monster....We won't have the option of simply making it a bit bigger.
Sure you do. You can just decrease the B field strength. Or am I missing something there?
My logic here may not be as crystal clear and unassailable as you have come to expect of me.

The first consequence may actually be that the assumptions are screwy. If my magrid is 100 cm on a side, then I only have 10 cm or so for the radial build of my coils, which is almost certainly not enough to shield a superconductor from industrial strength neutron fluxes. I'm not sure how we/you may want to fix this, but it underscores the fact that it is easy to make inconsistent assumptions if you don't do a complete design.

But back to the question of fixing confinement by building a bigger machine. If we are in a regime where we are limited by energy flux rather than coil size, then we have B^4 ~ R^-1, and total power P ~ B^4*R^3 ~ R^2. Quite a difference to Bussard's P ~ R^7. For the scaling of Q, we need some kind of model for the losses.

Bussard loss model (as near as I can tell): P_loss ~ R^2. Q = P_fusion / P_loss ~ R^2 / R^2 ~ constant. That is, either the thing works or it doesn't, but it doesn't work any bit better just by making it bigger.

Carlson loss model: P_loss ~ R/B ~ R^(5/4). Q ~ R^2 / R^(5/4) ~ R^(3/4). If I'm right about the scaling of the losses (even if I am wrong about the absolute magnitude), then it does indeed help to increase the radius, even if you have to simultaneously decrease the field to keep from burning up your first wall. But the improvement is real slow, and all the while the power rating and cost are rising. Unless you're real close to working at WB-100, you're unlikely to gain enough ground to get to breakeven by going to WB-200 or WB-1000.

TallDave
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Post by TallDave »

If my magrid is 100 cm on a side, then I only have 10 cm or so for the radial build of my coils, which is almost certainly not enough to shield a superconductor from industrial strength neutron fluxes.
Hmm? Wouldn't it be 3m a side?
That is, either the thing works or it doesn't, but it doesn't work any bit better just by making it bigger.
Ah yes, we're assuming the losses grow as r**2 too, so you would have more power but no more gain. Yes, if we're operating with power density at the first wall limit this would be a problem. But too much power density is probably a nice problem to have if we can get there. And again, a lot depends on a more detailed understanding of how exactly losses scale.

On the plus side, we could promise the funders we will never ask for a machine as big as ITER.
Unless you're real close to working at WB-100, you're unlikely to gain enough ground to get to breakeven by going to WB-200 or WB-1000.
...if you're at the first wall limit or the B field limit of current technology, yes.

KitemanSA
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Re: Q scaling when energy flux is limiting

Post by KitemanSA »

Art Carlson wrote:Bussard loss model (as near as I can tell): P_loss ~ R^2. Q = P_fusion / P_loss ~ R^2 / R^2 ~ constant. That is, either the thing works or it doesn't, but it doesn't work any bit better just by making it bigger.
DrB has several paragraphs on loss factors and scaling thereof in the Valencia paper. It is a lot more comprehensive than portrayed here, I think.

MSimon
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Post by MSimon »

Isn't there also the option of reducing density?

===

The 100 MW size is the sweet spot for conventional cooling (1 MW/sq meter). With more engineering effort sizes in the 200 MW to 500 MW range should be possible.
Engineering is the art of making what you want from what you can get at a profit.

Art Carlson
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Re: Q scaling when energy flux is limiting

Post by Art Carlson »

Art Carlson wrote:B^4 ~ R^-1
Art Carlson wrote:Bussard loss model (as near as I can tell): P_loss ~ R^2. Q = P_fusion / P_loss ~ R^2 / R^2 ~ constant. That is, either the thing works or it doesn't, but it doesn't work any bit better just by making it bigger.
Looking at Bussard's Valencia paper, I find this claim:
Tests made on a large variety of machines, over a wide range
of drive and operating parameters have shown that the loss
power scales as the square of the drive voltage, the square
root of the surface electron density and inversely as the 3/4
power of the B fields. At the desirable beta = one condition,
this reduces to power loss scaling as the 3/2 power of the
drive voltage, the 1/4 power of the B field, and the square of
the system size (radius).
Taking P_loss ~ B^0.25*R^2 and applying the energy-flux-limited scaling, I get P_loss ~ R^2.0625. Formally, that means the Q gets worse with increasing radius (Q ~ 0.0625), but let's just say "hardly changes".
Art Carlson wrote:Carlson loss model: P_loss ~ R/B ~ R^(5/4). Q ~ R^2 / R^(5/4) ~ R^(3/4).
The area of the "hole" scales with R/B, but the loses through that hole scale with R*B. (dummy!) P_loss ~ R*B ~ R^0.75. Q ~ R^2 / R^0.75 ~ R^1.25. This doesn't change my general conclusions. (Basically, the power density depends so sensitively on the field that the field doesn't have to change much to keep a constant wall loading when the radius changes, therefore the scaling of the losses with B hardly matters.)

KitemanSA
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Post by KitemanSA »

Thank you for clarifying that. :)

Does anyone know if he is right? :?

Art Carlson
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Post by Art Carlson »

In his Valencia paper, Bussard makes the claim:
In particular, it has been found, by detailed design studies, that
superconducting (S/C) magnets can not be used practically
in machines below a size of, typically 1.5-2 m radius. Below
this size, water-cooled copper coils occupy less total volume
(because of S/C LHe/LN2 cooling requirements) thus are
more practical to build. However, water-cooled copper coils
with optimal shape and configuration (for minimum electron
impact losses to coil structure), able to reach conditions
useful for significant fusion production, also can not be
made practically below a machine size of about 1-1.5 m
radius.
It is not clear whether he is talking about superconductors hardened against neutron flux from D-T. (That is the trouble of detailed design studies without the details.) Since he only mentions p-B11 in the abstract, I suspect he is not. That suggests that engineering constraints on a superconducting D-T machine require the side of the magrid (which I take to be twice the "radius"), to be on the order of 6-8 m. (Not quite ITER dimensions, but respectable.) This in turn implies that the field of a D-T machine will have to be substantially de-rated to avoid the technical limit on the wall loading. In fact, to match the wall-loading of ITER, the power density would have to be considerable less than in ITER, so that it is no longer obvious that the price per MW will be significantly less than that for a tokamak reactor. (I'm not sure where this train of thought is going, except to re-emphasize the importance of a complete and self-consistent reference design.)

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Post by TallDave »

It is not clear whether he is talking about superconductors hardened against neutron flux from D-T. That suggests that engineering constraints on a superconducting D-T machine require the side of the magrid (which I take to be twice the "radius"), to be on the order of 6-8 m.
I remember there are some posts in Design dealing with this issue. It was a while ago, but they seemed to indicate 1.5m radius isn't a problem. A layer of boron was going to absorb the neutrons, iirc. Here was MSimon on this more recently:
MSimon wrote:My admittedly BOE calculation says that 5 cm of H2O is enough to thermalize the neutrons and a few mm of B10 is enough to absorb them.
Presumably the water would be a coolant flow anyway.
In fact, to match the wall-loading of ITER, the power density would have to be considerable less than in ITER,
Not sure about that. What's the currently envisioned distance between wall and plasma in ITER? I found a couple conflicting sources on that.

Also, the Magrid intercept area is a lot smaller and the casings could be replaced more cheaply, so I'm not sure the wall-loading has to match.

It looks like ITER is expecting ~1MW/m^2 heat loads. OTOH, APEX is looking at ~10MW/m^2 heat loads. I'm guessing a 10MW/m^2 heat load limit pretty much solves our problem (maybe MSimon wants to do the math again to verify, or I could dig up his post).
so that it is no longer obvious that the price per MW will be significantly less than that for a tokamak reactor.
...if they reach the wall limit at similar sizes, which they probably don't.

It does look like Polywells might reach a point where further gains would have to come from better wall limits or new ways of reducing losses. But again, we probably need a better (empirically-driven) understanding of how losses scale before we can really say.

D Tibbets
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Post by D Tibbets »

A couple of questions based on the last few posts. I seams that there may be a convergence of understanding that the loss scaling might be ~ r^2. A. Carlaon has compared that with the power gain from size (r) as being ~ r^2. How did the claimed r^3 gain scaling get reduced to r^2 ?

Also, how did the 1.5 to 2 meter radius net power size get increased to 6-8 meters diameter, instead of 3-4 meters? Is there some modification to the scaling laws or heat load tolorances incorperated into this doubling of linier size? M. Simon has repeatedly estimated that the 'WB100' would have ~ 1 MW/M^2 heat loading. I don't know if this refers to the magrid surfaces or the vacuum vessel surface. How much further away would the vacuum vessel walls be compared to the magrids? Is this where the 6-8 meter estimated diameter comes from?


Dan Tibbets
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Post by MSimon »

M. Simon has repeatedly estimated that the 'WB100' would have ~ 1 MW/M^2 heat loading.
That is at the MaGrid casings. Vessel wall loadings would of course be lower.

A 10 MW/sq m loading would imply a maximum power of 1 GW.

All the above assumes pB11 alphas and no (significant thermally) neutrons.

===

The situation is different where neutrons predominate. Wall loadings would be relatively insignificant. All the heat would be generated inside the moderator. A situation that is relatively easy to deal with. OTOH you give up the advantages of direct conversion.
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Art Carlson
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time to shut up

Post by Art Carlson »

I need to shut up now (or soon) because my knowledge of engineering is getting stretched pretty thin. I think at least it is clear that there has to be a figure for the wall loading in any reactor reference design (which I hope we have some day).

It is important to distinguish between wall loading by neutrons and by charged particles, and possibly important to distinguish between energetic (fusion product, MeV) and "thermal" (10 - 100 eV) particles. There are limits due to melting (or sublimation) when the surface gets too hot. There are limits due to erosion. There are limits due to material damage. (The problem of heat flux to the superconductors is something that could and should be solved by using sufficient shielding.) The question is as complex as it is important, so I doubt we will be able to cook it down to one number.

We are still struggling a bit with terminology. May I suggest:
R = the radius of the high beta, nearly spherical plasma ball
S = the length of the side of the cube, on whose faces the magrid coils lie
R_coil = the major radius of the toroidal magrid coils
r_coil = the minor radius of the toroidal magrid coils, including conductors, cooling, and shielding

My guess is:
S = (0.5-0.8)*S
R_coil = 0.2*S
r_coil = 0.1*S

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Post by MSimon »

Art,

You are so correct on all your engineering points. As far as a practical reactor goes (assuming the physics argument get settled favorably) the first wall (esp for pB11) and thermal issues are uppermost in my mind.

One thing to keep in mind was that Bussard's specialty was practical thermodynamics.
In 1956, Bussard designed the nuclear thermal rocket known as project Rover.

http://en.wikipedia.org/wiki/Robert_Bussard
I have a little background in the subject from my Naval Nuke days and when I did my calculations I was amazed at how all the pieces fit together. At 1 MW/sq. m (MaGrid loading with pB11 fuel) he is right on the edge between difficult and exotic. Just right for a maximum size proof of principle design.
Engineering is the art of making what you want from what you can get at a profit.

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