How would you answer this Polywell FAQ?
How will power and gain from small machines like the WB-7 scale to break even and beyond?
Power & Gain Scaling? - DONE
Power & Gain Scaling? - DONE
Last edited by KitemanSA on Mon May 31, 2010 4:00 pm, edited 1 time in total.
Wait and see ??
We won't know until several live devices go 'over unity'...
Power scales at r^3*b^4.
Loss scaling, acccording to Bussard, is r^2*b^1/4. That may be overly optimistic, esp on the B term. At B*8 WB-8 vs WB-7 will tell us a lot in that respect. This is probably the biggest question mark for whether Polywell is useful tech or just an interesting science project.
Glad to see someone is paying attention to the FAQ.
Loss scaling, acccording to Bussard, is r^2*b^1/4. That may be overly optimistic, esp on the B term. At B*8 WB-8 vs WB-7 will tell us a lot in that respect. This is probably the biggest question mark for whether Polywell is useful tech or just an interesting science project.
Glad to see someone is paying attention to the FAQ.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
As pointed out, data is not avaible. We don't know what drive voltages and magnetic field tests have been used. Certainly WB7 and 7.1 may have expanded the range of conditions tested, compared to WB 6 But I doubt that WB7 could have pushed the voltage or magnetic field strengths very far beyond WB 6 so the measured changes probably wouldn't be large enouth to give good confidence intervals. At one time there was a claim that WB7 was 35 cm wide, compared to 30 cm for WB 6 . Everything else being equal, this would allow slightly more amp-turns for the magnets and ~ 40% greater volume. Considering that the WB6 neutron results had a confidence interval of ~ +/- 30%, it would be difficult to establish any quantitative trends with any confidence.
Assuming Bussard's claims are correct, the assumptions are that breakeven will be exceeded (perhaps by a factor as much as 10:1)in a D-D machine that is ~ 2-3 meters wide and has a magnetic strength of ~ 10 Tesla. This assumes that the magnetic field strength is increased in proportion to the volume. With superconductors and favorable radiation loads on the magnets, the magnets may scale faster and significantly decrease the necessary size as the magnetic scaling contributes most to the gain.
The gains of fusion output may scale as predicted, but if losses do not scale as expected (such as Bremsstrulung) the net gains may be much more modest and according to some it will never reach breakeven.
There are a lot of variables that have to be accounted for to be able to make confident predictions. Things such as ionization efficiencies, electron losses, ion losses, thermalization times, ion focus, other plasma effects and instabilities, etc. Certainly WB 7 and 7.1 greatly expanded the data base and probably significantly improved the confidence intervals (at least within the narrow scaling range possible between WB6 and 7). Also, data from other machines like WB5 redoubtably contributes greatly to expectations. The neutron counts are the most sexy bits of data, but other data measuring plasma behavior, wiffleball performance, thermalization characteristics, and confinement times are at least as important.
I suspect that the size and strength of WB 8 (along with continuing improvements in instrumentation) will provide scaling data (compared to WB 6, 7 and earlier machines) that will give greater understanding and answers with good confidence intervals. This should define the risks and expectations of further development. As R. Bussard said, it would then be an engineering problem, the physics are solved.
Also, keep in mind that the magnetic field strength and size are not the only variables. The number of faces, the spacing between the magnets, the shape of the magnets, the drive voltage, tricks with variable feeds and frequencies (like POPS) and the types of fuel and conversion systems may significantly effect the final gain/ loss ratios and thus the final scaling predictions.
It is not unreasonable from a fanboy perspective that the first generation of machines may be similar to the predictions above. Subsequent refinements in superconductors, geometry, and other inputs may greatly change the design of later generation machines.
Dan Tibbets
Assuming Bussard's claims are correct, the assumptions are that breakeven will be exceeded (perhaps by a factor as much as 10:1)in a D-D machine that is ~ 2-3 meters wide and has a magnetic strength of ~ 10 Tesla. This assumes that the magnetic field strength is increased in proportion to the volume. With superconductors and favorable radiation loads on the magnets, the magnets may scale faster and significantly decrease the necessary size as the magnetic scaling contributes most to the gain.
The gains of fusion output may scale as predicted, but if losses do not scale as expected (such as Bremsstrulung) the net gains may be much more modest and according to some it will never reach breakeven.
There are a lot of variables that have to be accounted for to be able to make confident predictions. Things such as ionization efficiencies, electron losses, ion losses, thermalization times, ion focus, other plasma effects and instabilities, etc. Certainly WB 7 and 7.1 greatly expanded the data base and probably significantly improved the confidence intervals (at least within the narrow scaling range possible between WB6 and 7). Also, data from other machines like WB5 redoubtably contributes greatly to expectations. The neutron counts are the most sexy bits of data, but other data measuring plasma behavior, wiffleball performance, thermalization characteristics, and confinement times are at least as important.
I suspect that the size and strength of WB 8 (along with continuing improvements in instrumentation) will provide scaling data (compared to WB 6, 7 and earlier machines) that will give greater understanding and answers with good confidence intervals. This should define the risks and expectations of further development. As R. Bussard said, it would then be an engineering problem, the physics are solved.
Also, keep in mind that the magnetic field strength and size are not the only variables. The number of faces, the spacing between the magnets, the shape of the magnets, the drive voltage, tricks with variable feeds and frequencies (like POPS) and the types of fuel and conversion systems may significantly effect the final gain/ loss ratios and thus the final scaling predictions.
It is not unreasonable from a fanboy perspective that the first generation of machines may be similar to the predictions above. Subsequent refinements in superconductors, geometry, and other inputs may greatly change the design of later generation machines.
Dan Tibbets
To error is human... and I'm very human.
How does this strike you all? Please note that the superscripts available in the wiki do not translate to this forum. R3 in the wiki is Rsuperscript3.
From basic physics, power scales at R3*B4. For constant scaling, all else being equal, this would be equal to R7.
Loss scaling in the Polywell, according to Dr. Bussard, is R2*B1/4; or R2.25.
Thus gain would be ~R7/R2 or about R5.
That loss equation may be overly optimistic, especially on the B term. Given that WB8 is supposed to have a B field eight times that of WB-7, the results of the WB8 testing should tell a lot in that respect.
It should be noted that no-one expects a full scale unit to be an "all else equal" scaling from the WB7. First and foremost, the magnets will almost certainly be some version of superconductor, so it is expected that the B field will grow much more rapidly than the dimension R.
True. I don't know just what growth factors Bussard considered in going from 30 cm diameter and 0.1 T in WB6 to 300 cm and 10T in a Demo machine. I do believe that he said it could be done with copper wires. By cooling the copper to liquid nitrogen temperatures and having enough coolent flow to carry away the ohmic heating loads, copper wires could carry eight times (or more) current.. If the magnet can proportions are kept the same, the amp turns that could be packed inside would increase by 2 for each doubling of magrid diameter*. That would add up to 10X gain from more windings (at the same current) and 8X gain from cooling (lower resistance in the wires). That gets you in the range of ~ 10 Tesla.KitemanSA wrote:...
It should be noted that no-one expects a full scale unit to be an "all else equal" scaling from the WB7. First and foremost, the magnets will almost certainly be some version of superconductor, so it is expected that the B field will grow much more rapidly than the dimension R.
Superconductors, could push the magnetic strength much faster, if it can be kept cold enough and other considerations (like limits on Teslas that the superconductor can tolerate, and the neutron or other radiation loads that the superconductor can tolerate) do not interfere.
* The internal volume of the magnet cans would increase 4X for each doubling of machine diameter, but the circumference would double- thus ohmic heating would double. Net gain would be 2X. This ignores the volumes that would be needed for cooling.
Dan Tibbets
To error is human... and I'm very human.
A variation of the above answer is now inserted in the FAQ. At this point, this topic is done. If you want to make further comments, either PM me directly or start a new topic please.From basic physics, power scales at R^3*B^4. For constant scaling, all else being equal, this would be equal to R^7.
Loss scaling in the Polywell, according to Dr. Bussard, is ~R^2*B^1/4; or ~R^2.25.
Thus gain would be ~R^7/R^2 or about R^5.
That loss equation may be overly optimistic, especially on the B term. Given that WB8 is supposed to have a B field eight times that of WB-7, the results of the WB8 testing should tell a lot in that respect.
It should be noted that no-one expects a full scale unit to be an "all else equal" scaling from the WB7. First and foremost, the magnets will almost certainly be some version of superconductor, so it is expected that the B field will grow much more rapidly than the dimension R.
If I may pose a followup question. . .
If the scaling formula proposed by Dr. B holds true, I imagine that, given current materials science (I think there is a limit to how strong of an electromagnet can be produced, even with superconductors?), what is likely to be the largest (in terms of power output) WB that can be constructed (ignoring cost effectiveness)?
Do we have any info on how the costs scale, such that prediction could be made on saying that beyond X power output, making the reactor larger might be possible, but begins to be less cost-effective than simply building an additional, smaller reactor?
Based upon the fact that you guys mentioned that the power output is supposed to scale as a power of the radius and magnetic field, it seems like, for the most part, unless costs also scale to an even larger power, that the larger you can make this, the cheaper (per W) the output power should be?
If the scaling formula proposed by Dr. B holds true, I imagine that, given current materials science (I think there is a limit to how strong of an electromagnet can be produced, even with superconductors?), what is likely to be the largest (in terms of power output) WB that can be constructed (ignoring cost effectiveness)?
Do we have any info on how the costs scale, such that prediction could be made on saying that beyond X power output, making the reactor larger might be possible, but begins to be less cost-effective than simply building an additional, smaller reactor?
Based upon the fact that you guys mentioned that the power output is supposed to scale as a power of the radius and magnetic field, it seems like, for the most part, unless costs also scale to an even larger power, that the larger you can make this, the cheaper (per W) the output power should be?
I suspect there is no real limit to the total output, after all, one can always make it bigger in size without going higher in magnetic power. But the power density is likely to be limited by material issues, heat flux, neutron flux...
There may be a final limit out there somewhere, but not till well beyond reasonable power sizes.
There may be a final limit out there somewhere, but not till well beyond reasonable power sizes.
A thermalized machine might scale in volume indefinitely, until it collapsed under it's own weight, or the stresses on the magnets became unbearable. But, in a near monoenergetic , radially dominated ion movement machine like a Polywell, as the diameter increased, the distance an ion, whether a fuel ion or fusion produced ion, traveled per orbit/ oscillation (multiplied by the expected orbits before being lost to the system) would increase. Once this approached , or exceeded the Coulomb mean free path for that particle (especially the fusion product ions which are traveling to fast to participate in the edge annealing process) there would be significanty increasing thermalization of the system, destroying the claimed advantages that make these machines work. You would eventually end up with a thermalized Tokamak like plasma that has poorer confinement compared to a Tokamak.KitemanSA wrote:I suspect there is no real limit to the total output, after all, one can always make it bigger in size without going higher in magnetic power. But the power density is likely to be limited by material issues, heat flux, neutron flux...
There may be a final limit out there somewhere, but not till well beyond reasonable power sizes.
[EDIT] Assuming these or other concerns do not apply, the maximum piratical size for 10^7 power scaling would be perhaps a diameter of 12 meters if the magnets are also scaled up. EG: If a 3 M X 10Tesla D-D machine generates 100 MW. A 12 M diameter machine with 40 Tesla magnets would produce ~1.5 Terra Watts. The input power costs (r^2) would go up ~ 16 X (perhaps several hundred MWif the starting input power was ~ 10 MW). And, assuming the reactor didn't melt into a pool of slag.
Something doesn't look right here. Where am I going wrong? I guess this is an example of how much more important the magnetic scaling is, especially if it is free (with steady state superconducting magnets). Having a machine that can can actually survive is more dependent on size scaling so that it can handle the thermal wall loads. In the example above, if the magnetic strength is maintained at 10 T, the power out would be ~ 6 GW
Dan Tibbets
Last edited by D Tibbets on Tue Jun 15, 2010 4:24 pm, edited 2 times in total.
To error is human... and I'm very human.
If you are using SC magnets the field is limited by the magnetic field quench limit.
What that means in practice (approximately) is that a 10T 2m magnet will be a 5T magnet at 4m. Other than using different wire with a higher quench limit there is nothing you can do about it.
In fact with SCs your power increases linearly for smaller sizes - limited by the physical size of the coils because of the B^4 scaling and magnet scaling. Perverse innit. Useful though.
What that means in practice (approximately) is that a 10T 2m magnet will be a 5T magnet at 4m. Other than using different wire with a higher quench limit there is nothing you can do about it.
In fact with SCs your power increases linearly for smaller sizes - limited by the physical size of the coils because of the B^4 scaling and magnet scaling. Perverse innit. Useful though.
Engineering is the art of making what you want from what you can get at a profit.
Since, according to the formulas, the power output should scale with both the radius of the magnetic 'wiffle ball', as well as the magnetic field, and since the magnetic field is being generated by electromagnets, can the output of a polywell, theoretically, be changed on demand by simply changing how much current is flowing through the electromagnets?
That is, if you have, say, a 100MW reactor, and market demand drops down to, say, 50MW, can the operator simply turn down the current to the magnets a little bit to reduce the power output?
I realize that, because of the scaling, if you try to drop the power too much, you'll end up in a situation where it requires more power to operate the reactor than it is generating, but if you have very precise control of the magnetic field, seems like you should be able to pick any power output above that break-even point?
That is, if you have, say, a 100MW reactor, and market demand drops down to, say, 50MW, can the operator simply turn down the current to the magnets a little bit to reduce the power output?
I realize that, because of the scaling, if you try to drop the power too much, you'll end up in a situation where it requires more power to operate the reactor than it is generating, but if you have very precise control of the magnetic field, seems like you should be able to pick any power output above that break-even point?
jsbiff,
I can't think of a reason why not offhand. But I'm not sure how they're planning on balancing the plasma density against the B field to hold the system at beta = 1; presumably this is a function of the electron/ion drives. The economics could be a bit unfriendly -- in a reactor you would probably want to run at max power as much as possible, because costs are r**3 -- but there might be circumstances where fractional power would sometimes be advantageous, say on a Navy vessel.
(As a sidenote -- the superconducting magnets in a reactor won't draw much additional current once they're running. They do no work, they just establish a boundary of sorts. This is a confusing detail (it certainly confused me when I was introduced to it) but once the magnets are powered up the only current is to replace losses from resistance (which will be tiny in a superconductor). This is different than, say, an electric motor, which does do work and needs a constant input.)
I can't think of a reason why not offhand. But I'm not sure how they're planning on balancing the plasma density against the B field to hold the system at beta = 1; presumably this is a function of the electron/ion drives. The economics could be a bit unfriendly -- in a reactor you would probably want to run at max power as much as possible, because costs are r**3 -- but there might be circumstances where fractional power would sometimes be advantageous, say on a Navy vessel.
(As a sidenote -- the superconducting magnets in a reactor won't draw much additional current once they're running. They do no work, they just establish a boundary of sorts. This is a confusing detail (it certainly confused me when I was introduced to it) but once the magnets are powered up the only current is to replace losses from resistance (which will be tiny in a superconductor). This is different than, say, an electric motor, which does do work and needs a constant input.)
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
Not with superconducting magnets. The whole advantage of them is that once you load them up with current, then they are steady state, without need for further energy input. If you drain some of the charge, you need to put in new energy to ramp the superconducter back up. You might have a supplemental copper coil magnet on the superconducting magnet, but why? Well, possible some oscillation of the magnetic field might end up being needed to optimize performance. But for merely adjusting the power output, you have two convenient control knobs. Either decrease fuel flow, and/ or decrease the drive potential. Response times should be small fractions of a second.jsbiff wrote:Since, according to the formulas, the power output should scale with both the radius of the magnetic 'wiffle ball', as well as the magnetic field, and since the magnetic field is being generated by electromagnets, can the output of a polywell, theoretically, be changed on demand by simply changing how much current is flowing through the electromagnets?
That is, if you have, say, a 100MW reactor, and market demand drops down to, say, 50MW, can the operator simply turn down the current to the magnets a little bit to reduce the power output?
I realize that, because of the scaling, if you try to drop the power too much, you'll end up in a situation where it requires more power to operate the reactor than it is generating, but if you have very precise control of the magnetic field, seems like you should be able to pick any power output above that break-even point?
Dan Tibbets
To error is human... and I'm very human.