Time for a possibly absurbly optimistic prediction

[D Tibbets]

Time for a possibly absurdly optimistic prediction.

Note the 'possibly' in the title. Using wildly optimistic, but at least possible, peramiters to figure the performance of an imaginary Polywell, and ignoring pesky problems like Bremsstrulung, plasma boundary arguments, thermalization, potential well shape, vacuum concerns, conversion efficiencies, material limits, etc, etc... a couple of example BFRs' (remember the threads proposing a name for a working Polywell fusion system?).
Estimates start from a base of 1 milliwatt output for WB6 , fusion crossection gains at higher voltages, and B4 r3 scaling.


Minimal Near break even size reactor:
Fuel D-D
Diameter = ~ 62 cm = ~ 10X size scaling
B -field = ~ 3.3 Tesla = ~ 1,000,000x scaling
Optimization of geometry = ~ 5X scaling
Potential well ~ 100,000 V = ~ 30X scaling

Multiply all of these together and the machine would have a fusion output of ~ 1,500,000 watts. Already near break even.
If the B- field was increased to ~ 6 Tesla, the output would be ~ 18 MW


WB 8 performance might be:
Fuel D-D
Diameter 43 cm (just for the heck of it) =~ 3X scaling
B-field = ~0.8 Tesla = ~ 4,000X scaling
Optimization of geometry (same truncated cube, but modification of nubs, spacing) = ~ 1.2 X scaling
Potential well ~ 30,000 volts = ~15X scaling

A maximal output for this imagined WB8 with these assumptions may be up to ~ 210 watts.

These are obviously extreme results, but they suggest that a 3 meter magrid diameter for a commercial reactor may be a very conservative goal, provided my assumptions are not too far off, and losses scale as hoped.

Such a reactor might have:
D-D fuel
Diameter = 300 cm = ~ 1000X scaling
B- field = ~ 3.3 Tesla = ~ 1,000,000X scaling
Optimization of geometry = ~ 5X scaling
Potential well = ~100,000 volts = ~30X scaling

Fusion output would be ~ 150 MW, even with this 'modest' magnetic strength. Even if there is no 'Optimization of geometry' gains past WB6 levels, only a mild increase in magnetic strength would compensate.
Losses for WB 6 was ~ 500,000 watts ( ~40 amp ( during the brief time when the machine was operating near Beta= 1 conditions) x 12,000 volts electron input, plus ~ 1000 amps x 12 volt magnet drive). I have seen Dr. Nebel mention 8 MW, but I don't know where this number came from, unless he was thinking of the power input for an anticipated break even system. I'm uncertain how the electron input energy would scale. If 80 amps at 100,000 volts is needed, that would be 8 MW. Increased power input to the stronger magnets would be relatively small even with copper wires (superconductors biggest advantage here may be avoidance of Ohmic heating and volume concerns, rather than need to maximize Q). How much more electron current would be needed to maintain a net excess of electrons over the increasingly heavy ion loading (and escaping charged fusion ion product unloading) is a mystery for me. I used a factor of two, merely because it matched my interpretation of Dr. Nebel's number (it is always convenient to cook the numbers ).


Dan Tibbets

[chrismb]

Time for a possibly absurdly optimistic prediction.

Note the 'possibly' in the title. Using wildly optimistic, but at least possible, peramiters to figure the performance of an imaginary Polywell, and ignoring pesky problems like Bremsstrulung, plasma boundary arguments, thermalization, potential well shape, vacuum concerns, conversion efficiencies, material limits, etc, etc... a couple of example BFRs' (remember the threads proposing a name for a working Polywell fusion system?).
Estimates start from a base of 1 milliwatt output for WB6 , fusion crossection gains at higher voltages, and B4 r3 scaling.

hmmm.....

Did I ever mention that tokamaks have got some extrapolated predictions too....? and they're based on actual experimental results rather than wild optimism!!

Not sure anyone will contest your figures, Dan, the questions, of course (as we well know) are; a) does it work as described, b) does it scale B^4? But, hey, let's get ahead of ourselves for a feel-good buzz. I'll always drink to that!

[MSimon]

Time for a possibly absurdly optimistic prediction. :wink:

Note the 'possibly' in the title. Using wildly optimistic, but at least possible, peramiters to figure the performance of an imaginary Polywell, and ignoring pesky problems like Bremsstrulung, plasma boundary arguments, thermalization, potential well shape, vacuum concerns, conversion efficiencies, material limits, etc, etc... a couple of example BFRs' (remember the threads proposing a name for a working Polywell fusion system?).
Estimates start from a base of 1 milliwatt output for WB6 , fusion crossection gains at higher voltages, and B4 r3 scaling.

hmmm.....

Did I ever mention that tokamaks have got some extrapolated predictions too....? and they're based on actual experimental results rather than wild optimism!! :wink:

Not sure anyone will contest your figures, Dan, the questions, of course (as we well know) are; a) does it work as described, b) does it scale B^4? But, hey, let's get ahead of ourselves for a feel-good buzz. I'll always drink to that!

Art Carlson, who is rather a sceptic, does not contest B^4 scaling. It is standard physics. What concerns Art is losses. On losses we have no handle at all.

[chrismb]

Art Carlson, who is rather a sceptic, does not contest B^4 scaling. It is standard physics. What concerns Art is losses. On losses we have no handle at all.

I may not dispute that 'a particualr mechanism' may scale as B^4, but the question is whether it is a dominant mechanism at the system level? The system will generally scale by the scaling of the most dominant mechanism.

Besides, I thought Art doesn't contest it because he views Polywell as functioning with a thermalised plasma? Not sure if his view would be different if you could persuade him to accept spherical ion beam convergence. I'll let him speak for himself...

[D Tibbets]

Time for a possibly absurdly optimistic prediction.

Note the 'possibly' in the title. Using wildly optimistic, but at least possible, peramiters to figure the performance of an imaginary Polywell, and ignoring pesky problems like Bremsstrulung, plasma boundary arguments, thermalization, potential well shape, vacuum concerns, conversion efficiencies, material limits, etc, etc... a couple of example BFRs' (remember the threads proposing a name for a working Polywell fusion system?).
Estimates start from a base of 1 milliwatt output for WB6 , fusion crossection gains at higher voltages, and B4 r3 scaling.

hmmm.....

Did I ever mention that tokamaks have got some extrapolated predictions too....? and they're based on actual experimental results rather than wild optimism!!

Not sure anyone will contest your figures, Dan, the questions, of course (as we well know) are; a) does it work as described, b) does it scale B^4? But, hey, let's get ahead of ourselves for a feel-good buzz. I'll always drink to that!

The problem with the Tokamac is that the extrapolated predictions seem to shrink as actual expermental results grow. With the Polywell ignorance is bliss!


Dan Tibbets

[Art Carlson]

Art Carlson, who is rather a sceptic, does not contest B^4 scaling. It is standard physics. What concerns Art is losses. On losses we have no handle at all.

I may not dispute that 'a particualr mechanism' may scale as B^4, but the question is whether it is a dominant mechanism at the system level? The system will generally scale by the scaling of the most dominant mechanism.

Besides, I thought Art doesn't contest it because he views Polywell as functioning with a thermalised plasma? Not sure if his view would be different if you could persuade him to accept spherical ion beam convergence. I'll let him speak for himself...

Are we talking about confinement time and power loss or are we talking about fusion power density? Fusion power density is E_fusion*n_1*n_2*<sigma*v>. There's not much to play with here. You have to do the <...> average right, which will depend on the velocity distributions, and you have to use the right profiles if you integrate to find total power. Then there's the pressure balance n*kT = B^2/2mu_0. This is a bit tougher. In its essence, this is Ampere's law plus the Lorentz force, pretty basic stuff. What I wrote as n*kT is actually a sum over all the species and all the velocities, and the equation should really be written as a differential. This form assumes a field-free plasma and a plasma-free magnetic field region, so you might have to watch the transition and be careful of where you measure the field (with curvature, the vacuum field will not be uniform). But all in all, the B^4 scaling of fusion power density is pretty robust, even with non-Maxwellian distributions.

Now the scaling of confinement time is a different kettle of fish ...

[Art Carlson]

The problem with the Tokamac is that the extrapolated predictions seem to shrink as actual expermental results grow. With the Polywell ignorance is bliss

Actually I suspect that ITER has always been within the error bars of the extrapolations. The reactor studies and PR hype have always concentrated on the optimistic side of the band. That's how life is. Unfortunately, as we have narrowed the error bars over the years, we did it by trimming off the optimistic side and leaving the pessimistic side where it was. Life is sometimes like that, too. It is legitimate statistics and legitimate science. No fraud involved. And no reason to expect ITER to work worse than predicted. (Which, I admit, is bad enough already.)

[chrismb]

But all in all, the B^4 scaling of fusion power density is pretty robust, even with non-Maxwellian distributions.

Now the scaling of confinement time is a different kettle of fish ...

Thanks for differentiating the two. I hadn't clarified that in my own mind, but that helps. Such that if confinement time scales as B^-4 then we're quits, and if it is B^-5, say, then we're where Zeta and pinches got to - ever-reducing stability at higher energies. Maybe it's a B^-2 term and there's some promise. Sounds like a guessing game to me at this stage.

[chrismb]

And no reason to expect ITER to work worse than predicted. (Which, I admit, is bad enough already.)

My main concern with ITER is that it carries 'false' objectives. It cannot produce viable energy, given, so its purpose is to develop stability and self-sustaining currents. Now I just think that's plain wrong-headed because a) we can do that with JET [sized] already and we should seek to get that 'right' and understood at that size first, there's plenty more to learn, and b)ITER carries so much energy in its plasma that in ELM disturbances the total wall/divertor loading becomes so high it can only take a few instances of this in its whole life, so it may be 'done-for' within a week of operation! Yet we don't yet know how to STOP these instances! So surely the money would be better spent improving understanding stability in JET sized experiments sufficiently (where the wall loading in ELM disruption events is tolerable) that we can then just make a single move to DEMO. I see ITER as a political compromise that achieves very little, possibly it may even mean tokamak research beings to fail because it's just the wrong thing to do and a negative result will raise questions on viability that just didn't need to be raised.

(Hey, cool, I've managed to tokamak-troll the thread into a different topic!! )

[EricF]

Time for a possibly absurdly optimistic prediction.

Note the 'possibly' in the title. Using wildly optimistic, but at least possible, peramiters to figure the performance of an imaginary Polywell, and ignoring pesky problems like Bremsstrulung, plasma boundary arguments, thermalization, potential well shape, vacuum concerns, conversion efficiencies, material limits, etc, etc... a couple of example BFRs' (remember the threads proposing a name for a working Polywell fusion system?).
Estimates start from a base of 1 milliwatt output for WB6 , fusion crossection gains at higher voltages, and B4 r3 scaling.

hmmm.....

Did I ever mention that tokamaks have got some extrapolated predictions too....? and they're based on actual experimental results rather than wild optimism!!

Not sure anyone will contest your figures, Dan, the questions, of course (as we well know) are; a) does it work as described, b) does it scale B^4? But, hey, let's get ahead of ourselves for a feel-good buzz. I'll always drink to that!

Art Carlson, who is rather a sceptic, does not contest B^4 scaling. It is standard physics. What concerns Art is losses. On losses we have no handle at all.

What category would solving practical problems such as losses fall under? Electrical or Mechanical Engineering, some branch of Physics?

[KitemanSA]

Art Carlson, who is rather a sceptic, does not contest B^4 scaling. It is standard physics. What concerns Art is losses. On losses we have no handle at all.

Didn't Dr.B. hve a section on loss mechanisms in his Valencia paper?

[MSimon]

hmmm.....

Did I ever mention that tokamaks have got some extrapolated predictions too....? and they're based on actual experimental results rather than wild optimism!! :wink:

Not sure anyone will contest your figures, Dan, the questions, of course (as we well know) are; a) does it work as described, b) does it scale B^4? But, hey, let's get ahead of ourselves for a feel-good buzz. I'll always drink to that!

Art Carlson, who is rather a sceptic, does not contest B^4 scaling. It is standard physics. What concerns Art is losses. On losses we have no handle at all.

What category would solving practical problems such as losses fall under? Electrical or Mechanical Engineering, some branch of Physics?

Measurement. To start. Once we know what we have we can more easily figure out who to ask.

[MSimon]

Art Carlson, who is rather a sceptic, does not contest B^4 scaling. It is standard physics. What concerns Art is losses. On losses we have no handle at all.

Didn't Dr.B. hve a section on loss mechanisms in his Valencia paper?

Yes. But it was theory. Mostly. What we now need is measurement.

A reactor that produces 100 mWf is probably good enough to get an idea of what is going on.

[Art Carlson]

But all in all, the B^4 scaling of fusion power density is pretty robust, even with non-Maxwellian distributions.

Now the scaling of confinement time is a different kettle of fish ...

Thanks for differentiating the two. I hadn't clarified that in my own mind, but that helps. Such that if confinement time scales as B^-4 then we're quits, and if it is B^-5, say, then we're where Zeta and pinches got to - ever-reducing stability at higher energies. Maybe it's a B^-2 term and there's some promise. Sounds like a guessing game to me at this stage.

The energy confinement time tau is defined as the energy content divided by the loss power, or equivalently the energy density divided by the loss power density. The coefficients depend on the assumptions you make, but the fusion power better be something close to the loss power if you want to make electricity. The energy density will be something close to the pressure. Putting it together,

tau_required ~ (W/V) / (P_f/V) ~ (n*T) / (n^2*<sigma*v>) ~ (n*T)^-1 * (<sigma*v>/T^2)^-1

(<sigma*v>/T^2) is a function of temperature that has a maximum near which we will want to operate (so that the requirement on tau is as small as possible), so (<sigma*v>/T^2) will be roughly constant near the operating point. The pressure (n*T) scales with B^2, so the confinement time *required* scales with B^-2, independent of the size. If the empirical confinement time increases with radius, then it helps to make the machine bigger, and if it decreases with field more slowly than B^-2, then it helps to go to larger field.

Thats the mathematical relationship, but I don't think it's very helpful, considering we have neither a verified theory nor published data.

[chrismb]

But all in all, the B^4 scaling of fusion power density is pretty robust, even with non-Maxwellian distributions.

Now the scaling of confinement time is a different kettle of fish ...

Thanks for differentiating the two. I hadn't clarified that in my own mind, but that helps. Such that if confinement time scales as B^-4 then we're quits, and if it is B^-5, say, then we're where Zeta and pinches got to - ever-reducing stability at higher energies. Maybe it's a B^-2 term and there's some promise. Sounds like a guessing game to me at this stage.

The energy confinement time tau is defined as the energy content divided by the loss power, or equivalently the energy density divided by the loss power density. The coefficients depend on the assumptions you make, but the fusion power better be something close to the loss power if you want to make electricity. The energy density will be something close to the pressure. Putting it together,

tau_required ~ (W/V) / (P_f/V) ~ (n*T) / (n^2*<sigma*v>) ~ (n*T)^-1 * (<sigma*v>/T^2)^-1

(<sigma*v>/T^2) is a function of temperature that has a maximum near which we will want to operate (so that the requirement on tau is as small as possible), so (<sigma*v>/T^2) will be roughly constant near the operating point. The pressure (n*T) scales with B^2, so the confinement time *required* scales with B^-2, independent of the size. If the empirical confinement time increases with radius, then it helps to make the machine bigger, and if it decreases with field more slowly than B^-2, then it helps to go to larger field.

Thats the mathematical relationship, but I don't think it's very helpful, considering we have neither a verified theory nor published data.

I'm aware the B^-2 result, which as you've shown, is the theory but that doesn;t even begin to address the lack of stability with respect to time. So I would suggest a realistic calculation cannot presume the instantaneous steady state, from which B^-2 derives, but must surely be worse than that because it's, frankly, just plain obvious that as the energy density goes up, stability drops and the B^-2 doesn't include a hint of accommodating stability - I guess??