looking for an equation, where is the main FAQ for polywell?

[Art Carlson]

No, I'm just arguing you shouldn't call them "Lawson" when referring to Polywells.

Alternate suggestions?

Lawson's criterion is a nice simple equation for a nice simple thermal plasma, and it applies nicely to magnetic confinement schemes where things are pretty similar.

It also applies, in the appropriate form, to inertial confinement fusion, where things are vastly different.

[TallDave]

How about just "requirements for net power?"

It also applies, in the appropriate form, to inertial confinement fusion, where things are vastly different.

Right. My point was just that all the magnetic confinement devices have basically the same thermal plasma with the same properties so Lawson's is a useful metric for all of them, whereas in IEC/Polywells there are so many different things going on (wiffleballs, electron oscillation/recirculation, anode heights, well depths, non-ambipolar losses,various schemes for power conversion, ion focussing, etc.) that Lawson's criterion doesn't do nearly as well in describing the basic conditions at which net power could be achieved for all such machines in all modes of operation.

[chrismb]

No, I'm just arguing you shouldn't call them "Lawson" when referring to Polywells.

Alternate suggestions?

Lawson's criterion is a nice simple equation for a nice simple thermal plasma, and it applies nicely to magnetic confinement schemes where things are pretty similar.

It also applies, in the appropriate form, to inertial confinement fusion, where things are vastly different.

Lawson's 1955 report [AERE GP/R 1807] *specifically* addressed "Some criteria for a useful *thermonuclear* reactor" and later was clear to state "It is of course easy to postulate..non Maxwellian [systems]. These systems are outside the scope of this report."

To spin Lawson into IEC applications surely must end up as an argument of reduction to the absurd - one ends up saying "useful power out > driving power in" which is obvious and need not be claimed to be a "Lawson" criterion. I cannot see what else there is to be drawn from trying to make parallels with the "Lawson criterion" and have no idea what useful analytical forms can be evolved beyond, as TallDave says, "net evolved power > 0"?!

[Art Carlson]

My point was just that all the magnetic confinement devices have basically the same thermal plasma with the same properties so Lawson's is a useful metric for all of them, whereas in IEC/Polywells there are so many different things going on (wiffleballs, electron oscillation/recirculation, anode heights, well depths, non-ambipolar losses,various schemes for power conversion, ion focussing, etc.) that Lawson's criterion doesn't do nearly as well in describing the basic conditions at which net power could be achieved for all such machines in all modes of operation.

1. wiffleballs
2. electron oscillation/recirculation
3. anode heights
4. well depths
5. non-ambipolar losses
6. various schemes for power conversion
7. ion focussing

1-5 affect the confinement time (or not) but they do not effect the minimum required value of the confinement time. 6 and 7 do not affect the relative requirement when comparing fuel cycles, but they do affect the absolute requirement, which is why I suggesting adding the conversion efficiency when interpreting the absolute numbers. Then instead of saying, like Lawson, "the product of n*T*tau must exceed 1e21 keV-s/m^3 for a thermal D-T plasma to ignite", you end up saying "the product of eta*n*E*tau must exceed 2e20 keV-s/m^3 for a reactor with a monoenergetic D-T plasma to break-even". [edit: adjusted numerical value down a factor of E_fus/E_ch = 5] I admit it can't beat the elegance of Lawson's criterion, but I insist it is a useful figure of merit and rough orientation on the feasibility of an IEC reactor. This is so obvious to me that I can't shake the feeling that Dave and Chris have some reason to avoid talking about hard numbers.

[MSimon]

Art,

I believe this point brought up by chris is telling:

Lawson's 1955 report [AERE GP/R 1807] *specifically* addressed "Some criteria for a useful *thermonuclear* reactor" and later was clear to state "It is of course easy to postulate..non Maxwellian [systems]. These systems are outside the scope of this report."

I think it is important to keep distinctions distinct. It makes language more useful.

[TallDave]

To spin Lawson into IEC applications surely must end up as an argument of reduction to the absurd - one ends up saying "useful power out > driving power in" which is obvious and need not be claimed to be a "Lawson" criterion.

Thanks, I think that's what I was trying to say. It's just not a good fit.

Lawson's paper, fwiw.

[Art Carlson]

Art,
I believe this point brought up by chris is telling:

Lawson's 1955 report [AERE GP/R 1807] *specifically* addressed "Some criteria for a useful *thermonuclear* reactor" and later was clear to state "It is of course easy to postulate..non Maxwellian [systems]. These systems are outside the scope of this report."

I think it is important to keep distinctions distinct. It makes language more useful.

I know Lawson limited himself to Maxwellian plasmas. I just made a straightforward extension of his calculations to fusion systems that rely on external drive. No problem with that, is there? If you're worried about the language, you're welcome to call it the Carlson criterion.

[Art Carlson]

To spin Lawson into IEC applications surely must end up as an argument of reduction to the absurd - one ends up saying "useful power out > driving power in" which is obvious and need not be claimed to be a "Lawson" criterion.

Thanks, I think that's what I was trying to say. It's just not a good fit.

Where's the problem? Lawson took the obvious statement that "useful power out > driving power in" and reformulated it in terms of plasma and confinement parameters for the case of self-heating plasmas. I took the same trivial statement and reformulated it in terms of plasma and confinement parameters plus conversion efficiency.

...

Hold the phone. Thank you. You have helped hone my thoughts. If the energy has to be converted by a thermal process, then eta is on the order of 30%. Detailed designs of direct conversion systems might give you up to 80%. Whatever. The important thing is that there is an upper limit: eta < 1. So let's just plug that in to eliminate the machine dependence that bugs Dave.

The product of n*E*tau must exeed 2e20 keV-s/m^3 for a reactor with a monoenergetic D-T plasma to break-even.

Does anyone think this statement is false? Does anyone think this statement is useless?

(I forgot to divide by 5 before, to account for the fact that I want to consider all fusion products, not just the charged products. This gives a more rigorous limit and is closer to the concept envisioned for IEC. What I am neglecting is the theoretical possibility to recover energy leaving the plasma as heat, rather than fusion products. That shouldn't be a big limitation, but I can even fold that in, if you insist. I have not recalculated <sigma*v> for a mono-energetic energy distribution. It should not be difficult, but it is not trivial because in a 3-D geometry you have to take collisions into account that are not head-on. I claim the number will be close to that for a Maxwellian distribution, but the important thing is not the actual value so much as the fact that such a number is well-defined.)

(I might also note that something always bothered me about the Lawson criterion, namely that too much physics is hidden in tau, whose value and scaling are complex and not known a priori. That doesn't stop the Lawson criterion from being universally considered useful.)

[MSimon]

the Carlson criterion

I like that.

[KitemanSA]

Polish and PUBLISH!!

[icarus]

MSimon:

Quote:
the Carlson criterion


I like that.

I would too if it was written up in one place with proper definitions, caveats, assumptions, sub-classes, legible equations, etc.

[hanelyp]

(I might also note that something always bothered me about the Lawson criterion, namely that too much physics is hidden in tau, whose value and scaling are complex and not known a priori. That doesn't stop the Lawson criterion from being universally considered useful.)

Yup, that tau factor hides a whole lot of complexity, including the differences between thermal and mono-energetic plasmas. So Lawson's criterion most certainly does apply to the polywell for the correct value of tau. What the correct value for tau is for a polywell may be a matter for further research.

[MSimon]

(I might also note that something always bothered me about the Lawson criterion, namely that too much physics is hidden in tau, whose value and scaling are complex and not known a priori. That doesn't stop the Lawson criterion from being universally considered useful.)

Yup, that tau factor hides a whole lot of complexity, including the differences between thermal and mono-energetic plasmas. So Lawson's criterion most certainly does apply to the polywell for the correct value of tau. What the correct value for tau is for a polywell may be a matter for further research.

In other words - with a big enough fudge factor I can turn road apples instantly into mackintoshes.

[chrismb]

There is an aspect of this discussion on 'Lawson' which has been overlooked, I think. The fact is that if the Lawson criteron had been found not to tie up with anything that was found experimentally, then it'd've been junked. As it is, this criterion, and even better the triple product, has become well-regarded because it has both a) a theoretical underpinning AND b) useful empirical value (extrapolation).

If (b) hadn't been found to hold for tokamaks, the Lawson criteria would've been forgotten long ago as an irrelevance. So, much as one might now seek some theoretical underpinnings for a polywell-equivalent criterion, it will be a very weak notion until empirical extrapolations show it is a practically useful figure.

[Art Carlson]

There is an aspect of this discussion on 'Lawson' which has been overlooked, I think. The fact is that if the Lawson criteron had been found not to tie up with anything that was found experimentally, then it'd've been junked. As it is, this criterion, and even better the triple product, has become well-regarded because it has both a) a theoretical underpinning AND b) useful empirical value (extrapolation).

If (b) hadn't been found to hold for tokamaks, the Lawson criteria would've been forgotten long ago as an irrelevance. So, much as one might now seek some theoretical underpinnings for a polywell-equivalent criterion, it will be a very weak notion until empirical extrapolations show it is a practically useful figure.

If you mean by that that we are flying blind with the polywell, I couldn't agree with you more. We don't even have one point of confinement time, much less the two points needed to make the most primitive and unreliable empirical extrapolation. The Lawson criterion is nice to put a variety of experiments on one graph to compare them and see how we are doing in the march to reactor conditions. Good for tokamaks, but far, far in the future for polywells. The Lawson criterion is also a handy way to get a handle on the relative difficulty of various fuel cycles. But until we have plausible evidence that a polywell can work with D-T, there's not much point in speculating about less reactive fuels.

I just got sucked into this game because there's nothing else to talk about. We need either some measured numbers from Rick or at least some bare details about the diagnostics he has available. How about it, Rick? Telling us how you diagnose particle energies and power balance wouldn't violate your NDA, would it?