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

[Art Carlson]

A more detailed treatment of the issues in shielding, and direct conversion is in the below link. Reference # 4 (if you can acess)apparently deals with the shielding issues of the fission rocket Bussard was involved with in the 1960's.

Is he thinking only of manned missions? He only mentions it once. I don't see why shielding would be such a critical problem for payload flights.

If you can get 98% efficient direct conversion, like he claims, then aneutronic fuels would have a big plus in lower cooling needs. On the other hand, this figure seems to be predicated on his statement, "Since the fast fusion product alpha particles from p11B fusion appear at relatively precise energies (a result of the unique decay scheme of 12C*)", which, as has been discussed before on this forum, is at least partial nonsense.

[TallDave]

The Lawson criterion most certainly does apply to the polywell, though in a modified form. In a D-T, thermal concept, 20% of the fusion power is available free for heating the plasma. In a polywell, instead of the fixed 20%, you need to take the product of the conversion efficiency of fusion power to electricity times the recirculating power fraction..

Sure, if you squint hard enough you can come up with something Lawson-y that sort of applies, but to shoehorn it in you're forced to include things outside the plasma to satisfy a plasma condition (ignition) that was defined under the assumption of a neutral thermal plasma and doesn't mean much in IEC anyway. Very kludgy. It's much simpler and more coherent to just say it doesn't apply because Polywells don't ignite.

[Art Carlson]

It's much simpler and more coherent to just say it doesn't apply because Polywells don't ignite.

I couldn't agree with you more. It complicates things terribly to ask under what conditions a device could produce usable power.

(It was D Tibbets that brought up the question of which fuel cycles were "harder". Let's blame him!)

But it's really not that painful. A polywell of a given volume and field strength will require some particular amount of drive power to sustain it. For a self-sustaining power plant, the conversion efficiency has to exceed drive power divided by output power. The fuel cycle with the larger output power will require a proportionately smaller conversion efficiency, which seems like a good figure of merit to evaluate the relative ease of various fuel cycles. Of course, if that efficiency is ridiculously high or ridiculously low for all fuel cycles under consideration, who cares? But if making your Mr. Fusion work is hard but not impossible, it's something you should keep in mind.

[TallDave]

It complicates things terribly to ask under what conditions a device could produce usable power.

That's a different and much more applicable question than whether it satisfies Lawson.

An even more applicable and complicating question would be where can it produce copious amounts of useful power, and even yet more interesting question would be where can it do so economically. Notice we are getting further and further, though, from properties of the plasma itself.

Possibly I'm just tired of people asking why it doesn't ignite.

I don't know where the idea comes from that "getting really high temperatures is very hard" in a tokamak.

Well, relative to IEC. The first tokamak was exciting because it reached 1 kEv.

[MSimon]

Art,

For SSTO cooling can be done quite effectively with the appropriate reaction mass. No radiators required.

For long missions a reduction from 50% waste heat to 15% is significant. It reduces radiator rqmts by a factor of 3. And if the radiators can be run at higher temps - even more.

[Art Carlson]

It complicates things terribly to ask under what conditions a device could produce usable power.

That's a different and much more applicable question than whether it satisfies Lawson.

But the numbers are the same. The thermal Lawson criterion is exactly the condition required to achieve excess power with eta = 20%. And the ratio of eta for different fuels is exactly the ratio of the Lawson criteria for those fuels.

An even more applicable and complicating question would be where can it produce copious amounts of useful power, and even yet more interesting question would be where can it do so economically. Notice we are getting further and further, though, from properties of the plasma itself.

A figure of merit always sweeps a lot of important things under the rug. It's useful nonethless.

Possibly I'm just tired of people asking why it doesn't ignite.

Things will improve one day, come the FAQ.

[ohiovr]

Things will improve one day, come the FAQ.

There is some work on a FAQ over here:

http://www.ohiovr.com/polywell-faq/inde ... =Main_Page

just fyi

[TallDave]

But the numbers are the same.

Well, not really, unless I'm missing something. Lawson's criterion was calculated assuming a Maxwellian distribution, wasn't it?

The volume rate f (reactions per volume per time) of fusion reactions is [unpastable] where σ is the fusion cross section, v is the relative velocity, and < > denotes an average over the Maxwellian velocity distribution at the temperature T.

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

In nuclear fusion research, the Lawson criterion, first derived[1] by John D. Lawson in 1955 and published[2] in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the products of the fusion reactions is sufficient to maintain the temperature of the plasma against all losses without external power input.

A Polywell doesn't heat the plasma with fusion products. The fusion products might indirectly power the electron drive to offset electron losses, or they might not, and either way we're introducing outside elements. I think it's a little too loose a usage of the term, given that Lawson's is intended for magnetic confinement schemes, and leads people to make confused assumptions. I suppose it's a minor quibble.

[MSimon]

Your quibble seems valid to me Dave.

How hot is a bullet that has a temperature of 4K if it is traveling at 2,200 m/sec? And for simplicity let us assume a Newtonian Universe so we can avoid frame of reference arguments.

We can say that the bullet temperature is around 300 K. But that confuses the picture. You are mixing domains. Esp. When plasma fusion by heating depends on the hot tail while fusion from acceleration depends on velocity (and yeah that is a broad brush picture - still).

Now this is not so important for those of us who have been in the game for a while. But it will confuse newbies. I have seen it.

[icarus]

MSimon:

How hot is a bullet that has a temperature of 4K if it is traveling at 2,200 m/sec? And for simplicity let us assume a Newtonian Universe so we can avoid frame of reference arguments.

Actually you do need to consider frame of reference arguments even for Newtonian mechanics, the seat of modern physics is Galilean transformations of Cartesian reference frame. For instance, I could be travelling at 2,200 m/s parallel to the bullet and measure a different energy of the bullet than the someone stood still (i.e. the guy who measured 2,200).

The question is does he measure the 4K temperature of the bullet in the ref. frame stood still or the frame moving with the bullet?

Of course, the root problem with this whole confusion is the ease with which some people switch between energy and temperature. They slip into conflating the definitions of bulk properties, e.g. temperature and pressure with definitions of individual particle properties, e.g. energies and momentums.

The Maxwell-Boltzmann distribution does relate bulk to individual properties to some extent, using a statistical distribution, but it is not that simple. Using temperatures for individual particles is nonsensical generally and therefore using E~kT is a fraught minefield for the uninitiated. In the case of the Polywell (and other IEC concepts), it is safer to stick to talking about "fusion energies" of particles rather than "fusion temperatures", which are more applicable in thermalised plasma situations where there are easily predictable relationships between bulk temperature properties and particle energy distributions.

Unless someone would like to rigorously define temperature for a point particle?

[ohiovr]

Unless someone would like to rigorously define temperature for a point particle?

Evidently it has been done before:

http://jick.net/~jess/hr/skept/E_M/node14.html

Can this be correct?

[icarus]

I rest my case. The confusion is complete and widespread.

Temperature is a bulk property, defined by the laws of thermodynamics and within a framework of other bulk properties like entropy, density and pressure. You can ascribe a "temperature" to a particle, using Boltzmann, but can you also give the particle a density, entropy or a pressure? It is nonsensical and introduces confusion to use temperature in that way.

[MSimon]

MSimon:

How hot is a bullet that has a temperature of 4K if it is traveling at 2,200 m/sec? And for simplicity let us assume a Newtonian Universe so we can avoid frame of reference arguments.

Actually you do need to consider frame of reference arguments even for Newtonian mechanics, the seat of modern physics is Galilean transformations of Cartesian reference frame. For instance, I could be travelling at 2,200 m/s parallel to the bullet and measure a different energy of the bullet than the someone stood still (i.e. the guy who measured 2,200).

The question is does he measure the 4K temperature of the bullet in the ref. frame stood still or the frame moving with the bullet?

Of course, the root problem with this whole confusion is the ease with which some people switch between energy and temperature. They slip into conflating the definitions of bulk properties, e.g. temperature and pressure with definitions of individual particle properties, e.g. energies and momentums.

The Maxwell-Boltzmann distribution does relate bulk to individual properties to some extent, using a statistical distribution, but it is not that simple. Using temperatures for individual particles is nonsensical generally and therefore using E~kT is a fraught minefield for the uninitiated. In the case of the Polywell (and other IEC concepts), it is safer to stick to talking about "fusion energies" of particles rather than "fusion temperatures", which are more applicable in thermalised plasma situations where there are easily predictable relationships between bulk temperature properties and particle energy distributions.

Unless someone would like to rigorously define temperature for a point particle?

It is worse than that. Do you define the temperature of the bullet by the average energy E=3kT/2? Or the most probable energy E = kT/2. So fundamentally you can't define the temperature of a particle. No matter what is says in some paper.

[Art Carlson]

But the numbers are the same.

Well, not really, unless I'm missing something. Lawson's criterion was calculated assuming a Maxwellian distribution, wasn't it?
...
A Polywell doesn't heat the plasma with fusion products. The fusion products might indirectly power the electron drive to offset electron losses, or they might not, and either way we're introducing outside elements. I think it's a little too loose a usage of the term, given that Lawson's is intended for magnetic confinement schemes, and leads people to make confused assumptions. I suppose it's a minor quibble.

Just what are we quibbling about? Lawson made a number of reasonable assumptions, but some of these may not apply to a polywell. Are you arguing that we should throw out the whole question of the conditions necessary for net power? Why not look at his derivation and see how it has to be modified? The main thing is that you want to use a more general velocity distribution. Feel free! You can even leave the velocity distribution open and optimize it according to some criterion, like maximizing the gain. That's what Lawson did with the temperature and fuel mixture. Whatever your distribution is, you can calculate a pressure (possibly a tensor quantity), and you can calculate the reactivity by averaging <sigma*v> over whatever distribution you have. The absolute numbers you get out will be at most a factor of 2 or 3 different from those with a thermal distribution, and the relative numbers will be closer still. A useful start for any discussion! The details may shift your answers a bit, e.g. including bremsstrahlung will generally lead you to choose slightly lower energies, but don't throw out such a helpful concept just because some people have trouble applying it properly.

[TallDave]

Lawson made a number of reasonable assumptions, but some of these may not apply to a polywell. Are you arguing that we should throw out the whole question of the conditions necessary for net power?

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

Why not look at his derivation and see how it has to be modified?

Sure, but then you have to ask a lot of questions whose answers may be different from one IEC device to another, or even within the same device in different modes of operation depending on how you're turning the knobs (e.g. bremsstrahlung at different anode heights and different fuel mixes, how and whether you're recirculating power from the fusion products into the electron drive). The interior of a Polywell is complex and dynamic. 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.