We need a new film on YouTube explaining the Polywell.

[hanelyp]

We have a good estimate of ion and electron Vmax. Particle Vmin are quantities we're not so sure of, relevant to how well annealing works.

[mattman]

Hello All,

I actually found it hard to find agreement in sources for the relative size and mass of electrons, ions and D2 gas.

Here is what I had in: "Taking a stab at simulation"




Below is where I got my Info.



1. Pauling, Linus. College Chemistry. San Francisco: Freeman, 1964: 57, 4-5

2. Hyperphysics. Nave, R. "Atomic Radii." Ionization Energy. Georgia State University, n.d. Web. 15 Nov. 2012.

3. Yoon, Jung-Sik, Young-Woo Kim, Deuk-Chul Kwon, Mi-Young Song, Won-Seok Chang, Chang-Geun Kim, Vijay Kumar, and BongJu Lee. "Electron-impact Cross Sections for Deuterated Hydrogen and Deuterium Molecules." Reports on Progress in Physics 73.11 (2010): 116401. Print.

4. Elert, Glenn, Michael P, and Judy Dong. "Diameter of an Atom." Diameter of an Atom. The Physics Factbook, 1996. Web. 04 Nov. 2012. .

[KitemanSA]

The $64 question.

Must be one of those "left as an exercise for the student" or it would have been a $64,000 question! :0

[happyjack27]

Hello All,

I actually found it hard to find agreement in sources for the relative size and mass of electrons, ions and D2 gas.

Here is what I had in: "Taking a stab at simulation"
...
Below is where I got my Info.



1. Pauling, Linus. College Chemistry. San Francisco: Freeman, 1964: 57, 4-5

2. Hyperphysics. Nave, R. "Atomic Radii." Ionization Energy. Georgia State University, n.d. Web. 15 Nov. 2012.

3. Yoon, Jung-Sik, Young-Woo Kim, Deuk-Chul Kwon, Mi-Young Song, Won-Seok Chang, Chang-Geun Kim, Vijay Kumar, and BongJu Lee. "Electron-impact Cross Sections for Deuterated Hydrogen and Deuterium Molecules." Reports on Progress in Physics 73.11 (2010): 116401. Print.

4. Elert, Glenn, Michael P, and Judy Dong. "Diameter of an Atom." Diameter of an Atom. The Physics Factbook, 1996. Web. 04 Nov. 2012. .

...and you didn't think to try wikipedia? they probably have all those sources and then some, and then a lot more.

[happyjack27]

But the issue is, in the center where things are densest, when the ion is Vmax and the electron is Vmin, how fast are they moving?

electrons in the center, if practice resembles theory and simulation, are quite cold. forming a hollow spikey-ball. a little faster at the cusps, where they spin.

inside the spikey-ball, they are naught. the spikey ball is hollow. where the most fusion occurs; where the ions are densest and fastest, there are no electrons. except for maybe some brought in by tugging from the ions. and this may be where more of the crux of the question lies. but the net tugging is zero - at every concentric surface, the sum of ke out equals the sum of ke in, statistically, at equilibrium, not counting fusions. so it's more of an "adding fuzziness" to the ball's surface, than a pushing in or out.

ion max velocity is of course determined by its Periapsis, and its min velocity by its Apoapsis, given the voltage gradient from center to outside.

i understand some contend that the ions would be non-thermal. i.e., they'd share basically the same min and max velocity. however, i don't think this is true. it seems to me that all orbits are valid equilibrium solutions, and so the solution is a superposition of all orbits. i.e. you'd have some ions that only orbit through half the voltage, some through the whole voltage, etc. so at the center you'd have a mix of different velocities, and the distribution of said velocities would follow the distribution of orbit periods. ($64 please! ) (another question is what is the distribution of orbit eccentricities? i would guess that they would remain pretty eccentric - but can't validate that with any hard reasoning.)

it think it would be nice to see a 2-dimensional plot, with Periapsis on one axis and Apoapsis on anther, and then probability density would be the z-dimension. also it would be nice to see the same thing, but instead with period and eccentricty as the x and y. i'm sure the orbits are by no means this simple, but i'm sure there's a way to get some sort of quasi-statistics like this out of it.

i.e peak voltage (= distance from center) of the "orbit" on one axis and kinetic energy at that peak (which by definition would all be axial) on another, and on the z-axis as usual would be the probability density. and here we'd call an "orbit" simply reaching a radial velocity of zero; a local maximum/minimum. and so every time that it's detected, we mark its voltage (or distance from center, either way) on one axis, and its axial KE on another. at the end we have a bunch of coordinate pairs, and then we can "bin" these into X by X squares and count them up so we can make a plot (or do a guassian convolution, or whatever, point is, we can turn the set of discrete samples into a surface) from the combination of the 2 coordinates we can determine if its a "quasi-Periapsis" or "quasi-Apoapsis". but it's no matter, anyways, since all of the quasi-Periapsis will be on one side of the graph and all the quasi-Apoapsis on the other; we can always in the end just draw a curve that splits the two. and then of course everything _on_ the curve is a circular orbit. and then we have a map of ion trajectories! the min velocities are all the axial ke's (converted to speed by solving Ke=mv^2/2 for v) on the quasi-apoapsis', and the max velocities are all the axial ke's on the quasi-periapsis'.

[happyjack27]

5.) is wrong. it should be:

net power = fusion power * conversion efficiency - losses.

you have:

net power = (fusion power - losses) * conversion efficiency

the losses are always 100%, regardless of the conversion efficiency. you're paying for your losses out of your power * efficiency budget. if that's below your losses, you're consuming more energy than you're getting out.

a subtle difference, but a big difference.

[ladajo]

Happy, I tend to think along your thinking as well for the core dynamics. However, it is a complex device, and there may be other factors at play. Of course these will change again as you make it physically bigger or smaller.

[happyjack27]

and to add to my question on eccentricty - my understanding of "annealing" with regard to ions, is essentially this logic: at the outer edge, the ions are at their apopsis, i.e. travelling the slowest, and therefore a) spending their most time, and b) at low KE. unlike celestial bodies, however, they will be interacting with each other via the electric force. at this point is mostly, since it's their apoposis, their KE is mostly axial, or more precisely, it has the highest ratio of axial ke to radial ke as it does in its whole orbit, except for possibly at its periopsis. and since they all repel each other and there's not a lot of electrons there (relatively) to "mediate" (cancel out or otherwise redirect their repulsion), they're going to go to, well, the "lowest energy", electromagnetically, which, while isn't neccessarily a net axial KE of zero from any absolute reference frame, IS neccessarily them all having the SAME axial KE and being evenly spaced. essentially you get the same situation as the electrons in the core, they, like ice, are nonlinearly attracted towards a "solid" phase where the ions are regularly spaced and have synchronized velocities.

essentially picture this: put a bunch of postively charged ball bearings inside a hollow ball, in zero gravity (e.g. outer space). they will space themselves out evenly on the surface. now shake the ball. what happens? all the ball bearings will start to spin, TOGETHER, in one direction.

now the picture is a bit more complicated, because you also have a force normal to that spinning pulling them back towards the center, and once it pulls them a bit, it's no longer normal to their current velocity vector, etc. and what you have is a considerably more complicated calculus problem, which gets more complicated pretty quickly when you start to consider not only the balls with the same r coordinate (in polar coordinates) but the ones at higher and lower r coordinates interacting with your r-coordinate sphere.

now it seems to me that it would have the effect of increasing the eccentricty of orbits. but i can't do that math in my head. in any case it is important to note that there are really two orthogonal questions here: orbit eccentricity distribution, and orbit apopsis (highest point) distribution. (how the orbit "spins" relative to the core is not really that important. we might as well just picture the core spinning relative to the orbit -- so what?) while the apopsis's might be thermalized - the eccentricities might not be.

[happyjack27]

... It would serve to increase the eccentricity of the orbits. Just picture each r=x surface as independent, them you have the same annealing effect between radii.

But then you could argue - well maybe at first, but can't it find an equilibrium where everything orbits at the same low eccentricity orbit? True, but two things:
1) you're dealing with a lot of particles, so there will be a lot of synchronizing towards the average velocity before it reaches equilibrium. (And the fact that it will be a lot faster in terms of radians per second close to the center is irrelevant - that's just a fact of geometry). 2) and gerr's the kicker: every orbit with axial velocity on one direction while approaching the center will have exactly the opposite velocity when going away from the center, thus the average axial velocity at every radii will always be exactly zero. (Discounting relative overall spin of the orbit -which can be considered as an orthogonal / separate effect altogether.)

Now the only thing left ...maybe... is the net "spin" of the whole ion cloud...


Oh, did I say "I can't do that math in my head."? It appears i just did! (Self adulation)

[happyjack27]

Happy, I tend to think along your thinking as well for the core dynamics. However, it is a complex device, and there may be other factors at play. Of course these will change again as you make it physically bigger or smaller.

if this was facebook I'd give you a like!

[KitemanSA]

But the issue is, in the center where things are densest, when the ion is Vmax and the electron is Vmin, how fast are they moving?

electrons in the center, if practice resembles theory and simulation, are quite cold. forming a hollow spikey-ball. a little faster at the cusps, where they spin.

inside the spikey-ball, they are naught. the spikey ball is hollow.

I disagree with your model. While in operation the electrons fill a rough sphere that includes most of the volume of the MaGrid. The electrons travel with significant radial motion frequently passing near the center. Wiffle Ball old boy!

[happyjack27]

Happy, I tend to think along your thinking as well for the core dynamics. However, it is a complex device, and there may be other factors at play. Of course these will change again as you make it physically bigger or smaller.

if this was facebook I'd give you a like!

As regards scale, though, your issues are engineering issues, and by tht I mean specifically structural issues. You can scale injection and e and m fields and vacuum pretty liberally. And by the time you run into engineering constraints, it's all about the magri an vacuum chamber and electron guns and puff gas I injection. And you can always make then small enough to get at least optimal performance from the other variables. So all the engineering issues are net power issues; all the physics are already solved at that point, otherwise the engineering issues are moot. So the thing to do is to solve the physics issues. And that means you have to make some simplifications, and go from there, and then after that figure out why they're wrong, and then find new ones that aren't wrong in that respect, and then repeat. Any method to solve a non-trivial problem will involve repetition. If you think there's a solution that involves less steps, ask a computer programmer. Thi computer programmer says that what he just said is true to the degree of his intellect.

[D Tibbets]

More accurately , net power out is = fusion power * conversion efficiency of fusion ion KE, plus conversion efficiency of heat from input power. If a steam cycle, the output conversion and input loss conversion may both be ~ 25-30%. or perhaps a little higher if heroic efforts are dedicated to the steam cycle. If direct conversion of fusion ions (like with P-B11 and to a lesser extent with D-D) the fusion output net electricity may be up to ~ 80% (or possibly higher) of gross fusion output. Input derived electrical output may still be ~ 30% as would be that portion of fusion ion or neutron energy, or gamma energy harvested thermally.

Steam conversion might be neglected if direct conversion is good enough. This eases some considerations but would not eliminate the need for active cooling.

An example for a P=B11 plant might be Fusion output of 100 MW, input power of 10 MW.
This could result in ~80 MW of electrical power from direct conversion, and 30 MW of waste heat. If the wast heat is run through a steam cycle, a further ~ 10 MW of electrical power might be generated and ~ 20 MW of residual waste heat would have to be disposed of.

Dan Tibbets

[D Tibbets]

The kinetic energy of the electrons and the ions at different radii in the Polywell is complex.
Electrons have a large component of radial velocity upon initial injection or recirculation. My impression is that this is ~ 80% of the total energy as the potential well is ~this strength relative to the injection voltage (in WB6). The electrons by themselves would be expected to quickly gain angular momentum/ transverse energy at the expense of radial speed. How much is dependent on this relaxation rate relative to the containment time and if there are any restoring forces. One restoring force is the ions. They tug the electrons inward to a modest (?) extent. Bussard mentioned this as the cause of a stable parabolic potential well formation versus a square (electrons in near circular orbits at the Wiffleball border) potential well that exists with the pure electron stage.

Ion presence also modifies the potential well due to confluence of the ions (along with tugging electrons inward). If there is any confluence the concentration of ions will increase towards the center. This not only effects the density/ fusion rate considerations, it also eats into the electron generated potential well. The potential well negative voltage drops back towards zero. This is referred to as the virtual anode and there are tolerable limits. Bussard mentioned (I recall) a maximum central virtual anode of ~ 20% of the maximum negative potential well. Much greater and things fall apart. This means there is a limit to the amount of ion confluence (central focus ) that is possible.

I am uncertain if the ions slow as they approach the middle due to the virtual anode as the net space charge remains negative (just not as negative), but the acceleration profile would be modified and more complex.
Add to this other variations in the potential well that might be occurring naturally due to plasma waves, etc; and then add additional intentional variations like with POPS and the potential well and the behavior of charged particles within it becomes extremely complex.

PS: If ions restores electron radial vectors, then it should increase the angular momentum of the ions (there are no free rides). Why this is permissable is presumebly due to annealing of the ions. Each time the ion reaches the Wiffleball border region its radial velocity drops toward zero and the annealing process constricts the ion velocities to a small range-resets the ion energy spread to a small number. I'm uncertain of the relationship between the ion radial velocity and transverse (angular momentum) velocity. I suspect that so long as a dominate portion of the ion velocity is radial the net vector velocity in the border region will be set to very low velocities because the sum of the velocities is still so low that the [edit- colisionality, not conditionality] results in a net average speed with a thermal spread close to zero. If the total energy is 1 eV radial and 100 eV transverse, the collisionality would force a net energy somewhere in between. Thus radial thermalization is is limited to a small range, and so is transverse thermalization, though perhaps only within limits.

Dan Tibbets

[happyjack27]

ya, no. you said nothing there to explain why ions would prefer one set of radial energies over another; one apsis over another.