forming a good wiffleball

[happyjack27]

from my simulation runs, it seems the most important thing is to get the electrons as close to zero kinetic energy at the exact center as possible.

short of starting them out that way (ionization?), i suppose to inject them there you'll have to start them out at zero energy at their electric-potential-counterpoint - i.e. a point outside the magrid with electric potential (i.e. voltage) exactly equal to the electric potential at the exact center. (this is where the positive charge on the magrid comes in very handy.) any closer (lower electric potential) and you'll have to start them out with higher KE to compensate, such that KE+PE = electric potential at center.

furthermore, to get them through the mag field, you'll have to shoot it right down the cusp, and your aim will have to be VERY accurate. and the stronger the mag field the more accurate your aim needs to be.

i'll post a video of a 3m radius iterated octahedron magrid where i started the electrons on the surface of a sphere at the center of radius 0.01m at zero KE. I cut off the first part of the video because it's very uneventful (in a good way).

(EDIT) here's the video:

http://www.youtube.com/watch?v=LfmoOYGGayU

[happyjack27]

conversely, btw, you presumably want the ions traveling at a very specific non-zero KE through the center. they will thus be oscillating back and forth. since they are so much heavier their speed will be so much less than the electrons and thus they will not be affected very much by the mag field. their behavior will be dominated by electrostatic forces, so they will pretty much act as any particle would in the presence of a point charge (radial voltage gradient), they will oscillate back and forth about it.

so your ion injection points and energies are ruled by completely different considerations. instead of their initial radial KE+electric PE being exactly equal to the electric potential at the center, you want it to differ by exactly the amount that will give it the largest cross-section for fusion. maybe a little more so that the region in which it is at peak fusion velocity is the surface of a small sphere, rather than a point. i'm sure some basic calculus could figure out the optimal point.

[D Tibbets]

Ideally, the ions would come to a point in the center at their greatest velocity. Bussard even mentioned a 'black hole effect' where the central ion density is so great that the ions collide so much during one pass through this region, there is essentially zero chance the ion could escape this region before participating in a fusion reaction. Of course, the real situation is different. Even with good central focus/ confluence. As the ions converge towards the center, the become dominate over the electron space charge and the ions start slowing as they build up a central virtual anode. Some of this may be desirable, but too much will destroy the potential well. I recall (I think) that ~ 20% central virtual anode formation(compared to the negative potential well) is the upper tolerable limit. As the ions have a lot more inertia, some electrons are dragged towards the center with the ions. This is what converts the initial pure electron based square potential well into an elliptical (or parabolic potential well.This would help to decrease the virtual anode, but it also can lead to more bremsstrung radiation. Despite what Art Carlson claimed (leading to bipolar cusp flows) the opposite does not occur in significant amounts, again due to inertia differences between the electrons and ions, but mostly because of the excess electrons in the system that created and maintains the negative potential well.

Also, I cringe when you speak of the magnetic field accelerating the particles towards the center. The magnetic fields turns the particles (electrons primarily) but do not accelerate them. Think of the magnetic field as a pool table. The ball will bounce off the edges, but the energy (acceleration) comes from the pool cue (E-Gun at low voltage and an accelerating magrid, or a high voltage E-gun alone (magrid grounded)).
The pockets of the pool table are the cusps. In part the Wiffleball effect can be visualized as converting the pool table, into a snooker table with smaller pockets/ cusps.

Also, remember Gauss's Law. The electrons see the positive charge on the magrid only when they are outside of the magrid. Inside of the magrid, neither the electrons or ions see the charge on the magrid . The potential well and complex interactions between the electrons and ions is derived only from the momentum of the electrons that is provided by their initial injection energy and direction (and of course the relative numbers of electrons to ions, radial and transverse thermalization issues, annealing, debye considerations, two stream instabilities, etc., etc.). Recirculation occurs as the electrons exit through a cusp to the outside of the magrid. I assume the electrostatic potential on the magrid then becomes the dominate interaction, and the old electron is reborn and is indistinguishable from a virgin young electron from the electron gun. Any ions reaching this height would immediately be accelerated to the walls. But this is apparently a rare occurrence because this distance from the center is beyond the potential well top for the 'normal' ions and edge annealing impedes otherwise troublesome up-scattering of the ions.

In your simulations, the magnetic field should be only a rebounding surface (thus Bussard's analogy to a Wiffle Ball Toy in which marbles bounce around inside and only occasionally escape because the holes are only slightly larger than the marbles), unless you wish to also include the mirroring effects which complicates the picture. For simplicity, the magnetic field can be ignored from the ions perspective, as their containment is purely due to electrostatic effects from the magnetically contained excess electrons. This isn't always completely true, but close enough..

Dan Tibbets

[happyjack27]

In your simulations, the magnetic field should be only a rebounding surface (thus Bussard's analogy to a Wiffle Ball Toy in which marbles bounce around inside and only occasionally escape because the holes are only slightly larger than the marbles), unless you wish to also include the mirroring effects which complicates the picture.

in my simulation the mag fields are biot-savart + lorentz force equations acting on individidual electrons (and/or ions), with relativists corrections via lorentz transforms (to "proper inertia" and back). magnetic mirroring is a consequence of the lorentz force, so with sufficient temporal resolution the magnetic mirroring effect is included in the simulation.

thanks for correcting. where i said "accelerate" i should probably have said something more like "pressure".

and thanks for the reminder of gauss' law (a hollow sphere has no voltage gradient). very poignant and helpful for me to visualize and understand the physics.

(the KE=0 at ~center simulation is still running, btw, as dense and stable as ever)

[chrismb]

Bussard even mentioned a 'black hole effect' where the central ion density is so great that the ions collide so much during one pass through this region, there is essentially zero chance the ion could escape this region before participating in a fusion reaction.

...jeezuz.... did Bussard actually say this?

We've done this before.. the best fusion cross-section of all time is 5E-28m^2, so assuming the core is no bigger than 10 cm, and with the best will in the universe, that'd mean the density was of the order of 1/[0.1]x[5E-28] = 1000 x atmospheric particle density.

The other part of it is that if each particle spent 1E-7s in the core (that's taking pretty much the slowest time possible for fusible velocities, of 1Mm/s as the particle velocity) then it means the 1E25 particles in that core would be reacting in that time scale, if they all get to react, so that'd be 1E32 reactions per second. Assume 5MeV per reaction and we get a power output of ~10^20W.

really?????...... Are we really talking about 100,000 petawatts from a 10 cm diameter, 1E28/m^3 reaction volume? Approximately a million times the average total power consumption of the planet?

Just excuse me a moment whilst I run away back to reality.....

[KitemanSA]

We've done this before.. the best fusion cross-section of all time is 5E-28m^2, so assuming the core is no bigger than 10 cm, and with the best will in the universe, that'd mean the density was of the order of 1/[0.1]x[5E-28] = 1000 x atmospheric particle density.

So what whould the output be if the core wasn't 10cm but 10μm? Its all about the sphericity. Or not.

[chrismb]

We've done this before.. the best fusion cross-section of all time is 5E-28m^2, so assuming the core is no bigger than 10 cm, and with the best will in the universe, that'd mean the density was of the order of 1/[0.1]x[5E-28] = 1000 x atmospheric particle density.

So what whould the output be if the core wasn't 10cm but 10μm? Its all about the sphericity. Or not.

It's a fair enquiry...

a reduction of the core to 10um would mean the density is now in the order of 1/[10^-5]x[5E-28] = 2E32/m^3 (20,000,000 x atmospheric density, a third the density of liquid water) which'd be around 2E17 particles. They'd spend at most 10 picoseconds in the core so if all of them were guaranteed to fuse that'd be a reaction rate of 2E28/s, or a mere 10 petawatts.

[pending possible arithmetic errors - feel free to re-calculate this for yourself...]

[happyjack27]

from the looks of these images of electric potential:

http://www.mare.ee/indrek/ephi/pef2/

it looks like you should be introducing the electrons at zero energy from right on the midplane of the coils, or even a tad closer. anything further back and you'd have to introduce a negative charge behind it to stretch back the well/hill, or shoot them in with a little KE so they're at zero KE when they reach the top.

it's like rolling a marble down a trapeze wire w/two big bumps in it, as slowly as humanly possible.

oh, and underneath the trapeze is a big lava pit.

[D Tibbets]

Bussard even mentioned a 'black hole effect' where the central ion density is so great that the ions collide so much during one pass through this region, there is essentially zero chance the ion could escape this region before participating in a fusion reaction.

...jeezuz.... did Bussard actually say this?

......

really?????...... Are we really talking about 100,000 petawatts from a 10 cm diameter, 1E28/m^3 reaction volume? Approximately a million times the average total power consumption of the planet?

Just excuse me a moment whilst I run away back to reality.....

No, in this case the reaction volume might be something like a cubic micron(?). The volume is extremely small, but the density is so great in this tiny volume, the MFP is so small, that there would be so many collisions occurring that the rare collision that results in fusion would still be statistically inevitable before the ion could escape this volume. I don't see any inconsistencies here. Of course the piratical issues of focusing the convergent beams to such a tiny volume, and the repulsion they would need to overcome are phenominal. I think Bussard might have been illistrating the conceptual limits of the system. He didn't say such conditions were impossible, but highly improbable.

So, the Polywell may work without any ion confluence (Nebel claimed this) or at levels where there are greater levels of confluence. This would result in smaller machines and possibly greater Q, up till some limit. The thermal wall loading limits may become intolorable, even with moderate confluence (with corresponding shrinkage of the machine), so while the fusion physics might allow 'black hole' like operational conditions, in the real world such is indeed silly.

Dan Tibbets

[chrismb]

Dan, you need to think through the basics sometimes.

The cross-section for fusion is known. The MFP to a fusion event is determined to be 1/(cs).(density). So we can work out the density.

Do you agree with my density calculations above?

Then, as the core is a load of dynamic particles that go in then out straight away, clearly there is a matter of continuity of their flux in to that reaction volume. If ions going towards that core have a 'total' chance of fusion then it means the MFP to fusion must be a lot less than the size of the core but, hey, let's say they are real lucky ions! Point is that if they are all heading that way and they all fuse, then the total reaction rate is the total number of ions in that reaction volume divided by the time they'll take to cross that volume, as they all get into fusion reactions.

So the reaction rate is total ion count/time in the reaction volume.

We know both of those, the first from the former calc and the latter because all light isotope fusion reactions require ion velocities of between 1,000 and 10,000 km/s.

Do you disagree with any of these points?

Or are you just saying that it'd be smaller than even 10 um? If so, how small do you want to run the calculation for?

It'd help if you [and other folks] could pinpoint the aspect that they think I have wrong, rather than run off at a different tangent and not deal with each point. hen we can deal with the particular point, or points in turn, that you think are wrong.

[TallDave]

from my simulation runs, it seems the most important thing is to get the electrons as close to zero kinetic energy at the exact center as possible.

I'm curious what you're maximizing there. Fusion power?

I'm not sure you can actually fine-tune the electron velocity at the center, though, since the well itself is just a result of the average position of the electrons. I think Rick has said electron behavior is stochastic.

[D Tibbets]

ChrisMB. I am not challenging your numbers. just the scales you choose to illistrate your point. Certainly as density goes up the MFP to fusion decreases. By manipulating these two parameters (within a fusion temperature range) you could create a 'black hole' core of any size that would result in the total fusion of ions converging towards the center in this spherical space. An equivalent comparison would be real black holes in Astronomy/ cosmology. Very massive galactic black holes may be as wide (distance to event horizon) as the inner Solar system, a stellar mass black hole may be a few kilometers wide, and a extreamly low mass black hole may be smaller than an atom.

And, using inertial confinement fusion/ fission methods (like a nuclear bomb), you can approach this 'black hole' core situation. Modern atomic bombs can fission ~ 60-80 percent of the of the plutonium present before the containment is overcome by the expanding fireball. In a thermonuclear bomb, the tritium/ lithium and deuterium fuse at high enough efficiencies in the core of bombs that considerable energy is generated. I don't know what percentage of these elements fuse, but if you assume it is 90% you are very close to the 'black hole' effect for fusion.

Bussards comments about these focused quasi-spherical inertially electrostatically containment systems conceptionally approaching this condition from a physics standpoint (even if it results in the energy densities of well demonstrated nuclear bombs) is not the point. The important point is not that a Polywell could be developed into a bomb (the engineering problems would be huge), but that if confluence can be pushed, the difficult problems of containment time and various thermalization issues become much less significant.

Dan Tibbets

[happyjack27]

from my simulation runs, it seems the most important thing is to get the electrons as close to zero kinetic energy at the exact center as possible.

I'm curious what you're maximizing there. Fusion power?

I'm not sure you can actually fine-tune the electron velocity at the center, though, since the well itself is just a result of the average position of the electrons. I think Rick has said electron behavior is stochastic.

in my simulations, thats the most important thing to getting the electrons to stay in the center. and it makes sense. if you want to minimize their chance of escape, then you essentially want escaping to be the "highest energy" from their current energy. and their is exactly one point in the system in which that is maximal: the absolute center at 0 KE.

[D Tibbets]

in my simulations, thats the most important thing to getting the electrons to stay in the center. and it makes sense. if you want to minimize their chance of escape, then you essentially want escaping to be the "highest energy" from their current energy. and their is exactly one point in the system in which that is maximal: the absolute center at 0 KE.

I'm not sure what you are getting at. Such assumptions may be convient for your modeling, but it doesnt describe the physical situation. There are several way to look at the electron distribution in the Polywell. If you inject several radial streams of electrons towards the center, the will initially be traveling in near radial directions, slowing as they approach the center on each pass. These electrons quickly thermalize both in radial and transvers directions. They would soon assume the picture of a random collection of electrons within the Wiffleball border. This is modified by the electrons tending to tag along with ions and to become trapped on magnetic field lines just outside the Wiffleball border. Keeping the electrons in the core (defined as the Wiffleball border) is due to the magnetic confinement. Any convergence of the electrons towards the center is due to the initial radial motions that have not yet been fully randomized, or aborted by magnetic field line capture. The important issue here is the dynamics of the system. The cusp, and cross field transport losses remove these thermalizing electrons before they can reach this final state. This is easily achieved, but only at great cost. The trick, that Bussard claimes to have achieved, is that this dynamic process can be feed at rates that does not cost too much. The efficient confinement needs to be good enough, but not so good that the electrons can thermalize completly. Apparently there is a window of operation where this can occur (especially if recirculation resets the thermalization process for those recirculating electrons).

I see two basic potential well morphologies. One is a thermalized bag of electrons . Any ions outside this bag willl be accelerated towards the center.The problems here is that the ions are deflected by the magnetic fields in this area, so they do not collapse to as small of a core. This would (I think) be represented by a square potential well. If there is some remaining central convergence of the electrons the ions would see a more elliptical, or parabolic well. The electrons tagging along with the ions would promote this also and somewhat impead the vertual anode formation.

The actual picture is probably somewhere in the middle.

Dan Tibbets


Dan Tibbets

[happyjack27]

The actual picture is probably somewhere in the middle.

you say this as i'm watching the actual picture on my computer screen.

(i'll make a video for you guys. i've got to find software to speed it up.)