Spheroidal Foci and POPS?

[D Tibbets]

In a spherical cusp system like the Polywell I believe the results would be the same, though with perhaps complications.

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

Dan Tibbets

Dan,

The pictures of the permanent magnet polywell in your pressure cooker seem to show a spherical grid cathode. Do you have an electron gun for it?

MSimon can probably suggest the cheapest vacuum tube to break to get one...

Given the success of your first attempt, it would be interesting to set up a wiffleball without the grid.

It depends on the amount of cathode current needed. 6L6s and variants are common for the 100 ma or so range. A 12AX7 or 12AT7 is good in the 10 ma range. The versions made by the Soviets (now Russians) are considered good and not too expensive.

The difficulty I see is that they are linear and not point sources. Some collimation may be required. and that complicates things.

Thoriated tungsten wire may be a better bet.

Tom Ligon used filamented auto headlights as emitters.

I had never thought of using a vacuum tube, interesting, though as you say a point source or beam would be better. I played with passing 12 volts through a Tail light bulb, but at more than a small current it only nociably flooded the vessel with light. Playing with varous grids, I've found that an open ended tube at moderate negative voltages produces a a nice aimed beam, presumably an electron beam. But, with perminate magnets the central grid cathode is not a problem as the electrons/ plasma are quickly hitting the magnet poles anyway. I didn't know perminate ring magnets could be given an axial field, but I did see them on the linked supplier. I guess it makes sence since that was presumably the makeup of WB1 and 2. I'm currently playing with other smaller containers as vacuum vessels to try to ease the load on my old pump and decrease outgassing problems. It is too small to hold a microwave magnet array. The pressure cooker pictures are mostly eye candy. It is too leaky (and contaminated with vaporized gunk) to do more than visual demo work.
I will say though, that with the ~ 10-30 ma of current, and a few thousand volts of potential. The cusp areas were demonstrated and the curving edge of the magnetic borders possibly were pushed out some(?) with invreasing voltage and current. but the morphology did not visibly change, so I assume my conditions do not come close to those needed for potential wiffleball conditions( if even possible with the poles on the faces of the magnets). Even with my weaker magnets, my currents have been ~ 1000 times less than WB6 (~ 40 amps of electron current at beta=1).

Dsan Tibbets


Dan Tibbets

[D Tibbets]

As far as the ions turning around beyond the Wiffleball border, I think that depends on your definition of the Wiffleball and the shape of the potential well. If the Wiffleball is dependent on the electron density and vectors only , then yes. If the ions are contributing to the Wiffleball expansion, then it is more complex.

I've always understood the term "wiffleball" to be a like for like description - a hollow sphere with holes in it. That would refer to the magnetic containment of electrons to form a virtual grid.

I've not seen any suggestions that the ions contribute to the formation of the wiffleball, only that enough of them cause it to collapse.

Same here, though presumably a Wiffleball could be formed by a pure positive ion injection instead of a pure electron injection. I'm guessing it would be much harder to achieve and maintain because the current flow of the ions out of the cusps would be significantly greater at all stages. What I wonder is if the ions injected into the already formed Wiffleball has a reinforcing, neutral, or distructive effect on the Wiffleball at operating conditions; and if the effect is significant or not.

Dan Tibbets

[TallDave]

The greatest density of ions is in the centre, but that's because of the spherical topology.

It's because of the well.

They spend half their time outside the wiffleball slowing down and turning round.

Hrm, maybe I'm looking at this wrong but I don't think that's possible. If that were true, the B field would be adding a lot of transverse momentum to the ions, which seems like it would be very bad. (If an alpha at MeV energies is forced into 1000 transits and out a cusp, what's going to happen to a mere KeV fuel ion, which is actually slowing to zero radial velocity?) It's also hard to believe any number of ions can leave virtually the entire population of electrons behind. I don't think Rick sees it this way either, because (iirc) he talked about the edge having both ions and electrons, meaning it was within the WB boundary.

Chacon made no such statement. He calculated a spherically symmetric system. No cusps.

His statement was about upscattering being a red herring for this kind of machine.

What does that mean? "Generally neutral" or "only quasineutral"?

"Generally quasineutral" as opposed to "locally quasineutral."

I still favor 100 mW as the minimum design goal.

Heh, I'm still 99.999% sure that was a typo. I doubt you can even measure a net output that small when your drive is 10MW.

I sure wish I could get a look at this code:

These have been readily modelled successfully by a major
plasma phenomenological code (the EIXL code) developed
by EMC2 since 1990. This is a 1.5- dimensional Vlasov-
Maxwell code, in which diamagnetic expansion of B fields is
included, particle collisions are estimated from density and
energy distributions, fusion rates and output are calculated
and bremmstrahlung losses are included, and which includes
such phenomena as central core inertial-collisionalcompression
effects which can apply to core ion
compression in Polywell devices.

[TallDave]

Same here, though presumably a Wiffleball could be formed by a pure positive ion injection instead of a pure electron injection.

Someone correct me if I'm wrong, but I don't think space charge limits would allow anything like either of those. The well and wiffle-ball require only slightly more electrons than ions, and it sounds like neutrals get ionized and fall in as electrons are injected.

As the neutral gas filled the machine interior, fast injected
electrons created ionization in this gas. The ion and electron
densities produced by this fast ionization were too low to
drive the system to the electron beta=one condition.
However, the low energy electrons resulting from this
ionization rapidly cascaded with additional neutral atoms,
being driven by electron/electron collisions with the
incoming injected fast electrons, and made still more low
energy electrons. The cascade time e-folds at a rate of
1/(no)(sigmaizn)(veo), where (no) is neutral density,
(sigmaizn) is ionization cross-section for low energy
electrons at speed (veo). Typically, for no = 1E13 /cm3 (i.e.
ptorr = 3E-4 torr), veo = 1E9 cm/sec (Ee = 100 eV), and
sigmaizn = 1E-16 cm2, the cascade e- folds with a time
constant of about 1E-6 sec (one usec). Thus all of the
neutral gas is ionized and the system is filled with low
energy electrons in only a few usec. Wiffle Ball trapping
works very effectively here. If all the electrons were still at
ca. 100 eV, the surface beta would be about beta = 0.01, at B
= 1000 G.
However, the low energy electrons are heated by fast
collisions with incoming fast injected electrons. The
Coulomb energy exchange time for this process is also about
1 usec. Thus the device will reach beta = one conditions
when the mean electron energy is about 2.5 keV, in ca. 20
usec. Beyond this point excess electron density will be
driven out beyond the beta = one limit; the field will have
expanded as far as it can within MHD stability limits.
...
Only a very slight fractional
negative deviation (1E-6) from charge neutrality (of ions vs.
electrons) is required to make potential wells nearly as deep
as the electron drive energy.

[alexjrgreen]

...

57th International Astronautical Congress (IAC 2006)

[alexjrgreen]

Someone correct me if I'm wrong, but I don't think space charge limits would allow anything like either of those. The well and wiffle-ball require only slightly more electrons than ions, and it sounds like neutrals get ionized and fall in as electrons are injected.

The trouble with the plasma soup model is that Art will gleefully prove that it can't work.

There has to be enough structure for stable jets to form.

[D Tibbets]

Responce to some of the above 'TallDave' posts.

I'm not certain, but I believe the convergence (central focus with hugh central density) of the Polywell, while driven by the potential well, is possible, or at least hughly augmented by the 3 dimensional spherical volume. Consider a potential well in the center of a very thin cyclinder. The dynamic motion of the ions- slow at the ends, and fast in the center. Because of their speeds the ions would spend most of their time near the ends. I suspect things would average out so that there was an even distribution of ions in this 2 dimensional space. It is the 3 dimensional volume of a sphere that allows the density buildup in the center. If I'm thinking right, it would be like comparing my 2d model, but adding thousands of them together, all intersecting in the center. If my estimates are right, the density in this intersecting area would be a 1000 times higher than the density anywhere else in the 'near' 2 dimensional
cydlinders (ignoring vertual anode dampening and assuming the ions maintain dominate radial motions).

I had read that Bussard quote several times and it confused me. The cascading ionization , starting from one high energy electron's energy being finally distributed over several hundred secondary free electrons would result in a bunch of low energy electrons. How would all these low energy secondary electrons be reheated to high energy by a single new high energy electron? Reading your post, it occured to me that this would be possible because of the proportion of secondary electrons to primary electrons being lower, ie- one high energy electron produces 100 ions and 100 secondary electrons from the neutral gas that is injected. If the ions created last ~ 100 times as long as the primary and secondary electron mix, then there would be an almost 1:1 mix of primary and secondary electrons with an average energy halfway between. Say the primary electrons are 10,000 eV and the just created secondary electrons are 20 eV (ionization energy ~11 eV) then the average energy would end up as 5,010 eV. If the ions last 200X, 300X, or longer than the electrons, the average electron energy would progressively come closer to the primary electrons' energy levels.
If the potential well depth, after overcoming the penalty of injection (~85% efficiency) is near this value, then the ions' lifetimes must be many hundreds, if not thousands of times longer than the electrons' lifetime. So even if the upscattered escaping ions carried significant amounts of energy, it would be trivial compared to the electron losses, which fits Bussard's claim that the ion energy losses could be ignored, and the ion losses were only important in preventing charged particle buildup outside the magrid that could lead to arcing. I assume that the secondary electrons that are created with random vectors are converted to near radial vectors due to the much higher energies of the colliding high energy primary electrons.

Someone (not me) could presumably calculate the ion lifetimes, and average density obtainable within the Wiffleball based on electron containment time (assume 100,000 passes at 10 million meters per second in a 1 meter machine = 10 ms (actually less than this if the drive voltage is higher than the 12,000 volts in WB6 that the speed was taken from)), electron current (assume 100 Amps), near equality in the numbers of electrons and ions within the Wiffleball, potential well depth (how close it comes to the drive potential) and the exterior density that could lead to arcing (assume 10 microns). The magnetic field strength could be ignored as that is incorperated into the electron lifetime and current(?). Making an assumpion on how much convergence there is would allow calculation of central ion density.

If using ion guns, I have heard mention that powers of at least several amps would be needed per gun. Looking at needed power output of ~ 10 ^20 fusions per second (100 MW), I think this would be equivalent to ~ 20 amps of ion current (1 amp = 6 x 10^18 ions (plus 1 charge) per second). If the ion lifetimes are 100 times as long as the electrons, this would suggest an electron current of ~ 2,000 amps. At 100,000 volts that would add up to a lot of watts. If I haven't confused myself, the effective containment time of the electrons must improve considerably over this baseline with increasing B-fields, and raduis(?)

Dan Tibbets

[D Tibbets]

It's not likely ions ever get out that far (Luis Chacon is apparently pretty confident about this).

Chacon made no such statement. He calculated a spherically symmetric system. No cusps. ....

In such calculations, does it make a difference whether you have a smooth sphere as opposed to a lumpy sphere (Wiffleball) in which the lumps (cusps) are on symmetrically opposite sides of the ball?

Dan Tibbets

[D Tibbets]

Same here, though presumably a Wiffleball could be formed by a pure positive ion injection instead of a pure electron injection.

Someone correct me if I'm wrong, but I don't think space charge limits would allow anything like either of those. The well and wiffle-ball require only slightly more electrons than ions, and it sounds like neutrals get ionized and fall in as electrons are injected.

Mmm.. perhaps you are right. I may be confused by the sequential steps used to turn on WB6, unless it is actually a compromise process. The initial injection of electrons equivalent to that 1 part per million, that is within the spece charge limit, forms an immature Wiffleball, the subsuquent injection of equal numbers of electrons and ions then provide the density to finish development of the Wiffleball. In one of Bussard's papers he describes two methods of forming a Wiffleball. I didn't follow his brief discriptions.

Dan Tibbets

[MSimon]

Heh, I'm still 99.999% sure that was a typo. I doubt you can even measure a net output that small when your drive is 10MW.

Depends on how you measure it. Neutrons for D-D. Alphas (inside the vessel) for pBj.

I can easily measure 100 mW of fusion confounded by a 10 MW electrical signal.

[hanelyp]

If using ion guns, I have heard mention that powers of at least several amps would be needed per gun.

Hall effect thrusters come to mind for the application.

[TallDave]

Heh, I'm still 99.999% sure that was a typo. I doubt you can even measure a net output that small when your drive is 10MW.

Depends on how you measure it. Neutrons for D-D. Alphas (inside the vessel) for pBj.

I can easily measure 100 mW of fusion confounded by a 10 MW electrical signal.

Sorry, I think I was unclear there. You're not measuring 100mW of fusion, you're measuring the .1 watts in 10,000,000.1 watts of fusion.

My point is that you're trying to measure a 0.000001% difference in input over output, and I doubt either is anywhere near steady enough for that to make sense. I think you'd have to look for something closer to 1%, like 10kW.

[TallDave]

Someone correct me if I'm wrong, but I don't think space charge limits would allow anything like either of those. The well and wiffle-ball require only slightly more electrons than ions, and it sounds like neutrals get ionized and fall in as electrons are injected.

The trouble with the plasma soup model is that Art will gleefully prove that it can't work.

There has to be enough structure for stable jets to form.

Shrug, it can still have structure regardless. But I'm not sure where you're going with jets.

[D Tibbets]

Someone correct me if I'm wrong, but I don't think space charge limits would allow anything like either of those. The well and wiffle-ball require only slightly more electrons than ions, and it sounds like neutrals get ionized and fall in as electrons are injected.

The trouble with the plasma soup model is that Art will gleefully prove that it can't work.

There has to be enough structure for stable jets to form.

Shrug, it can still have structure regardless. But I'm not sure where you're going with jets.

My understanding is that using terms like jets or beams is the same as saying there is convergence in a spherical device.. With a gridded real cathode (or anode), jets which effectively increase the transparency of the grid wires (Star mode) is real. With virtual grids - see above. It doesn't mean that discreate jets can't form, but that they are not required.

[EDIT] I could come up with all sorts of speculations where discreate jets might form and have an effect on performance through effects on thermalization, injection, contaainment, etc.; but for once I'll limit my rambling. Except, of course, for this rambling edit.....


Dan Tibbets

[alexjrgreen]

The trouble with the plasma soup model is that Art will gleefully prove that it can't work.

There has to be enough structure for stable jets to form.

Shrug, it can still have structure regardless. But I'm not sure where you're going with jets.

Then it works by magic, right? Cool...

The wiffleball has holes in it. If we have plasma soup then the plasma just falls out the holes in a horribly lossy way as Art keeps trying to make everyone understand.

Some people seem to think that the holes magically seal up to give us a nice pretty quasi sphere. That just flat contradicts what Dr Bussard had to say about electron recirculation, but if you can handwave that away, Art has his cannons charged and ready.

So if the device works we don't have plasma soup. We have structure.

Ions are heavier than electrons and take longer to stop, so the first piece of structure is that the wiffleball is covered by a layer of ions. That should make for some interesting calculations.

The second piece of structure is that the plasma falls out of the holes in jets, actually tubular double sheets, focussed by the magrid.

Proving that those jets turn back on themselves and return the plasma to the wiffleball, rather than spraying it all over the wall, is this week's exercise...

The clues are Rick's insistence on collective mechanisms and Art's insistence that where the electrons go, the ions follow and vice versa.