F.O. Question to Collision:Fusion Ratios - DONE

[D Tibbets]

To partly answer Chris' objection: A fast particle sweeps though volume faster. But the slower particle will have more time for collisions as it sweeps through a distance. So the number of collisions is proportional to distance covered * cross section, velocity canceling out.

Sort of. My understanding is that fusion (or coulomb collision) rate is: dependant on the distance traveled / mean free path .
Or, restated = velocity / crossection / density. Hopefully I am not confusing myself too much.

A coulomb collision becomes more likely as you relax the limiting definition- in this case- the angle of deflection. Coulomb collisions are electromagnetic interactions and obey the inverse square law. My hand waving mussings are that as the distance between the ions closet approach as they fly by each other is doubled, the force applied between is cut to 1/4th, so the angle of deflection is 1/4th. The number of collisions that come within this 2X greater distance is 4, or D ^2. In effect the crossection increases at D^2 , but the effect decreases at D^1/2 so the net effects would be similar so long as the velocity is not changed.
But, subsequent collisions can add or subtract from the net deflection, this random walk process decreases the net contribution of smaller angle deflections to ~1/2 of their effect per collision. Thus, if my reasoning is right it would take 200 one degree deflecting collisions to match 1 ten degree deflecting collision.

Lets see how this fits with the calculation from this link:

http://hyperphysics.phy-astr.gsu.edu/Hb ... rosec.html

Crossection at 100 KeV for deuterium
Deflections of at least 10 degrees per collision= 212 Barns
Deflections of at least 1 degrees per collision = 21384 Barns
This matches well my reasoning that the effective thermalization rate is dependent on the number of collisions times their relative effect, not on just the number of collisions alone. Note that this does not address my further argument of even lesser effects of the weaker collisions due to the random walk process. Also, note that I am only talking about the angular deflection contribution of collisions , the upscattering and downscattering component may need additional head scratching, but these are irrelevant when only the radius of the effective core is addressed*.
So Chrismb's tactic of using coulomb crossections at progressively smaller effects to inflate the crossection numbers is a red herring.

Thinking about the decreasing coulomb crossection as the speed increases, the accelerating force applied as an ion passes another ion, is time dependent. Accelerating force is defined per unit of time (eg:m/s^2), so the less time it spends near it's target the less total force is applied (within limits). So, acceleration at 1 m/s^2 for 10 seconds gives a velocity of 10 M/s. For 0.1 second gives a velocity of 0.1 m/s. This translates into how much angular momentum could be imparted so it makes sense that higher speeds would result in smaller crossections relative to some limiting angular deflection. Again, upscattering collisions might complicate the picture.

These are simple two particle interactions. It becomes vastly more complicated with more particles. Also, in the Polywell the geometry, position within the Wiffleball and the energy at that position, partial restoring forces (like annealing), and shorter lifetimes of the ions as they upscatter all contribute to the calculation.
For more detailed discussion with plenty of math, see:

http://www.askmar.com/Fusion_files/EMC2 ... ration.pdf


* So long as the ions stay out of the magnetic domain.

Dan Tibbets

[WizWom]

The idea is that the supply of ions is significantly less than the supply of electrons, so that there is always a negative potential well in the center.

In this situation, the ions are strongly attracted by coulomb force to the electrons, which are kept in the center by the magnetic fields of the magrid.

These ions are not in a Maxwell-Boltzmann thermal distribution, because the escape through the "cusps" favors the low energy particles, and the magrid pushes harder at the faster particles. Thus there is "automatic" clipping at both the high and low end tails of the distribution curve.

[D Tibbets]

The idea is that the supply of ions is significantly less than the supply of electrons, so that there is always a negative potential well in the center.

In this situation, the ions are strongly attracted by coulomb force to the electrons, which are kept in the center by the magnetic fields of the magrid.

These ions are not in a Maxwell-Boltzmann thermal distribution, because the escape through the "cusps" favors the low energy particles, and the magrid pushes harder at the faster particles. Thus there is "automatic" clipping at both the high and low end tails of the distribution curve.

Actually, things are a lot more complicated. My understanding changes, sometimes reversing. I once wondered how the electrons maintained radial paths, but decided that they bounced elastically off the magnetic field to maintain a central convergence of electrons and establishing a elliptical potential well. More recently I've decided that the picture of the electrons congregating near the Wiffleball border (bouncing around at shallow angles or being trapped on magnetic field lines)as far away from each other as possible is more real. Rewatching Bussard's Google talk reinforced this. It is only after the ions are introduced and fall into the square potential well provided by the pure electron population that an elliptical potential well forms. The in falling ions drag electrons with them and this establishes the elliptical potential well. Since it is not a one for one relationship, a virtual anode forms in the center and actually limits the ion convergence that is tolerated. Keep in mind that the electrons are dragged along by ions much easier than visa versa because the electrons are much lighter. Because of Gauss law considerations, and the inertia differences the ions do not follow (at least not much) the escaping electrons through the cusps. Electrons tagging along with ions towards the center is favored by the local coulomb forces acting without any significant opposing forces. But, in the ions case, they are not tagging along with the electrons escaping through cusps because the excess electrons inside the machine exert a general (space charge) inward directed force and this dominates over the local coulomb forces between ions and the relatively few escaping electrons. This would be more of a problem if this was a neutral plasma (like A. Carlson always assumed), but it is not.

I believe that the slow ions do not escape through the cusps . It is the faster upscattered ions that are more likely to escape the potential well and thus have an opportunity to exit through a cusp. As mentioned by Bussard this may actually be good as it slows the development of the high energy ion tail without costing much energy. Only the excess gained energy is left after the ion climbs out of the potential well and I'm guessing that the lifetimes of these progressively upscattered ions is short enough that the upscattering opportunities are limited, so most of the upscattered escaping ions do not have a chance to gain much energy in excess of the potential well.
Since the space charge is negative inside the magrid and ~ 80% of the positive potential on the magrid the ion that has escaped beyond the magrid will only be accelerated by ~ 20% of the magrid voltage (need to consider inverse square law in here somewhere as the potential well is further away than the magrid at this point). Presumably the percentages of ions escaping per cycle is much less that the number of electrons lost per cycle, so the contribution of upscattered lost ions is trivial compared with the electron losses. At the same time this ion loss mechanism is beneficial as it limits ion upscattering cumulative effects, such a electron heating, bremsstrulung, etc.

I've never had a good handle on what happens to the downscattered (slow ions). Annealing would help some.

Dan Tibbets

[ladajo]

I have been thinking on this as well. As the wiffleball forms, why would not ions combine with electrons in the shell near the magrid, and form a quasi-neutral layer? Is that what is meant with annealing? This layer would in effect become a shield layer, so ions attempting to transit would have collisions, and be slowed, and then in turn would fall back into the well accellerating to the center (Begs the question on how fuel ions get in...hmm you could have fast insertion and hope that they collide with neutrals and slow down enough to get captured???). You would have a higher density <quasi> neutral "crust", and then the potential well inside with an increasing curve to the core of the plasma of ion and electron <effective> density as they all aim for the center convergence. It may well even be that the core itself has an effective diameter based on the averaged densities. Working from outside to center, I see a crust, a drop in density, then increasing to a plateau whose width represents the size of the effective fusion core. ie. enough stuff moving at each other fast enough to have significant fusion events. A kind of critical distance point from center, where there is not enough fuel and it is not moving fast enough. Ok, now I am think to hard on it again, my head is starting to hurt.

[KitemanSA]

Still no words to modify hanelyp's answer. Anyone?

[93143]

I might try to finesse it if I had managed to get my simulation running and obtain some solid results. Unfortunately I've been somewhat distracted by my Ph.D. research (spray modelling is actually fairly similar in principle to particle kinetics, only even more complicated in some ways)...

I had conjectured that a Polywell actually exhibits a dense multiple-well structure, essentially a pattern of standing Langmuir waves. The annealing would happen not just at the edge, but in each wave trough. I have, sadly, no evidence whatsoever of this at the moment, meaning that it definitely doesn't belong in a FAQ...

On second thought, even at the level of evidence provided by a set of successful quasi-1D simulations, I doubt I'd include it...

To partly answer Chris' objection: A fast particle sweeps though volume faster. But the slower particle will have more time for collisions as it sweeps through a distance. So the number of collisions is proportional to distance covered * cross section, velocity canceling out.

True. Specifically, mean free path = 1/(sqrt(2)*number density*cross section). Also worth repeating at this point is that velocity does show up in the cross section calculation. So the mean free path should be significantly shorter in the dense edge region than in the interior.

How much shorter depends on how much residual energy the ions have at the edge, which depends on injection temperature, well focus, and interior single-pass thermalization...

[ladajo]

"I had conjectured that a Polywell actually exhibits a dense multiple-well structure, essentially a pattern of standing Langmuir waves. The annealing would happen not just at the edge, but in each wave trough. I have, sadly, no evidence whatsoever of this at the moment, meaning that it definitely doesn't belong in a FAQ... "

That would be more likely if you injected an RF Field. If your polywell enclosure was sized right to the frequency, you could create standing waves. Maybe Dan T needs to take apart a microwave and use the magnetron on his pressure cooker!

[TallDave]

I had conjectured that a Polywell actually exhibits a dense multiple-well structure, essentially a pattern of standing Langmuir waves. The annealing would happen not just at the edge, but in each wave trough. I have, sadly, no evidence whatsoever of this at the moment, meaning that it definitely doesn't belong in a FAQ...

That still sounds to me like the picture of things most consistent with physics and experiment (such as we can infer, bleah). It sounds similar to what Joel modelled as well (he was taking Debye slices).

I wonder what Rick has seen this month? WB-8 is supposed to have been delivered almost a month ago now...

I've never had a good handle on what happens to the downscattered (slow ions). Annealing would help some.

Well, slow ions at the edge have high potential energy, and in addition to evening their energy spread they will also tend to anneal longitudinal velocity into radial (because they have to give up radial velocity to get out of the well, they'll tend to have higher longitudinal velocity and lower radial velocity in the high-collision edge area). Slow ions at the core aren't going to stay slow for long, and the energy they pick up from collisions will tend to be radial because of where they are. A neat trick, if it works.

[D Tibbets]

I've never had a good handle on what happens to the downscattered (slow ions). Annealing would help some.

Well, slow ions at the edge have high potential energy, and in addition to evening their energy spread they will also tend to anneal longitudinal velocity into radial (because they have to give up radial velocity to get out of the well, they'll tend to have higher longitudinal velocity and lower radial velocity in the high-collision edge area). Slow ions at the core aren't going to stay slow for long, and the energy they pick up from collisions will tend to be radial because of where they are. A neat trick, if it works.

Well, I was thinking of slow (downscattered) ions that have a subsequent lower potential well peak that does not reach the 'edge' annealing region. As these ions accumulate deeper in the well and the upscattered ions leave the machine, the average (and mean?) ion energy would drop. Subsequent slow/ fast ion collisions would slow the accumulation of slow ions some, but as the upscattered ions leave the system, the net average ion energy would drop. Taking it to the extreme, the older aging and progressively slower ions may finally accumulate in the center and the machine may act more as a beam- target system instead of a beam- beam system. Multiple zones (or broadening zones) of annealing would slow the process, but not stop it. Heating the ions with microwaves may be a good mechanism to maintain desired populations over the fusion lifetimes. I have the impression that handling the downscattering ions may be a lot more tenable than trying to handle the upscattered ions if they did not preferentially leave the system (without much energy loss compared to the dominate electron losses). In that case, I'm guessing that untenable potential well voltages would be needed, as A. Carlson (and Rider?) championed .

Dan Tibbets

[TallDave]

Yep, I think you'll get some velocity spread in the "mantle."

As these ions accumulate deeper in the well and the upscattered ions leave the machine, the average (and mean?) ion energy would drop.

I don't think that's possible. With no signficant loss of upscattered ions (Nebel and Chacon agree upscatter is a red herring in this kind of system, and Joel finds no ion current) there's nowhere for the energy to go. It can spread, but it can't be lost (except via brem, which may be a serious obstacle for p-B11).

At one point we were thinking ions would be pulled out, because we were thinking the exterior was essentially ion free, but upon further review it was pointed out that would probably have required ridiculous potentials in the system (a competing notion appears to be that we can ignore, or at least mitigate, the needed potentials and the pull because the charge on the Magrid balances the excess electrons). To merely lack sufficient potential for an ion current, because of different ratios of density and ion/electron ratios, is not as tall an order as an ion-free exterior that fails to pull out ions, and seems to jibe better with what little we know experimentally (no hotspots on the wall in WB-7, the PZL effect).

(I think Joel's simulation finds cold electrons bunching up at the cusps, with ions at the edge not seeing a pull because the Magrid balances them. The electrons are all squeezed into the cusps, so they see some pushback from each other locally (more than they see from the Magrid, because it's farther away), resulting in WB confinement. I hope that's close, anyway )

the machine may act more as a beam- target system instead of a beam- beam system.

It better not, or it won't work as a reactor. Beam-target scaling is much less friendly.

[D Tibbets]

Yep, I think you'll get some velocity spread in the "mantle."

As these ions accumulate deeper in the well and the upscattered ions leave the machine, the average (and mean?) ion energy would drop.

I don't think that's possible. With no signficant loss of upscattered ions (Nebel and Chacon agree upscatter is a red herring in this kind of system, and Joel finds no ion current) there's nowhere for the energy to go. It can spread, but it can't be lost (except via brem, which may be a serious obstacle for p-B11).

At one point we were thinking ions would be pulled out, because we were thinking the exterior was essentially ion free, but upon further review it was pointed out that would probably have required ridiculous potentials in the system (a competing notion appears to be that we can ignore, or at least mitigate, the needed potentials and the pull because the charge on the Magrid balances the excess electrons). To merely lack sufficient potential for an ion current, because of different ratios of density and ion/electron ratios, is not as tall an order as an ion-free exterior that fails to pull out ions, and seems to jibe better with what little we know experimentally (no hotspots on the wall in WB-7, the PZL effect).

(I think Joel's simulation finds cold electrons bunching up at the cusps, with ions at the edge not seeing a pull because the Magrid balances them. The electrons are all squeezed into the cusps, so they see some pushback from each other locally (more than they see from the Magrid, because it's farther away), resulting in WB confinement. I hope that's close, anyway )

the machine may act more as a beam- target system instead of a beam- beam system.

It better not, or it won't work as a reactor. Beam-target scaling is much less friendly.

No ions outside the machine? Where does that come from? My understanding is that the Polywell magnetically confines electrons because magnetic fields do not contain ions well. The potential well confines the ions. Once an ion is upscattered to velocities great enough to escape the potential well, the only barrier to their escape is the magnetic field. They can possibly become trapped on magnetic field lines and exit at cusps, or exit directly through a cusp (there are other transport loss mechanism but they are probably minor). As far as magrid potential effects, no charged particles would see them until they reached a radius equal or greater than the radius to the mid plane of the magrid- at least if Gauss's Law is real.

The key to the Polywell is not that it contains ions absolutely, but that it contains them (electrostatically due to the excess electrons) well enough that necessary density gradients can be maintained between the inside and outside of the machine (wiffleball trapping factor) in order to get useful fusion rates (both in the sense of useful power production, and shortening the mean distance / time to fusion so that the effective containment is sufficient), and maintain outside densities low enough to prevent arcing to the machine walls. The actual ion current leaving the magrid is substantial, I have not seen published numbers but mention of ion guns of several amps capacity being needed makes me think that the escaping ion current is perhaps in the region of 1-10% of the electron current. As Bussard said, the ion loss rate in the Polywell is limited by the need to maintain this density gradient without arcing (and therefor within exterior magrid volume vacuum pumping capacity). In this regard the energy balance is not the issue in making the machine work.

To make the machine work profitably (Q>1) the energy carried away by the escaping ions must be low compared to the electron losses.
My understanding of this is that it is accomplished by both the ratio of the ion to electron loss rates (assume 1%)* and the energy each escaping ion carries. If the upscattering ion leaves soon after it has accumulated enough energy to escape the potential well, it will only have the energy it picks up from the magrid as it is accelerated towards the wall plus whatever small(?) velocity it retains after breaching the top of the potential well. If there is some local interaction between the ions and electrons in this region outside the magrid (an ion dragging an electron along with it) there would not be any net acceleration of the escaped ion in this region (no additional energy loss) and for piratical purpose the ion - electron pair could be considered as a recombined neutral atom, with a net energy equal to the ions upscattered energy it contained as it exited the magrid + the upscattered electron energy that allowed it to escape recirculation. So there would not be the magrid potential added to the escaping ions velocity. If these arguments apply, then the escaping ion might have a minimal energy that is a small fraction of the magrid potential. Thus the energy loss would be trivial compared to the electron losses both because there are significantly fewer ions escaping, and the lost energy per ion is small. I think this turns A. Carlson's argument on it's head as it only applies in this exterior region of the machine. The excess electron space charge inside the magrid (combined with mass difference between the ions and electrons) would prevent the undesirable situation- which would be escaping electrons tugging ions along with them.

As for cusp plugging , etc, I have little understanding of it, except that after WB5 Bussarard realized any system that depended on it (without open cusps allowing recirculation) was hopeless.

As far as energy balance in the machine, any preferential escape of upscattered ions would decrease the remaining energy of the plasma within the machine. Along with other loss mechanisms like bremmstrulung, and black body radiation, the temperature of the plasma would continually decrease. Of course the injection of new energetic ions would mostly restore the system and through collisions speed up the slow ions. But this would be a thermalizing process- controlled to limit its spread, but defiantly not a monoenergetic system. I think this confuses people (it does me). Perhaps if some term other than monoenergetic was used it might not get people so excited. What word would describe conditions of a narrow (not monoenergetic) thermal spread?

* The ion vs electron input currents I'm considering presumably applies to a machine where the ions lost through fusion reactions is relatively tiny. If the "few amps of ion gun capacity" applies to a power producing reactor- with ~ 10^20 fusions per second, or ~ 5-10 amps of ions consumed per second, then this would imply that the rate of ions lost through exiting the magrid would be much less.

Dan Tibbets

[ladajo]

Would it also not help in consideration that the "crust" would also act as a higher density area, thus providing an opportunity for upscattered ions to collide with the quasi-nuetral layer, be slowed, and re-captured by the potential well?

[D Tibbets]

Would it also not help in consideration that the "crust" would also act as a higher density area, thus providing an opportunity for upscattered ions to collide with the quasi-nuetral layer, be slowed, and re-captured by the potential well?

Yes, depending on the degree to which the radial ion motion has been upscattered or downscattered. The upscattered ions would travel through this region faster, and therfore have less coulomb collisionality. It would buffer the process somewhat, but not prevent a significant portion of the most upscattered ions from exiting the potential well. Of course if you consider Nebel's estimate of 1000 magnetically confined passes before an alpha escapes being similar to how many passes an upscatterd fuel ion passes (transits or orbits) before probable escape, then there would be many chances for the annealing to 'recapture' the upscattered ion. So it is a struggle for upscattered ions to maintain or increase their speed untill they can find a cusp. How this adds up to the percentage of ions escaping and their upscattered mean energy and range of energies is way beyond my pay scale. Perhaps because of these required multiple passes through the annealing region the potential well reclaimes practically all of these 'average' upscattered ions, except for those rare ones that happen to hit a cusp and exit on their first few tries. Note that upscattered ions that reach the dominate magnetic regions are more likely to be diverted transversely and be lost to the core. Bussard mentioned that it is actually advantageous to let these ions go , as apparently they promote the further thermalization of better behaved ions.

It occurs to me that downscattered ions may broaden and flatten the potential well, in effect moving the annealing region towards the center, so the machine may self regulate this process, with the continuous energetic electron injection being a knob to control and prevent this decay of the potential well. Another example of the dynamic nature of the machine.

Using the Goldilocks analogy,the electron current / loss represents the ideal compromise. It's not too hot and it's not too cold. It's just right!

Dan Tibbets

[TallDave]

No ions outside the machine? Where does that come from?

It was a point of discussion. As best I can tell there's really nothing in Valencia that speaks to it one way or the other, not sure about other papers. Joel's simulation has only a small number outside. It's not so much "no ions at all" as it is "not enough ions for anything like quasineutrality." It's hard to get away from quasineutrality.

As far as magrid potential effects, no charged particles would see them until they reached a radius equal or greater than the radius to the mid plane of the magrid- at least if Gauss's Law is real.

That may be overly idealized for the WB devices. Isn't that supposed to be for the case of a spherical shell? And how would that be affected by local Debye screening? In any case, Joels picture does indicate cusp plugging at those midpoints.

As Bussard said, the ion loss rate in the Polywell is limited by the need to maintain this density gradient without arcing (and therefor within exterior magrid volume vacuum pumping capacity).

Hmmm? Not sure that's really what he meant. If you were losing enough ions to affect the Paschen arcing or the pumping requirements, I think you'd be losing WAY too much energy to hope for breakeven at anything like the sizes contemplated.

What word would describe conditions of a narrow (not monoenergetic) thermal spread?

"Partially relaxed" is how Chacon's paper described it.

Your understanding is mostly the same as mine on the rest of the above. If we disagree, it's on the scope of the upscattered ion losses, but 1% of electron losses might be reasonable. My point was just that it seems to be small enough to ignore for purposes of looking at energy balance or downscattering.

[D Tibbets]

....

Your understanding is mostly the same as mine on the rest of the above. If we disagree, it's on the scope of the upscattered ion losses, but 1% of electron losses might be reasonable. My point was just that it seems to be small enough to ignore for purposes of looking at energy balance or downscattering.

Agreed. Again though, I'll restate my understanding of Bussard's emphasis on the Wiffleball trapping factor being more important for practical fusion levels, not for minimizing energy loss. The fewer ions that escape at any energy, the better in an energy balance, if other concerns are not considered. But, if ions upscatter too much without escaping it will have detrimental effects such as I beleive A. Carlson alluded to. Also, keep in mind what Bussard said about upscattered ions- if they reach the magnaticically dominate regions they will gyro turn on a magnetic field line that is always somewhat convex to the center, and thus increase their angular or transverse / longitudinal (?) motion, no longer transiting the core and being much less useful for fusion, and contribute more to angular collisions in the bulk of the machine. If an upscattered ion is quickly annealed to a desired energy- good, otherwise it is best to get rid of it, especially if it doesn't carry away much energy per ion ,or the energy loss per upscattered ion is large but there are few of them so that the loss is small compared to the limiting electron losses.

As I mentioned earlier the internal density gain is important. Pashin arching between charged particles and neutrals- to the non magneticically insulated walls or other fixtures will start at densities of ~ 10^- 5 or -6 atm.
This would be equivalent to ~ 10^19 particles / M^3. This density is two low for practical fusion. Also, the MFP to fusion would be longer and the fusion rate to loss rate would suffer (?). With a Wifleball trapping factor of ~ 1000 (or greater), the internal density is boosted to ~ 10^22 particles/ M^3, giving the predicted fusion density and efficiency. The increased internal density/ pressure can be tolerated without arcing because of careful attention to surface smoothness and curvature and because all of the internal structure (essentially the magrid) is magnetically insulated. In other words the ion energy losses are expected to be small in any case compared to the electron loss rate. But the density gradient between the inside and outside is of paramount importance. In the case of the electrons this density gradient and the energy balance were both paramount. That is why the electron recirculation in WB6 was so important.

Annealing- I think I have seen mention of edge annealing moderating the thermalization via upscattering or downscattering. I'm not sure if it has a similar effect on angular thermalization.

As far as Gauss's Law. In several threads here in the last ~1-2 years I have been informed that the lumpiness or continuity of the shell is not important. A wire grid would do as well. In fact the Faraday cage in the WB6 experiments was a rectangular wire mesh grid.and acted via Gauss's law.

Dan Tibbets