Fusion product Alpha particle

[WizWom]

I'd been meaning to work out the cyclotron radius of the fusion product alphas for some time, so I finally did.

Cyclotron radius:
r = mv/qB
For an alpha particle in a p-B11 polywell, we have:
m = 6.64424*10^-27 kg
v = 1.16*10^7
q = 3.20*10^-19 C
B = 10 T
so, r = .0242 m
That's significantly tighter than I expected, actually.

Also, there would be no magical physics reason the alpha particles would get treated any differently than the rest of the ions in the plasma.

Which, I guess, brings up a question - won't these hot alphas poison the reaction?

Edit: fixed q & r

[93143]

Rick addressed this a while ago. Basically, the alphas rattle around in the wiffleball for about a thousand passes on average, then shoot out the cusps. They're poorly confined due to their relatively large gyroradius, which is one of the two big reasons neutronicity is expected to be so much lower than Wikipedia says (the other is the non-Maxwellian distribution, which suppresses p + ¹¹B -> ¹¹C + n - 2.8 MeV). And at 3 MeV, the collision cross section with anything else is fairly low, so they shouldn't really do much to disrupt the plasma.

We were all very pleased to hear this, since we had been assuming the alphas would simply smash into the magrid, heating it intensely and liberating vast quantities of neutrals (like you, we hadn't gotten around to actually calculating the gyroradius...). Reactor design is much easier when you don't need SSME-nozzle-class cooling of the superconducting coils, never mind a solution to a sputtering problem of that magnitude... not to mention the direct conversion system for non-monoenergetic particles; beam spreading or no, it's vastly easier to electrostatically convert non-monoenergetic alphas if they come out in some semblance of a beam rather than just radiating outwards from the core in all directions...

In a D-T tokamak, you want alpha confinement to be good, since it's supposed to be the primary source of plasma heating in the "burning plasma" regime, making external heating (which is difficult in a tokamak) unnecessary. In a Polywell, external heating is dead easy; it's inherent in the operating principle, and alpha confinement doesn't need to be good (and sure enough, it isn't). This is why it's often said that Polywells don't ignite.

[D Tibbets]

As mentioned the coulomb crossection for particles at such a high energy is much smaller than the crossection of the fuel ions. Also, the containment of the high energy alpha's is almost purely magnetic, as their kinetic energy is much greater than the potential well. I find it interesting that Nebel's estimate of the magnetic confinement time (passes) for the alphas is close to the wiffleball traping factor for electrons ( and thus ions as they are in almost equal numbers within the Wifflebal. This suggests that the wiffleball trapping allows for charged particle confinement (if there were not an electrostatic confinement of fuel ions added onto this) dominated by cusp losses, not transport across magnetic fields, (random walk process, plus others) even with energetic alphas which have a significantly greater gyroradii and with the modest sizes compared to Tokamaks.

As pointed out by Chris MB in another thread, the confinement time for the ITER tokamak might be 800 seconds (if edge instabilities don't cause a problem), A FRC device might be ~60-80 seconds. But, because of the Polywells advantage of greater density, monoenergenicity and possibly confluence, the otherwise dismal confinement times of a fraction of a second for the Polywell is sufficient to surpass the fusion limited lifetime of the fuel ions. This limited ion lifetime (due to fusion) is also important in that , at least according to Bussard, the ions are consumed before they can thermalize, thanks to the geometry and dynamics of the Polywell.

Dan Tibbets

[chrismb]

We were all very pleased to hear this

Were we, indeed!? More 'bemused' that 'pleased' for some individuals, I think.

[chrismb]

Which, I guess, brings up a question - won't these hot alphas poison the reaction?

This minor issue has been mentioned before.

The response is usually to say that they all disapear down the multi-million litre/s vac pumps, before they scatter everything else into a thermalised mass of inconsequence.

[93143]

What happens to the helium after it leaves the collectors is a separate issue. The collector design may be driven largely by this consideration.

[TallDave]

Well covered by those before me -- I would only offer a small addendum to Dan's post, that fuel ion confinement is probably very high, due to the excess of electrons everywhere and the virtual cathode inside the WB. Rick ignored ion pressure entirely when he did the ITER comparison.

Also in this vein -- most of you probably realized this a while before, but it only occurred to me yesterday that the implication of cold electrons in the cusps is that they create only a shallow gradient for fuel ions -- i.e., they aren't very good at sucking them into the cusps, as they can't accelerate them nearly as much as the central well does. That clarified the confinement picture for me a bit. (Previous statements from Joel Rogers about "ions being confined by cold electrons" had caused me some muddle.)

[chrismb]

most of you probably realized this a while before, but it only occurred to me yesterday that the implication of cold electrons in the cusps is that they create only a shallow gradient for fuel ions

That hasn't occurred to me. Why is this?

[D Tibbets]

Speaking of ions in the cusps, I assume (a dangerous activity) that cold electrons in the cusps (down scattered electrons) might be acting to plug the cusps aome. I don't understand electrostatic plugging much, except to say that multiple efforts with Penning trap devices, and Bussard's earlier work, did'nt seem to work (or at least not well enough).

Joel Rogers simulation did show ~ 30 amps of electron current to the walls, while there was no ion current to the walls. So, at least in his simulation, it seems he showed non- ambipolar flows out of the cusps (which of course would equal the non- ambipolar flow into the cusps (either directly through electron guns and ion guns, or indirectly through electron guns and neutral gas puffers)).
I've wondered how long the ions lasted compared to the electrons. Due to some comments I heard about the needed strength of ion guns (for a WB7 or 8 type machine?) being ~ several amps compared to ~ 40-50 amps electron gun currents, I guessed that ion containment was ~ 10 times that of the electrons. This suggests that the ratio may be much more. If the electron lifetime (with recirculation) is ~ 2 milliseconds, the ion lifetimes may be 50-100 or more milliseconds. I think that the mean time to fusion for the average ion was ~ 20 milliseconds, then almost all fuel ions would be consumed by fusion and very few would be escaping. I recall Bussard saying that the thermalization time for ions was longer than the fusion lifetime due to the dynamics of the Polywell, and that was without invoking restoring forces like annealing. That is important, because if the fuel ions were not consumed by fusion, then the longer confinement times would allow more thermalization.

Dan Tibbets

[TallDave]

Dan,

Yeah, that might mean we're somewhat limited in how much we could "throttle down" fusion rates by well depth. There may be a range of well depths at which ion lifetimes become too long for the machine to produce net power. Of course, we'd need a lot more data to say what the range was.

I'm not sure the flow out of the cusps is important. Bussard's b^.25*r^2 seems to only deal with cross-field transport and unshielded surfaces. He must have expected the "hot" tail of the electron distribution that could make it to the wall was small.

[D Tibbets]

Dan,

Yeah, that might mean we're somewhat limited in how much we could "throttle down" fusion rates by well depth. There may be a range of well depths at which ion lifetimes become too long for the machine to produce net power. Of course, we'd need a lot more data to say what the range was.

I'm not sure the flow out of the cusps is important. Bussard's b^.25*r^2 seems to only deal with cross-field transport and unshielded surfaces. He must have expected the "hot" tail of the electron distribution that could make it to the wall was small.

If the WB6 conditions represents an acceptable base line, a reactor could range from this level (10 KV on up to ~ 100 KV) this would give a throttler range of ~ 10-11 X in yeild/ input based on this factor alone.. Increased drive voltages would be better for eficiency as the fusion rate is faster, and the thermalization rate is slower (except at the low energy edge). As the fusion rate is faster at thehigher voltages, the individual ion lifetime before fusion would also be shorter. On issue not considered in this picture is the amount of neutrals that might be present, presumably this will (has to) be kept relatively small.

Actual electron cusp leakage is relatively small in terms of what is tolerable, but this is still a lot of current. If it was ~ 40 Amps in WB6, it would be ~ 4000 amps in a 150 cm radius machine (everything else being equal and accepting that electron losses are the dominate loss mechanism in the Polywell).
One thing not obvious in the available WB 6 results is the amount of thermalization of the electrons over their lifetime of a few milliseconds. Sense the WB6 only operated at 'steady state" for only about a 10th of this time. WB 7 may have run longer. And, the magnetic confinement time of WB 6 was ~ equal or less than the test time. The recirculation accounted for the rest. If recirculation serves to recycle the electrons at the original input voltage (and direction?), then the WB6 did cover the entire lifetime of the electron dynamics in the machine. Other than current, and photometryI don't know what diagnostics were aviable in WB 6 or 7 to measure electron behavior.

Dan Tibbets