recirculation vs. line cusps

[hanelyp]

The simplest magnetic well configuration, 2 coils like poles together, was rejected by Dr. Buzzard on account of the equatorial line cusp, a clear leaky zone. But I believe that decision was made before WB-6 and a proper understanding of recirculation. A large population of electrons outside the magrid, and electrons circulating in and out, isn't a major problem except as those electrons are lost. Given proper recirculation might this configuration work? Might other configurations with leaky wells also work?

The symmetries in this configuration should make it comparatively easy for me to simulate.

[charliem]

Remember that recirculation is never 100% perfect, some of the electrons that get out dont come back, so there is still the neccesity of making cusps losses as little as possible.

With only two opposed coils you'd have mirror confinement but from that field geometry no wiffle ball could be formed, and according Bussard's Valencia paper mirror confinement is less efficient than wiffle ball confinement.

Better confinement means a higher ratio of electron density inside to outside (and ion density ratio?). Keeping low external densities is paramount to minimize energy losses.

[seedload]

Bussard basically moved from the idea of extraordinary confinement with some recirculation to very good confinement with exceptional recirculation when he went to the WB6.

Bussard wrote:

This means that the ONLY Polywell systems that can be made to work are those in which there is NO metal surface exposed - this requires open cusp, recirculating electron flow, around B field coils that are spatially conformable to the magnetic fields surfaces that they produce.

He accepted that line cusps will exist and focused on getting better recirculation. He also changed the meaning of the Wiffleball. This is what he said.

This also makes the WB trapping factor simply a measure of electron density ratios (inside and outside) rather than a measure of "losses" to containing walls and structures. And, because of this, it is not necessary to achieve Gwb values greater than, at most, 1E4 - rather than the 1E6 required for non-recirculating machines.

He is accepting cusps in any form in these statements but insisting on almost perfect recirculation and high electron densities "inside" the machine as opposed to outside of it.

So, if you can come up with a recirculating configuration that has lots more electrons inside than out, then it should work.

[charliem]

Bussard basically moved from the idea of extraordinary confinement with some recirculation to very good confinement with exceptional recirculation when he went to the WB6.

He accepted that line cusps will exist and focused on getting better recirculation.

He is accepting cusps in any form in these statements but insisting on almost perfect recirculation and high electron densities "inside" the machine as opposed to outside of it.

The way you say it looks like Bussard abandoned the wiffle ball confinement idea for any other fields shape that would allow recirculation.

More like he took the wiffle ball concept from a purely ideal form to a practical (doable) one by allowing recirculation (given the impossibility to 100% shut cusps).

As always, confinement is still the key, and obtaining it with a magnetic mirrors machine looks harder than with a w-b one.

[seedload]

Bussard basically moved from the idea of extraordinary confinement with some recirculation to very good confinement with exceptional recirculation when he went to the WB6.

He accepted that line cusps will exist and focused on getting better recirculation.

He is accepting cusps in any form in these statements but insisting on almost perfect recirculation and high electron densities "inside" the machine as opposed to outside of it.

The way you say it looks like Bussard abandoned the wiffle ball confinement idea for any other fields shape that would allow recirculation.

More like he took the wiffle ball concept from a purely ideal form to a practical (doable) one by allowing recirculation (given the impossibility to 100% shut cusps).

As always, confinement is still the key, and obtaining it with a magnetic mirrors machine looks harder than with a w-b one.

Didn't mean to sound like that entirely. The point was that he relaxed his ideas about required electron containment by two orders of magnitude but insisted on great recirculation. That was it. Agreed that you still need very good containment with a huge ratio of inside to outside density of electrons (1E4). Agreed that Bussard thinks you can only do this with the WB field. Agreed that he would say that mirrored coils wouldn't do it. I just didn't want to stomp on creativity.

[dch24]

The point was that he relaxed his ideas about required electron containment by two orders of magnitude but insisted on great recirculation. That was it. Agreed that you still need very good containment with a huge ratio of inside to outside density of electrons (1E4). Agreed that Bussard thinks you can only do this with the WB field. Agreed that he would say that mirrored coils wouldn't do it. I just didn't want to stomp on creativity.

It just occurred to me that Bucky Fuller might possibly approve of this concept - "waste not, want not" - by eliminating losses even if confinement went down a lot.

Not that it matters...

[TallDave]

A large population of electrons outside the magrid, and electrons circulating in and out, isn't a major problem except as those electrons are lost.

It's a problem because the ratio of inner to outer density controls how deep the well can be before arcing to the outer walls occurs. IIRC, Bussard believed a ratio of 1000:1 was the the minimum for fusion.

Bussard actually distinguishes between "mirror trapping" and "cusp trapping" in the Valencia paper. With the latter, he says you can get a ratio in the tens of thousands.

As previously noted, no Polywell can operate at all if arcing
occurs outside the machine, between the walls and the
machine, because this destroys the ability of the driving
power supplies to produce deep potential wells. Thus the
mean free path for ionization outside the machine (inside the
container) must be much greater than the external
recirculation factor, times the machine-to-wall distance.
Since the mfp for ionization is inversely proportional to the
product of the local neutral density and the ionization crosssection,
this condition can ALWAYS be satisfied, IF the
external neutral gas pressure is made sufficiently small. In
order to avoid external arcing, the densities thus required are
very much too low to be of interest for fusion, thus the
density inside the machine (at its boundary) must be very
much higher than that outside. This ratio is the Gmj factor,
which is the ratio of electron lifetimes within the machine
with B fields on, to that without any B fields.
In contrast, in order to be of interest for fusion, the interior
density must be above some numerical value for any given
size of machine. Typically this requires electron densities at
the interior boundary of order 1E13/cm3, or higher. While
the exterior densities (of neutrals able to be ionized) must
typically be below 1E10/cm3 or less. Thus a minimum value

exists for Gmj (here, typically 1E3), below which no
machine can give significant fusion or net power,
independent of the unprotected wall loss problem. Both
must be solved simultaneously
In any realistic device, the effective overall trapping factor is
reduced from the pure WB mode by circulation through the
semi-line-cusps at the spaced corners, which allow much
greater throughflow per unit area than through the point
cusps of the polyhedral faces. The line-cusp throughflow
factor is called Glc. These two effects act as parallel lossflow
channels, and combine to produce an overall trapping
factor Gmj, which is the inverse sum of each of their
contributions, as weighted by their fractional areas involved.
Thus the overall trapping factor for inside/outside density
ratios, is given by 1/Gmj = fwb/Gwb + flc/Glc, where the
fractional areas are flc + fwb = 1. Solving this algebraic
identity gives the effect of corner flow paths on the entire
Gmj system as Gmj/Gwb = 1/[fwb + (Gwb/Glc)flc]. If
corner flow paths are not to dominate the trapping, the
second term in the denominator must be kept small relative
to the first (WB) term, thus flc/fwb << Glc/Gwb.
Analysis shows that line cusp corner spacing flow factors are
roughly equal to the square root of the mirror reflection
coefficient Gmr for point cusps at the corner field strength,
thus Glc = SQRT(Gmr). Gmr values may be as high as 80-
100 in suchmachines, thus Glc = 10 is a reasonable value for
the corner flow. Using this, and noting that fwb must be
close to unity, gives the approximate result that flc <<
10/Gwb for effective operation. In a truncated cube
configuration Gwb = (BR)^2/110E, for B in Gauss, E in eV
and R in cm. Typically, machines may have Gwb > 1E4,
thus the fractional corner cusp flow area must be flc << 1E-3
as required to maintain good density ratios from the interior
to the exterior, to prevent arcing, and retain high enough
density inside for useful fusion.

http://www.askmar.com/ConferenceNotes/2 ... 0Paper.pdf

[charliem]

One aspect of P-W operation I dont see clearly is what happens if we increase B field strengh and internal density, but dont modify electron injectors potential nor net charge.

My intuition says that it would not work, but I can't justify it so I'm most probably wrong.

Anyone?

[MSimon]

One aspect of P-W operation I dont see clearly is what happens if we increase B field strengh and internal density, but dont modify electron injectors potential nor net charge.

My intuition says that it would not work, but I can't justify it so I'm most probably wrong.

Anyone?

If we get the device fusioning then we can probably turn the electron injectors off. You have 1E21 alphas leaving the reaction space every second. That is 1E21 electrons left behind. That is a current on the order of 1,000 Amps. Those kinds of electron guns are hard to buy and difficult to make.

[drmike]

Talldave - thanks, I don't remember reading that.

I think we can play games with electron density using POPS like processes. The thing that Bussard was worried about was that external electrons create electric fields that draw out ions as well as cause arcing to the external wall. By dynamically pushing the ions back thru the cusps we can help the fusion process and reduce the losses because the electrons will try to follow the ions.

If it can work for 10 or 20 microseconds without any help, we'll have proof of principle. After that, it's "just engineering details".

[StevePoling]

Talldave - thanks, I don't remember reading that.

I think we can play games with electron density using POPS like processes. The thing that Bussard was worried about was that external electrons create electric fields that draw out ions as well as cause arcing to the external wall. By dynamically pushing the ions back thru the cusps we can help the fusion process and reduce the losses because the electrons will try to follow the ions.

If it can work for 10 or 20 microseconds without any help, we'll have proof of principle. After that, it's "just engineering details". 8)

if one of the factors limiting voltage is arcing to external walls, why not push the walls farther out. Or insulate them? Aside from expense, what's to prevent setting up the apparatus in a larger vacuum chamber and cranking up the voltage?

Are such experiments feasible in space? Is NASA still running their "getaway specials" for small-time researchers? Or ask the next Google billionaire going up on Soyuz to smuggle an experiment in his duffel bag.

[drmike]

Building a BFR in space with no outer wall makes some sense, but you can't get too close to it. Large chambers were discussed here once before, and the conclusion was that it is not a problem.

It boils down to an efficiency issue though. If Wiffle Balls make fusion work, we can deal with efficiency problems later. If it doesn't work, no point in dealing with it.

I sure hope it works!