All that can go wrong with recirculation

[kcdodd]

Well, as I see it there are only two possibilities for keeping the potential in the outer region within the boundaries of the machine. Either there are ions there to balance the electron's charge, as you say, or the electron density is just not very high outside to begin with. And, like I already said, I don't see how you could hope to keep even one ion in that region, much less get a high density. So assuming that ions cant stay in the outer region that only leaves the electron density outside being rather low, at least to the point that the potential generated from the spatial electron's is below that generated between the magrid and wall from the external power source.

Let me know if we are agreeing or not on those two points before I go on.

[Art Carlson]

Hmmmm? Bussard addresses that here:

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.

Well, that's nice. Can you help me understand what he says?

What's important inside is the electron/ion/plasma density (and the neutral density better be doggone low). What's important outside is the neutral density. (Don't know about you, but I've been making the mistake to think it was a question of electron density outside.) Biggest question: What does "the ratio of electron lifetimes within the machine with B fields on, to that without any B fields" have to do with the ratio of plasma density inside the machine to neutral gas density outside the machine?

[Art Carlson]

The cusps plugging with low-energy electrons was my interpretation of the behavior of PXL-1 (a closed-box machine) in one particular configuration. Dr. Bussard did not think that was correct, although he was certain some "two-color electron" effects would be important.

Whatever was happening, PXL-1 did drop percipitiously into a low-leakage state, presumably evidence of a wiffle-ball state, where drive current limited to about 50 mA. When the magnetic field was switched off while it was still at high voltage and in this state, all hell broke loose. The effects were similar to accidents I've seen described with electron storage rings. I witnessed very high reverse current in the magnets (blowing a large damper diode open, then arcing past a magnetic blowout contactor) with EMP-like effects damaging other equipment in the lab.

Has this been published? How was "leakage" measured? What is the evidence that the drop in leakage was due to whiffle-ball confinement instead of something else (like cusp plugging)? Are we both using the term "whiffle-ball confinement" in the same way: Effective loss area on the order of several times the gyroradius squared due to high beta effects?

[Art Carlson]

Well, as I see it there are only two possibilities for keeping the potential in the outer region within the boundaries of the machine. Either there are ions there to balance the electron's charge, as you say, or the electron density is just not very high outside to begin with. And, like I already said, I don't see how you could hope to keep even one ion in that region, much less get a high density. So assuming that ions cant stay in the outer region that only leaves the electron density outside being rather low, at least to the point that the potential generated from the spatial electron's is below that generated between the magrid and wall from the external power source.

Let me know if we are agreeing or not on those two points before I go on.

I'm with you. Please go on. I'm especially interested in the part about how you recirculate electrons when there are none outside the machine.

[Tom Ligon]

Art,

I was just running the thing, not doing the analysis. PXL-1, when run with a "hot cathode", would be expected to have high cusp losses as the chamber walls would have attracted electrons. Upon being initially switched on, it would draw everything the power supply had to give (about two amps) for a couple of seconds. Then there was a sudden drop out of the limited condition, stabilizing at about 50 mA of cathode current. The pattern reproduced nicely from run to run, as we worked up to higher voltages.

My initial impression was dispenser cathode poisoning, but turning off the magnets too soon convinced me the machine was simply filled with every electron it could hold, at high kinetic energy. Your objections regarding cusp losses would have been perfectly valid for PXL-1, as that 50 mA would have been lost to the walls ... there was no prospect for recirculation in the closed-box machine.

I don't know if the PXL-1 results were ever published. I don't recall ever getting it to a state in which fusion would have been expected. It had some technical flaws. I believe WB5 was designed in an attempt to correct those flaws. In the end, the whole "closed box" approach was abandoned as a dead end, with the realization of how important the electron recirculation offered by the form of WB6 was.

[Art Carlson]

I am just pointing out that the picture on the table (pure electron plasma outside the cusps with a significant density) is not consistent. A polywell machine will certainly do something, and that something will certainly be consistent with the laws of physics. I don't think we understand yet what we should expect it to do.

Let me make a stab at this, myself. The easy way to do fusion would be with a magic wall that totally reflects ions. The second best thing would be a magic wall that totally reflects electrons, because the ions won't dare to go much at all beyond the outskirts of the electron cage. The closest we can come to such a magic electron wall is a magnetic field. Topologically, the magnetic field cannot be parallel to the surface everywhere (except on a torus - but that's a dirty word here), so magnetic cusps are unavoidable. (Up to here the standard polywell tale.)

The cusps punch holes in our magic wall. First, electrons leak out. They might be reflected back in with the right configuration of external electric fields, and some of the electrons might pool up and create an internal electric field that reflects other electrons back. Are these electrons doing their job? Not really, since the ions follow the electron distribution, plus a sheath, they will be able to leak out where the electrons are leaking out. This might not look too bad, but if the leaky electrons are pushed back by external fields, these same fields will pull out the ions. If the leaky electrons are able to plug their own hole, then the ions will come along and unplug it again.

The ions are also confined a bit by the magnetic field, so we could ask if this is enough to help. (Note that this goes against the catechism of the polywell, but let's be tolerant.) The answer is no, because the loss rate of ions from a line cusp is the same as that of electrons (assuming equal temperatures and no electric fields). The loss of ions from a point cusp is even greater than that of electrons.

I conclude that either electrons or ions or both will be lost through the cusps at at least the rate determined by the cusp, and there can be no credit for recycling.

Is there any way out? The only loophole I can see at the moment is that if the ions are cold at the edge (as they are according to polywell othodoxy), then the energy loss associated with the ion particle loss may be small. (Alternatively, the ion cusp loss rate may be small because the gyroradius is small.) If you pick this scenario, I will give you a hard time about maintaining a two-temperature distribution, but we can save that for tomorrow.

Do you concur with my argument up to the point that the net particle losses will be on the order of the cusp loss rate, i.e. that recycling as we know it is not possible, except perhaps to shift the species lost from electrons to ions?

[bcglorf]

Let me make a stab at this, myself. The easy way to do fusion would be with a magic wall that totally reflects ions. The second best thing would be a magic wall that totally reflects electrons, because the ions won't dare to go much at all beyond the outskirts of the electron cage. The closest we can come to such a magic electron wall is a magnetic field. Topologically, the magnetic field cannot be parallel to the surface everywhere (except on a torus - but that's a dirty word here), so magnetic cusps are unavoidable. (Up to here the standard polywell tale.)

The cusps punch holes in our magic wall. First, electrons leak out. They might be reflected back in with the right configuration of external electric fields, and some of the electrons might pool up and create an internal electric field that reflects other electrons back. Are these electrons doing their job? Not really, since the ions follow the electron distribution, plus a sheath, they will be able to leak out where the electrons are leaking out. This might not look too bad, but if the leaky electrons are pushed back by external fields, these same fields will pull out the ions. If the leaky electrons are able to plug their own hole, then the ions will come along and unplug it again.

Now, I only took my physics to an undergrad level, so forgive my ignorance. I'm going to ask what I hope is a stupid question. You do realize that the electric field that is supposed to recirculate the electrons comes from the positive charge being held on the magnetic grid, correct? And also that the ions are introduced inside the grid between it's positive charge and the negative potential well inside? As such, ions are only able to reach the magnetic grid if they upscatter enough and are guaranteed lost if they pass it as the positive charge that is drawing the electrons back will push them out. And again, forgive me for pointing out something so basic since I'm pretty sure that there are just more complex factors going on that I'm just not following your real argument.

[Art Carlson]

Let me make a stab at this, myself. The easy way to do fusion would be with a magic wall that totally reflects ions. The second best thing would be a magic wall that totally reflects electrons, because the ions won't dare to go much at all beyond the outskirts of the electron cage. The closest we can come to such a magic electron wall is a magnetic field. Topologically, the magnetic field cannot be parallel to the surface everywhere (except on a torus - but that's a dirty word here), so magnetic cusps are unavoidable. (Up to here the standard polywell tale.)

The cusps punch holes in our magic wall. First, electrons leak out. They might be reflected back in with the right configuration of external electric fields, and some of the electrons might pool up and create an internal electric field that reflects other electrons back. Are these electrons doing their job? Not really, since the ions follow the electron distribution, plus a sheath, they will be able to leak out where the electrons are leaking out. This might not look too bad, but if the leaky electrons are pushed back by external fields, these same fields will pull out the ions. If the leaky electrons are able to plug their own hole, then the ions will come along and unplug it again.

Now, I only took my physics to an undergrad level, so forgive my ignorance. I'm going to ask what I hope is a stupid question. You do realize that the electric field that is supposed to recirculate the electrons comes from the positive charge being held on the magnetic grid, correct? And also that the ions are introduced inside the grid between it's positive charge and the negative potential well inside? As such, ions are only able to reach the magnetic grid if they upscatter enough and are guaranteed lost if they pass it as the positive charge that is drawing the electrons back will push them out. And again, forgive me for pointing out something so basic since I'm pretty sure that there are just more complex factors going on that I'm just not following your real argument.

No harm asking, and it's not a stupid question. It's just based on the overly simple picture that is always used to explain how the polywell is supposed to work. The trouble is that the picture is 1-d (spherically symmetric), but when you start to look at losses (or ion convergence), you need to think at least a little bit in higher dimensions. You can start with a sphere of electrons confining a sphere of ions, but when you add the cusps, electrons leak out along them, so your electron sphere now has spikes like a blowfish. Since the ions are only confined electrostaticly by the electrons, they can only be where electrons are, but they can be everywhere that electrons are. So the ions start creeping out along the spikes, too. You might think of the cusps as a tunnel that allows the ions to get through the wall of high potential and hemorrhage into space.

If you can't follow me, feel feel to ask for clarification.

[drmike]

I didn't see this thread when I posted a comment in another one. "Recirculation" means bouncing inside the coils. Bussard states in only a few places that all particles that get past the coil radius are lost. In this sense Art is correct - all the particles that get out of the cusps don't help confinement any more.

Bussard's thought process was along the lines of: electrons are injected into the center and they bounce around the inside of the coil region until they escape out the cusp regions. He was computing his systems to have at least 1e5 bounces between center and coil before hitting the loss cone.

It remains to be proven if this can happen.

Simon is right - "recirculation" is a bad term because it conjures up "circles".
"Bouncing" or "oscillation" makes a lot more sense.

[TallDave]

Art,

I'm assuming Bussard made a typo there. Since the 1e10 vs. 1e13 difference is the same as the necessary density ratio, the parenthetical about neutrals doesn't really make sense. He must be talking about the electron density.

[TallDave]

You can start with a sphere of electrons confining a sphere of ions, but when you add the cusps, electrons leak out along them, so your electron sphere now has spikes like a blowfish. Since the ions are only confined electrostaticly by the electrons, they can only be where electrons are, but they can be everywhere that electrons are.

Welll.... okay, but if those tiny spikes are symmetrical the focus of the well is still in the core. I don't think any significant number of ions will venture that far out.

[TallDave]

I didn't see this thread when I posted a comment in another one. "Recirculation" means bouncing inside the coils. Bussard states in only a few places that all particles that get past the coil radius are lost. In this sense Art is correct - all the particles that get out of the cusps don't help confinement any more.

Bussard's thought process was along the lines of: electrons are injected into the center and they bounce around the inside of the coil region until they escape out the cusp regions. He was computing his systems to have at least 1e5 bounces between center and coil before hitting the loss cone.

It remains to be proven if this can happen.

Simon is right - "recirculation" is a bad term because it conjures up "circles".
"Bouncing" or "oscillation" makes a lot more sense.

Hmm, I don't see how that squares with Bussard's statements about inside vs. outside density ratios and electron flows around the coils.

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. And this forces the coils to be spaced at a
significant interval at their corner “touching“ points, to allow
free electron flow through these points. This also makes the
WB trapping factor simply a measure of electron density
ratios (inside to outside) rather than a measure of —losses“
to containing walls and structures.

[Art Carlson]

Simon is right - "recirculation" is a bad term because it conjures up "circles".
"Bouncing" or "oscillation" makes a lot more sense.

Why not call it "cusp confinement", then?

[TallDave]

Art,

I'm assuming Bussard made a typo there. Since the 1e10 vs. 1e13 difference is the same as the necessary density ratio, the parenthetical about neutrals doesn't really make sense. He must be talking about the electron density.

Here's the other place he talks about neutrals:

In both of these,
neutral density in/out ratios needed to avoid Paschen arc
breakdown outside the machine (for a very short time), was
achieved by fast puff gas input directly into the machine
interior edge.

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.

[MSimon]

Art,

I'd say you were pretty much on track if static analysis is the correct way to describe the machine. If you have a lot of interacting dynamics (oscillating beams) I don't think you have covered it.

Tokamacs are amenable (first order) to static analysis. I don't think that would be a correct statement for BFRs.