Cusp Ion Plug

[rcain]

...The first question, which I'm not sure has been answered yet, is how energy efficient the external recycling of the electrons has to be in order to make a reactor, assuming you cannot live with thermalized electrons.

iirc, the claim has been made that recirculation doesnt need to exist/be efficient at all, for Polywell to work as an effective fusion device; so long as we get rid of them from the core, if they ever exist at those energies. (attentuated) recirculation, is just a bonus afforded by the geometry.

[TallDave]

1. As I now understand it, the magrid magnetic field contains the electrons, except at the cusps, where they jet out, but are recirculated due to the positive magrid. So no need to plug electrons at the cusp.

Close. The WB effect squeezes the cusps, limiting electron losses, and this may involve cusp plugging from oscillating electrons. It also seems unlikely electrons can "recirculate" to other cusps given that field lines go out to the wall.

If a polywell is driven in a way that is not ambi-polar, then the losses will not be ambi-polar.

Don't the parabolic potential well and the not-ambiplolar losses from the edge and cusps imply the cusps are ion-poor, and the ions that do reach the cusps are low energy?

I think it's a mistake to assume local quasineutrality only ends at the wall. It's also possible it ends at the cusps, which therefore eject electrons because the electron drive is injecting them. This seems more likely given the limited amount we know about the WB machine results.

Bussard said the electron density dropped by 1e4 from the WB interior to the outside. That implies there's a similar drop along the inside of the cusp, which helps explain why they wouldn't bleed ions: the electrostatic slope still points the wrong way for ions, esp with the Magrid out there.

[TallDave]

The system net energy gain ��balance�� will be little af��
fected, since most energy loss is due to electron escape
through the cusps. Note that this gain is reduced by the
factor of increased electron injection energy required to
create a deeper well to hold upscattered ions versus the
minimum well depth needed for core ion energy alone.
But deeper��than core��energy wells are required anyway,
to allow ion injection deep enough within the magnetic
field surface to avoid excessive transverse ion momen��
tum generation in core ion recirculating flow.

Heh, we were just talking about the problem of upscattered ions picking up transverse momentum last week. This solution is pretty obvious: the bulk of the ions never leave the well because they start inside it.

[KitemanSA]

Polywell Definitions:

RECIRCULATE: To exit a cusp, stop due to MaGrid charge, and reenter the same cusp. The electrons recirculate.

UPSCATTER: To gain energy due to random collisions. Upscattered ions can leave the well and are occasionally lost through a cusp.

[rcain]

.. surely this has got to be resolvable (visualizable), with a fairly simple 1d (1.5d) model, and Lorentz force alone (collisions/upscaterring, can be bought in as a second step).

the numerical computations are beyond me (...ehem) at present, though i suspect some here will show them trivial at this level.

i was thinking of a simplified model of 'containment cylinder', at a couple of well chosen angles though the machine. much along the lines of simple Paul/quadrapole trap or TOf Mass Spectrometer (esp. use of Reflectron - http://en.wikipedia.org/wiki/File:TOF-reflectron.png ).

i've not seen anything like this so far (Indreks nearest i suspect). any volunteers?

[TallDave]

Maybe we can borrow EMC2's PIC code.

Of course, I'm pretty sure I already know what that looks like...

I found Bussard's Debye length calculation interesting.

[TallDave]

Polywell Definitions:

RECIRCULATE: To exit a cusp, stop due to MaGrid charge, and reenter the same cusp. The electrons recirculate.

UPSCATTER: To gain energy due to random collisions. Upscattered ions can leave the well and are occasionally lost through a cusp.

Did we ever get a page of those together?

It does help to agree on the meaning of words.

[rcain]

Maybe we can borrow EMC2's PIC code....

i'm not sure we even need to get that complicated at this stage, sort of charged balls rolling between two hills would do me to start.

In what way were Bussards Debeye calcs interesting?

(btw - re 'RECIRCULATE' - shouldnt we mention 'possibility'/opportunity of recirulation between cusps, outside the magrid, supposing suitably configured container - i know this doesnt really figure yet, but i always thought of 'recirculationn though the same cusp as 'oscillation'/orbiting. if, when, we eventually get to consider how to direct useful energy out of the device, and how perhaps to implement homeostasis/control, we might need to extend our definition of recirculation. anyone agree?)

[TallDave]

rcain,

It's fine for an exercise, but I'm not confident they can tell us much that's useful. I'm suspicious of simulations anyway. Rick has pointed out you can get wildly different results by modifying your assumptions slightly. That seems to call for more experimental data to nail down your assumptions.

Re the Debye calculation:

These are limited to those contained within a sphere
around each particle with radius equal to the Debye
shielding radius
LD
=
kT
4�� ne2
���� ��
���� ��
0.5
��8��
For ion core energies Ec > 1 x 103 eV, the Debye sphere
will contain a very large number of ions for any density
&#56256;&#56324; < 1 x 1019/cm3,

Bleah, equations don't paste very well. Someone beat the ANSI folks over the head till they put them in.

[rcain]

TallDave - well, its that exercize that would sort of help me right now i think. sure, we do not hope to capture all complexity, to start, but it sets a stage.

as to wildly different results depending on assumptions (initial conditions), that is sort of the point. such an exersize at least allows us to circumscribe regions of the space where we know things are either certain or uncertain, stable or unstable. indeed we are sort of relying on such criticalities being identified (and existing,) for the Polywell to work at all.

whatever the experimental results (and i agree with you on their importance), we still need a coherent simplified model, that works, and that we can all (well, some of us), get our heads around. otherwise, we have no idea what we are doing or what we are talking about (not that i'm really suggesting that, of course).

re. Debeye quote - was that from Valencia paper - to me, all it suggests is we have a confined plasma under some effective pressure (and turbulence).

ps. surely gyroradius is going to have a critical (dominant?) role at corner cusps in determining ion/electron distribution. (remembering criticality of coil spacing). (unless/until it actually bursts - Art's follow my leader scenario)?

[Art Carlson]

I think it's a mistake to assume local quasineutrality only ends at the wall. It's also possible it ends at the cusps, which therefore eject electrons because the electron drive is injecting them. This seems more likely given the limited amount we know about the WB machine results.

I didn't assume the cusp plasma must be quasi-neutral. I calculated it. Of course, if you have a solid surface, quasi-neutrality can break down in the last Debye length. There is no reason for it to freak down in the middle of nowhere.

[chrismb]

I've never really bought into the argument that Polywell would be "a sphere - but with holes in it". It would be, I rather think, a ball with spiky bits. They are all, and one of the whole, the same thing. Looking at it that way you suddenly find yourself with a set of much simpler questions - what happens at the termination of the spiky bits? The nature of 'the cusps' then becomes somewhat irrelevant.

I do not see why the electrons wouldn't migrate and be 'held' in the same topology, even if there is the claimed radial polarisation that goes on. If the sought-after central polarisation occurs in a stable fashion, I would then suppose that the higher electron density would simply be a facimile of this spikey ball, and the spikes of increased electron density would run up into the cusps.

[alexjrgreen]

ps. surely gyroradius is going to have a critical (dominant?) role at corner cusps in determining ion/electron distribution. (remembering criticality of coil spacing). (unless/until it actually bursts - Art's follow my leader scenario)?

kcdodd modelled the shape of the wiffleball at the edges and corner cusps and the behaviour of particles there.

Unless a particle flies straight down the barrel it gets turned round by box corner reflection, so the losses are low.

[alexjrgreen]

Maybe we can borrow EMC2's PIC code.

Of course, I'm pretty sure I already know what that looks like...

Why don't you post your version? It might inspire others...

[alexjrgreen]

I've never really bought into the argument that Polywell would be "a sphere - but with holes in it". It would be, I rather think, a ball with spiky bits. They are all, and one of the whole, the same thing. Looking at it that way you suddenly find yourself with a set of much simpler questions - what happens at the termination of the spiky bits? The nature of 'the cusps' then becomes somewhat irrelevant.

I do not see why the electrons wouldn't migrate and be 'held' in the same topology, even if there is the claimed radial polarisation that goes on. If the sought-after central polarisation occurs in a stable fashion, I would then suppose that the higher electron density would simply be a facimile of this spikey ball, and the spikes of increased electron density would run up into the cusps.

This is good. Go on.