Of Line Cusps

[tombo]

as described by Art, the wiffleball will have an irregular shape

I wouldn’t call the line (corner) cusp an irregular shape. I would call it a “Y” shape.
I prefer to be more precise and give it less mystery.

If you figure out what Dr. Bussard was getting at with the gyroradius stuff, maybe you can explain it more simply!

The conclusion of that paper is that 1.95 is the minimum and 2.87 is the maximum so it is not as fuzzy as saying it is 2 or 3.
I made myself a little summary of that paper to help my own understanding that I would share if anyone wants to see it.
(I’ve been a bit humbled by some of the work I’ve seen here lately and am trying to shut up a bit. This is not up to that level.)

if the Magrid is a Faraday cage then ions can't see the electrons

I don’t have a lot of confidence in the screening ability of a coarse faraday cage with holes this large when the electrons and ions are seeing it from up close.
This is one of the things that keeps bothering me.

[drmike]

Tom - that's why I'm itching to build hardware!! There's a lot of fun physics here...

tombo - the virtual cathode in the center along with the ions moving radially creates a central virtual anode, and the whole thing oscillates. A double well was described by the Japanese paper early on in this forum. So the inner most core is really small, but it helps keep the electrons around, and those in turn help keep the ions around. It's not so simple as a Faraday cage - it is more like a series of grids. They are not real grids, but "virtual".

The main problem is that it can not be a static system. It has to be dynamic. I think the fundamental question is can we create a dynamic system that is stable long enough to get net power out? So far, all fusion research to date has failed to do that.

Challenging problems are the most fun!

[Art Carlson]

I understand (hopefully correctly) that (1) tokamaks have problems partly because it's really hard to magnetically confine the positive ions which are massive and we have to get to a really high average temperature for some fusion to occur, (2) the polywell has the advantage of trying to magnetically confine much less massive electrons rather than positive ions (and the electrons hopefully induce the motion necessary on the part of the ions to result in fusion at or near the center of confinement, and high average temperature is not necessary), (3) ...

I know you're repeating the common wisdom here, but this simple picture doesn't make a lot of sense. Both the tokamak and the polywell are trying to confine a quasineutral plasma with magnetic fields. In either machine, if you can succeed in confining the electrons, the ions will be confined automatically by the electric field. In either machine, the ions and the electrons are stongly coupled and have to be considered self-consistently. There are big differences, for example that the tokamak has closed magnetic flux surfaces but also has large regions of bad curvature, but this "confine electrons instead of ions" business doesn't get at them.

Here's one idea for an alternate geometry. Confine electrons using a toroidal magnetic field (maybe a large-in-size field) which does not (hopefully) have cusps for electrons to escape. Allow or inject ions into the region of electron confinement. ...

Unfortunately a torus is not just a cylinder without an end. The curvature of the magnetic field results in a drift that will shove your electrons against either the ceiling or the floor in short order. If you add an equal number of ions, their electrical attraction will prevent this (and also allow you to go to much higher density), but then the EXB drift will shove them both against the outer wall. To prevent this, you need a toroidal current (or some other source of a rotational transform). Oops. We just reinvented the tokamak.

[Art Carlson]

As i've mentioned before, it seems to me they will either oscillate with a period equal to the electron transit speed, or they will bunch up and form a stationary cloud. Either way, it seems like the hole is going to get pluged by a "virtual electrode."

And what are the ions doing all this time? What looks like a plug to electrons looks like marching orders to ions.

[MSimon]

As i've mentioned before, it seems to me they will either oscillate with a period equal to the electron transit speed, or they will bunch up and form a stationary cloud. Either way, it seems like the hole is going to get pluged by a "virtual electrode."

And what are the ions doing all this time? What looks like a plug to electrons looks like marching orders to ions.

But every thing is oscillating Art.

How do you figure that out? May I suggest a real time reactor simulator capable of dealing with about 10^30 particles. i.e. experiment.

[Solo]

When I looked at one of Indrek's slices thru the corner of a polywell showing B-field strength, I noticed two things about the semi-line cusps: one was that the field right between the coils where they almost touch (the midpoint of the line) is greater than the field at the center of the 'corner cusp,' which is also greater than the field at the center of a point cusp. So there is some difference between these semi-line cusps and your traditional ring cusp in that the field strength of the cusp throat changes as you move along the line cusp.

The other thing I noticed was that the gradient in the field strength was much steeper as you approach the midpoint. I don't know what effect the gradient has on mirror/cusp confinement. Most of the calculations for mirror reflection in a cusp just assume the gradient is low enough to ignore. I'm not sure how high it'd have to be to get interesting, nor what it would do in that case. (Bussard uses (Larmor rad.)*(gradient_z of (lnB)) <<1, so that the B-field gradient doesn't change much over a gyroradius.) I would speculate, though, that the reflection coefficient would not suffer if the gradient went up. Could this be the source of the 'whiffle-ball' effect?

[ravingdave]

As i've mentioned before, it seems to me they will either oscillate with a period equal to the electron transit speed, or they will bunch up and form a stationary cloud. Either way, it seems like the hole is going to get pluged by a "virtual electrode."

And what are the ions doing all this time? What looks like a plug to electrons looks like marching orders to ions.

I meant this condition would plug electrons. You are of course right about this. If either a stationary cloud, or a group of oscillating electrons form in the cusp region, it will act as a lure for ions. The pull on the ions will be proportional to the quantity of electrons involved.

I think what we are all hoping is that the magnetic field will constrain the electrons going through this hole to a very small trickle, and that this small trickle of electrons will somehow represent a very small effect on the ions. ( I think I saw someplace where you calculated the initial leakage.)

On the other hand:

I have read your assesment that (if I understand you correctly) no matter how small that trickle is, it will attract some ions, which will then attract further electrons which will result in a cascade effect of blowing a big hole through the cusp. Very Bad.


If this is true and insurmountable then the design is probably hopeless. You make a good argument and it may very well be true, but we are all hoping it is not. I can only speak for myself, but I suspect many others are relying on the belief that Dr. Bussard looked at this and concluded that it could be made to work. I hope he based this belief on sound physics principles and not the power of positive thinking.

To my observation, there seems to only be about 4 or 5 people in this forum that can competently discuss this design on your level. I , of course am not one of them, and for that reason I have refrained from bothering you or the others with my comments. In my opinion, when the adults are talking the children should be quiet!

In any case, You have a good argument, and I can't say i've seen a good refutation.


David

[Art Carlson]

I have read your assesment that (if I understand you correctly) no matter how small that trickle is, it will attract some ions, which will then attract further electrons which will result in a cascade effect of blowing a big hole through the cusp. Very Bad.

We'll, maybe not quite that bad. I see it more like, both elecrons and ions are leaky, and if you try to stop up one of them with an electric field, you make the other one that much worse, so you don't gain much and usually lose a little bit.
An example of a similar phenomenon is the heat load to a metal surface in a plasma (a subject I have done work on). If the object is electrically floating, there is a particular heat load. If it is biased positive, the electron energy doesn't change, but more electrons come from the tail of the Boltzmann distribution and so the heating goes up. If it is biased negative, the ion current doesn't change, but each ion brings more energy because it falls through a larger potential, again increasing the heating. Since the floating potential is near the minimum of this curve, small bias voltages don't change the heat load much.
Another example is free expansion. Since the electrons are faster, they move ahead of the ions, but this creates an electric field that pulls the ions along. The net result is expansion at the sound speed, sqrt(kT_e/m_i). Note that the electrons and the ions flow together, but the electrons contribute the pressure and the ions contribute the inertia.
If the polywell is neutral, I expect the loss rates of electrons and ions to be equal. (The electrons see a smaller hole, but they are faster.) If you bias the polywell negative, you may be able to supress ion losses, but the electron losses can only get worse. If you plug the cusps for electrons, you will be opening them up for ions. It would surprise me if the net power loss changed much no matter how you set up the bias, but it's hard to say in detail, and I wouldn't be too surprised if a net reduction by the order of the square root of the mass ratio is possible. I think we can rule out a reduction by 1000-10,000.

[rnebel]

1-D PIC simulations say the following:

1. Electrons leave the well at the same rate they are injected.
2. Ions can only leave if they are upscattered out of the well and have a much longer confinement time.

This is the answer you get if the ionization rate is small. There is no mass dependence.

[Tom Ligon]

Art,

You have a good general principle there: there are a lot of things you can do to attempt to benefit one species which kill you for the other species. My understanding is, all attempts to fiddle with repeller plates in HEPS and WB-5 were unproductive ... electrostatically blocking the electrons in a "closed box" machine produces an ion sink.

I recall a few attempts to place insulators at the cusps, particularly a couple of single-turn copper tube experiments, the MPG machines. The MPG machine I watched run had the tubing shaped in squares to form a trucated cube, with the vertices held together by alumina or similar insulators. All sorts of fireworks were emitted from the insulators. I surmise that as they charged up with electrons, they attracted ions, and you lost both, and considerable energy.

Physics won't let you cheat. A magrid machine, i.e. an Elmore-Tuck-Watson machine with a magnetically-insulated grid, is the only "honest" configuration. (We await the experimental results to see if "honest" is also "workable.")

You want nothing but ions and electrons in this thing, and you don't want both at low energy (tens of eV) at the same point. Where the electrons are slowest (the center) you want the ions moving fast, and where the ions are slowest (just inside the magrid) the electrons must be at high kinetic energy. Anything trying to get around this is trouble.

I would offer that I've run a couple of magrids extensively, runs long enough to observe the plasma at leisure. Clearly, there is some leakage out the corner and face cusps, evidenced by faint whisps of plasma seen there, but I've never seen hot-spots on the walls where an ion beam would be hitting. That's as opposed to a fusor run in Paschen discharge mode, which puts out a hellacious e-beam that makes an obvious hot-spot and can damage the walls and make x-rays. From this I surmise the plasma outside is from ionizing background gas in an imperfectly pumped system. This is admittedly subjective, but it appears to me the far brighter glow inside the magrid appears well-contained, and I've never seen any bright spots in the cusp that one might expect from a cloud of spent electrons pulling ions out into the cusps. I suspect one could rig experiments to investigate this.