Can we contain the electrons only with the Magnetic field?

[mattman]

Hey all,


Can we contain the electrons ONLY with the Magnetic field pressure?

It would make the polywell simpler.



Why won't this work?

[hanelyp]

That would be pretty much the case attempted prior to WB-6. The wiffleball magnetic field is an open field line configuration, which leaks to some degree no matter what you do. By applying an electric field around the magrid AND allowing space between the coils for electrons to pass, most of the electrons escaping the wiffleball can be pulled back in. And those upscattered electrons with more energy than the electric field can stop lose energy to the field. Drop the electric field OR the magrid spacing and electrons escaping the wiffleball represent automatic lost energy.

[D Tibbets]

The short answer is that yes, electrons are only contained by the magnetic fields. Of course things become more complicated when you consider recirculation. EMC2 tried to contain the electrons with the magnetic fields and attempted to 'plug' the cusps with electrostatic repellar plates. I don't know if the repellar plates helped on the electron confinement but they were devastating on the ion confinement. I don't know at what radii the replellars were placed in WB5. I assume they were negatively charged plates placed near the mid plane of the magrid.

Recirculation due to a positive charge on the magrid surface does not actually help in containing the electrons. This electric field is not seen by the electrons (or ions) so long as the charged particle is at a smaller radii from the center than the mid plane of the magrid magnets. Once past the mid plane the electron is officially lost to confinement. The positive charge on the magrid acts as a direct energy converter, converting the electrons outward momentum into potential energy stored in the magrid electric field. If the electron is not brought to a stop, most of the outward KE is harvested and available for reuse. If the escaped electron is brought to a stop it is now the same as the low voltage electrons from the electron gun. It will be accelerated back into the magrid through the cusp. It doesn't matter from an energy perspective whether the individual electrons are recirculated, only that their KE (or most of it) is recovered at high efficiency. Contrast this to the energy recovery that might be obtained with the high energy electron hitting the vacuum vessel wall and heating it- steam cycle to generate electricity. Efficiency of ~ 90 to 99% (?) versus 25-30 %. There are other issues with vacuum control, sputtering, arcing, etc. but from an input energy perspective this is it.

You might (correctly?) argue that the electron guns act as repellar plates, but as mentioned in the patent application, the radii past the magrid is critical. The E-guns need to be far enough away that they do not overly interfere with the potential well due to the contained electrons, but not so far away that electron injection through the cusp suffers too much. Collimation of the e-gun electron output is another element of efficient electron injection (as opposed to omnidirectional (isotropic) emitting hot car light filaments. In WB6 it took about 45 amps of E-gun current to build and maintain the Wiffleball. I don't know if the required current might have been less if better E-guns were used- something that might have been addressed in WB8

Dan Tibbets

[KitemanSA]

Sorry, the short answer is no. Any time they tried using only the magnetics (i.e., putting the chamber wall right at the magnets) the electron loss was just too high. Recirculation seems to be a "must have".

[ltgbrown]

In recirculation, what causes the electrons, once outside the magrid, to recirculate? hummmmmm. Isn't it the magnetic field lines? Soooo, if recirculation is the mechanism for "containing" the electrons, then isn't the magnetic field "containing" the electrons?

So the short answer IS yes.

[ladajo]

I agree. I think that this is a matter of terminology alignment and somewhat about folks talking past each other.
In the basic concept, (e-) confinement is about magnetics. (+) confinement is about electrostatics.
That said, I also fully agree that in an up and running full scale machine there are some other dynamics at play, but the basic concept remains (IMO).

[KitemanSA]

In recirculation, what causes the electrons, once outside the magrid, to recirculate? hummmmmm. Isn't it the magnetic field lines? Soooo, if recirculation is the mechanism for "containing" the electrons, then isn't the magnetic field "containing" the electrons?

So the short answer IS yes.

The ever lengthening answer is still no. What causes the recirculation is the charge on the MaGrid that stops and returns the electrons. The B field is pretty disperse outside the MaGrid and given the proximity of the chamber wall (Faraday cage in WB6 case), it looks like the electrons would certainly impact the wall before getting all the way around. Remember, electrons drift toward the weaker field, and the weaker field is directly in line with the radial vector out of a cusp. The electron wants to go directly out. But the E field stops it and pulls it back in. The B field may help funnel the electrons back through the cusps, but they won't guide them around into another cusp.

Just by way of a thought experiment, look at how close the e-emitters are in the WB6 set up. The electrons will have a tough time getting any further that that distance when they escape the MaGrid at the cusps.

[ladajo]

I am not so comfortable to think that the (e-)s exit a cusp and re-enter another as "recirculation". I am more of the mind that they oscillate back in where they "got out" as "recirculation". In machine pics that I have seen, it does not appear that there is enough space from the coils to the faraday cage to allow for cusp to cusp circulation.

[KitemanSA]

My point, thank you for your support.

[ltgbrown]

I have to say, Ladajo's description seems much more accurate.

[D Tibbets]

One can be forgiven for thinking that recirculation was the escaping electron looping around the field line outside the magrid and reentering through another cusp. This was a prominent view here at one time, there is even a U tube video that shows this. Art Carlson argued against this as he felt there was not enough room for the outside loop to be completed (the apex reached) before outside structure was hit.
And in actuality, again in the patent application, Bussard pointed out that this is undesirable and must be prevented by placing intercepting structure outside the magrid. This is because if the escaping electron has been up scattered it can / will have greater outward KE than the accelerating (inward) voltage on the magrid surface. So it will not be stopped and then reversed back through the same cusp. It is still effected by the magnetic field though so it could loop around with it's residual KE, then pick up another dose of accelerating voltage as it approaches another cusp and re enters the magrid. It would result is a self feeding process where up scattered electrons obtain increasing energy on each escape/ re entering loop. The high thermal tail of the electrons would be reenforced. This would continue until the magnetic loop associated with the up scattered electron did hit the wall. Either that or the up scattered electron shares it's energy with other electrons- raising the average temperature of the electrons. Neither is desired, so intercepting surfaces will intentionally be distanced outside the magrid so that this doesn't occur.

As the up scattered electrons have a higher speed, they complete their allotment of machine transits (~ 10,000 in WB6) and hit a cusp and escape earlier (their lifetime is shorter). These up scattered escaping electrons return much of their KE back to the potential energy of the magrid. Any excess is carried away and is lost as the electron hits a wall. The important point is two fold.The high thermal tail of the electrons are removed from the system rapidly. This restoring effect limits the development of full thermalization of the high thermal tail. This is important for Bremmstruhlung considerations, and possibly other concerns. The second point is that this favorable process is carried out at discounted energy costs since a probably large percentage of the KE is recovered. Assuming that all 'normal' electrons are stopped and re accelerated back through the cusp, the up scattered electrons are decelerated so that they only have their excess KE left. Ignoring possibly many other contributors, this may be reflected in the ~ 90 % efficiency claimed for recirculation. ie: 10% of the electrons (or the energy equivalent ) is carrying this excess energy and are eliminated from the system.

I think this would also apply to the down scattered electrons. As they exit the cusp at a lower KE (below the magrid potential voltage) they are quickly decelerated , stopped, and re accelerated back through the cusp. Gauss Law dictates that the charged particle will be accelerated the same with a given potential accelerating force, irregardless of the distance it starts at. So even though the down scattered electron stops at a lower distance past the mid plane of the magrid, it will have the same imparted inward KE as any other electron irregardless of starting position (1 mm to 1 billion KM away). This applies to any electron from the e-gun, or escaping electron with the qualification that the electron starts with zero velocity. This eliminates the electrons that are not fully decelerated and hit the walls, or if not controlled as above, those electrons that loop around to another cusp. You are adding net energy to the down scattered ion so it is not energy free, but it does restore the down scattered electron to the desired "mono energetic state".

So there are restoring mechanisms for both up scattered electrons (elimination after recovering most of the KE) and down scattered electrons (at the cost of modest input energy). Electron thermalization is impeded and importantly, it is done so at much lower energy costs that simply replacing the escaping electrons with new ones.

Electron average life time is 10,000 passes. In WB6 6 this represents 3,000 meters (30 cm diameter * 10,000 passes). The speed is ~ 10 million M/s at energies of ~ 10 KeV, so the lifetime before escape through a cusp and exposure to the recirculation process was ~ 3,000 M / 10,000,000 M/s = ~ 300 micro seconds. This is consistent with claimed lifetimes. The distance traveled per average electron before escape was ~ 3,000 M. The MFP under these conditions may be less than this, and some thermalization may occur. The tight initial mono energetic nature may not last long, but full thermalization- especially of the high energy tail is also suppressed. It seems reasonable to claim that the system is not in thermal equilibrium. Conversely, using a narrow term like "mono energetic" may be misleading.
These conditions seem reasonable for WB 6. How this translates to larger machines with increased density and KE is an open question. Nebel hinted at this in one of his comments.

Dan Tibbets

[KitemanSA]

I have to say, Ladajo's description seems much more accurate.

Than yours? Quite true.

[mattman]

I reserve judgment until a model can be done.

Modeling can go places experimenters cannot.

Four input variables makes modeling, instabilities, competing physical effect, ect,.. simpler.

Consider...



Any “Rules” you could find could be applied to the bigger or real system.

A rule, could be a way to reduce recirculating electrons.

[D Tibbets]

To understand the Polywell you must have an understanding of Gauss Law and it's consequences on the physics inside and outside the magrid. You cannot use a single electrostatic force parameter, it is totally dependent on the radii you are looking at relative to the magrid radius.

An excellent free video lecture series is available here:

http://ocw.mit.edu/courses/physics/8-02 ... -lectures/

I think it was lecture 3 [edited] that is most relevant to this discussion.

Dan Tibbets

[mattman]

Dan,

If I had the funding I would seek optimization with these 4 inputs by comparing different physical mechanisms.

These would be the mechanisms, minus the outside E-field.