Question: How is the electron not getting into the machine?

[Robthebob]

That cant be true. At a given set of parameters (geometry, config, B field strength, electron beam current, etc) there is a well depth that's achieved at input/loss equilibrium, usually is far below beta=1. You cant get to high beta without WB effect, not without putting in some outrageous amount of electron beam current.

I'll buy that as you increase the beam current, thus increase N in the core, the core plasma is increasing in volume. It's either the volume is staying the same and the density is increasing or the volume and perhaps the density is both changing.

I dont know what cross field diffusion is, so please explain this to me.

I dont think any of this explains how electrons are generating fields to push the machine field back (and of course ultimately explain the WB effect).

[happyjack27]

the system is not at absolute zero temperature, so there will no doubt constantly be perturbations away from equilibrium. feedback forces will push the system back towards equilibirum, but that doesn't always mean pushing the same electrons. meaning there will always be some leakage across the wiffleball border (in both directions), as well as everywhere else. there will be a finite electron loss / leakage, even at b=1. electrons always have a non-zero probability to drift across field lines.

even without considering statistical mechanics, quantum electrodynamics shows that an electron can still, with finite probability, travel through an electrical barrier that according to classical physics is impassible.

[KitemanSA]

I dont think any of this explains how electrons are generating fields to push the machine field back (and of course ultimately explain the WB effect).

Rob,
Imagine your screen is a slice thru the core if a Polywell with the bottom of the screen pointing toward the center and the top toward the magnet. The mag field lines are going from left to right. They are weaker at the bottom and stronger at the top.

An electron that has been injected thru a cusp and passed near the center is now traveling outward (bottom to top of screen). As it encounters the strengthening field, it curves normal to the screen and eventually heads back down. This path describes half of a solenoid winding wherein the field inside the solenoid counters the ambient field and that outside strengthens it. Given the myriad electrons following similar paths, the field at the bottom gets on average weakened and that at the top gets strengthened. The ambient field gets "pushed out (up)".
You wind up with a bubble of no field at the center surrounded by a very rapid rise to a strong field at the average distance the electrons make it outward. The more you inject high energy electrons, the further out you push the field until eventually the curvature become concave and it effectively pops. The point just before popping is beta = 1.
Does that help?

[Robthebob]

Okay, you're saying the mirror effect, which causes the electrons to reflect, the reflected electrons' motion generates an opposing B field to push the field out?

The problem with this argument is first that, you have to count all electrons' motions, if there are equal amount of electrons going in both directions, then there's no net flow, and no net flow means no current and no B field. Second, it's true charge particles are diamagnetic as they travel down B field lines, original electron gyromotion and reflected electron gyromotion are the same, so it wouldnt just be the reflected electrons that are pushing the machine B field out, it would be both.

[hanelyp]

Okay, you're saying the mirror effect, which causes the electrons to reflect, the reflected electrons' motion generates an opposing B field to push the field out?

Yes.

Consider an electron hitting a wall of magnetic field crosswise to its path. The electron will be turned in a particular direction crosswise to both its initial path and the magnetic field, circling until it exits the magnetic wall. In the process it generates a magnetic field opposing the field that turns it. The reflection is quite like light in a mirror.

You can also consider if the electron is pushed and doesn't push back, action-reaction is broken.

[KitemanSA]

Okay, you're saying the mirror effect, which causes the electrons to reflect, the reflected electrons' motion generates an opposing B field to push the field out?

To echo hanelyp... yes.

The problem with this argument is first that, you have to count all electrons' motions, if there are equal amount of electrons going in both directions, then there's no net flow, and no net flow means no current and no B field.

Sorry, but there is no net flow past a solenoid either, but there is a net Ixr which is true in the core of a Polywell too.

Second, it's true charge particles are diamagnetic as they travel down B field lines, original electron gyromotion and reflected electron gyromotion are the same, so it wouldnt just be the reflected electrons that are pushing the machine B field out, it would be both.

There may indeed be a contribution from gyro motion following the original field lines, but even then the field is not uniform with radius so the gyro motion is kind of egg shaped, tight radius, high counter field on the outside and larger radius, lower field on the inside. As the ambient field gets pushed out, the gyro motion will change to a longer and longer ellipsoid, perhaps even eventually changing over to an electron that transits the full well diameter.

[KitemanSA]

I'm strongly considering building a polywell for my PhD, I'll start the process of gathering information and details soon (not that I havent been doing that).

Dr. B wanted to run two more small scale MaGrids before going to full scale, one being a square planform cubeoctahedron and another being a higher order form. You could do some real research by making two units, a round planform WB6 like machine and a square planform equivalent. Keeping all else the same, Dr. B thought the square would perform ~5 times better than the round. Real data would help a lot.

Personally, I think a bow sided square planform would be slightly better still, but I have no modeling to back that up.

This is what a bow sided... Looks like.

[Robthebob]

what's lxr? sorry like i said, im dumb.

Second, I later did realize that given the gyromotion of the electrons alone, there has to be opposing field. Hell, even if the electrons are just circulating the field line in place, it would still have that effect.

So the diamagnetic property of the plasma is a function of the amount of electrons on field lines, I'll buy that. WB effect has to assume that there are more on field electrons on the interior of the polywell than there are on field electrons on the exterior of the polywell, and I'll even buy that.

It's a misconception then, it's not the core off field electrons pushing the field back, it's the core on field electrons, which increase with the core off field electrons, because the core off field electrons can randomly get back on field, and the core on field electrons can get off field easily by curvature drift. There's an equilibrium that's achieved by this on and off field exchange. Nevertheless, more off field electrons implies more on field electron implies more diamagnetic property implies the machine field on the interior of the polywell gets pushed out.

[KitemanSA]

... implies more on field electron implies more diamagnetic property implies the machine field on the interior of the polywell gets pushed out.

Ok.

...
Sorry, Ixr = I cross r

[Robthebob]

I got that, what's l? is it like moment of something?

[KitemanSA]

I got that, what's l? is it like moment of something?

"I" ... current. "r" radius. of course it has been so long that I don't remember if it is rhr or lhr. No matter, you figured it out for yourself.

Oh, and I think it is 1/r, not r.

the first three things that go with age, your hair, your stamina, and umm... er ... hmm; where was I?

[Robthebob]

What's the current vector cross radial position vector? If it's something really obvious, sorry.

In other news, if we're talking about diamagnetic property of electrons, we can not be talking about the core off field electrons. They're not on B field, thus they dont have gyromotion to oppose the machine field. This includes all of the core off field electrons, now I dont know what kind of current or flow and what kind of effect they have, but it makes no sense to say the core off field electrons plays a part in WB formation as we described it.

Perhaps these type of field pushing events arent observed in other machines because they either dont have magnetic fields or have too high of field or beta is too low. In polywell, we have the extreme of both, the field at the core region is low, and this is also a high beta machine, so this type of first order? effect can actually be observed. This means any MHD simulation wont be able to account for this, because they disregard this effect when they go to guiding center frame. In the limit of low beta, this is fine.

This however turns into a chicken and egg problem, because we're using the assumption of the machine being at high beta to prove that it can go to high beta. For WB effect to happen, machine needs to be at high beta, but in order for the machine to be at high beta, it needs WB effect... (maybe beam current can get beta high enough for this effect to happen)

[TallDave]

I dont know what cross field diffusion is, so please explain this to me.

My understanding is that reflection isn't 100%, there's a random walk that allows some fraction of electrons to skip all the way to the coils. Rick seemed to think it was hard to predict in Polywells.

I don't know how to predict cross-field diffusion on these devices. The gradient scale lengths of the magnetic fields are smaller than the larmor radii and the electrostatic fields should give rise to large shear flows. On top of that, the geometry is 3-D.

On the WB effect... the machine starts at low beta with a very leaky WB, at high beta the field gets pushed out and we get a much tighter WB. Joel's simulations suggest cold electrons may sit in the cusps and help plug them as well.

I believe electron behavior in the interior is supposed to be essentially stochastic, as opposed to collapsing into a Debye sheath at the field boundary or anything like that.

[D Tibbets]

First, while the electrons are magnetically contained, and the ions are considered to be dominantly electrostatically contained by the slight excess of electrons, remember that both species population only differes by ~ 1 PPM. Both the electrons and ions are contributing to magnetic effects. Any charged particle in motion creates a magnetic field. If the charged particles have a preferred /dominate direction, such as in a Tokamak they can create a net strong magnetic field of their own. In the Polywell there is no preferred direction , motions tend to cancel each other out, so there is no gross (as in large scale) magnetic field produced by the plasma. Here things become less certain, but I accept that the plasma excludes the magrid magnetic field. Bussard, etel mentions the plasma pressure pushing out against the magrid B fields much as a gas pushes against an elastic balloon, and in fact the (mostly) electrons bounce off of the magnetic fields from the Magrid much as neutral gas bounces off of a balloon surface and the effect of this ' pressure' inflates the balloon. The difference is the turning mechanism, instead of bouncing off of a solid surface, the charged particles bounce through orbiting a containing field line. As repeatedly pointed out , this orbit is not circular but extended, even extremely extended into long elliptical orbits with the minor radius being perhaps a mm while the long radius is perhaps several meters (irnorring the B fields that would eventually be encountered on the other side of the machine. That is how fast the B field drops off due to the Wiffleball compression of the B field. Once on the long side of the orbit the charged particle is passing through other charged particles, but since their motion is in all directions (or +/- radial directions if highly confluent) so magnetic intractions between the particles are a net zero on the gross scale. As the particle travels away from the turning B field line it transits the machine before reaching the long radius of the orbit. It hits the opposite side Magrid field where it again is turned by the minor radius of the elliptical gyro orbit at that position. Simple gas pressure principles apply on a practical level. As you heat a gas and or increase the density it will push out more on a containing surface whether that surface is a solid or a magnetic field. If this seems inconsistent, consider the Sun. It creates a magnetic bubble due to the outward motion of the Solar wind and this pushes out the galactic magnetic field until the Heliopause is reached. In this case the charged particle motions are mostly outward so there is a net Solar magnetic field, otherwise it is very similar to a Polywell. Another frequent example is water falling from a facet and hitting the sink bottom. It forms an area that pushes out the standing water in the sink. In this case the falling water splashes outward, inward, etc, so it doesn't have a radial favored direction (once the facet input and the drain output are canceled out). Nor does it have an initial preferred angular motion direction. Soon Coriolis forces produces a favored angular momentum direction, but that still allows for the outward net pressure that excludes the standing water in the sink.

Note that the pressure created by the electrons 'banging' against the Magrid B field may be different than the ions. The Patent application mentions this. Because the ions are contained mostly by the electrostatic potential well they do not hit the electron containing B field line much. This changes some of the consequences, but not the basic picture above.

The important point is that the charged particle transits from one side of the machine to the other side between gyro orbit turns. Thus the particle pushes outward on both sides. If there was not this rapid gradient between the strong B field on the periphery of the core and the effectively zero B field towards the core, the gyro orbits would be much more circular and the charged particle would not leave that field line unless there was a collision. In that case I do not think you could build up internal pressure unless you allowed for the charged particles to have a preferred direction so that an excluding plasma gross magnetic field could form (like in a Tokamak?). Another way to look at it is that the charged particle motions inside the machine do create magnetic fields and these fields exclude the Magrid B fields. Note that I said fields. Very many B fields associated with the motions of individual particles in relation to their close neighbors. The differences is that all of these micro fields cancel each other out so that on the gross/ average scale the effects are like having no fields, or rather no net fields. The electron may be nudged one way as it approaches another, but soon it is nudged the other way as it approaches another. The net effect is that on the gross scale the filght of the charged particle is a straight line (if you magnify the view enough the line is reveled to be a jagged squiggle that is ~ a line. The magnetic fields are there and you could consider this as pushing outward, but within the plasma it has no net effect on the charged particle vectors.

I ignored Coulomb collisions for the most part. Just as with a gas, the MFP may be much shorter than the machine diamater (actually perhaps not in the WB6 plasma), so the electron may bounce around a lot, but the net effects on the containing wall is still the same.

If you are thinking that the electrons/ charged particles adiabatically bouncing off of the magnetic walls must transfer some KE to the walls in order to inflate it, perhaps this is the case. But just like a balloon (assuming elastic collisions- no heat generated) the energy of the system is not changed. Some of the energy is transferred to the balloon walls due to the elasticity of the walls (stored as potential energy) but it is still part of the system. In this sense the magnetic fields are absorbing some energy as they turn the particle. If the particle has a nearly circular narrow gyro orbit the effect is local and self canceling (?). In the Polywell the effect is similar but more complex and on a larger scale. Also, cyclotron radiation implies that B fields do not truly adiabatically turn charged particles, but this effect is so small it can often be ignored.

Note also that all of this discussion uses bouncing or turning as adjectives for bouncing off of a wall. A charged particle in a near circular gyro orbit (because the B field gradient is nearly flat) spirals around that field line and 'Mirroring or Bouncing" in this context means the reversal of the direction of the spiral. This does not apply to the above discussion. It might apply to reversing direction parellel to the field lines in cusp regions but that is a different discussion.

[D Tibbets]

Charged particle transport, diffusion, drift across magnetic fields are loss mechanisms. I have seen all of these terms used synonymously.

From the Nuclear Plasma texts I have read there are three types of diffusion: ExB, ExY and ExX (or is that ExZ?). ExY and ExX diffusion or drift refers to a charged particle on a field line moving towards a pole of the field line or equatorially across field lines at the same field strength.

ExB diffusion is the important one from the perspective of charged particle containment , and is independent of cusp concerns. In a cuspless system like the Tokamak the containment is limited by ExB diffusion. Ignoring macro instabilities it is what limits the size of the machine. Start with a charged particle trapped on a field line with a given gryoradius. In a collisionless plasma like a Penning trap with a few antimater particles the density is so low that Coulomb collisions are very rare and this is what drives ExB drift. The gyroradius is dependent on the mass (momentum) of the particle and its KE or speed. In fusion plasmas the density has to be much higher and the KE (temperature) has to be much higher. The Coulomb collision rate scales as ~ density squared and temperature to the 1/1.75 power.
If you want useful amounts of fusion you need a relatively high density (eg:~10^19 to 10^22particles per M^3). The magnitude (distance traveled) of the ExB drift is proportional to the momentum of the particle/ B field strength and is always equal to the gyroradius under those conditions.
The movement is described as a random walk process. A Coulomb collision may knock the test particle up one or down one gyro radius. As the density is greater on the inside of the confining B field, the particles will drift outward till they eventually hit the magnet wall/ vacuum vessel wall. A deuterium or tritium has a mass ~ 12,000-18,000 times that of an electron At the same temperature, the momentum difference is the square root of this. This means that the ion will have ~ 100 times the momentum of an electron and this means that the gyro radius will be ~ 100 times as great.

An example of this is that if an electron has a gyro radius of 1 mm, a deuterium ion will have a gyro radius of ~ 100 mm. No need to adjust for Z here as both have a charge of one.
Assume it takes takes about 1000 collisions within this magnetized plasma for ~1/2 of the particles to travel 10 gyroradii deeper into the magnetic field. That would be a distance of ~ 1 meter of ExB drift for the ions. If the distance from the magnetic field containing field line to the magnet can is this distance then half of the ions would be lost within this number of passes/ distance traveled/ time . Half of the remaining ions would ground on the case in the next interval, etc. Thus the ion density decays and to maintain the density energetic ions need to be replaced at the same rate. By increasing the strength of the magnets and the distance from the nominal confinement magnetic strength (field line)to any surface will proportionatly increase this time interval. Thus very strong magnets with multiple meters of standoff distance is needed to confine neutral plasma long enough to meet the triple product requirements. That is why Tokamaks need to be so big. And this ignores other complicating issues like macro instabilities and thermalized variations in the ion temperatures.

Note that I compared electron gyro orbits to ion gyro orbits. The electrons gyro orbits will be ~ 100 times less than the ion gyro orbits, and thus the distance traveled with each random walk collision driven ExB drift event will be ~ 100 times less and electron confinement will be ~ 100 times better in this regard. This is why Bussard said that magnetic confinement of ions or neutral plasmas is no darn good. This is because ExB ion losses are too painful at any given density . Electron ExB losses are a different matter, and this is why Bussard used magnetic confinement of electrons as the primary confinement limiter (in a cuspless system). By injecting excess electrons a potential well is created and this electrostatically confines the ions so that the ExB drift problem is almost eliminated.

There are a number of tradeoffs that this enables. It becomes much easier to heat the ions (accelerate them with a potential well). It allows for greater densities, and as fusion scales as the fourth power, and ExB drift scales at the second power this is a significant advantage. The numbers for the triple product is changed tremendously. This is confinement time* temperature* density. The density can be increased with ExB limited confinement losses increasing at a slower relative rate. A smaller, potentially much cheaper machine is possible. Add to that claimed thermalization advantages, possible significant confluence, and potential for direct conversion and the advantages are potentially tremendous.

The above discussion focuses on ExB drift losses being the limiting containment issue. The Polywell is cusp loss limited and actually this is much worse than the Tokamak losses through ExB losses. But, once the triple product is considered, the obtainable density advantage at these relative loss rates more than makes up the difference. The Polywell cusp limited loss rates are mentioned as being ~ 10-100 times worse than the ExB electron loss rates in the Polywell. I don't know if this is before or after the recirculation advantages found with WB6. It does put a limit on the improvement theoretically possible with the Polywell. If the electron cusp loss/ recirculation efficiency can be improved 10-100 times, then the physics of ExB drift losses would be the limiting factor. There are several other effects that theoretically could extend the performance further and these are mentioned in the patent application. In any case, I suspect that thermal wall loading issues and magnet technology issues will probably limit the Polywell size/ performance before the theoretical limits are reached.

Dan Tibbets