What if there were no electrons?

[D Tibbets]

What if there were no electrons?

What if electrons were taken out of the picture initially. Perhaps all this concentration on magnetic field effects are obscuring the actual primary driving force of the Polywell. At it's heart the force driving the positively charged ions towards the center is the positively charged magrid. Imagine a hollow sphere with an adequate positive charge. Magically place sone ions inside and they will be accelerated through the center and decelerate as they approach the opposite wall. This back and forth oscillation is what allows for collisions that results in fusion. No magnetic field needed. Ignoring upscattering the ions would be contained indefinitely until 100% of them had fused. The problem with this ideal system is that not many ions could be contained because to much 'pressure' could blow up the vessel! So, while efficiency would be large, the rate would be small because of the limit of how many charged ions could be stuffed into the vessel.

Now add an equal number electrons. The net charge inside the vessel would be zero, so you could pack many more ion- electron pairs into the sphere so the efficiency would still be 100 %, but the rate would be much higher due to the much higher density. The problem would be that the electrons would quickly fly into the positively charged shell and be lost. OK, lets replace the lost electrons with new electrons to keep the balance in check. The problem is the power needed to inject new electrons and the power needed to overcome the neutralizing effects of the electrons that hit the positive shell.

Well, maybe we can use some force other than electrical that would keep the electrons from being lost to the shell, Ureka!
Magnets can divert the electrons so that they will never reach the shell (without seriously effecting the behavior of the ions).
So, the magnets in this imaginary system do nothing to the ions. All the action on the ions comes from the electrostatic field. The purpose of the magnets is just to confine the electrons and avoid the terrible losses associated with their consumption and replacement. Finally, a high efficiency and high power system to solve the energy needs of the world (of course you have 100% efficient electrical conversion of the fusion energy, etc)

Now comes the complications. There have to be holes in the sphere to let in ions and electrons, and you cannot have a perfectly spherical magnet shell. Plus you have to account for upscattering. Perhaps we can approach a spherical shell by using multiple magnets in a 'quisipherical' shape. And, perhaps if we can make the holes small enough- something like a 'Wiffle Ball' we can keep the efficiency /losses good enough that the high relative density allows net power production at usable levels.
But, what about upscattering of ions, and electrons either hitting the shell of escaping through one of the holes(cusps). Perhaps if we inject a (very) few extra electrons that are kept further from the shell (by the magnetic field) than the top of the orbits of the average ions, perhaps this will have a breaking force on those upscattered ions that would otherwise reach the shell. And perhaps the electrons would have a supercharger effect on the ions, adding to the centrally directed accelerating force provided by the positively charged shell.

What, the electrons are still escaping through or hitting the edges of the holes in the shell because the magnetic field is less there, and because of the attractive force of the positively charged shell? Well, lets enlarge the physical holes- of course without enlarging the magnetic holes, so that the electrons will not hit the edges of the holes. And, lets go green. Lets recirculate those electrons that escaped, without paying for it of course.

Finally, despite the complications of the real world, we have a winner!


Obviously, I am ignoring the many complexities and questions that have been raised. But, hopefully this emphasizes the nature of the beast (at least from a layman's perspective ). It seems many threads become ensnared by the magnetic questions and complexities and lose sight that the Polywell is at it's heart an electrostatic beast, and the magnetic fields can be considered as only a containment/ salvaging mechanism to control costs.


ps: What are the relative contributions of the positive grid -vs- the contained electrons on the driving force accelerating the ions towards the center (and limiting their outward excursion)?

Dan Tibbets

[Art Carlson]

What if there were no electrons?

What if electrons were taken out of the picture initially. Perhaps all this concentration on magnetic field effects are obscuring the actual primary driving force of the Polywell. At it's heart the force driving the positively charged ions towards the center is the positively charged magrid. Imagine a hollow sphere with an adequate positive charge. Magically place sone ions inside and they will be accelerated through the center and decelerate as they approach the opposite wall.

Yikes! Stop right there and learn some elementary electrostatics. Start with the Faraday cage.

[D Tibbets]

I'm not sure of your point. My example is an imagined and impossible model that I used to try to illistrate the seperation of the electrostatic forces driving the ions, and the magnetic forces confining the electrons. I have heard arguments about how few unbalanced charged particles can be contained befor the energy to contain them becomes huge. In this regard , the electrons are acting to prevent this charge buildup with the suggested benifit of increasing ion density, while the positive grids are what does most of the acellerating work. The electrons are acting like a buffer in this model that is somewhat fanciful, but I used it to give another perspective of what is (?) going on inside the Polywell.


Dan Tibbets

[Art Carlson]

I'm not sure of your point.

Do you understand the Faraday cage?
What is the electric field inside a spherical shell of charge, like a positively charged mag-grid?
What is the force on an ion when the electric field is zero?
Anyway, I have to let somebody else take care of this. I'm neglecting my daytime job too much.

[blaisepascal]

Dan,

What Art is trying to get at is that within a closed uniform shell of charge(of any shape, but it's easier to show with a spherical shell) there is no net electrostatic force on any charged objects within that shell.

With a sphere, look at an arbitrary narrow cone whose vertex is at an ion inside the sphere. The cone will intersect a circular patch on the sphere with a charge proportional to the square of the distance to the ion. The force on the ion is proportional to the charge and inversely proportional to the square of the distance to the distance to the ion, so the total force in that direction is constant, regardless of the direction, distance, etc. Since the force is the same in all directions, the net force is zero.

So in your hypothetical example of a positively charged case around the polywell apparatus with no free electrons inside, any ion is only going to see electric forces from other ions, not from the wall. An isolated ion is going to float freely; a pair of ions will flow away from each other; a ball of ions will explode with mutual repulsion.

The only reason the ions in a BFR will converge on the center is because of the ball of electrons held in place by the magnetic fields.

[drmike]

Dan, This is a great way to learn physics. There are two parts to your
question - one is about the force between particles and the other is about
what happens when you get a lot of particles (in this case a shell).

The electric force is huge. I vaguely remember a homework problem
where we had to compute the force from one coulomb of +charge on the
top of a saturn 5 and one coulomb of -charge on the ground. The full
engine blast would not get it off the ground! Since everything starts
neutral (for practical purposes) you'd have to do a lot of work to
separate out as much charge as you are talking about.

Because the force is so powerful, charges in a metal move fast. For every
charge inside a gage, each one will create a mirror charge on the wall
evenly distributed which exactly balances it. The net end result is that
the particles see no forces acting on them. That is not good for
confinement.

For the physicists, this is pretty basic. If you've never heard about a
Faraday cage, then it might seem like magic. It's not - but math really
helps to see how things really do cancel out and you get nothing left.

Hope that helps, keep throwing stuff out there!

[Aero]

We seem to be using the noun "ball" and "shell" interchangeably. Do the electrons form a ball, inferring something (more electrons) inside and net forces inside, or do they form a shell, inferring a vacuum inside with no net forces.

[blaisepascal]

We seem to be using the noun "ball" and "shell" interchangeably. Do the electrons form a ball, inferring something (more electrons) inside and net forces inside, or do they form a shell, inferring a vacuum inside with no net forces.

I'm not sure it matters. The way I envision it the ions travel far outside the bounds of the ball/shell of electrons before falling back in. From far outside, the ball/shell looks like a point charge, and by the time the ions are within the ball/shell, they are going fast enough that the charge distribution doesn't effect it much anyway.

Of course, I could be wrong.

[Aero]

Yes, but with no charge within a shell, there is claimed to be no effect on the ion trajectories as they pass through the polywell. With a charge within a ball, I envision a small effect that would bend the trajectory ever so slightly toward the center so the next pass would be closer to the center of the ball. This would be a focusing effect increasing the probability of a collision.

Maybe it doesn't work like that but the polywell is not a Faraday Cage, either, because ions do transport charge from outside to inside and outside again, exactly what a Faraday Cage blocks.

[D Tibbets]

Yes, indeed I'm confused. And to further extend my confusion I'll argue further. First, my understanding of a a Faraday cage is that it is a barrior against electrostatic fields, it doesn't say anything about what fields may exist within or outside of it.
http://searchsecurity.techtarget.com/sD ... 82,00.html

"A Faraday cage is a metallic enclosure that prevents the entry or escape of an electromagnetic field (EM field). An ideal Faraday cage consists of an unbroken, perfectly conducting shell. This ideal cannot be achieved in practice, but can be approached by using fine-mesh copper screening. For best performance, the cage should be directly connected to an earth ground".

If, you prefer, make the initial sphere a grounded Faraday cage, and place your anode spherical grid (not a continous surface) immediatly inside it (enough distance to prevent dielectric breakdown). The amount of charge this grid could hold would be limited (like a capaciter) but the potential could be anything the dielectric could withstand. The space inside the grid is a perfect vacuum. I can accept that the electrostatic field is uniform, and relatively nonexixtant inside the sphere. But once charged particles are is introduced, they have an electrostic field, and will act with any other electrostatic fields. What I find confusing is that it would not act locally with a charged surface. If the sphere is extreamly large , and the ion is very close to a surface, the sphere would approach a flat plane in geometry. Would not the like charged partical be repelled from the nearby surface with a force equal to the inverse square law?
I realize that if you have a 'Faraday cage' with a surface potential, that can be considered as zero within it's frame of reference. And if a like charged partical could then be introduced, it could see the Faraday as neutral, but if the charged particle is of opposite charge, would it still see the cage as neutral? What if a pos charge particle and a neg charged particle is introduced at the same time. They would interact with each other, but not the charged wall? I can see the wall being set realitivly neutral to one particle, but not both. Perhaps this is where I'm being confused, combining rules in a perfect pure system with messy nonpure conditions. Going back to my modification of the positive grid inside the Faraday cage. If it is also a perfect sphere then you could argue that I've mearly placed one spherical Faraday cage inside another, and again you cannot have any localizing effect. If the positive grid is not quite spherical, does it change the conditions? If it is slightly leaky- not a perfect Faraday cage does it then allow profound interactions eventhough the 'leakyness' is tiny?

And, to further confuse the issue, a least for me, consider the following-
Have a 2 dimensional hollow square with a charge. Place a oppositly charged particle exactly in the center- it would experiance no net accelerating force because all opposite sides are equaly far away. But, place the particle sligtly closer to one side and it will experiance acceleration towards the nearest side. Increase the number of sides untill a practical circle is formed and the same should apply, Expand into 3 dimensions (sphere), and I assume the same should still apply.

I better stop here, as I'm drifting and only further confusing myself. Sufice it to say a Faraday chage acts as a limiting condition- setting the initial conditions to zero. But if the physical surface of the cage has some property, like charge, I do not see how it could not interact with a particle that has a different charge.

Dan Tibbets

[bcglorf]

Yes, indeed I'm confused. And to further extend my confusion I'll argue further. First, my understanding of a a Faraday cage is that it is a barrior against electrostatic fields, it doesn't say anything about what fields may exist within or outside of it.
http://searchsecurity.techtarget.com/sD ... 82,00.html

"A Faraday cage is a metallic enclosure that prevents the entry or escape of an electromagnetic field (EM field). An ideal Faraday cage consists of an unbroken, perfectly conducting shell. This ideal cannot be achieved in practice, but can be approached by using fine-mesh copper screening. For best performance, the cage should be directly connected to an earth ground".

If, you prefer, make the initial sphere a grounded Faraday cage, and place your anode spherical grid (not a continous surface) immediatly inside it (enough distance to prevent dielectric breakdown). The amount of charge this grid could hold would be limited (like a capaciter) but the potential could be anything the dielectric could withstand. The space inside the grid is a perfect vacuum. I can accept that the electrostatic field is uniform, and relatively nonexixtant inside the sphere. But once charged particles are is introduced, they have an electrostic field, and will act with any other electrostatic fields. What I find confusing is that it would not act locally with a charged surface. If the sphere is extreamly large , and the ion is very close to a surface, the sphere would approach a flat plane in geometry. Would not the like charged partical be repelled from the nearby surface with a force equal to the inverse square law?
I realize that if you have a 'Faraday cage' with a surface potential, that can be considered as zero within it's frame of reference. And if a like charged partical could then be introduced, it could see the Faraday as neutral, but if the charged particle is of opposite charge, would it still see the cage as neutral? What if a pos charge particle and a neg charged particle is introduced at the same time. They would interact with each other, but not the charged wall? I can see the wall being set realitivly neutral to one particle, but not both. Perhaps this is where I'm being confused, combining rules in a perfect pure system with messy nonpure conditions. Going back to my modification of the positive grid inside the Faraday cage. If it is also a perfect sphere then you could argue that I've mearly placed one spherical Faraday cage inside another, and again you cannot have any localizing effect. If the positive grid is not quite spherical, does it change the conditions? If it is slightly leaky- not a perfect Faraday cage does it then allow profound interactions eventhough the 'leakyness' is tiny?

And, to further confuse the issue, a least for me, consider the following-
Have a 2 dimensional hollow square with a charge. Place a oppositly charged particle exactly in the center- it would experiance no net accelerating force because all opposite sides are equaly far away. But, place the particle sligtly closer to one side and it will experiance acceleration towards the nearest side. Increase the number of sides untill a practical circle is formed and the same should apply, Expand into 3 dimensions (sphere), and I assume the same should still apply.

I better stop here, as I'm drifting and only further confusing myself. Sufice it to say a Faraday chage acts as a limiting condition- setting the initial conditions to zero. But if the physical surface of the cage has some property, like charge, I do not see how it could not interact with a particle that has a different charge.


Seeing as I only minored in physics maybe I can explain it in a way that makes more sense even if it may also be less accurate.


Dan Tibbets

A shell with a charge will exert a force on any charged particles inside it. The thing is, no matter where inside the sphere the charged particle is, the part of the sphere closest will be pulling the particle to the outside exactly as strongly as the rest of the sphere is pulling the particle back.

Strictly speaking the charged shell has no NET force on a charged particle inside it as the force pulling the particle out equals the force pulling it in, no matter where the particle is in the shell.

[blaisepascal]

Yes, indeed I'm confused. And to further extend my confusion I'll argue further. First, my understanding of a a Faraday cage is that it is a barrior against electrostatic fields, it doesn't say anything about what fields may exist within or outside of it.
http://searchsecurity.techtarget.com/sD ... 82,00.html

"A Faraday cage is a metallic enclosure that prevents the entry or escape of an electromagnetic field (EM field). An ideal Faraday cage consists of an unbroken, perfectly conducting shell. This ideal cannot be achieved in practice, but can be approached by using fine-mesh copper screening. For best performance, the cage should be directly connected to an earth ground".

I suspect that Art confused you slightly. A Faraday cage is a solid conductive shell used as a shield against electric fields. By definition, a perfect conductor is always at a single potential, and charges on a conductor rearrange so that electric field lines terminate at the conductor and are perpendicular to the conductor. Inside a Faraday cage there are no electric fields except those caused by charges within the cage.

That principle is related to, but not identical, to the idea that within a closed surface of uniform charge there is no net electric field caused by the surface. In the absence of an external electric field, the net charge on a Faraday cage would arrange itself uniformly to achieve that result, but that's not what's going on here.

If, you prefer, make the initial sphere a grounded Faraday cage, and place your anode spherical grid (not a continous surface) immediatly inside it (enough distance to prevent dielectric breakdown). The amount of charge this grid could hold would be limited (like a capaciter) but the potential could be anything the dielectric could withstand. The space inside the grid is a perfect vacuum. I can accept that the electrostatic field is uniform, and relatively nonexixtant inside the sphere. But once charged particles are is introduced, they have an electrostic field, and will act with any other electrostatic fields. What I find confusing is that it would not act locally with a charged surface. If the sphere is extreamly large , and the ion is very close to a surface, the sphere would approach a flat plane in geometry. Would not the like charged partical be repelled from the nearby surface with a force equal to the inverse square law?

What about the force from the far-away surface?

Let's throw some example numbers at this. Imagine a uniformly charged sphere 1m in radius and a test particle 1cm from the inside surface. The particle is 1cm from one side, and 199cm from the other side. If we look at a double cone situated symmetrically on this diameter, its vertex at the test particle, and its angle of 0.1 radian, the area of the local wall contained within the cone is pi*sin(0.1)^2*1cm^2, with a charge proportional to that. The force by that charge is inverse-square the distance, so it's proportional to pi*sin(0.1)^2. The area of the far wall is pi*sin(0.1)^2*199cm^2, and the force is proportional to that divided by r^2, or pi*sin(0.1)^2, the same as the near-wall force, but in the opposite direction, for no net force.

I realize that if you have a 'Faraday cage' with a surface potential, that can be considered as zero within it's frame of reference. And if a like charged partical could then be introduced, it could see the Faraday as neutral, but if the charged particle is of opposite charge, would it still see the cage as neutral? What if a pos charge particle and a neg charged particle is introduced at the same time. They would interact with each other, but not the charged wall? I can see the wall being set realitivly neutral to one particle, but not both. Perhaps this is where I'm being confused, combining rules in a perfect pure system with messy nonpure conditions. Going back to my modification of the positive grid inside the Faraday cage. If it is also a perfect sphere then you could argue that I've mearly placed one spherical Faraday cage inside another, and again you cannot have any localizing effect. If the positive grid is not quite spherical, does it change the conditions? If it is slightly leaky- not a perfect Faraday cage does it then allow profound interactions eventhough the 'leakyness' is tiny?

Notice I never mentioned the polarity of the charge of charged spherical shell or of the test charge. It doesn't matter. Nor did I mention the magnitude of the charges. it doesn't matter.

A nonspherical shell makes the maths more complicated to prove the result, but it doesn't change it drasically.

And, to further confuse the issue, a least for me, consider the following-
Have a 2 dimensional hollow square with a charge. Place a oppositly charged particle exactly in the center- it would experiance no net accelerating force because all opposite sides are equaly far away. But, place the particle sligtly closer to one side and it will experiance acceleration towards the nearest side. Increase the number of sides untill a practical circle is formed and the same should apply, Expand into 3 dimensions (sphere), and I assume the same should still apply.

I agree with your assessment in 2-dimensions, but expanding it to 3 dimensions is where things fall apart. The major difference is that the perimeter of a hollow square expands linearly with increased side length (or the circumference of a circle expands linearly with the radius). The amount of charge "far" from the off-center point is proportional to the distance from the point, and the force is inversely proportional to the square of the distance, so the force falls off linearly with distance. The close wall pulls stronger than the far wall, and it falls towards the close wall.

In three dimensions, however, the surface area of a hollow cube/sphere grows with the square of the side/radius of the cube/sphere. The amount of charge "far" from the off-center point is proportional to the square of the distance, and the force is inversely proportional, so overall the distance cancels out and the force is constant -- in all directions, so there is no net force.

I better stop here, as I'm drifting and only further confusing myself. Sufice it to say a Faraday chage acts as a limiting condition- setting the initial conditions to zero. But if the physical surface of the cage has some property, like charge, I do not see how it could not interact with a particle that has a different charge.

It does -- all over, every bit of charge in the anode grid interacts with every ion. It's just that, overall, the interactions cancel, exactly, within the area of the shell.

In your example -- grounded spherical wall, charged concentric anode separated by a dielectric from the wall -- there is a very potentially very strong electrostatic field between the wall and anode, but no net field within the anode. Any charged particle caught between the two would experience a net electrostatic force, but not within the anode.

[Aero]

So it doesn't matter if the polywell is a ball of electrons or a spherical shell, the geometry will give the same result to first order. Of course the polywell is not an ideal sphere, but it's departure from spherical can introduce only second order effects. These second order effects will be different for a dodec than for a truncube, because of the different distribution of the cusps but at this stage of research we don't know if they will be significant, or even observable.

[blaisepascal]

So it doesn't matter if the polywell is a ball of electrons or a spherical shell, the geometry will give the same result to first order.

Assuming that the electrons are a tight ball/shell in the center of device and the ions go relatively far outside the electrons, then yes. This is the mode I've assumed that the device worked.

However, cross-thread, there's mention that the ions don't actually go that far out of the area of containment of the electrons. In that case, I don't know what to expect .

[D Tibbets]

I agree with your assessment in 2-dimensions, but expanding it to 3 dimensions is where things fall apart. The major difference is that the perimeter of a hollow square expands linearly with increased side length (or the circumference of a circle expands linearly with the radius). The amount of charge "far" from the off-center point is proportional to the distance from the point, and the force is inversely proportional to the square of the distance, so the force falls off linearly with distance. The close wall pulls stronger than the far wall, and it falls towards the close wall.

In three dimensions, however, the surface area of a hollow cube/sphere grows with the square of the side/radius of the cube/sphere. The amount of charge "far" from the off-center point is proportional to the square of the distance, and the force is inversely proportional, so overall the distance cancels out and the force is constant -- in all directions, so there is no net force.

Thanks, I think I understand now. I failed to consider that the surface area behind a particle moving away from the center of a hollow sphere increases proportionatly faster than it does in a 2 dimensional circle, thus resulting in a net neutral effect on the particle.

This requires me to modify some of my perceptions about fusors. I had thought that in a gridded fusor (central wire cathode) the ions acellerated inward untill they passed the nearest grid, then decellerated till it reached the center, acellerated again till it passed the opposite grid, then decellerated till it stoped to begin a new cycle. But, I guess that the ion is on its' own while within the hollow cathode grid. What still confuses me is what was going on in the pos gridded machines- like the Elmore, Tuck and Watson (?) variation.
And in the Polywell, I guessed that the electron cloud confined by the magrids extended close to the magnets, but to allow for ion acceleration most of the electrons must spend alot of their time near the center of the machine.

Which begs the question- why is the magrid charged to a high positive potential? I'm guessing that if the ions are immune to effects of the pos charged grid, then it would not contribute directly to acceleration of the ions. But, would the pos charge on the grid add to the neg charge on the confined electrons to give a greater cumulative driving potential ( eg: +10,000 grid volts plus ( or would it be minus?) -10,000 volts of the contained electrons giving a difference of 20,000 driving volts)? If so, why not just drive the electrons at a higher potential. Is there engineering concers that faver this splitting the volts this way. Does it make it easier (less magnetic field strength) or more efficient to contain the electrons?
If the positive charged magrid acts as a charged hollow sphere, then it would not effect the internal electrons or ions. So, would it have no purpose in being charged, just grounded? In this case, is the pos charge soley used to aid in recirculation ( pulling back on the electrons that have escaped through the cusps so that they bounce back befor reaching the vacuum chamber walls( or orbit, if this unpopular option is real)?

Dan Tibbets