Electron recirculation

[93143]

Perhaps I described it a bit sloppy. Without the grid between the magid and the outer shell, the electrons outside will see the magid will see the magrid at a MV or so lower electrical potential than the surrounding and rush for the higher electric potential. A trap grid isn't needed for direct conversion as the alphas would be similarly attracted to the magrid if the trap grid was missing.

Quite true. However, that would require the magrid to have a net negative charge, which violates one of the basic principles of its operation. I was assuming the magrid to be positive, which would result in 50-150 kV positive voltage with respect to the next object outward (trap grid or wall, whichever is first).

A point repeated many times in basic circuit theory class, because so many had a tough time grasping it, is that ground, 0V potential, is a reference point. We could validly assign ground to the alpha collecting grid, the trap grid, the magrid, or any other convenient point in the device. Just so long as everyone concerned knew where ground was assigned. Electric potential is not an absolute, but a relative measure.

But electric charge IS absolute, and if the magrid is at a lower potential than its surroundings (whatever the floating voltage is), it MUST be negatively charged, and it will NOT form a wiffleball. So without a trap grid you have the choice of either a working direct conversion system or a working magrid.

[hanelyp]

Quite true. However, that would require the magrid to have a net negative charge...
But electric charge IS absolute

I think you're confusing Coulombs and Volts. Coulombs are absolute. But I'm thinking in terms of volts, and electric field deriving from a difference in volts between 2 shell or grid levels.

The magrid has a potential higher than the trap grid. both magrid and trap grid have a potential much lower than the collector shell. What that translates to in coulombs is a messy calculation, and not needed to determine the electron and ion behavior.

So without a trap grid you have the choice of either a working direct conversion system or a working magrid.

This much we agree on.

[93143]

I think you're confusing Coulombs and Volts. Coulombs are absolute. But I'm thinking in terms of volts, and electric field deriving from a difference in volts between 2 shell or grid levels.

The magrid has a potential higher than the trap grid. both magrid and trap grid have a potential much lower than the collector shell.

Consider what would happen if you had a hollow sphere with the outer wall at ground. The potential inside is uniform. Probably you would call it zero.

Now add a magrid at the center. What is the net charge on the magrid? Who cares? But it generates an electric field due to that charge. Since this is a conservative field, the magrid can be said to be at a different potential than the outer shell. If the field points towards the magrid, it will attract positive charges and repel negative charges, and the potential of the magrid will be negative with respect to the outer shell.

Also, regardless of the exact value of the charge on the magrid in this case, you DO know it is negative.

This remains true even if the outer shell is not at ground - if it is highly charged itself. Due to Gauss' Law, the potential inside an empty sphere is uniform regardless of the charge on the sphere, so a negative perturbation in the potential requires the presence of a negative charge.

So what happens if you stick an electron gun into this configuration and try to form a wiffleball?

Abject failure, that's what. A magrid at the bottom of a negative potential well in the MV range would leak electrons like a sieve.

Now consider the trap grid case. The magrid is only slightly more positive (in potential) than the extremely negative (compared to the outer shell) trap grid. But once again, if the magrid weren't there, the potential inside the trap grid would be uniform. Thus an absolute positive charge on the magrid is required to produce the upward perturbation in potential.

The only problem with the electrons now is that you have to get them to the electron gun through the trap grid, which is simple high-voltage electrical engineering. Once they're injected, they only see the field from the magrid and that's where they go.

What that translates to in coulombs is a messy calculation, and not needed to determine the electron and ion behavior.

It's not that messy a calculation. A spherically-symmetric ball of charge (or a reasonable approximation thereto) has the same effect outside it as an equal point charge at its center. All you have to do is integrate the field from the next shell out (trap grid or wall) up to the outer surface of the inner sphere to get the potential difference across the interval. Do it analytically and you can then reverse the equation, feed it the actual potential difference and obtain the total net charge existing within the inner spherical volume you integrated up to.

[pstudier]

Due to Gauss' Law, the potential inside an empty sphere is uniform regardless of the charge on the sphere, so a negative perturbation in the potential requires the presence of a negative charge.

To pick a nit here, the volume inside any conducting shape is of uniform potential. If the sphere is not conductive, then an asymmetric charge on the sphere can cause gradients inside.

[93143]

To pick a nit here, the volume inside any conducting shape is of uniform potential. If the sphere is not conductive, then an asymmetric charge on the sphere can cause gradients inside.

Fair enough. All the components in this case are conducting (perhaps I should have specified), and they are also pseudo-spherical, so I felt no need to mention the arbitrary closed surface thing. But it's certainly true - a potato-shaped trap grid would still have basically zero internal field, and hence uniform potential throughout its internal volume.

[TheRadicalModerate]

Fair enough. All the components in this case are conducting (perhaps I should have specified), and they are also pseudo-spherical, so I felt no need to mention the arbitrary closed surface thing. But it's certainly true - a potato-shaped trap grid would still have basically zero internal field, and hence uniform potential throughout its internal volume.

So, we have:

1) A spherical (conducting) decelerator shell, which produces no E-field inside the device.

2) A quasi-spherical (conducting) magrid, which also should produce no E-field at radii less than the magrid itself, and which should act like a point-charge for radii greater than the magrid.

3) A big ball of electrons, maybe a ten-thousandth of a coulomb's worth.

Superpose all of these and it seems as if the voltage profile for the whole machine is nothing but a negative E-field inside the magrid radius, and a completely flat field outside the magrid. In other words, you get no help from the magrid in coralling wayward electrons, but at least the deceleration grid doesn't make things worse.

Of course, this begs the quesiton: How does the deceleration grid deceleratate anything if it's a spherical conductor?

[93143]

So, we have:

1) A spherical (conducting) decelerator shell, which produces no E-field inside the device.

2) A quasi-spherical (conducting) magrid, which also should produce no E-field at radii less than the magrid itself, and which should act like a point-charge for radii greater than the magrid.

3) A big ball of electrons, maybe a ten-thousandth of a coulomb's worth.

Superpose all of these and it seems as if the voltage profile for the whole machine is nothing but a negative E-field inside the magrid radius, and a completely flat field outside the magrid. In other words, you get no help from the magrid in coralling wayward electrons, but at least the deceleration grid doesn't make things worse.

Of course, this begs the quesiton: How does the deceleration grid deceleratate anything if it's a spherical conductor?

No no. In that configuration you can't decelerate the alphas. You need a trap grid in between the wall and the magrid. So from outer to inner, you have:

1) The shell. No effect on anything inside it except when alphas actually hit it.

2) The trap grid. Attracts alphas strongly, but only outside the closed surface it approximates. This means that the alphas basically shoot straight out from the core at ~constant speed until they pass the trap grid, at which point they start slowing down rapidly and (ideally) just barely make it to the wall. The potential within the volume of the trap grid is not truly uniform because of the presence of the magrid+wiffleball; the effect this has on the alphas is discussed below.

3) The magrid. It is positively charged, and this makes for a positive potential well outside it (superimposed on the uniform negative potential inside the trap grid with respect to the wall) that attracts electrons (from the electron guns or from cusp losses) and repels ions (including alphas). This means that the alphas accelerate slightly as they cross the space between the magrid and the trap grid, but this potential difference is only a few tens of kV and is dwarfed by the potential difference between the trap grid and the wall. Electrons in the space between the trap grid and the magrid only see the magrid+wiffleball and will thus recirculate unless they hit something or get past the trap grid.

4) The wiffleball. Created largely through magnetic trapping of negative charge within the magrid, this generates a negative potential well (with respect to the magrid) of maybe 80% of the magnitude of the positive potential well generated by the magrid (with respect to the electron guns). This means that the positive charge on the magrid has to increase as the wiffleball builds up in order to maintain the same potential geometry outside it. The ions are generated within the magrid, and the reactor shell, trap grid and magrid are all invisible to them. All they see is the wiffleball. Electrons within the wiffleball don't like it there, but there's not much they can do about it, and if they ever do get outside the magrid they change their minds quickly.

Here's a thought that helped me understand: Consider two conducting closed surfaces, one contained within the other. If their potential is equal, the inner one has no net charge. This is true irrespective of the charge on the outer one.

Also remember that a uniform potential, however large, is essentially a mathematical construct (so far as modern physics is concerned). It just means there is no electric field in that volume.

[tombo]

Thank You 93143 that is much clearer to me now.

Ok so now…
Where does the current return to the chamber to complete the circuit and do useful work? (I.e. where do the electrons leave?)

1 The ion guns? But they are balanced by the electron guns.
Also they could be replaced by neutral gas injections.

2 The electron guns? But they are pushing electrons into the chamber.

3 The magrid power supply? But it is being hit by alphas too, so removing + charges from the chamber.
This could be countered by the electrons drifting into the magrid.
But that is a parasitic loss that would not happen in a perfect machine.

4 The trap grid? It is negative so flows the wrong way.

Those are all the connections I see.

Somehow electrons must leave the well at the same rate as the alphas leave.
Otherwise, it will build up more and more negative charge until the well “blows out”.
Whatever this connection is, it needs to be beefy enough to handle 100MW.
That is one whale of an ion gun.
Or, it is one huge inefficiency with the electrons hitting the ~+20kV magrid doing negative work (i.e. forcing the power supply to do more work).

[93143]

I hadn't really thought about it.

I think your #3 is most likely, since that is where the electrons from ECR ionization would go. Also remember that it doesn't have to be 100 MW - it's just 50 amps, and at 20 kV, 50 A is just 1 MW - ie: 1% of reactor output.

[dch24]

tombo, you ask a good question: where is the "ground" that returns current generated by the trap grid and outer wall?

As I think about it, the first thing I am unclear on is how the current is generated.

In full operation, the trap grid is negatively charged, so when alphas pass it they start to decelerate. Eventually, the alphas have given up their kinetic energy and they "kiss" the outer wall, where they pick up an electron. So electrons are being sucked up by the outer wall; current flows out of the outer wall. The outer wall is positively charged relative to the trap grid, and it is that potential difference that's capturing energy from the alphas.

This is the part I am unclear on - where does the current come from? As far as I can tell, the trap grid is not capturing electrons when the outer wall is capturing positively charged alphas.

I think I'm too focused on recirculation -- trying to keep as many electrons "unattached" so they can fall into the potential well in the center. But really, that is the magrid's problem. Does the trap grid capture electrons after all?

Maybe it's a combination of the trap grid and the magrid, both capturing the "stray" electrons, though they are at different potentials?

[drmike]

Potential energy = kinetic energy. If you have a voltage, it's a potential. But you have get the energy from somewhere to keep that potential hill. The alphas can be used to push against a potential - just like a weight can push on a lever to work on a wheel.

All the currents have to sum to zero, so electrons come out of ground to meet the ions at the outer surface, but they get pulled from the MaGrid to make it positive. If the currents don't match smoothly, nature will make them match violently.

Here's a recent article on a typical method in tandom mirrors. MHD guys have been looking at this for many decades.

[tonybarry]

The electrons do have to match, or the whole polywell would rapidly acquire a huge - and growing - static charge.

As it turns out, when you ionise boron you get 5 electrons; when you ionise the hydrogen to get the proton you get another electron. That makes six electrons.

When the p and the B11 are fused, you get three alphas of +2 charge, which require six electrons to fully neutralise. No net static charge. The electron accounting is zero.

The +1.8MV alpha neutralise - collection grid would act like a regular battery, charged to 1.8MV. As alphas collect on it, they charge the grid even higher, and as we allow current to bleed off the grid, helium is produced. The charge decreases as we bleed more current, or increases as we bleed less current.

Regards,
Tony Barry

[charliem]

The P-W generator Positive Terminal is the collector grid/s for the alphas.

As more and more alphas get out from the device center plasma, its net charge grows increasingly negative. That makes those electrons remaining inside try to escape harder and harder, so more and more of them will flee from confinement.

Most electrons leaving the wiffle-ball end up impacting the magnet shells. That's the Negative Terminal.

BTW, alphas hitting the magnets will only be a portion (<40%), while 99% plus of the electrons will end up there, so there's no complete neutralization.

[tombo]

OK. Here is a possible solution:
The well will build up a negative charge threatening to blow out through the coils/cusps.
One of the coils or cusps could be weaker than the others to deliberately leak electrons before the others blow out.
They could then be collected on a negatively charged power electrode, perhaps the trap grid.
This would equilibrate at the alpha production rate (x2).
I think of it as a pressure relief.

[dch24]

Very interesting stuff! Ok, I read the abstract of the article for tandem mirrors (CUSPDEC). I haven't ever doubted the idea would work but didn't understand exactly how the electron flow worked.

I think I was just hung up on avoiding any electrons colliding with the magrid. Thanks for the explanations.