regarding recirculation

[D Tibbets]

Your math/ assumptions are not right. Perhaps you are assuming a population of ~ 10^22 electrons/ M^3 in the Wiffleball and the associated coulomb repulsion (which would be huge)...

I didn't consider any particle-particle interactions, just the grid. The question was if he was using SI units, i.e. C and C/m. If thats the case I interpret the first "wb32" video (xyz-view) as him having a ~10C/m charge on the grid. Since the length of the 15cm "wb32" grid is about 7.4m that is a total of ~74C on the grid and a potential of ~ 4.4*10^12V in the center (compared to 0V at infinite radius). I then compared this to the potential at 3m giving a difference of about 4.3TV (should perhaps have been 3 radii = 0.45m and 3.8TV).

I neglected the particles because the net charge was set to 10^-8C << 74C
(By the way, is this total or per particle? Doesn't really matter in this case.)

Perhaps I'm confused, but I don't follow your reasoning. Particles can interact with particles, but I believe the charged particle interactions are dominated by space charge considerations. Fusion plasmas are generally weakly coupled. This means that the behavior of the plasma is not dominated by the oppositely charged particles pairing up. There is some of this effect (it is what helps to form a parabolic potential well) but for containment issues it is a minor influence.

The space charge (the force pulling in or pushing out against individual charged particles) is determined by the net excess of one charge over the other. Again this is ~ determined by the excess electrons in a ration of ~ 1.000001. This makes the plasma non neutral. I used the density of ~ 10^22 charged particles / M^3 as this is a claimed capacity of a large Polywell. In this case there would be 10^16 excess electrons /M^3, and it is only this number of negative charged particles that creats the negative space charge. The other electrons and ions cancel each other out. In this example there is ~ 0.001 Coulombs of net negative charge/ M^3 within the Wiffleball, and this is what helps to create the potential well. The pressure against the magnetic field is a cumulative effect of all of the charged particles. But this is due to their kinetic energy, not their individual charges (the individual charges are nessisary for them to interact with the magnetic field, but does not contribute much to the pressure directly. There is discussion of the pressure effects against the magnetic field (that inflates it) in the 2008 patent application.

So, my understanding is that the Polywell will have perhaps 10^-3 Coulombs of unbalanced charge that tries to push the electrons out and pull the ions in. Of course inside the magrid , the charged particles ignore any potential on the coils. The pressure on the magrid generated field is something like P= n* V^2. The velocity is squared, so it has a dominate effect on the pressure. A balanced neutral plasma would interact with the magnetic field much like a gas in a balloon. the inflation is dependent on the density and temperature. The charge is irrelevant (except of course you have to have individually charged particles to interact with the magnetic field like a gas does with the surface of a balloon).

I don't know what parameters the sims are using, but the above illustrates the the charges in a Polywell.

Also, I don't know what you intend when you state a potential needed to contain the electrons. That is nonsensical to me. The electrons are not contained electrostatically, but magnetically. There are two (or three considerations if you consider recirculation). The magnetic field strength has to be strong enough to turn the high speed electrons at the bottom of their potential well before they reach the magnet can surface, and the cusps need to be small enough that the electrons hit these sites rarely. The electrons that hit the cusps and pass outside are lost from containment. But recirculation cheats and reclaims most of these escaped electrons. Because of inneficiencies in electron injection. The potential on the magrid can reclaim (and reset the energy) of these escaped electrons unless they have been upscattered by more than ~ 20%.

Thermalization issues are important. The originally monoenergetic electrons collide repeatedly within the Wiffleball and tend towards thermalization, but the lifetime of the electrons before they hit a cusp is short enough that full thermalization does not occur before escape. I don't know if there are any other thermalization impeding effects for the electrons as there are for ions (annealing). So the high energy tail does not fully develop, and a presumably large portion of this developing high energy tail electrons are still below the 20% limit so they are reclaimed and reset by recirculation.. Those above the ~ 20% limit fly to the wall and are removed from the system so they cannot continue to contribute to thermalization. Of course all of this implies energy loss, but in balance it is tolerable and beneficial to the operation of the machine.

Talking of the ions, which are electrostatically contained, A. Carlson claimed that several million volt potential wells would be required to contain most of the upscattered ions, but this was based on thermalized plasmas and ignored the claimed annealing. In one paper Bussard gave a number ~ twice the desired potential well to contain most of the upscattered ions. I assume this reflects the efficiency of the claimed annealing. Of course, I don't know how you could have an accelerating potential well that was different from the containment potential well. In that case, Bussard recognized that the mildly upscattered ion could climb above the potential well (extend past the Wiffleball border), but it would not escape unless it hit a cusp. It would be turned by the magnetic field. This tends to decrease convergence, but hangs on to the ion. This is not as bad as pure magnetic ion confinement schemes, because only a minority of the ions reach this condition, so ion ExB drift and ion cusp losses are restrained, apparently to such an extent that most of the ions (or at least enough of them) are expected to fuse before they manage to escape.

Dan Tibbets

[erblo]

total. so divide by 14336 to get per particle. also, i am using SI units, but the magrid charge is in coloumbs per square meter (surface area), or in the case of 0 thickness coils coloumbs per linear meter. and the slider for that one i haven't checked to see if i'm multilying it to the right constant scaling factor. so its "some quantity" times coloumbs per square meter.

i understand that since when its on the mag fields and plasma flow make it so the capacitance on the coil surface is not uniform throughout the coil and thus neither is the charge, so this isn't fully accurate. but modelling that is a whole nother ball of wax and i don't imagine it makes that big of a difference, really.

How do you calculate the the surface? Is it the surface of the coils approximated as cylinders/tori: L*2*pi*r? Then the results in my previous post should be divided by about 30 (using 5mm radius), not considering the unknown scaling factor.

Regarding the actual charge distribution on the coils: Using a homogeneous distribution leads to a higher potential on the inside than the outside of the coils and also where the coils are close to each other. These coils are still fairly thin and far apart, so it's probably not important.
Also, any space charge is of course going to affect the coils, but it'll need to be bigger (compared to the grid charge) than in the current simulations.

[D Tibbets]

total. so divide by 14336 to get per particle. also, i am using SI units, but the magrid charge is in coloumbs per square meter (surface area), or in the case of 0 thickness coils coloumbs per linear meter. and the slider for that one i haven't checked to see if i'm multilying it to the right constant scaling factor. so its "some quantity" times coloumbs per square meter.

i understand that since when its on the mag fields and plasma flow make it so the capacitance on the coil surface is not uniform throughout the coil and thus neither is the charge, so this isn't fully accurate. but modelling that is a whole nother ball of wax and i don't imagine it makes that big of a difference, really.

How do you calculate the the surface? Is it the surface of the coils approximated as cylinders/tori: L*2*pi*r? Then the results in my previous post should be divided by about 30 (using 5mm radius), not considering the unknown scaling factor.

Regarding the actual charge distribution on the coils: Using a homogeneous distribution leads to a higher potential on the inside than the outside of the coils and also where the coils are close to each other. These coils are still fairly thin and far apart, so it's probably not important.
Also, any space charge is of course going to affect the coils, but it'll need to be bigger (compared to the grid charge) than in the current simulations.

Again, I may be confused. Talking of inductance on the magnetic coil casings, there are two points that may be important. The coil surfaces are metal and highly conductive so I wonder how much difference could develop on the inner and outer faces. Also, due to Wiffleball trapping an electron density difference of ~1000 or greater exists inside. But 99.9999% of this is canceled by the pos. ions present inside also. So, between conduction and the small differences between charge inside and outside, is there any noticable induction induced charge seperation on the magrid metal surfaces?

Dan Tibbets

[erblo]

Perhaps I'm confused, but I don't follow your reasoning...

Seems like we're talking past each other. I was just commenting that the charge on the grid looked like it was quite far from a realistic polywell and wondered why it still didn't show any recirculation of the electrons. The simulation I'm commenting on has a ~7T B-field (I think) and (-)10^-8C net space charge from the particles. The grid has an unknown charge, but from the settings it looks to me like it's on the order of a few C at least. This would result in a potential of gigavolts or more inside the grid compared to the wall.

The simulation shows the electrons leaving the grid and traveling to the wall without slowing down. Shouldn't this require insane amounts of energy (GeV-TeV) being transferred to the leaving electrons, regardless of if they are following B-field lines or seeing the tiny influences from the other particles?

[erblo]

So, between conduction and the small differences between charge inside and outside, is there any noticable induction induced charge seperation on the magrid metal surfaces?

Dan Tibbets

No, I don't think there will be much either, on a real polywell with conducting casings. I was talking about the simulations were he's using a homogeneous charge distribution on the surface of the coils, not a constant potential.

(Indrek's Ephi-page has some nice pictures and calculations regarding the charge distribution required to get a constant potential.)

[happyjack27]

Perhaps I'm confused, but I don't follow your reasoning...

Seem like we're talking past each other. I was just commenting that the charge on the grid looked like it was quite far from a realistic polywell and wondered why it still didn't show any recirculation of the electrons. The simulation I'm commenting on has a ~7T B-field (I think) and (-)10^-8C net space charge from the particles. The grid has an unknown charge, but from the settings it looks to me like it's on the order of a few C at least. This would result in a potential of gigavolts or more inside the grid compared to the wall.

The simulation shows the electrons leaving the grid and traveling to the wall without slowing down. Shouldn't this require insane amounts of energy (GeV-TeV) being transferred to the leaving electrons, regardless of if they are following B-field lines or seeing the tiny influences from the other particles?

i'm not sure the charge is that high. it's on a logarithmic scale and the scale is pretty large right now, i need to narrow the min and the max on the slider to get finer control. but in any case given 1E5.292 amp turns, at about 1E3 whatever-the-unit-is is about the point, experimentally, where electrons start running into the magrid, i.e. where the coloumb force can exceed the magnetic mirroring effect, i.e. where you go from essentially 0 grid losses to non-zero. at that point, since i'm using a log scale, its very sensitive, so you go from 0 to very high very quickly.

[happyjack27]

How do you calculate the the surface? Is it the surface of the coils approximated as cylinders/tori: L*2*pi*r? Then the results in my previous post should be divided by about 30 (using 5mm radius), not considering the unknown scaling factor.

come to think of it, with the new formula for the field of a finite line charge i put in i'm not sure i turned on wire radius for the charge. so in that case its acutally a line instead of a surface right now.

but in any case the idea for the surface is i just subtract "r" from the distance, so each line segment becomes, approximately, a cylinder with a hemisphere cap on each end. that gives you an extra sphere of charge at the intersections, though. but if one really wanted they could just put a point charge of opposite polarity at each intersection to cancel that out.

[erblo]

...but in any case the idea for the surface is i just subtract "r" from the distance, so each line segment becomes, approximately, a cylinder with a hemisphere cap on each end. that gives you an extra sphere of charge at the intersections, though. but if one really wanted they could just put a point charge of opposite polarity at each intersection to cancel that out.

That's an interesting approach, I'll have to think a little on what it should result in. I thought that you calculated the field as from a 0 radius wire at the center of the coil but simply said that the electrons are lost if they hit the surface (at distance r from the center)...

[erblo]

One thing is that you will still have an infinite electric potential (and field) at the surface of the coil. Doing it the way I described will result in a finite and easily changed (but not quite constant) potential and field at the surface.

(That way you could set the (average) potential on the grid as "insert value" Volts compared to the wall.)

[happyjack27]

So, my understanding is that the Polywell will have perhaps 10^-3 Coulombs of unbalanced charge that tries to push the electrons out and pull the ions in ... I don't know what parameters the sims are using, but the above illustrates the the charges in a Polywell.

fwiw, in the sims i usually keep the unbalanced charge around 10^-8 (1E-8) coloumbs. mostly due to the aforementioned particle count limitations.

...The charge is irrelevant (except of course you have to have individually charged particles to interact with the magnetic field like a gas does with the surface of a balloon).

i get it, so it's in a sense the average outward radial momentum of the electrons at that point vs. the lorentz force produced by the cross product of the momentum vector and the mag field.

Thermalization issues are important. The originally monoenergetic electrons ...

the sims show that electrons are pretty uniformly cold in the center and warmer as you go out. i don't remember if the momentum view of them showed this trend to be monoenergetic or not. but i'm not sure it really matters for the electrons, which after all arent' the fusion reactants. so long as their cold where the fusion is happening to keep bremstralg (sp?) losses at a minimum.

Talking of the ions, which are electrostatically contained, A. Carlson claimed that several million volt potential wells would be required to contain most of the upscattered ions, but this was based on thermalized plasmas and ignored the claimed annealing. In one paper Bussard gave a number ~ twice the desired potential well to contain most of the upscattered ions. I assume this reflects the efficiency of the claimed annealing. Of course, I don't know how you could have an accelerating potential well that was different from the containment potential well. In that case, Bussard recognized that the mildly upscattered ion could climb above the potential well (extend past the Wiffleball border), but it would not escape unless it hit a cusp. It would be turned by the magnetic field. This tends to decrease convergence, but hangs on to the ion. This is not as bad as pure magnetic ion confinement schemes, because only a minority of the ions reach this condition, so ion ExB drift and ion cusp losses are restrained, apparently to such an extent that most of the ions (or at least enough of them) are expected to fuse before they manage to escape.

the ions do appear to "see" the grid charge. and with as low of a net plasma charge imbalance as i have, i suppose there isn't much other charge for them to see in my sims. in any case this alone seems to actually confine them pretty well. in my sims the ion starts with zero ke w/in the magrid so they don't start w/enough initial energy to escape in the first place. this is probably not the case for all ions in real life, but i figure coloumb forces should spread out their ke's over time to what they would reach in equilibrium, anyways. as to their thermalization or not i have a 3rd video of radial momentum vs. position space after running the sim for a few hours i suppose i should upload.

EDIT: i've posted said video in the sims thread.

[happyjack27]

That's an interesting approach, I'll have to think a little on what it should result in. I thought that you calculated the field as from a 0 radius wire at the center of the coil but simply said that the electrons are lost if they hit the surface (at distance r from the center)...

for now i think that's what i'm doing actually (0 radius wire). it may actually turn out to be a better approximation. it certainly doesn't result in the extra sphere of charge at intersections.

[D Tibbets]

@happyjack27
Are you modelling the chamber as a simple loss radius? Just make sure to remember that the electric potential at the chamber is nonzero (and also different at different positions). I checked the 1m radius dodec - the potential at 2m is about half of that in the center of the grid and at 3m it's about 1/3...

(To get a grounded conducting spherical chamber is easy enough - use image coils)

when an electron reaches a distance of 3 times the radius of the magrid from the center its position is reset. by reset i mean its introduced in one of the "electron guns", which for now is just a random position inside the magrid. (a rough sim of introduction by ionization of a nuetral gas)

I've held off due to plans of referencing my thoughts, but instead I'll give less defended comments. In the 2008 Pollywell patent application it is mentioned that the escaping electrons need to stay 'stuck' to the magnetic field lines. To do this the vacuum vessel wall (or other grounding structure) needs to be within a given radius of the magrid. I cannot recall the number but I believe it was somewhere around 1.5 times the radius of the magrid.

Also, when reintroducing the electrons back into the magrid to make up for these lost electrons, placing them randomly inside with random energies is far from how electrons are actually placed into the magrid enclosed reaction space. The electrons are injected towards the center with a narrow energy spread. They slow as they approach the center, reverse and continue this radial oscillation until they scatter into more random directions or escape. Those that escape are recirculated with energies and directions similar to the original injection. Those upscattered electrons that reach the wall (or reach the magnet surfaces), are replaced with new electrons from the electron guns, and enter the magrid with energies and vectors towards the center just like the recirculated electrons. Note that the electrons are not expected to reach all the way to the center, but into a sphere near the center, that is reflected by the potential well being ~ 85% of the drive voltage.

The easiest way to do this in this simulation(?) is to introduce these replacement electrons into the center ( or randomly within a core radius consistent with the potential well/ drive voltage ratio) Also, these electrons should have zero or some low energy comparable to what the real electron gun injected electrons would have as they reached the core where they are at the top of their potential well.

Dan Tibbets

[jcoady]

I my web based 3D simulation of electron trapping I noticed that when the electron escapes the polywell it never returns. I am just simulating a single electron of a given kinetic energy moving around in the polywell based on the Lorentz force. You can view the simulation in 3D in your web page here.

http://members.shaw.ca/johncoady/polywell.html

You can configure different options for the polywell such as magnetic field strength, radius size, electron energy and then watch how it behaves in the polywell. However, once the electron escapes the polywell, it follows some long trajectory away from the polywell and never returns.

Also a similar simulation of an electron trapped in a magnetic mirror can be found here.

http://members.shaw.ca/johncoady/magneticmirror.html

[93143]

Are you including the effect of the magrid's positive charge? 'Cause that's what's supposed to recirculate the electrons...

[jcoady]

No I did not take into account a charge on the magnetic grid in my simulation. The simulation is just based on the motion of an electron of a given energy and the magnetic field generated by the polywell. I think the term recirculation refers to the electron moving moving around inside polywell and doesn't necessary refer to the electron moving outside of the polywell and coming back inside. Here is a paper by Bussard about recirculation.

http://www.askmar.com/Fusion_files/EMC2 ... lation.pdf

He uses the the term Gj to refer to recirculation and shows in Figure 7 at the end of the paper that you can get up to 100000 recirculations of the electron inside the polywell under the right conditions. I think I read somewhere that for fusion to work the ions need to recirculate a couple of thousand times through the core before there is a likelihood of a collision and the electrons need to recirculate on the order of 100,000 times before they exit the polywell.