regarding recirculation

[rjaypeters]

...some electrons get stuck the the grid. so i turn down the charge on the grid to get them off.

I thought for a second you had turned the "happy holidays magrid" back on.

[happyjack27]

momentum view of the phase space, after running overnight.
steady state.

http://www.youtube.com/watch?v=KbaV5iSG2jY

near the end of the video i show cross-section on the z-axis, vs. the y axis (radial momentum)

[happyjack27]

now that i have the charged magrid, from all the sims no matter where i put the relative charge at, if the electrons have enough momentum to make it to the coils (as far as their distance from the center is concerned), then they have enough momentum to reach all the way to the chamber walls. (presumably they get their momentum from mutual repulsion.)

so that supports my theory. it's not because of recirculation that you can't put any metal in front of the fields -- any electron that hits that plane is lost anyways -- it's because the metal is a conductor and as such it warps the electromagnetic field around it. and this _changes_ the trajectory of the electrons, presumably so as to make the losses much greater.

so it's not so much that electrons run into the plate (any electron that reaches that surface is as good as lost anyways), but that the plate, simply by being there, changes the electromagnetic fields for the worse.

[D Tibbets]

Your finding of total electron loss if the electrons reach the radius of the magrid is totally contrary to the claim of recirculation. If this is true in your sims, a possible explanation without throwing out recirculation (and thus any hope for break even) is your assumptions. I assume you are introducing/creating your central electrons at the same potential as the magrid voltage. But, remember that the potential well for the electrons is only ~ 80% of the electron injection energy(potential on the magrid). This is due to inefficiencies in the injection process. In that case an escaping electron would have to be upscattered by 20% before it reached velocities that would not be reversed by the magrid. That is simple electrostatic theory. If your election average (birth) energy equals the magrid potential, then any escaped electrons would be decelerated to zero speed just as they kissed the vessel wall. This might explain your observation of electrons accumulating outside the magrid. There would be a lot of slow electron in this low energy halo that would not ever quite reach the edge of the sim, or fall back towards the magrid (within the precision of your math and considering the high coulomb collisionality of this cold electron plasma and the time scale of your sims). Within the lifetime of your simulation, this accumulation of electrons could even partially negate the potential difference between this region and the the magrid. Even with a lower initial electron energy VS grid potential, this would eventually reach this state as the upscattered electrons accumulated in this region, unless you remove them from the system (much as they would be by colliding with a real vacuum vessel wall).

Recall the claimed density difference between the internal and external electrons of over a thousand fold. The magnetic containment and recirculation of electrons is a dynamic process. The relatively high (but tolorable) currents of electrons into the machine is exactly matched by the loss of electrons to magrid or vessel wall surfaces. And the energy distribution of these electrons is also an important component. The replacement electrons are relatively monoenergetic, while the escaped upscattered electrons are at a thermal distribution around their average upscattered energy (with a offset due to decelleration as they pull away from the magrid (In a WB6 example this would be 10,000 eV average input (birth) energy plus the upscattered energy minus 2000 eV (magrid voltage of 12,000 volts). My understanding is that due to another component of Gauss Law, any upscattered electron that has not accumulated more than 2,000eV of energy will be reversed and accelerated back through the cusp at the same energy as the virgin electrons from an electron gun. This reverse acceleration is the same for any escaping electron. The only difference is how far they climb before being reversed. Or, in the case of electrons upscattered by more than 2,000eV, they will be slowed but not reversed. This is very important as it provides a mechanism for removing these excessively accelerated electrons at ~ 12,000 eV less cost than would otherwise apply. It is very important to remove these undesirable electrons (at low cost) in order to prevent/ delay the thermalization of the other electrons.

I wonder if your sims account for this dynamic process. A pulse of electrons into the center, then watching how they move, is interesting, but only represents a portion of the physics. Pulsing input of electrons (or better yet a continuous stream) on timescales short enough and at appropriate energy near the center of the machine, combined with a arbitrary periodical removal of electrons outside a chosen radius outside the magrid would better approach the true(?) Polywell physics.

Dan Tibbets

[happyjack27]

i just dont see it. its really not like a hollow sphere. its a very poor approximation. its clear that the ions really do see the charge from the magrid quite clearly. and in any case there's a point on the line through the face of a coil where the net electric potential from the coils is maximal. with the magnetic field off an electron will at best oscillate around this point, but far more probably run right into the magrid. you have to turn the mag field on to insulate the magrid. and at 7 tesla (~1E5.3 ampturns on a 15cm wb-6), by the time you have some visible electrons bouncing back via the magrid charge, the grid losses are huge. maybe w/thicker coils it would be more like a hollow sphere, but still... if an electron can get to that peak voltage, even if it did oscillate about it, well it's already on average so far from the center it's not really contributing to the potential well anyways.

[D Tibbets]

Of course, without the magnetic fields an electron would fly straight towards the nearest magrid surface. But this ignores the momentum of the electron, and Gauss Law. You do not have to have a perfect sphere for Gauss Law to apply. Even the bench top demonstration apparatus in classrooms, have a fairly large hole in the sphere to allow you to insert the test sphere. The degree of 'absoluteness' of the sphere continuality is dependent on the frequency of the test charge. Just like a Faraday cage which can be made of separated wires and easily stop AM radio signals. Higher frequency FM signals need closer spaced wires. Also, a container does not need to be spherical for Gauss Law to apply, a cube, pyramid, irregular shapes, etc work equally well. This was hashed out in another thread, where I gained this hopefully accurate understanding.

Back to the Polywell. For an electron inside the magrid, despite it's openings, and non spherical surfaces (towards the center), Gauss Law applies well enough (I don't know if it would be absolute). No magrid charge is seen by the electron until they are past the radius of the mid plane of the magrid . At that point they are immediately attracted to the nearest magrid surface. Of course with the magnetic fields they are turned at a given gyroradius. Remember that due to the small cusp sizes and their locations at equal distances from opposing magrid surfaces, the electrons will experiance no lateral force, only the net inward accelerating force, at least in pure terms. Of course, unless the electron is traveling exactly down the center of the cusp, there will be some spiraling along a field line. Also Coulomb scattering will push some of the electrons closer to a magnetic surface. I assume that this is why Bussard said, 3-5 gyroraddii separation is needed. During the transit of this narrowest portion of the cusp (closest to the opposing magnet surfaces), there may be up to ~ twice(?) the number collisions compared to the number of gyroradii allowed for. Each collision will knock one of the pair of colliding electrons one gyroradii deeper into the magnetic field and the other is knocked one gyroradii further away. This needs to be allowed for so that this ExB drift does not result in too many electrons hitting the magrid surface in these tight edge ('funny cusp') regions, as they did in WB4. This scattering process in the cusps is also probably, at least in part, why a potential well of only ~80-85% of the drive potential can be obtained.

In the magrid designs where the magnets are not symmetrical in shape and size, there may be net displacements of electrons passing through a cusp and move more towards one magnet. I don't know if this would result in a problem.

Dan Tibbets

[erblo]

@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)

[happyjack27]

@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)

[erblo]

OK, that was what I thought.

I've looked trough your recent videos of the "Escape from Coruscant"-sims and I haven't really seen any recirculation, just as you said. Once the electrons are outside they don't seem to be affected much by the grid which makes me wonder:

Is this true as you zoom out, are they being slowed at all in the 2.85 m to the "wall"?
What happens if the electrons are introduced outside?
What is the effect of the ratio between the E and B field strengths? - It should work like a fusor for low B-fields, right?
Are you using SI units for the line charge, i.e. ~10^1 C/m in the first video? That would mean quite impressive numbers: to get to the wall from the middle of the 15cm radius 32 coil grid the electrons would need about 4.3 TeV (when only considering the grid and assuming my calculations are correct).

[happyjack27]

OK, that was what I thought.

I've looked trough your recent videos of the "Escape from Coruscant"-sims and I haven't really seen any recirculation, just as you said. Once the electrons are outside they don't seem to be affected much by the grid which makes me wonder:

Is this true as you zoom out, are they being slowed at all in the 2.85 m to the "wall"?
What happens if the electrons are introduced outside?
What is the effect of the ratio between the E and B field strengths? - It should work like a fusor for low B-fields, right?
Are you using SI units for the line charge, i.e. ~10^1 C/m in the first video? That would mean quite impressive numbers: to get to the wall from the middle of the 15cm radius 32 coil grid the electrons would need about 4.3 TeV (when only considering the grid and assuming my calculations are correct).

tried that. yeah, zooming out no good. they dont reverse.

[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)

Your arbitrary distaqnce from the center befor removal may help to elminiate the accumulation of external charge, though I don't know how you arrived at the distance. Bussard's stipulation of how far the electron guns need to be from the center (1.5 X the radius of the mqgrid I think) might be a reasonable distance as apparently that far away, any electrons that are going to recirculate will. Any electron with residual outward radial velocity after overcoming the magrid reversing potential, will fly directly to the wall unless scattered*. The mean free path of electrons in this region is presumably long enough that this probably wouldn't happen much. And unless they assumed a perfectly circular orbit around the magrid, further collisions would decelerate them enough that they would be recirculated, or accelerate them so that they would hit the vacuum vessel wall. The lifetimes of the upscattered electrons would not be long. In fact I think the relative lifetimes would be in the order of 1/ (WB trapping factor * recirculation factor) or somewhere around 1/100,000 th lifetime

Your scheme for reintroducing electrons may be reasonable for your current sims. But as they evolve, you will need to not only transplant the position of these electrons, you will also need to give them an appropriate radial velocity/ energy. ~ equal to the potential well level energy if introduced on the edge, and near 0 energy if introduced at the center.

* this is a simplification. Most of these electrons will probably be following along magnetic field lines, but these fieldlines wil probably/ possibly intersect the vacuum vessel walls before the electron can loop around to the neighboring cusp. This suggests that you do not want your vacuum vessel diameter to be too great in proportion to the magrid diameter.

Dan Tibbets

[D Tibbets]

OK, that was what I thought.

I've looked trough your recent videos of the "Escape from Coruscant"-sims and I haven't really seen any recirculation, just as you said. Once the electrons are outside they don't seem to be affected much by the grid which makes me wonder:

Is this true as you zoom out, are they being slowed at all in the 2.85 m to the "wall"?
What happens if the electrons are introduced outside?
What is the effect of the ratio between the E and B field strengths? - It should work like a fusor for low B-fields, right?
Are you using SI units for the line charge, i.e. ~10^1 C/m in the first video? That would mean quite impressive numbers: to get to the wall from the middle of the 15cm radius 32 coil grid the electrons would need about 4.3 TeV (when only considering the grid and assuming my calculations are correct).

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 think WB 6 actually operated more in the range of 10^18 or 19.

Remember the charge is dependent on the ration of negative charges compared to positive charges. Polywells are supposed to operate at ratios of ~ 1,000,001 electrons per 1,000,000 positive ion charges. This difference is what provides the electrostatic confinement of the ions.
The electrons (in excess) are of course not confined in this manner, but if allowed would quickly disperse due to this excess negative space charge. It is the magnetic fields that confine the electrons against this electrostatic charge. If there was 1.000000 *10^22 pos deuterium ions, there would be 1.000001 *10^22 electrons. This would be an excess of 10^16 electrons. If you plugged that number into your calculation you would get the Positive potential well nessisary to contain them. But this is misleading as there is no electrostatic containment of electrons within a given sized magrid. That is the magnetic fields job. This is one of the key features of the Polywell. As Bussard ~ said, 'magnetic fields do not contain ions worth a darn, but they can contain electrons much better'.

In fact the ability of a magnetic field that can turn electrons extends only up to a certain energy. At 10 Teslas, I suspect this maximum tolerable electron energy may be in the region of 10's of millions of eV. Essentially the electrons gyroradius would be greater than the radius of the machine and they would hit the magnet or vessel walls on the first pass.

As far as electrons being introduced outside the magrid, that is basically how the Polywells operate. But, they cannot be randomely introduced. With the positive charge on the Magrid the electrons need to be introduced at low voltage from an electron gun aimed down the throat of a cusp. Release elsewhere will further impede the development of a deep internal potential well, and result in a greater accumulation of electrons outside (bad). Already, a well of ~ 80-85% of the potential on the magrid is the maximum obtainable.

Dan Tibbets

[happyjack27]

remember my major limitation is particle count. i only have 14k particles to represent an entire virtual population. i don't feel comfortable pushing that up past about 1E-5 gross space charge.. that's already a representation ratio of over 1E10 to 1. anything else, however, is essentially unlimited.

[erblo]

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.)

[happyjack27]

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

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.