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

[Robthebob]

I see, my understanding of well depths may be incorrect. I was under the impression that geometry can improve confinement and reduce loss rates, thus more electrons confined in the machine, which means well depth would be deeper.

for machines of similar sizes and dimensions, more electromagnets of similar strength would mean each cusp is smaller? (because they're packed closer together) This should help with the mirror effect at the core of the machine. (While this also means you gotta pump in more current to maintain the higher number of electromagnets, not sure if this is worth it or not). This also reduce loss rates by increasing the quality of confinement, then there's the whole x-cusp business.

To me, this means less electrons are escaping and gone forever or running into something and gone forever, which means electron life time in the machine would be higher, which means higher electron density, which should be deeper well depth... On another note, I dont quite understand what you mean by well shape.

[D Tibbets]

The B field in the center of a cusp is indeed zero, but like Bussard's use of lines for the magrid structure in his models, this is a misleading condition. The B field is zero in the center, but this center is by definition a line or point that is infinitely small. In the real world the electrons that would travel down this infinity tiny channel is miniscule. This realization is what lead to the spacing in WB6. You cannot avoid electrons entering into non zero B field regions in the cusp (except for an infinitely few), and thus the electrons assume relevant gyro radii. To accommodate for this (along with some collisional random walk scattering (ExB drift)) the magnet grids were separated by 2-5 gyro radii, presumably calculated on the gyro radii of the B fields at the Wiffleball border. If you consider a computer model of the truncated cube Polywell where the magnets are treated as lines, then each corner would be the same as an X cusp, except with three arms instead of 4. This would lead to the conclusion that charged particle gyro radii were zero in the funny cusps and thus no ExB drift needed to be considered (as it apparently was not considered in WB4). It was not until the testing of WB5 that Bussard, etel discovered the fallacy of this computer model.

In the x-cusps the same would apply, as the corners of the x- cusp is approached. The ExB drift at some point exceeds the cusp leakage. In the 2008 Patent application with the truncated cube, it was mentioned that cusp electron leakage was ~ 10-100 times greater than the ExB drift losses. I don't know if this was before or after recirculation contributions. This does show the imaginary electron confinement efficiency if the cusp losses were zero. ExB magnetic confinement losses cannot be eliminated, just like in a Tokamak. But, one of the keys of the Polywell is that only electrons are confined magnetically, their gyro radius is <1/60th that of hydrogen ions, and 1/120th(?) of deuterium ions. Thus confinement times are much longer than the neutral plasmas where the confinement time is limited by the ion ExB dynamics (if macro instabilities can be controlled). An obvious question would be - why not inject excess electrons into a Tokamak. I don't know the answer, but that the plasma is magnatized throughout in a Tokamak probably plays a role.

There is a tradoff. As higher polyhedra are utilized, apparently the cusp losses will decrease. But at the same the ExB drift losses increase. There is a diminishig return. Bussard felt that performance would peak at ~ 3-5 times that of the truncated cube. Whether that is reached at the 2,3,4,... polyhedra order is the question
Also, I don't know if Bussard's preferred square form arrangement was before or after recirculation and real ExB concerns were addressed. Experiment would answer the question.



Dan Tibbets

[KitemanSA]

Correction, the B field in the center of an X-Cusp (or funny cusp) is zero. In the center of a point or line cusp the fields are generally very large. It is the tangential component of the field that is zero.

As to your confusion, remember that the expectation is to have a plasma near beta=1. Once you reach that, the depth won't change much. But if you can make the MaGrid less leaky, you can maintain beta=1 (max depth) with a much lower electron current.

[ladajo]

As to your confusion, remember that the expectation is to have a plasma near beta=1. Once you reach that, the depth won't change much. But if you can make the MaGrid less leaky, you can maintain beta=1 (max depth) with a much lower electron current.

Key point. It is about loss control, which in turn means efficiency and Q.
Power in v. Power out. The trick is having a "deep" well, with minimal (or no) drive current. This is where Bussard and Nebel both had thoughts that in a full scale device, you would not need to drive the well, as there could be sufficient neutrals stripping of fuel to keep the machine in (e-)s.

[happyjack27]

but i thought it needed to kept with a few excess electrons. there will always be some electrons loss, so there will always be the need for some electron input.

[happyjack27]

I see, my understanding of well depths may be incorrect. I was under the impression that geometry can improve confinement and reduce loss rates, thus more electrons confined in the machine, which means well depth would be deeper.

for machines of similar sizes and dimensions, more electromagnets of similar strength would mean each cusp is smaller? (because they're packed closer together) This should help with the mirror effect at the core of the machine. (While this also means you gotta pump in more current to maintain the higher number of electromagnets, not sure if this is worth it or not). This also reduce loss rates by increasing the quality of confinement, then there's the whole x-cusp business.

To me, this means less electrons are escaping and gone forever or running into something and gone forever, which means electron life time in the machine would be higher, which means higher electron density, which should be deeper well depth... On another note, I dont quite understand what you mean by well shape.

from my understanding you are correct in all this. more sphericity means better confinement means deeper well depth. but that's all assuming the same mag field strength and all that, for the same net power input. etc. it's assuming that you can keep all of the other variables the same when you change the geometry.

if, for instance, going to a higher order polyhedra means more coils, means smaller coils, well then you have to look at how that effects the mag field strength and the current (power) needed to maintain that mag field. the change in the mag field strength could have a much bigger effect on confinement than the change in polyhedra order does. and the change in current a much bigger effect on the power in/out ratio.

so it's not straightforward as change in polyhedra order can effect other variables, esp. in smaller machines. and those other variables can have much more significant affects.

re: plan form magnets: making the mag shapes non-conformal just means more electron losses to the coil housing. unless you're talking about the major axis rather than minor-axis - they you're talking about increasing sphericty. would still have an impact on electron losses, and would have different mechanical strain distribution, of course.

[happyjack27]

There is a tradoff. As higher polyhedra are utilized, apparently the cusp losses will decrease. But at the same the ExB drift losses increase. There is a diminishig return. Bussard felt that performance would peak at ~ 3-5 times that of the truncated cube. Whether that is reached at the 2,3,4,... polyhedra order is the question
Also, I don't know if Bussard's preferred square form arrangement was before or after recirculation and real ExB concerns were addressed. Experiment would answer the question.

Dan Tibbets

my sims seem results suggest to me that higher order polyhedra would pay off at larger sizes. when its' big enough to get mag field strength and all that easily into peak fusion velocities, well then you're left with fusion volume * fusion density * fusion density / power loss. so you'd adjust your mag field and all that to maximize volume *density^2 at optimal velocity, and your power loss vectors are primarily driven here by surface areas and lengths and counts. so you look at how polyhedra order - sphericity, coil count, etc. - effects these spatial components, and it seems to me that the optimal polyhedra order increases monotonically with machine size.

[ladajo]

but i thought it needed to kept with a few excess electrons. there will always be some electrons loss, so there will always be the need for some electron input.

Yes, but the thought is that the neutral stripping would be a sufficient source to replace actual e- guns during run. That does not mean that initial start-up will not need to have the well driven. But, as I recall that was also part of the discussion.

The key take away remains that behaviour will be significantly different at full scale, and Bussard's whole argument about just going big.

[KitemanSA]

I was under the impression the a degree of drive current would be required to maintain the mono energetic nature of the electrons. The current would heat the cooler electrons while the overheated ones would escape to the wall, recycling most of their energy.

[ladajo]

I was under the impression the a degree of drive current would be required to maintain the mono energetic nature of the electrons. The current would heat the cooler electrons while the overheated ones would escape to the wall, recycling most of their energy.

I will need to go back a look again at what was said, but as I recall, the thought was that no input would be required, and distribution would be maintained given dynamics of core travel, upscatter, downscatter and edge interactions.

[D Tibbets]

Correction, the B field in the center of an X-Cusp (or funny cusp) is zero. In the center of a point or line cusp the fields are generally very large. It is the tangential component of the field that is zero.

As to your confusion, remember that the expectation is to have a plasma near beta=1. Once you reach that, the depth won't change much. But if you can make the MaGrid less leaky, you can maintain beta=1 (max depth) with a much lower electron current.

I disagree. The point cusp is no different than the line cusps in terms of opposing fields. In fact, my current understanding is that this is why the face center cusps leak more than the corner cusps. The distance to the electromagnet casing to the center is greater (greater separation). The B field drops of as the inverse square of the distance. It is a greater distance to the center point cusp than the corner line cusp. The the line cusp (what used to be the equatorial cusp has a length but the field strength compensates for this somewhat. That is the whole idea begind the polyhedron versus the biconic opposing mirror machines.

Also, consider that the cusps are formed by two opposing magnetic fields. Not only distance to the casing is important, but also the distance to the opposing casing. With equal B fields at the center between the magnets there will always be a region of zero strength,otherwise how could concieve of a cusp at all? The rapidity of the fall off depends on the initial strengths and geometry, but by definition there has to be this zero strength in the middle. My previous point was that this was assumed for electrons reaching the center of the cusp, but this represents only a tiny fraction of the electrons, depending on where you choose to place your limits (some small gyro radii that you round down to zero).
The horrendous leakage in a line, equatorial cusp in a two magnet mirror machine, is because of the line componet (length). If the magnets are placed apart a distance equal to the diameter of the magnet, the B field drop off is the same (which reaches zero at the center). The difference is that a point cusp (with a loss area of say 1 cm^2 in which the falling B field and charged particle dynamics result in increasing likelihood of the loss cone being satisfied) on either end is the full loss area. The line cusp is the same in one dimension, but is a line, not a point Yo have to multiply the width by the length, which is 2 PI R. If the magnets are 1 meter wide this would result in a total loss area of 100 CM ^2. You can move the magnets closer together, and this will increase the gradient of the B field strength near the center of the cusp, effectively decreasing the width of the cusp where mirror confinement fails. This is part of the idea behind the Polywell. The increased strength on each side of the mid line makes the cusp thickness less. At some point this will compensate for the circumference multiplier on the losses. The problem is that as the magnets are moved closer though is that the internal confinement volume decreases. The The truncated cube or higher polyhedra over comes this tradeoff by maintaining the volume despite having most of the confining magnets close together. You get your cake and eat it too!

I do not conceive of how you could consider an x cusp as being different. In a two magnet opposing mirror machine, there are the described point and line cusps. In the Truncated cube the funny cusps is an adaptation based on metal being in the way, otherwise there is no difference. . It wasn't that Bussard didn't recognize this, it was that he considered the intervening metal (magnets) to be lines, which means infinitely thin. And this meant there was no surface area for the electrons to hit , even if the electrons gyro radius was greater than the separation of the lines as they in turn approached each other. This is easy to setup in a mathematical model, but didn't represent reality as Bussard , etel finally realized. This is described clearly in his Google talk.

As for Beta condition that has nothing to do with the width of the cusp in the midline of the magnet, except that above 1 the cusp starts expanding. Below 1 the cusp midline width does not change, what changes is the cusp throat. It gets flattend out, thus the Wiffleball analogy. There can be some confusion.It depends on how you define the cusp. If you define it as the collection are where a charged particle is trapped on an ever deepening path into the cusp where it will inevitably pass through the tightest portion of the cusp and then exit, then the Wiffleball shrinking hole analogycan be a description of the cusp shrinkage. If you describe the cusp as the diameter of the path between the opposing magnets where they are closest (midline) as defined by some border where the B field is below some limit, then This is not changed at Betas below 1. My perspective is that the holes in the wiffleball do not shrink. What happens is that the holes stay the same size while the overall Wiffleball grows. The expansion of the Wiffleball diameter and thus surface area increases to a limit, while the cusp stays the same. It is like a billiard table. At certain approach angles the ball will fall directly into the pocket, or bounce off the bumpers several times on the edge of the hole till they fall. With Wiffleball inflation the total size of the table increases, there are more areas where the ball bounces away from the hole, but the holes and 'collecting' areas are unchanged. That is not a perfect analogy, I prefer the funnel analogy , but I think it gets the point across.

This does lead to less input electrons to maintain the balance as you said, but I do not think that is the whole story. You do not want the electrons to thermalize over their lifetime, so a certain amount of leakage is not only unavoidable, it is desired. Various parameters determines where the best compromise can be made once some minimum confinement efficiency is reached.

After my rambling, the points are that all cusps have zero strength in the middle by definition. And this zero strength is only asmall contributor to the overall behavior of the cusp confinement. It is at what diameter the field is weak enough for the charged particles to get through and not be mirrored back . Add to this collisional effects where the electron will knocked towards the walls of the magnet lateral to the cusp.

As a further ramble, consider that the plasma is collisional- it has to be for fusion to occur. Even if you evoke the null B field in the midline of the cusp and claim that the escaping electrons must travel straight down this line, several things become obvious. First since the cross section is tiny, the density of electrons must be considerable. A billion electrons escaping through a 1 cm area per second, has a density of 1 billion per square cm/ sec. If the hole is much smaller, say a square mm where the B field has decreased to the point where gyro motion becomes negligible, then the density has increased a hundred fold and the collisions have increased ~ 10,000 fold. Many of the electrons would be scattered laterally and enter non negligible B field areas. ExB drift now manifests (which is just scattering limited to discreate distances before being trapped by the next field line) and electrons are lost to the magnet walls and cannot be recirculated. And, if you persist is saying the B field is very strong in the midline of the x- cusp, this implies strong gyroradii for the electrons. The distance between the magnets are small but the current is only half the general current, and the x cusp is essentially two crossing line cusps that terminate in the corners. The electrons will not hit the exposed metal at the ends of the line, more importantly due to gyroradii and associated ExB drift many / most(?) will hit the walls before the corner is reached. As I mentioned though, the x cusps are small (short distance between the magnets)and possibly stronger* despite 1/2 the amp turns and occupy a small portion of the surface area, so the tradeoffs could conceivably be positive.


*Note that stronger her refers to the distance from the center of the cusp (which has a zero B field) where the B field is strong enough to mirror most of the electrons. This is somewhat different from recirculation of electrons. Here the electrons pass through the cusp with some variable gyro radius depending on how close to dead center they enter the cusp and their vector(plus any scattering). There has to be room for them to spiral through the mid plane of the cusp where the metal surfaces are closest without hitting metal, then be pulled back in.

Dan Tibbets

[KitemanSA]

Comments in red.

Correction, the B field in the center of an X-Cusp (or funny cusp) is zero. In the center of a point or line cusp the fields are generally very large. It is the tangential component of the field that is zero.

As to your confusion, remember that the expectation is to have a plasma near beta=1. Once you reach that, the depth won't change much. But if you can make the MaGrid less leaky, you can maintain beta=1 (max depth) with a much lower electron current.

I disagree. The point cusp is no different than the line cusps in terms of opposing fields. Indeed, that is what I said. Point cusp, line cusp, high field, no transverse component. In fact, my current understanding is that this is why the face center cusps leak more than the corner cusps. Dan, you have invented two terms which have no general meaning and you haven't defined them sufficiently to be communicative. What do you mean by "face center" and "corner" cusps and how do they relate to the generally defined point, line, and funny cusps?

[KitemanSA]

Correction, the B field in the center of an X-Cusp (or funny cusp) is zero. In the center of a point or line cusp the fields are generally very large. It is the tangential component of the field that is zero.

As to your confusion, remember that the expectation is to have a plasma near beta=1. Once you reach that, the depth won't change much. But if you can make the MaGrid less leaky, you can maintain beta=1 (max depth) with a much lower electron current.

The B field drops of as the inverse square of the distance. It is a greater distance to the center point cusp than the corner line cusp. The the line cusp (what used to be the equatorial cusp has a length but the field strength compensates for this somewhat. That is the whole idea begind the polyhedron versus the biconic opposing mirror machines.

Not according to Dr. B. He seemed desirous of getting rid of the line like cusps and replacing them with funny like cusps. The equations he used showed that the line like cusps were the controlling factor in leakage. Thus I suspect your understanding is faulty.

[KitemanSA]

Correction, the B field in the center of an X-Cusp (or funny cusp) is zero. In the center of a point or line cusp the fields are generally very large. It is the tangential component of the field that is zero.

As to your confusion, remember that the expectation is to have a plasma near beta=1. Once you reach that, the depth won't change much. But if you can make the MaGrid less leaky, you can maintain beta=1 (max depth) with a much lower electron current.

Also, consider that the cusps are formed by two opposing magnetic fields. Not only distance to the casing is important, but also the distance to the opposing casing. yada yada yada. You get your cake and eat it too!

Dr. B. has done the math in several documents. Please read them. He mentioned at least once that he wanted to use square planform magnets (planform, not cross section) in order to reduce the length of the line like cusps (making them more funny like by the way) and expected an improvement of 3 to 5 times IIRC. I'll take his understanding over yours.

[KitemanSA]

Correction, the B field in the center of an X-Cusp (or funny cusp) is zero. In the center of a point or line cusp the fields are generally very large. It is the tangential component of the field that is zero.

As to your confusion, remember that the expectation is to have a plasma near beta=1. Once you reach that, the depth won't change much. But if you can make the MaGrid less leaky, you can maintain beta=1 (max depth) with a much lower electron current.

I do not conceive of how you could consider an x cusp as being different. In a two magnet opposing mirror machine, there are the described point and line cusps. In the Truncated cube the funny cusps is an adaptation based on metal being in the way, otherwise there is no difference. And this defines your misunderstanding of the whole issue. The funny cusp is NOT defined by metal being in the way, it is defined by four or more alternating B Fields meeting at one point. It just so happened that in Dr. B's patent, there would have been metal in the way. The X-Cusp is simply a funny cusp without the metal in the way. It wasn't that Bussard didn't recognize this, it was that he considered the intervening metal (magnets) to be lines, which means infinitely thin. Nonsense! The importance of metal being in the way didn't strike him until AFTER WB-5. It was the AHA moment that caused WB-6 to have a round cross-section FOR THE FIRST TIME. Please get your timeline straight. And this meant there was no surface area for the electrons to hit , even if the electrons gyro radius was greater than the separation of the lines as they in turn approached each other. This is easy to setup in a mathematical model, but didn't represent reality as Bussard , etel finally realized. This is described clearly in his Google talk. Time stamp please. I'd like to hear this interesting revelation for myself, thank you.