Does the Gyroradius of an Alpha fit in a cusp?

[D Tibbets]

I've been wondering about the passage of fusion alphas from P-B11 fusion, and to a lesser extent the tritium and Helium3 fusion ions from D-D fusion.
With the spacing of ~ 3-5 electron gyroradii between the coils of WB6, and WB7(?), there is plenty of room for electrons with their small gyroradii at ~ 10 KeV to pass back and forth between the closest approaches of the magnets.
Fuel ions would presumably have similar or smaller gyroradii because they are at the top of their potential well and moving slowly. So any fuel ions that escape electrostatic confinement possibly would not gyrate wide enough to hit the magnet casing. But this is completely different for the fusion alphas. They generally have ~ 700 KeV , 2.8 or 4 MeV depending on which reference you use.
At these energies, these relatively high energy ions would have much wider gyroradii than the electrons. Thus I would think that they might frequently hit the magrid casing on their way through the cusps- especially the 'funny cusps'- the area where the magnets are closest together. This would play havoc with direct conversion and increase sputtering and cooling concerns.
Is this indeed a problem?

The only way I could see to avoid this is if the fusion ion is directed into the center of the cusp where the opposing magnetic fields are all but cancelled. so the motion of the fusion ion would be almost linier in this region.
The other possibility is that the length of the gyroradius corkscrew motion is such that it passes the closest approaches between the magnets while in a position parallel to the width of this 'funny cusp'. I don't know how this would work.

The square magnet casings with the vertexes meeting as in one of the magrid designs would seem to minimize the area where the magnet casings are close together. This might minimize the vulnerable area.

Dan Tibbets

[TallDave]

Rick said they expect them to average a thousand passes before exiting. I took that to mean some proportion will hit the casings, but probably not a very large proportion, and very small relative to the MW of electrons.

One could probably calculate roughly the number expected to hit the casings to be sure, though I doubt sputtering will be a major concern.

[D Tibbets]

I think you are referring to a separate issue. In areas away from the cusps, if an energetic ion like an alpha exits the Wiffleball- magnetic field free zone and enters the magnetic domain it will complete a half of a gyroradius before reversing and again exiting the magnetic domain as it starts another pass through the Wiffleball. If the magnetic field strength is strong enough compared to the Wiffleball ball border to magrid casing distance the gyroradius will be shorter thus the ion will not reach the magnet. I don't know how accurate it is, but I recall hearing somewhere that the threshold B field strength for this to occur with a P-B11 fusion alpha is ~ 3.5 Tesla in a several meter size machine.

The issue I'm asking about is different. The above characterizes the alpha's dynamics when it hits the perpendicular magnetic field surface/ domain away from the cusps. In the cusps this meeting is mostly parallel. and the alpha will not reverse as it escapes through the narrow cusp, but it will spiral along the nearly parallel magnetic field lines. This gyro radius guided spiraling may be many cm in width .

Dan Tibbets

[KitemanSA]

The issue I'm asking about is different. The above characterizes the alpha's dynamics when it hits the perpendicular magnetic field surface/ domain away from the cusps. In the cusps this meeting is mostly parallel. and the alpha will not reverse as it escapes through the narrow cusp, but it will spiral along the nearly parallel magnetic field lines. This gyro radius guided spiraling may be many cm in width .

I was under the impression that the line-like cusp between the coils are too tight to allow alphas out. They are effectively corner reflectors. Only at the point cusps will the alphas exit.

I'm not sure where I got this impression.

[D Tibbets]

I'm not sure how the line like cusp regions would oppose the Alphas motion in order to prevent them from reaching the surface of the magrid. The only effect the magnetic fields have on charged particles is to turn them. This turning occurs through a certain radius that is the gyroradius or Lamar radius. In a homogenous magnetic field this is straight forward and results in the charged particle assuming a spiraling path along a field line. In the Polywell with a Wiffleball border the magnetic field strength varies over very short distances, but the same principles would apply except that the gyro orbit would be more oval or parabolic (essentially hyperbolic if the Wiffleball diameter is less than the otherwise parabolic orbit of the charged particle (in areas where the the magnetic border is nearly perpendicular to the vector of the alpha). With the fuel ions the potential well and collision considerations complicates this significantly. But the fusion alphas are essentially a collisonless subset of particles within the machine.

Where the alphas vector is nearly parellel to the magnetic field surface (field lines) the alphas will be turned at some angle, but provided this new vector is still outward the ion will continue outward. The escape cone or angle of a point cusp is often discussed with mirror machines. But this also applies to line- equatorial cusps. If this was not the case then opposing magnet biconic cusp mirror machines would be just as good as {olywells for ion or electron confinement.

One work around that might apply is that instead of considering the turning radius of the alphas in regions away from cusps as defining the minimum size, and B field strengths necessary to to prevent alpha grounding on the magrid surfaces facing the center of the machine, you consider the turning radius in the cusps, which would be compared to the opposing B field strengths and the distance between the magnets.
The B fields are compressed in these areas and this would result in smaller gyro radii. I could not calculate the relationship, but I would accept the arguement that there is a balance. In the electrons case this 'funny cusp' electron gyroradius is adiquate, but minimized (~ 3-5 electron gyroradii) to optimize confinement while still allowing recirculation of the electrons. The corresponding electrons striking the magnetic border away from the cusp would have wider gyroradii but still turn befor coming near the madrid surface. With Wiffleball formation these non cusp magnetic surfaces are also compressed so that the electron gyroradii are smaller, while the distance to the magrid surface is also reduced, perhaps to an amount that the distance from the magnetic surfaces to the magrid surface approaches this distance relationship in the cusps.

The problem as I see it is that this electron gyroradius distance tolorance may be easily met, even the fuel ion gyroradius tolerance may be met (and it may also be mostly moot as the potential well may provide the vast majority of the confinement mechanism and also greatly reduces the energy of most of the ions that are upscattered so that they can turn with small gyroradii)).
But the alphas lose only ~ 10% or less of their kinetic energy to the potential well so they may be ~ 9 times as energetic as the fuel ions. This would result in gyroradii much wider than the electrons.

I suppose the ratio of the magnetic field strength over the standoff distance to the magrid surface in various areas may suggest an equivalence (if one area is adequate, then all areas are adequate (due to increasing opposing magnetic field strengths where the magnets come closer together). This may apply to the mathmatical assumption of line like magnets that do not have any diameter, but as Bussard discovered this convienant assumption mislead him for years. Magnets with finite crossections led to the need for spacing in WB6 and I speculate woyuld also modify this alpha guiding issue. In the face centered point cusps and the corner 'point like' cusps the electron gyroradii may be much less than the distance to the magrid surface- perhaps to such an extent that even the much greater alpha gyroradius also fits. But at the close approaches this cannot hold. The spacing is required to prevent the electrons from grounding on the grid surface due to a combination of the electron gyroradius and some scattering (thus several gyroradii spacing). This to keep the electron exposure to grounding surfaces below ~ 1part per 10,000.
The alpha has much larger gyroradii , but is essentially collisionless so that helps some. Also, the alpha bombardmant reaching the surfaces may still be a small fraction of the total alpha flux, so it may be a tolorable condition that does not subtract from direct conversion efficiency much. It would require attention to the local heating of the magrid in these areas. It might be an additional argument against bridging interconnecting nubs between the magnets.

I'm thinking that the spacing chosen for optimal electron confinement and recirculation (confinement efficiency determines the Wiffleball density achievable, while recirculation determines the input energy efficiency) must have consequences for grid transparency to the alphas. This compromise will have engineering consequences but not be a show stopper. M. Simon was at one point calculating the heat loads with the assumption that the Alphas were hitting the magrids as a function of the magrid surface area as a percentage of the overall spherical surface area at a given radius. This consideration may ease the concern, but not eliminate it as I once thought.

Dan Tibbets

[hanelyp]

If a fusion alpha makes an average 1000 passes before escaping, that translates to the cusps having an area of 1/1000 of the sphere, as seen by the alpha. Assuming for simplicity each of the (6+8+12) = 26 cusps is the same size, each cusp has an area of 4pi/26*1000 = 0.000483322 steradians. Assuming circular cusps, each cusp has a radius of 0.012403474 radians, or 0.71066672 degrees. I'm thinking that the funny cusps where coils kiss are longer parallel to the coils, narrower the distance between the coils. Looks like plenty of space for alphas to get through.

Looking from another direction, given the magnetic field at the cusp and highest alpha energy, what gyro-radius is calculated? How does that relate to the cusp dimension and compare to the gap between the magnets?

[happyjack27]

my sims seem to suggest that most losses would be through point cusps, as the mag field is quite strong on the edges. ("funny cusps") due to the close approach. though i'm not sure i found near beta=1, those conditions might prove a different scenario for the WB "surface" at least.

as far as sputtering, sims also suggest it to be pretty low. due to the high mag field for electrons, and due to electrostatic repulsion for ions. ion sputtering looks to be practically nonexistent. but electron grid losses could be a non-negliglbe loss pathway, esp. given their very high energy that far away from the center, and that a charged grid provides electrostatic attraction.

on that note, mag field strength seems like a huge factor in confinement efficiency. but the higher the mag field, the harder it is to introduce electrons ala guns or electrostatics. at high field strength neutral gas injection really starts to win out. but the higher the field strength the faster that gas is going to ionize.

[D Tibbets]

As far as sputtering, the elecrtrons have relativelty low momentum, aso even though the may hit the magnets due to cross field trasnport while at their higest energies the effect will be minor compared to ions. Fuel ions contained by the potential well are not a problem. The fuel ions that are upscattered are probably a minor concern due to annealing and the probability that the upscattered fuel ions will escape before they can accumulate too much energy.
The situation is different with fusion ions. With energies of ~ 10-20 times that of the potential well, and if they are not turned by the magnetic field (or decelerated by outlieing conversion grids) they will hit with considerable force.

The gyroradius vs depth of magnetic field vs angle of impact vs degree of compression of the magnetic fields vs the increasing magnetic field strength as the magrid is approached vs the seperation of the magnets in a cusp (especially the 'funny' cusps between adjacent magnets) and the frequency of fusion ions hitting various portions of cusps is what confounds me.

As mentioned, the frequency of alphas escaping through the narrower cusps may be the saving grace. If 90 % of the alphas escape through distant point cusps (distant from magrid surface) then the problem is much less significant.
What worries me is that the spacing of WB6 decreased electron losses (mostly from impacts on the magrid surface ) by a factor of ~ 10X, then a similar mechanism may apply to the alphas. The difference is that a seperation of a few mm sufficed for electrons, but for alphas, this clearance may need to be much more. Increasing clearances in the 'funny' cusp regions decreases primary electron confinement and this directly effects the Wiffleball efficiency, density, and resultant fusion rates.


Dan Tibbets

[TallDave]

The issue I'm asking about is different. The above characterizes the alpha's dynamics when it hits the perpendicular magnetic field surface/ domain away from the cusps. In the cusps this meeting is mostly parallel. and the alpha will not reverse as it escapes through the narrow cusp, but it will spiral along the nearly parallel magnetic field lines. This gyro radius guided spiraling may be many cm in width .

I guess I'm not sure why that matters. It's not a constant field -- as they gyrate, they see the stronger fields closer to the casings. I think they end up being reflected there same as anywhere in the interior.

Polywells have good magnetic curvature toward the coils everywhere, even in the cusps.

mv/qB

[D Tibbets]

The issue I'm asking about is different. The above characterizes the alpha's dynamics when it hits the perpendicular magnetic field surface/ domain away from the cusps. In the cusps this meeting is mostly parallel. and the alpha will not reverse as it escapes through the narrow cusp, but it will spiral along the nearly parallel magnetic field lines. This gyro radius guided spiraling may be many cm in width .

I guess I'm not sure why that matters. It's not a constant field -- as they gyrate, they see the stronger fields closer to the casings. I think they end up being reflected there same as anywhere in the interior.

Polywells have good magnetic curvature toward the coils everywhere, even in the cusps.

mv/qB

The cusps at the closest approach, are spaced apart specifically to allow the electron's gyroradius to be accommodated, plus some leeway for ExB drift. The Alphas will have ~ 40-400 times as much energy, thus their gyroradius will be proportionately larger.

For that matter, this couple of mm spacing accomidates the electron gyroradius at 10 KeV. If the voltage in increased to ~ 100,000 volts, the electrons will have ~ 80 KeV. Does that mean the magnets need to be spaced even further apart? Will that effect the Wiffleball Trapping Factor. How will it interact with larger diameter machines and how will it effect the magnetic scaling?

Dan Tibbets

[TallDave]

I think you're referring to this:

Design, building and parametric testing of WB-
7 and WB-8, the final two true polyhedral coil systems, with
spaced angular corners, to reduce “funny cusp“ losses at the
not-quite-touching points, and yet provide very high B fields
with conformal coil surfaces. These would be topologically
similar to the original WB-2 and PZLx-1, but without their
excessive unshielded surface losses, and with pure
conformal coils and small intercept fractions. These latter
can be achieved by appropriate spacing between the corner
junctions (typically several gyro radii at the central field
strength between adjacent coils) to allow free circulation of
electrons and B fields through the “funny cusp“ regions,
without direct B field line impact on or intersection with the
coils themselves.

I assume you meant to say the coil casings are spaced, not the cusps. The idea seems to be that since the electrons are going out the cusps anyway, best to keep the casings out of their path.

But remember, the electrons are trying to get to the Magrid; that's why they spiral along the field lines. The alphas, otoh, want to get away from the Magrid. A simulation would be good to see, but I think they'll tend to bounce off the regions of stronger field/charge and head along their merry way.

Also, given that entering the cusp they should tend to have their velocity pointed out, it doesn't seem reasonable they can spiral out of the cusps into the Magrid, but maybe that's just one of those counterintuitive things.

[Roger]

I thought Rick said alphas exit out the 8 tri faced cusps, the truncated corners of the cubes.

?

[D Tibbets]

A cusp is a cusp, If the triangular shape of the corner cusps are ignored, then they agree probably smaller- tighter than the face centered point cusps. It depends on the transition to the 'funny cusps at the magrid magnets closest approach. I'm not sure how the ratios would work out. I at one point thought the corner cusps were larger, but I was convinced that this probably is not the case.

One thing that I have ignored is the strength of the B- fields. I mentioned the distance from center facing B- fields and the need to have > ~3.45 Tesla fields and some space. What this ignores is how close the Wiffleball border is to physical surfaces in these transverse fields compared to the near parallel cusp fields. There may not be much difference at Beta=1. Also with the B field 35X stronger (or more) the gyroradius will decrease proportionatly for any charged particle.

I may be asking the wrong question. With B field and radius gain and loss scaling. I have mentioned in other threads that the cusps stay about the same size as the size and B- field go up at appropiate rates.
EG: WB100 with 1.5 M radius, 10 T B fields, with corresponding 100X greater surface area and 1000x greater volume, and 10,000 greater density.
Alphas may or may not hit the magnets in the cusps, but what is more important is the effect of drive voltage on the electron confinement.
The cusp area/ total surface area of the Wiffleball would change 1/100 if the voltage was maintained at 12,000 V. But for D-D or P-B11 optimization the voltage may be increased by ~10X to 20X.
This would result in increased electron gyro radii. To allow for recirculation the spacing between the magnets may need to be increased. eg: increased 10X to 20X. This would still allow for a 10X improvement in confinement of the electrons, but it would result in ~ 100/10X improvement in density, so the B density scaling would be only B, not B^2. That would be bad. The electron collisionality may decrease by a factor of ~ 50-1000 though (due to higher KE) and this may allow less necessary compensation for ExB drift, perhaps only 1.5 times the electron gyroradius instead of the 3-5 gyroradii . The density would also increase, thus increasing Coulomb collisionality. But if my speculation holds the lower density gain would relax this somewhat.
So, it this speculation has any real effect the density gain with B field growth may be intermediate between B and B^2, so fusion gain may be closer to ~ B^3

This brings up another thought, but I will continue in another post. I have probably confused myself and others enough for one message.

Dan Tibbets

[D Tibbets]

Another thought...

In a WB 100 at 10 Tesla and 1.5 M radius. The cusps would stay the same area ( the B field is 100 times greater, but so is the Wiffleball surface area. So, the cusp loss area to total surface area would be 100X less , but the actual cusp area would remain constant in this situation (provided the drive voltage is not changed).
In terms of electron confinement transits, the electron containment would increase by ~ 100 transits without recirculation and > 1000 with recirculation. In terms of time this would be approaching 1 second with recirculation. I had seen that number mentioned and I now understand how it would be possible.

But, if the drive energy is increased ~ 10X (120,000 Volts, the KE would be ~ 10X greater and the Velocity Would be ~ 3X faster. In this case the transit containment would still be an increase of ~ 100 X passes, but the containment time without recirculation would be~ 30 X longer than the baseline. Assuming ~ 0.2 ms primary electron confinement for WB6, the result would be electron confinement times of ~ 6 ms.

If there is any hope of keeping the electrons from thermalizing, even with recirculation, the drive voltage and corresponding KE must be considerably higher than 10- 20 KV. I think Bussard mentioned ~ 80,000 volts for D-D (or was it ~ 80 KeV potential well?), even though Q is only mildly better at these more harsh conditions.

I can see the electron thermalization time staying ~ the same if the Coulomb collisionality decreases ~ 100X and the density increases ~ 10,000X, and importantly the electron input in increased ~ 100X. Better confinement * 100X increased current (R^2 input current scaling (actually it would be ~ 300X increased current due to the additional B^0.25 input scaling)). The problem is that the electron lifetime before recirculation also increases by a factor of ~ 30X (in this WB100 at ~ 120,000Volt example). The ~ 100X (or 300X) increased electron current needed to maintain the Wiffleball against losses might modify this to an advantage . a ~ 10 X advantage advantage instead of a 30X disadvantage- I need to think about this more

Again, IF my reasoning is sound, there are two modifiers that would help this situation if needed.
Increasing the radius faster than the B field. The density and confinment would be less, but the larger size would compensate. The electron lifetime would go down, while the electron input current goes up. Probably only small changes would be needed to create significant effects. An alternative may be to increase the spacing between the magnets. This would also have similar effects, but recirculation might improve with the corresponding resetting of the electrons energy along with perhaps improving on the electron input requirements.
Secondly, pushing the voltage to even higher levels would help (You need to do this anyway for P-B11 fusion).

Dynamics of the gas puffing ion creation approach would introduce further head scratching as electrons are left behind as fusion ions leave the system. This may be especially significant for high Z fuels. The 2008 EMC2 patent application mentions that with P-B11 gas puffing. so many electrons may be left behind, that electron input needs may almost disappear. How this would effect the electron energy dynamics is unknown.

The Polywell is fascinating. There are so many competing and synergistic dynamics and possible adaptations that this seemingly simple system provides endless cognitive challenges.


Dan Tibbets

[Joseph Chikva]

The Polywell is fascinating

If still it worked how has been conceived and particles wouldn't deviate from radial direction.