Loss of potential well in corner cusps

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D Tibbets
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Loss of potential well in corner cusps

Postby D Tibbets » Sat Jan 02, 2016 7:05 pm

Loss of potential well in corner cusps

Dr Parks has reported that having a positive charge on the magrid results in the potential well- negative space charge droping to zero in the corner cusp areas. As such the electrostatic confinement of ions suffer. He uses this to argue that a positively charged magrid is not a viable option.
I have been ruminating on this and have several considerations that may modify this viewpoint. Then again, it may be flawed thinking.

First, this may be a real measured effect, but misinterpreted. I have invoked Gauss Law multiple times in the past, and it is convenient to consider the magrid as a conductive metal sphere with a radius equal to the midplane of the magrid cans. This actually has two modifiers though. First the holes compromise the absolute manifestation of Gauss Law. It may still be dominate, but needs some fudging. Plasma frequency or other oscillations within the plasma may effect the significance of the hole size. But, here I am emphasizing a possible oversight in the interpretation of the observed results. Bussard, etel considered the magrid as a structure made up of lines- no width. This flaw in reasoning was not appreciated until WB6, where the physical dimensions of the magrid was considered. The ring magnets are not mathmatical one dimensional lines, but three dimensional cans with significant width and height along with length. As such the center of the magnet can radius was not representative for some considerations, but the can surfaces were. This resulted in ExB losses - cross field diffusion of charged particles through the magnetic fields, being a major concern, while before they were mostly ignored. It changed the perspective that the magnets needed to be as closely approximated as possible- the "Funny Cusp " analogy. Before, with line representation of the magnet cans in simulations, there was no surface area, so ExB losses could be ignored, though obviously ExB diffusion was a major concern with ion magnetic losses in any magnetic machine. But by decoupling the ions from magnetic confinement, only the electron ExB diffusion was an issue, and the attitude was apparently that these could be ignored as the electron cusp losses were highly dominate. This was a flaw in reasoning admitted by Bussard, and was not appreciated despite repeated reviews untill WB4 and WB5 results were analyzed. With the significant can surface area to intercept electrons as they diffused through the magnetic fields- well before reaching the radius from the center represented by the mathematical line representing the center of the magnets. This more realistic consideration lead to the spacing of the magnets so that the electrons would have to diffuse through several gyroradii distances before loss to the can surface. Bussard estimated this separation needed to be about 3-5 electron gyroradii. In "Mini -B" this separation is even more, perhaps representing improved electron confinement via cusp confinement without bridging nubs, compared to ExB losses in the cusp regions.
This modified the view that "Funny Cusps" with zero cusp losses (because the cusp was squeezed to near infinate thinness with the magnet cans almost touching) was desirable. It also decreases the impression that the corner cusps were effectively point cusp instead of highly modified continuous line cusps. This led to the appreciation of the need for significant magnet separations and need for minimization for any bridging structures across the cusps in the region that was previously viewed as "Funny Cusps".

This issue of perspective (line representation as opposed to 3 dimensional can perspective) may also apply to the corner cusp space charge consideration that is the concern of this thread.

With a line perspective, the radius from the center to the middle of the magnet cans is considered as the radius of the machine for Gauss Law Considerations. At any radius less than this the charge on the magrid is not seen by any charged particle. But with the appreciation that the magnet can has real 3 dimensional measurements, this perspective needs to be changed. In WB6 the can minor radius (thickness) was ~2.5 cm. This implies that for Gauss Law considerations, the location of the hole starts at the magrid radius (as measured to the magrid mid plane radius) minus 2.5 cm. With some gradation, the charged particle starts seeing the charge on the magrid at this smaller radius.

This has several consequences. With a positively charge magrid, the electron starts decelerating as it passes outward 2.5 cm earlier than may have been appreciated. As such it slows and reverses sooner. As the electrons slow, they accumulate locally (traverse the same distance slower). This local collection of cold electrons create their own space charge that competes with the central space charge that forms the potential well that is of interest for confining ions. This results in ions near these cusps being 'drawn out' of the central potential well. This cold electron cusp plugging may have benefits for electron contaminant, but is harmful for electrostatic ion containment and may harm electron injection. It is similar to what was found with WB5 with it's intentional electron cusp plugging. The same thing would occur with the line representation of the magrid, but this would occur 2.5 cm further out. This is especially significant for a small machine , perhaps less so for a large machine depending on several other considerations.

`Why the corner cusps and not the center face point cusps? This is simply due to inverse square law considerations. In WB6 patterned machines. The radius of the magnets is approximately two times that of the seperation in the corner regions. This means that any fixed charge on the magnet cans will have only ~ 1/4th the effect on charged particles in the cusps. Decelleration and thus turn around distance is greater. The cold electron cusp plugging effect is less. In the patent Bussard, etel stressed that the low voltage electron guns (effectively a cold electron collection) needed to be a at a significantly greater radius from the center than the positively charged magrid (perhaps twice as far) to prevent this cold electron cusp plugging effect from being too harmful. With a grounded magrid and high voltage electron guns located even further away, these concerns are much diminished. This may be why WB8 and Mini B depend on a grounded magrid and distant high voltage electron gun/s. The conclusion that positively charged magrid is not viable for the above considerations, but with out the modifier that the cans are of real dimensions.
The real dimensions are important, not only for the imposition of Gauss Law considerations relative to the radius to the midplane of the magrid (need to subtract several cm or even more in larger machines- though the proportions would remain the same). This effect is at a smaller radius from the center than the narrowest part of the cusps (at the magrid midplane radius) The cold electron cusp plugging is closer to the center, perhaps even less that the actual cusp distance (narrowest portion of the cusp at the magrid midplane distance. I don't know how fast the electrons accelerate (decelerate) as they experience any charge on the magrid cans. The inverse square law considerations coupled to the curvature of the cans play a role. As the electrons cool with Bremsstruhlung losses and down scattering, they may accumulate even more in the regions just inside the cusps (corner cusps mostly) compounding the problem.
The measured space charge reported near the corner cusps as falling to zero may be due to the competing space charges created by the hot injected electrons (considered as a central dominate negative space charge (ion attracting) versus a local near cusp electron accumulation that balances out the central charge so that the local measured potential some distance between the influences falls to zero. The actual measured potential versus radius data would be revealing.


Secondly, what are modifications that may minimize this effect.
If the curving metal cans with a positive charge is decelerating the electrons before the center of the cusps are reached, the same would apply to any ions in the region. The would be repelled back towards the center to an equal degree. At first this might seem to balance out the concerns. The decreased central potential well diminution is balanced by ion repulsion from the magrid as the ions enter the inner 1/2 half of the magrid can radii before the center of the cusp. But, this would not be the case as the plasma is not net neutral. The electron excess creates the central potential well and any local near cusp space charge effects would maintain this ratio (I think), So ion electrostatic containment suffers, as may peak acceleration/ confluence of ions towards the center.

The simplest solution is to ground the magrid and accelerate the electrons with distant high voltage electron guns. This may not be the best solution though due to concerns with electron injection efficiencies. It appears that this is a major and perhaps limiting concern with this approach. Mini B injection efficiency may have been only a few percent. Without significant improvement break even may be unobtainable. An electron beam created distant from the target cusp will spread due to mutual repulsion. High voltages may help as the electrons have less time to spread before the electrons reach the cusp, but current will need to be scaled up even more in a break even machine so beam spread and resultant mirror rejection of electrons at the cusp will probably be worse. Some type of intermediate focusing will probably be needed. This complicates the machine and near machine magnetic and electrostatic picture, and of course also applies to any direct conversion possibilities.
The alternate solution is the positively charged magrid. It should help to focus an electron beam to improve injection efficiency without cluttering up the exterior space, presumably simplifying any direct conversion scheme, etc. The problem (by my reasoning) is mostly the positive charge on the inner portion (facing the center and at a smaller radius than the magrid midplane radius), not the positive charge on the outer can surface. The simplest solution is to only charge the outside portion of the magrid cans. A ribbon of conductive metal located outside the midplane radius of the cans, or perhaps several cm beyond the midplane would serve to accelerate new electrons and focus them into the cusps, while moving the recirculating cold electron nucleus further outward by perhaps 2.5 to 5 cm (using WB6 dimensions). A positively charged wire may even be suspended further above the can surface, though trad offs may become increasingly unattractive.

I have mentioned before that a compromise may be the best solution. A distant electron gun at intermediate voltage coupled to an intermediate voltage on the magrid may give the best compromise between electron injection efficiency, eletron recirculation , and ion containment. Without the appreciation of the magrid cans real dimensions, the charge on the magrid is absolute- none/ grounded, or some selected voltage though out the surface of the can. With this appreciation the voltage on the magrid cans are localized to taylor both injection efficiency and ion containment efficiency (avoiding cold electron plugs near the cusp centers) at the same.

Changes in the geometry of the magrids may also effect this picture.

Dan Tibbets
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hanelyp
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Re: Loss of potential well in corner cusps

Postby hanelyp » Tue Jan 05, 2016 8:00 am

I'm wondering how much it might help if the electrostatic can was closed down some, leaving holes little larger than needed for electrons to pass freely through cusps.
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ladajo
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Re: Loss of potential well in corner cusps

Postby ladajo » Tue Jan 05, 2016 12:56 pm

This would make the cusp areas larger, and more than likely have cascading impacts.
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D Tibbets
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Re: Loss of potential well in corner cusps

Postby D Tibbets » Tue Jan 05, 2016 11:52 pm

hanelyp wrote:I'm wondering how much it might help if the electrostatic can was closed down some, leaving holes little larger than needed for electrons to pass freely through cusps.

I'm not sure what you are suggesting. The electron cusp loss hole will always be ~ 1 electron gyro radius. With the magnets closer together and at the same B field strength at the can surface will perhaps have a smaller loss hole- the B field gradient will be greater, though the Grad claimed loss hole at Beta=1 is one electron gyro radius (assuming the ions are not contributing to the net effect(they are well contained electroswtatically)). The gyro radius will be smaller or not, I admit that I am uncertain about the relationship in the cusp versus away from the cusp. The electrons push out and compact the B field mostly where the radial motion of the electrons approach perpendicular to the B field. In the cusps, the electrons are traveling almost parallel to the B field. Here the B field compression is presumed to be mostly (even at Beta=1) due to the opposing B fields pushing against each other. Mt funnel anallogy may apply here. The cusp throat or collecting area is flattened out but the cusp (mid portion) is changed very little. As such moving the magnets closer together does compress the cusp and, I think, decrease the gyro radius proportionally.

The problem is that the distance to the can surface is also less, so fewer ExB diffusion jumps are needed to reach the can surface. At some point ExB losses in the cusps will exceed the cusp losses themselfs. Kiteman Sa likes to promote the square planeform magnets with long sides very close together. This produces long "Funny Cusps" where cusp losses are minimized because of the very narrow cusp and the small area in the corners compared to round magnet plane forms. The ExB losses though become limiting. The patent application that showed this arrangement was presumably before Bussard, etel realized the flaw in their reasoning (assuming the magnets had no surface area for ExB diffusion to contact) that eventually led to WB6 .

Another approach and this may be what you are suggesting is to make the face centered point cusps smaller by making the magnets fatter, more oval in shape. That way the B field that you can generate at the can surface is closer to the mid point of the ring magnet and thus the cusps are smaller. I suspect there is some room for improvement here, especially as these cusps are suggested (my understanding) to already dominate the losses over the corner cusps in the round magrid can WB6 design. This is one of the modifications that I considered when speaking of geometry modifications. The illustration that was in one of Park's presentations suggests other shape modifications. All of the shape, local size modifications effect both cusp losses (or possibly cusp transparency to injected electrons) and ExB losses. The best compromise may require considerable computer modeling, or if too complex, experimental testing.

As per this thread topic, while geometry is adjustable, it is the radius at which a positive charge is located and it's effect on decelerating and possibly reversing (recirculating) escaping cusp electrons occurs. If this collection of cold electrons is too close to the center it adversely effects electrostatic ion containment. The effect would be similar to what was found in WB5. Without geometry changes, simply grounding the magrid except for a ribbon on the outward facing surface of the cans moves the electron decelerating region at least a few cm further out. In a large machine this might be several dozen cm further out. This may mitigate some of the concerns that I believe that Dr Parks was referring to when he said that positive charged magrid was not a viable option.

There are two considerations for positive magrid (partial surface or total surface) and a low voltage distant E gun versus a totally grounded magrid surface and high voltage distant E guns. First is the recirculation of electrons at high efficiency, perhaps 90%, through the same cusp after climbing only a limited distance above the cusp midplane. This is different from electrons looping around on magnetic field lines to reenter/ recirculate through another cusp. This seems to be the mechanism persued in the Lockheed design and the magrid can surfaces are grounded at zero volts. The electron recirculating in this manner may not have the advantage of having upscattered electrons removed from the system and thermal electron runaway may be a problem.This is one concern that I think Art Carlson expressed. With the positive magrid - same cusp recirculation, only returns/recircuates the electrons that have a KE less than the potential well. The up scattered electrons are removed by impacts with outside surfaces- a scrape off layer if you will. Most of the KE is recovered back to the magrid through direct conversion, so not much actual energy is lost even though the electron is. This action is not too far beyond the cusp midplane radius (actually too close if I understand Dr Parks comment correctly). This leaves exterior room for direct conversion of positively charge fusion produced ions with high energies. I suspect such would be impossible or at least much more difficult to do if the escaped electrons at full energy were also traversing this exterior space as they recirculated to the neighboring cusp.

The second consideration is that the positive charged magrid may help to focus an incoming high intensity electron beam so that it does not spread as much and injection efficiency improves as the injected electrons avoid mirroring outside the machine. As such isolating the positive charge further out on the magrid may improve injection efficiency with tolerable effect on the internal potential well and thus ion containment.

I speculate that a converging beam or collection of electron beams may be pointed at the cusp from distant intermediate voltage E- guns, and positive charge on the magrid surrounding the injection cusp/s helps to further accelerate the electrons to desired energies and limits the beam spread and thus reduces electron rejection.

The escaping electrons, because of the reduced positive charge combined with the greater radius before onset of electrostatic recirculation has less harmful effect on the potentail well, The down side is that less of the escaping electrons KE will be recovered (energy recirculation) The potential well is less than the injection energy though, so there may be some wiggle room here. Bussard felt that a potential well ~ 80% of the injection enerfgy was possible. With WB 6 the injection energy of ~12 KV- almost entirely due to the positive charge of 12 KV on the magrid, produced an internal potential well of ~ minus 10 KV .The average electron would still be recirculated with a modestly decreased magrid potential- with the difference made up in the E-gun potential. Each subsequent recirculation event for a selected electron would proportionately drop in energy, but again, it is the tradoffs that reach the best compromise among a number of competing processes. Microwave heating or other supplemental heating may be necessary to keep the temperature up against Bremsstruhlung losses, these losses, etc. But, if the penalty is less than the losses associated with poor injection efficiency , direct conversion of fusion products possibilities, etc. the game may be won.

Dan Tibbets
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D Tibbets
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Re: Loss of potential well in corner cusps

Postby D Tibbets » Wed Jan 06, 2016 12:32 am

PS: Continuing from the previous post. 'Cusp size just large enough for electrons to easily pass through' is a two way street.
At low Beta I suspect the amount of mirroring from inside and outside is similar. Electrons leak out about as fast as you can inject them. You might contain electrons for 10 or 100 passes, but if only ~ 1/10 or 1/100 electrons are getting in- you are going nowhere fast. You cannot build up concentrations and thus increase Beta. If you can improve injection efficiency while maintaining the same containment you may gain some ground, provided you can keep up with other energy losses like Bremmstruhlung and electron ExB losses. Once Beta starts to climb beyond some threshold, the containment will improve, so injection efficiency becomes less critical. I am moderately sure that the geometry of the cusps from the perspective of external electrons are almost unchangedweather low or high Beta, so injection efficiency (and recirculation efficiency) should be constant from low to high internal Beta.The difficulty of reaching that threashold is the pertinent question. Dr Parks achieved this with 'Mini B' with a suplimental blast of plasma*. The high energy electron injection was then adiquate to start building up the population of hot electrons inside the machine. The hot input electron current/ efficiency was ~ the same, but containment improved. Thus the build up of hot electrons and associated Bremsstruhlung, at least until the supplemental plasma cooled with the resultant loss of high Beta. Beta is proportional to the density and temperature of the plasma versus the strength of the B field.. The injected electrons was contributing little to the total plasma temperature and density product, so it was not effecting Beta much. It was along for the ride.

After an initial blast of plasma to create high Beta conditions the goal would be to maintain high energy electron injection current to become the dominate contributor to maintaining Beta, perhaps supplemented with microwaves. The startup plasma could then be gradually replaced with a fusion fuel and hopefully generate more energy than is consumed. This is one permutation. If electron gun current and injection efficiency can be improved enough then a more straight forward buildup of Beta may be possible.

WB6 claimes of high Beta based on observation of a peak in glow discharge brightness may have been flawed as it assumed constant input electron current AND efficiency. As B field strength was swept upward though, electron injection efficiency probably suffered. The team in Sidney has suggested this. As such, the peak glow was not at a Beta of one with falling glow as Beta exceeded one, but was a result of the product of increasing Beta, or at least increasing B field strength with corresponding better low Beta confinement; and falling injection efficiency. Where along the spectrum the peak was occurring is unknown. Beta of one was not demonstrated, instead confinement versus injection efficiency was . Better confinement does not mean higher Beta alone. It is the product of B field strength and Beta. I'm uncertain, but if the B field was held constant, while the input current was swept from low to high, the different confinement due to B field strength alone would have been eliminated. The injection efficiency variation may also have been avoided, at least that portion directly related to the B field strength. Increased E-gun current/ denser beams would lead to increased beam spread and mirror rejection, even at constant B field strengths. This might show the relative merits of beam focusing, high voltage E-guns versus high positive voltage magrid for electron injection efficiency at various currents and/ or B field strengths. It may provide a quick and adequate method to quickly evaluate various designs and trad offs. Note that Dr Nebels did say that the glow intensity measurement (PMT measurements) were consistent with a more refined density measurement. As such this easy measurement is useful, it is just that the increased density was not isolated to Beta effects alone. The Mini B results by Dr Parks is much less ambiguous.

Dan Tibbets
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prestonbarrows
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Re: Loss of potential well in corner cusps

Postby prestonbarrows » Sun Jan 24, 2016 4:14 pm

D Tibbets wrote:Dr Parks has reported that having a positive charge on the magrid results in the potential well- negative space charge droping to zero in the corner cusp areas.


Source?

D Tibbets
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Re: Loss of potential well in corner cusps

Postby D Tibbets » Mon Jan 25, 2016 5:56 pm

prestonbarrows wrote:
D Tibbets wrote:Dr Parks has reported that having a positive charge on the magrid results in the potential well- negative space charge droping to zero in the corner cusp areas.


Source?



http://iec.neep.wisc.edu/usjapan/16th_U ... lywell.pdf

Slide 12

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KitemanSA
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Re: Loss of potential well in corner cusps

Postby KitemanSA » Wed Feb 10, 2016 8:24 pm

It is because they haven't used a bowed, square planform, X-Cusp configuration. JMHO.


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