Electron Injection mussings

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D Tibbets
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Electron Injection mussings

Postby D Tibbets » Thu Jun 11, 2015 4:27 pm

Some meat, or perhaps some pseudo-meat for the theory forum. Recent Polywell efforts have seemed to imply that electron injection is a critical componet of the overall picture of not only efficiency, but viability.
In WB6 the electron injection was accomplished by an array of electron guns at low voltage placed ~ 1/2 the radius beyond the mid magrigid radius from the the center. This was done to allow for adequate electron injection efficiency without excessive slow electron plugging of the cusps. The acceleration of the electrons was via high positive voltage of the magrid metal cans. Having the electron guns too close to the magrid radius was demonstrated as being bad in WB5 where electron repellars were placed immediately outside the cusps in an effort to improve primary electron confinement. It may have helped in this regard, but it competed adversely with the desired internal potential well and its subsequent ability to electrostatically confine positively charged ions. The electron confinement may have been helped some, electron injection may even have been helped, but only at the cost of demolishing ion containment.
Compare this electron injection scheme to that used in Mini-B and apparently (based on pictures) of WB8. In these machines the electron injection was via a single high negative voltage electron gun placed several radii beyond the magrid. The magrid of Mini- B was grounded, and presumably so was the WB8 magid. The total accelerating voltage for the injection electrons was ~ the same, but the method was somewhat different. This has two possible consequences on electron injection efficiency and retention, and also consequences for electron recirculation.

Injection issues are two fold.

1) Injection efficiency as a percentage of electrons that fall within the cusp loss cone and thus gain entry, as opposed to being mirrored external to the magrid. This is a function of the B field strength and geometry,and the degree of collimation of the electron beam propagating from the E-Gun.

2) Injected electron tendency to traverse the magrid internal volume and immediately egress through the opposite cusp. This has been mentioned as a concern for the quasi-spherical cusp geometry. If you focus an electron beam through a cusp with a near parallel beam, as would be the case with a distant e- gun with a narrow emitter cross section, the beam may retain enough collimation, with minimal collisional scattering to be focused and transmitted well through the opposite cusp. This suggests that if you have a tight beam that is required for good injection efficiency, you also have as nearly as good of a tight beam exiting the opposite cusp with only one pass. This is completely useless.

Expansion on #1. An electron gun may operate via several processes, the primary method is thermionic emission of electrons from a surface due to temperature. Because of the electrons small mass it will boil off of a solid surface easily. Once this happens one of two things will occur. The electrons will hang around the surface and accumulate, drift away slowly, or fall back into the solid. The amount of electrons that can boil off depends on a goodly supply of electrons dwelling in or transiting the metal solid- current of electricity available from a power supply. Without quick replacement of the electrons that boil off, a retarding positive charge would quickly build in the solid wire. Secondly, if the free electrons are not quickly transported away , they will accumulate in the immediate vicinity and again retard further emission. Thus, the need for an extractor. This is an accelerating voltage that speeds the emitted electrons away from the thermoionic emmiting surface at reasonable speeds. Different substances, and surface area and temperature determines the absolute emission limits. Surface area is limited by various considerations, and temperature is limited by the melting point and also the tolerable erosion due slower but potentially significant ion emission and associated spalling. Material choices can allow for some variation in emission per unit of surface area.
The surface area ideally would be very small, this would allow for a very tight beam. But,this ignores the mutual electron repulsion which would tend to widen or diverge the electron beam. Electrostatic and/ or magnetic focusing could longer focus and preserve the tightness of the beam, much like the e- gun/ beam found in old cathode ray TV screens. After focusing considerations, the electron beam will spread in a cone dependent on mutual repulsion/ current, and speed- accelerating voltage. A larger emitting surface if shaped into a parabolic(?) surface may emit a stream of electrons that might be focused to a tight beam distant from the emitter- and near to the radius of the magrid cusp. This might not only allow for a higher current beam, but also a more efficient injection of electrons as less would be rejected/ mirrored outside the magrid. This is somewhat similar to what George Miley did in his bipolar focus efforts. Here he was not trying to transit the cusp in the center of a ring magnet so much as concentrate electrons in and near this single cusp in order to create a virtual cathode. He found that having a magnetically shielded anode to counter the mutual repulsion of electrons increased the electron density he could maintain with this scheme. I'm uncertain how this would apply to a system where cusp transit was the primary aim. It is noted though that this mimics the WB6 situation with high positive voltage on the magrid, compared to the grounded magrid of WB8, and Mini B. The biggest difference is that this bipolar single magnet might create a small reaction volume, as compared to the relatively large reaction volume with two magnets spaced apart- ie: an opposed magnet mirror machine. Now of course the losses through the line cusp between the separate magnets becomes the critical consideration, thus the evolution to the Polylwell concept.

The electron gun, as mentioned is limited by the available surface area, this can be increased by using a larger emitting surface, perhaps in a parabolic shape, or by clustering multiple E-guns, and combining their beams. The important consideration is that combining many beams into a common beam aimed at a cusp, implies a higher current/ electron density, and thus a more rapid spreading of the beam- so that more of the beam will be mirrored at the cusp and lost. By having the beam converging towards the cusp, as opposed to traveling in a single originally parallel beam may have benefits for injection efficiency. The placement of structures outside the magrid at certain distances may be the limiting consideration in designs as interactions with other aspects of the machine such as direct conversion and recirculation, and adverse cold electron cusp plugging need to be considered.

In Mini- B and presumably WB8, the single electron gun placed distant from the cusp limited the available electron current that could be injected towards the machine interior through a cusp, but also the efficiency as efforts to use a more intense beam is directly proportional to the spread of the beam and thus the percentage that falls onto the mirroring part of the cusp B field. This is essentially the same consideration as when talking about electron confinement within the machine at low Beta. What is the percentage of electrons that are transmitted through the cusp verses the percentage that is mirrored away. Good confinement implies, at least to a degree, poor injection efficiency.

I mentioned geometry, Dr Park did present an illustration of a more complex geometry for the individual magnets, with non round minor radius shapes. I presume this is an effort to modify the loss cones of the cusps depending on weather the path is inward versus outward. With Wiffleball formation, the interior to outward cusp loss cones are considerably modified, not pinched, but effectively smaller. This changes the relationship of confinement versus injection efficiency considerably, but it doesnot directly address the the injection efficiency issues, and without antiquate injection efficiency, the ability to build or maintain Wiffleball conditions becomes increasingly problematic. This is why Dr Parks resorted to the axillary method of creating Wiffleball conditions- a messy blast of intense plasma injection.

Note that a converging beam of electrons may be better for injection once adequate current is considered, but this beam would diverge more (I think) on the inside of the cusp and thus not immediatly exit the opposite cusp as efficiently. It may be doubly benificial.
The second point about electron escape immediately through the opposite cusp is important. Bussard stated that this was not a concern, but at least in WB6, he was using 4 separate electron guns aimed at four different corned cusps. These four beams would converge towards the center of the machine and as such generate ~ 4 times the central density on the first pass as any one of an equivalent E gun at the same incremental current would. With 4 times the density the Coulomb scattering collisions would occur ~ 16 times more rapidly, thus significantly disrupting the electron trajectories from the injection cusp to the opposite exit cusp. Additional e-guns aimed through a single cusp at modest angles, or especially multiple e- guns aimed through multiple cusps would considerably ease the concerns about electron escape on the first pass. I don't know if this may have been an issue with WB8 or Mini-B. I have not seen any discussion in this regard. But, if it was a minor or major problem, I would expect WB-6 to have suffered from this issue at by least 16 times less.
The issue of having high electron acceleration on a distant E- gun with a grounded magrid versus a low voltage E- gun with acceleration (extraction) by a positively charged magrid may effect injection efficiency in addition to the issue of recirculation. If an electron is mirrored outside of the machine with a grounded magrid it will bounce back around the B field to another cusp. In a collionless plasma, the electron would be on a stable mirroring confinement. With collisions, some of the electrons would eventually enter the cusp and others would be deflected to the walls, and some would hit the magnets- essentially ExB diffusion processes. This may correspond to some of the ideas in the Lockheed scheme, though I don't know how they address the ExB issues, especially for the ions which may have similar distribution as the electrons (if they do not have an internal potential well).

In WB 6 the Faraday cage was purposely positioned so that electrons could not loop between cusps before grounding on the Faraday cage. Without this outside intervention run away thermal electrons looping around may be a problem. This is especially true if the magrid has a positive charge. Any up scattered escaped, or rejected electron, could loop around and those up scattered electrons could repeatedly gain excess energy on each pass. Not good. With interception, and a grounded grid this problem is avoided, but so is the opportunity for most of the mirrored external electrons to gain entry on another attempt.
With a positively charged magrid, the shape of the E- gun electron beam may be different and may be more amiable to shaping for optimal injection efficiency, especially with geometry considerations. The recirculation of escaped electrons is also fundamentally different. There is no recirculation between cusps, any up scattered electrons are picked off before they can complete a loop so that there is not an electron temperature runaway. Non up scattered escaping electrons would be stopped, and reverse through the same cusp, if they escaped, they are on a course that permitted their escape and recirculation would be the exact reverse of this. Recirculation should be very efficient, limited only by collisional effects within the cusp and very near it that knocks some of the electrons onto mirroring paths. Even with this little energy should be lost as they give their energy back to the magrid as they pull away. So long as these escaped electrons hit something away from the magnets, the energy loss is minimal. This is not the case with ExB diffusion to the magnet cans them selfs, or to intervening nubs.

In short, the use of multiple E-guns at multiple cusps mitigates any concerns about single pass electron escape, and allows for more injection current without as much electron beam spread leading to external mirroring and low injection efficiency. Electron beam shaping- having a focus as opposed to an initial collimated beam, that can only spread without further manipulation, and by playing with the geometry of the magnetic field. I think that a positively charged magrid would serve as a focusing lens for the electrons, helping them to achieve cusp penetrating trajectories.

Based on the above ramblings, I think that WB-8 and Mini- B had significant problems getting electrons into the machines. I some ways WB-6 was a better solution, but it also, had problems . The e-guns were headlight filaments- a cluster of several at each of four cusps(?). As such the low voltage filaments spewed electrons in almost omnidirectional vectors (in all directions) and these were then collected , accelerated, and focused towards the center of a corner cusp. Apparently the corner cusps had tighter cusps than the face centered point cusps , so mirror rejection of the electrons were probably significantly greater. In this case the face centered point cusp injection of Mini-B and WB 8 (?) was probably better. The losses was further compounded by the nubs that traversed the ends of these corner cusps in WB 6. Note that this may have had other significant effects that I will mention if anyone desires. I once did a BOE calculation that WB 6 electron injection efficiency was only ~ 2-5%. In Mini-B the efficiency may have been even less because of the smaller dimensions, increased B field strength, and considerations such as those I expounded upon above. WB 8 injection efficiency is more uncertain because of unknown operating conditions.

There are easy modifications that may significantly improve electron injection. If gains beyond this is needed it becomes increasingly difficult.

Dan Tibbets
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Re: Electron Injection mussings

Postby hanelyp » Thu Jun 11, 2015 7:43 pm

Some time back it was suggested that with cold gas fuel injection and positive ion (fusion product) loss few electrons would need to be injected to maintain the net negative charge.

The problem I see with a larger area electron injector is the limited magnetic flux bundle passing through the cusp. Any electron falling outside that flux bundle would tend to be mirrored. The cusp is larger for high energy electrons, and higher current may be possible without space charge limits, but then the injected electrons have a limited time to thermalize with the rest of the plasma before they find a cusp and escape.
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D Tibbets
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Re: Electron Injection mussings

Postby D Tibbets » Fri Jun 12, 2015 1:03 am

hanelyp wrote:Some time back it was suggested that with cold gas fuel injection and positive ion (fusion product) loss few electrons would need to be injected to maintain the net negative charge.

The problem I see with a larger area electron injector is the limited magnetic flux bundle passing through the cusp. Any electron falling outside that flux bundle would tend to be mirrored. The cusp is larger for high energy electrons, and higher current may be possible without space charge limits, but then the injected electrons have a limited time to thermalize with the rest of the plasma before they find a cusp and escape.

This is mentioned as a theoretical but unlikely result in the EMC2 patent application. As the fuel is consumed and the alphas leave the system, the remaining electrons may come close to maintaining the 1 ppm electron excess without any further electron input. Without ignition heating this then begs the question of how you maintain the temperature of the plasma via the energetic injection of new hot electrons that establish and maintain the potential well. Also, without these new mono energetic electron injection the issue of electron thermalization becomes even more intractable. This situation implies already well established Wiffleball conditions, and good confluence of fuel ions. It is is a different mode of operation from that nessisary to build to this postulated condition. If the startup conditions can be achieved, this impressive steady state condition offers up a different set of problems that need to be addressed.

Grad postulated that under Wiffleball conditions- Beta=1, the cusp loss holes are equal to the electron gyro radius at that energy. Certainly at 100 KeV versus 10 KeV the hole will be larger (linear relationship?). To have the same loss hole size for the hotter electrons you have to increase the B field strength accordingly. I am not sure how this correlates to the external electron vectors that would allow for non mirroring injection through this high beta cusp because the high beta modification would only apply to the interior B field contours, not to the exterior B field contour (no high Beta condition outside the Magrid). If the cusp hole size is greater due to high injection electron energy it would ease electron injection, but also increase low Beta electron escape. There is a trade off. Some means to bias this relationship needs to be employed. Magnet minor radius geometry, and aiming of injection electrons seem to be the two most obvious possibilities. The shape of the injecting electron beam may be more managable as the space charge effects of the beam dispersion may be the dominate process. Inside the machine, as the density builds, the collisional processes may become dominate for the electon behavior. This defocusing effect due to local collisions versus space charge effects may alternate behaviors such that internal and external processes and the knobs to control them are different. As the Wiffleball forms the interior and exterior densities of electrons becomes much different. The difference may be as much as 10,000 X, or according to Grad, as much as 100,000 X inside versus outside. Keep in mind that even with the vast difference in density (outside limited by Pashin arcing concerns, and inside limited by the Wiffleball trapping factor beyond this) The inter electron collisions will go way up, but the space charge will not change much because there will be a constant ~ 1 part per million excess of electrons. Any more would not be containable. This of course means that the positive ion population must increase equally with the electrons. This provides for a complex transition from low Beta to high Beta. Neutral gas injection allows for this naturally, ion injection is more delicate, but perhaps more controllable.

Of course any focused electron beam would have to intercept the B field contours so that it fell within the loss cone for the cusp. The point is that by starting with a convergent electron beam, from a wider emmiter, once the magrid radius was reached, the mutual electron repulsion would ideallyresult in a narrow beam that mostly falls within the cusp loss cone. Because of the focusing, this approach might allow for a higher density/ current of the electron beam without as much dispersion at the critical distance where the beam enters the cusp. This as opposed to an initially tight narrow beam that is diverging from the get go.

Thermalization of the electrons is slower at higher temperatures, and as such scattering away from the opposite cusp is less. It shifts the question somewhat but does not change the proportional consideration of central density of the first pass electrons, at least when converging beams from multiple cusps are used. I think as Coulomb scattering as two processes. One is thermalization into a Maxwell distribution. of energies. The other is a scattering of near parellel traveling particles into a near random vector distribution. I'm uncertain if both processes proceed apace. As for vector scattering I believe that several , perhaps only one collision is nessisary, for KE thermalization a few more collisions may be necessary., especially to reach full thermalization with a high energy tail. There is a window where one may be taken advantage of while the other is not limiting. Add into this foggy picture the consequences of the electrons being in a potential well with central convergence, where the low energy electrons in the center have much higher collisional cross sections, and that any scattering here has to be mostly radial, confounds the picture. Even energy renormalization at low energies of the core electrons may have some annealing effects, somewhat like ion edge annealing. The consequences of the spherical convergence on local densities and corresponding local temperature within the potential well for both the electrons and electrons is interesting, to say the least . Even with higher electron injection energies, by the time they reach the center they are at the top of their potential well, are cool and have correspondingly increased collisional cross sections. How this gradient changes with increasing injection energies is unknown to me

.The only handle I have on the picture is Bussard's comment in the Google talk, where he points out that the injected electrons on their own, quickly disperse to near the confining magnet confinement radius with shallow orbits (little radial componets) with a resultant square potential well forming. With the introduction of ions, the electrons are dragged along to a degree, and have more radial orbits, resulting in a parabolic potential well. The reverse of this local partial coupling is not so much for the ions due to the momentum differences between the ions and electrons. The ions are governed mostly by the space charge of the potential well, which is evolving during start up conditions depending on the electron and ion or neutral gas injection modalities and timing. For a superficially simple system, the complexities are profound. This adds to the uncertainty, but it also adds to the possible knobs that might be employed.

Perhaps near neutral beam injection from outside (electrons and ions) may allow for some improvement in electron beam spreading and thus injection efficiency. Two stream instability is a concern,but perhaps a compromise would give the best combination of results. Such a neutral beam fired at a cusp with a positive charged magrid would accelerate the electrons (hopefully) into the cusp. The positive ions would slow, giving up kinetic energy to the magrid (the energy would be conserved) till they entered the cusp with residual low energy and related gyro radii perhaps comparable to the electrons. These ions would be at a low energy above the potential well energy, but further cooling via radiative loss processes may bring them to the desired top of potential well energies. The near neutral beam (possibly 1 ppm excess of electrons) would initially consist of low energy electrons and high energy positive ions (two separate guns located well beyond the magrid) so that the initial velocities might match or the ions may be somewhat faster.. This situation would reverse as the charged particles approached the magrid. Such a relationship may be tunable to the best compromise for combined electron injection efficiency and desired ion injection energies. It might allow for the guns to be placed at greater radii without as much penalty in injection efficiency. Other considerations may apply, but I think I will stop here as this is enough for me to chew upon.

PS: With the cusp hole size being quoted as the electron gyro radius, this obviously ignores the ion gyro radius hole size at the same conditions. But, part of the basic Polywell premise is that the ions do not reach the cusps ideally, and if they do, they are very near the top of their potential welll, and thus at much lower energies with corresponding smaller gyro radii., perhaps even smaller that the electron gyro radius at that radii. The exception would be the hot fusion ions, Protons,Tritium, Helium3 or Alphas depending on the fuel. These would have considerable KE even after climbing the potential well, and would find correspondingly large cusp escape holes. Again, this negates any concerns or desires for ignition as these high energy fusion ions escape before they can thermalize. Their confinement time versus their Coulomblomb collision cross sections is too small.

Dan Tibbets
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Re: Electron Injection mussings

Postby DeltaV » Sat Jun 13, 2015 5:19 pm

Maybe something of interest here...

Spatial-temporal evolution of the current filamentation instability

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