Electron injection as an engineering issue

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D Tibbets
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Electron injection as an engineering issue

Post by D Tibbets »

Some speculations on electron injection in the Polywell and vacuum issues.
In other threads there has been some discussion about the efficiency in electron injection into the Magrid volume of the Polywell. This is some further exploration using number comparisons and arm waving.

The electrons must enter the magrid through a cusp. The confinement is primarily limited by cusp size and geometry. Considered here is only the two way nature of the cusp. Electrons approaching the cusp from either the inside or outside will pass through or be reflected back. With the Wiffleball formation the geometry of the inside side of the cusp is different from outside approach- at least what I refer to as the cusp collection area. But these differences are mostly ignored for this consideration.

WB6 had an electron lifetime of ~ 0.2 milliseconds for primary magnetic containment. Recirculation at ~ 90% efficiency resulted it total effective confinement/ lifetime of 2 milliseconds for electrons.
In the WB6 report the input E gun current was ~ 45 Amps during the Beta= 1 condition. The electron density inside the the machine at this time is assumed to have been ~ 10^13 electrons/cc. The internal volume is estimated to have been ~ 10,000 cc. That implies that there was ~ 10^17 electrons inside the machine (and most of these came from injection, not from ionization of neutral gas inside the machine). This means that every 2 milliseconds 10^17 electrons had to be replaced.

A Coulomb of electrons is ~ 6* 10^19 particles. This means there is a need to replace ~ 1/600th of a Coulomb per 2 milliseconds. This is equivalent to ~0.002 Amps per 2 milliseconds, or ~ 1 Amp of current if electron injection was 100% efficient. Since ~45 Amps was actually used this suggests that injection efficiency was ~ 2% efficient. The remaining electrons from the E- guns was reflected and never entered the magrid. This means that ~ 43 Amps of the current from the e-guns was wasted. This does not necessarily imply a huge energy loss though. As the electrons approach the Magrid they are accelerated to ~ 12,000 eV. If they are reflected though, they pull away from the magrid and decellerate to near the E-gun potential- perhaps 12 volts. They then can try again for the cusp, or more likely ground on a surface.

The energy loss through this injection inefficiency may be as small as ~1% of the total electron losses. It may be of miner concern. But this also implies that there are~ 50 electrons outside the magrid as inside at any given time. Though these electrons are low average energy (at the time of grounding) they do contribute to the external charged particle density inside the vacuum vessel, and as such they place limits on the Pashin discharge density limits within the vacuum chamber. This effect may be highly dependent on the external volume compared to the internal volume. If ~ 50 times greater, then the electron density outside the machine may be similar to the electron density inside the machine. It depends not only on the relative volumes but also the lifetime of the electrons outside the magrid. The external reflected electrons may have a presumed average velocity of ~ 1,000,000 M/s or ~ 2,000 M/2 milliseconds. This would result in an exterior electron lifetime of perhaps ~ 1-2 micro second., so this would effectively reduce the external density to perhaps only 0.001 that of the internal electron density. This might allow the ~ 1000 fold increased density inside the machine due to Wiffleball trapping to be maintained, while the external electron density remains slightly below the tolerable density limited by Pashin arc breakdown ( ~ 0.000001 atmospheres).
This is consistent with the densities reported by WB6 and suggests that this inefficient electron injection was not the limiting factor in the machine. But with increased internal confinement times (with stronger B fields the internal density may reach as high as a claimed 10^ 16 electrons/cc. With the same injection efficiencies and the same relative internal to external volume ratios, the external electron densities might increase by as much as a thousand fold. This would be intolerable, as the external electron densities (with balanced ion densities (neutrallity must be nearly maintained)), would result in destructive Pashin arc breakdown. You could not reach the desired internal electron densities due to this limit, even if your containment would allow it.

There are several ways to combat this limit. One is to better insulate external surfaces so that Pashin arc breakdown is delayed. This is a limited partial and compromised solution (you have to allow for the escaped up scattered electrons to ground on something before they have a chance to renter through another cusp). A second partial solution is to increase the external volume relative to the magrid volume and couple this to very good vacuum pumping. Finally, and most directly is to increase the injection efficiency of the electrons from the electron guns. If the electrons leaving the guns are more collimated and aimed straight down the throat of the cusp and are at an optimized distance from the cusp, efficiency (lack of reflection) may be much greater. An efficiency approaching 90% may be possible and required to achieve the densities advertized.

This is why (I suppose) that EMC2 is interested in much better electron guns than the simple crude headlight filaments used in WB6, and WB7(?). It is not an issue of energy costs as much as it is an issue of vacuum level outside the magrid. It is an engineering issue.


Dan Tibbets.
To error is human... and I'm very human.

hanelyp
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Re: Electron injection as an engineering issue

Post by hanelyp »

An electron that is reflected back to the emitter doesn't contribute to current through the emitter. 45 amps DC at 10kV comes to 450kW any way I look at it.
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D Tibbets
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Re: Electron injection as an engineering issue

Post by D Tibbets »

I disagree, or at least I think I do. My uncertainty in this area is not trivial. The e-gun current was 45 Amps and ~ 12 (or 24,36...) volts The power output of the e-guns was ~ 500 to 1000 Watts. The vast majority of the subsequent power input came from the magrid potential. This was ~ 12,000 volts. This voltage 'grabbed a hold' of the low energy e-gun electrons, and accelerated them to ~ 12 KeV (10 KeV is the energy of the elections once inside the magrid- or rather that is the potential well depth). This consumes about 480,000 Watts. This gets you ~ 3*10^ 21 electrons moving towards the magrid anode per second at 12KeV. This represents a one shot dynamic- a pulse if you will. Of all these high energy electrons, only ~ 2 percent are getting in (if my analysis is not too far off) and contributing to the potential well (~10^17 electrons/ ms or ~ 10^20 electrons per second). What happens to the remaining electrons that are at this high energy? They are reflected by the magnetic field, that is they reverse direction before reaching the plane of the magrid radius. Because they are reversed, they are traveling away from the magrid anode and as such they are climbing a potential well and slowing. This is a direct conversion , the KE of the electron is traded for potential energy in the anode. This is much like recirculation.

This is where my uncertainty grows. What happens to these now slow electrons, how slow are they? Do they reflect/ bounce back again and go through the whole process again, do they ground at a surface? Do they undergo ExB drift till they hit the magrid (at high KE)? Do they accumulate to densities where they can conduct significant current between structures (Pashin arcing)?

The simplest result is that they only contribute perhaps a small amount to the energy input relative to the ~ 10-20 KW consumed in getting the 2 % of the electons inside. The energy loss from these external 98% of the electrons may be intermediate, or perhaps even very close to the 480KW necessary to accelerate the initial electron population. Does it make a difference whether you are talking about the initial pulse of power needed, or the steady state requirements? How would this effect the Q?

Certainly the initial pulse of electrons accelerated towards the magrid requires a power input to the magrid of ~ 480,000 Watts*, but how much of this is recovered as the high percentage of electrons are reflected back and give up the KE they had initially acquired?

* With 45 Amps of electrons being accelerated towards the anode magrid, you would need ~ 45 Amps of 12,000 volt current through the anode to prevent voltage droop. This is two separate circuits though. Since the E-Gun electrons are not reaching the anode surface (not much) due to magnetic shielding the circuit is not completed. The results would be the same though, except that the reflected electrons return potential energy to the anode (potential energy is equivalent to voltage). After the initial pulse, this cyclic electron energy distribution would balance out and not contribute much to the continuing high voltage current that would have to be supplied to the magrid anode. I think the situation would be much like a transformer. Initially high current would flow through the primary to establish the fields that induces current in the secondary, but once established the current through the primary would be minimal and only match the power draining from the secondary. Note that I said power. If most of the current from the secondary is low voltage, the power is correspondingly reduced in the primary.

Dan Tibbets
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prestonbarrows
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Re: Electron injection as an engineering issue

Post by prestonbarrows »

First, are you sure that 45A is the electron beam current and not just the heating current through the filament? "45 Amps and ~ 12 (or 24,36...) volts" is about right for a resistive element; imagine a plain old 500W DC incandescent car headlamp or laying a resistor across a car battery.

This seems like way too much current for simple thermionic emission from a filament without any lenses. (especially at 10's of volts...)

Just some back of the envelope calculations, the maximum current that can be pulled from a surface is given by the Child-Langmuir Law

Image

Assuming 10000 volts between emitter and grid and a distance of 30 cm from the grid to the filaments, you need about 1.8 m^2 of emission area to get 45 A total current! (someone check that math haha) In the real world, you will get significantly less current density than this ideal 'two flat plates' model and would need even more emitter surface area. The best I have seen from big dumb filament electron sources like this is more on the order of 100's of mA to maybe an Amp of emission current. It is not exactly my area of expertise though. IIRC, Nebel claimed more like 5 A total electron current across multiple emitters.

The problem with thermionic emission is the electrons leave the surface with only a few eV of energy, essentially not moving. After a number of boiled off into space, they begin to produce a repulsive electric potential by Poisson's equation. In the current limited case above, this self-inflicted electric field pushes any new electrons back into the surface.

Higher currents are certainly possible, but require biased lenses near the emission surface. Good performance can require significant design work to get the optics right. The lenses set up a strong e-field to accelerate and focus the electrons to pull them away immediately to keep the local charge density (and accompanying space charge and fields) at a minimum. This essentially makes d in the above equation a few mm instead of fractions of a meter.

D Tibbets
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Re: Electron injection as an engineering issue

Post by D Tibbets »

Thermionic emmision of electrons from a filament is certainly temperature dependent, and the resulting space charge from the low voltage electrons boiled off of the wire needs to be removed. A n ecternal voltage gradient will do the second- in this case the high positive voltage anode of the magrid. The distance from the filament to the magrid is ~ 5-10 cm(a guesstimate).

The 45 Amps was the measured current from the filament e-gun to ( or towards the magrid). I don't know what current passed through and stayed within the headlight filaments, but at ~ 12 volts, even several hundred Amps would not cost much energy- perhaps ~ 2000 Watts. The filament could be heated by this internal current. Also, plasma impacts against the wire will heat it. In a fusor with only a few dozen milliamps of current introduced to the system, it is mostly the high energy plasma (and charge exchanged- accelerated neutrals) impacts that heats the cathode wire to incandescent temperatures.

In the Polywell, available pictures do not show brightly glowing cathode wires, so I'm guessing they are mostly heated by internal current to only dully glowing temperatures. Low energy electrons near the cathode wires and the rarefied plasma in this region does not apparently cause much impact heating. Remember that the external volume (outside the magrid) is at a pressure of well under 1 Micron under start up conditions, and there is relatively feeble impact heating of the wire. At the end of the test when the pressure builds to Pashin breakdown voltage/density conditions the wire might start to glow briskly, but the tests are only a few milliseconds and there is little time for the thermal mass of the wires to heat up to bright incandescence. If tests were run longer this might change and may or may not be an issue.

PS: Based on pictures of the oblong E-guns, I suspect each consisted of several filaments, and there were four assemblies, one at each top corner of WB6. If each filament provided ~ 5 Amps of electrons, then the numbers are reasonable. If the total was reported as 5 Amps then there is a discrepency.

Dan Tibbets
Last edited by D Tibbets on Fri Mar 21, 2014 12:19 pm, edited 2 times in total.
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D Tibbets
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Re: Electron injection as an engineering issue

Post by D Tibbets »

I still maintain that the reflected electrons lose energy as they pull away from the magrid. The same physics apply whether you are talking about recirculation of internal electrons, direct conversion of fusion ions, or excluded external electrons from the e-guns.

In an ideal system these rejected electrons would return to low KE and ground on a grounded or low voltage surface.

But, it occurs to me that this is far from an ideal condition. Some of the e-gun sourced electrons that are rejected/ mirrored may reach the magrid surface(which is at 12,000 volts in this example) through ExB drift and deposit their high energy upon impact. I've assumed that this is a minor process, though if these electrons are mirroring back and forth for a long time without grounding on a low voltage surface away from the magrid, there might be enough electron- electron collisions to drive ExB losses to significantly higher levels.

But, again, I have ignored another perhaps profound consideration. It occurs to me that ExY (?) diffusion may be a tremendous consideration. In WB6 and WB7.0 the nubs or bridges between the magnets were at high voltage (continuous metal surface) and crossed the cusps. They were not magnetically shielded to a significant degree so ExB drift/ diffusion does not need to be invoked for the high energy electrons to reach them. They may be a ravenous beast that suck up the electrons that are mirrored, and importantly do so at the full accelerating potential. ie: the fate of most of the reflected external electrons is not to ground on a low voltage surface away from the magrid where the electrons have decellerated back to low KE, but to impact the exposed high voltage nubs at their maximal KE. This means that the energy expended to accelerate the 45 Amps of current to 12,000 KeV results in ~ 2% (or whatever the injection efficiency is) of the energy entering the magrid, and most of the rest heating the nubs. So the 480 KW is fully consumed, there is little direct conversion recovery of this input energy. This is not nessisarily bad from a predictive stand point. It is a constant (?), so extrapolations about voltage, B field strength, and size scaling could still be explored. But it does increase your baseline starting point, and thus the final parameters needed for breakeven.

Nebel mentioned that nub heating was a reconized problem in WB7.0. I've always assumed that this represented losses of internal confined electron recirculation losses through EyB drift. But, with the e- gun injection efficiencies of less than 10%, it may be the rejected electrons that are doing most of the heating.

Moving the nubs outward or going to wall standoffs may help this, at least if these nubs or standoffs are insulated from the magrid surface high voltage. M. Simon mentioned this electrostatic insulation. I don't know if he was considering this external rejected electron perspective, but this is the first time I have appreciated this

Improving the e- gun performance so that a higher percentage of the electrons get into the magrid on the first try, and possibly even moving the e- guns to the face centered point cusps rather than the corner cusps (with their bridging nubs) as was the case in WB6 may help.

What is the significance of this? I already mentioned the external density and Pashin arc concerns.
The other consideration is the resultant baseline input energy consideration. An example may illustrate this.
Using WB6 as the baseline, if the input electron energy was 450KW consumed to get ~ 10-20 KW of energy into the machine (the rest is waste heat) and this ratio was maintained as you scaled to WB100 at 10 Tesla and 3 Meters diameter, and ~ 10 KV, then the numbers would be fusion output of ~ 100 MW and input costs would be ~50 MW (ignoring Bremsstruhlung losses, etc.). Higher voltages could be used with increased gains, but that is irrelevant at this point. Assuming that modifications to the nubs/ external insulation (electrostatic insulation and magnetic insulation) improves the injection energy efficiency to ~ 50%. This would translate into an input baseline of ~ 20 KW. Scaled up to WB100 parameters, this would give fusion output of ~ 100 MW, and electron injection costs of ~ 2 MW. This is a tremendous advantage, and perhaps would be applicable to P-B11 fusion where Q margins are more critical.
Even if injection efficiency (from an energy standpoint) is only doubled, it would still be significant. In the above example, the electron input costs would be reduced from 50 MW to 25 MW. A


Also, engineering considerations are applicable. There would be much less heating in the small areas of the nubs, which otherwise might melt in a steady state machine.

ll of this is dependent on my conclusion about the injection efficiency in the WB6 (and WB7.0?). But I think my numbers are reasonable, and my presumptions about the electron current AND voltage/ KE contributions when the electrons complete the circuit- are removed from the system apply.


Dan Tibbets
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hanelyp
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Re: Electron injection as an engineering issue

Post by hanelyp »

We should consider under what conditions an injected electron makes it into a wiffleball.

I'm seeing modified magnetic mirror dynamics on electron injection. A magnetic flux tube passes through a cusp and expands some going outwards.
- An electron injected inside this flux tube with a velocity within certain limits will make it in every time (unless scattered in route).
- An electron injected inside this flux tube with a velocity outside bounds will be reflected by the magnetic mirror effect.
- An electron injected outside this flux tube will not make it inside, but may make it to a zone between the wiffleball and the magrid.

So what I'm seeing is a need for the injector to be both compact and moderately directional. A plate behind the filaments to push electrons towards the magrid should help on both accounts. A cluster of filaments hurts us by not being compact. A needle tip "cold" cathode may be a very good option if it can deliver enough current to a vacuum.
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D Tibbets
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Re: Electron injection as an engineering issue

Post by D Tibbets »

hanelyp wrote:We should consider under what conditions an injected electron makes it into a wiffleball.

I'm seeing modified magnetic mirror dynamics on electron injection. A magnetic flux tube passes through a cusp and expands some going outwards.
- An electron injected inside this flux tube with a velocity within certain limits will make it in every time (unless scattered in route).
- An electron injected inside this flux tube with a velocity outside bounds will be reflected by the magnetic mirror effect.
- An electron injected outside this flux tube will not make it inside, but may make it to a zone between the wiffleball and the magrid.

So what I'm seeing is a need for the injector to be both compact and moderately directional. A plate behind the filaments to push electrons towards the magrid should help on both accounts. A cluster of filaments hurts us by not being compact. A needle tip "cold" cathode may be a very good option if it can deliver enough current to a vacuum.
Good and concise points. I'm guessing that the electrons that become traped outside to Wiffleballbut inside the magnetic fields eventuall ground on the magrid case through ExB drift- full energy loss. The nubs is similar but different. The electrons oscillating in the B field, but outside of the Wiffleball can impact these high voltage surfaces with little or no ExB drift. It may be a faster process and thus dominate the high energy losses even though the relavent surface areas are much less. That is why I stressed the possible improvements that magnetically shielding, or simply electrostatically shiielding these expose surfaces could help. They are currently at high voltage, thus the electrons that hit them are at that voltage. Shielding them and / or placing them in better positions may mildly to greatly decrease these orphin electron losses. They would still ground but on surfaces at low voltage, provided they were far enough outside the magrid proper that they have decelerated before they reach there By pulling away from the magrid proper.

As you say, improving the aiming of the e-guns will increase injection efficiency from an electron number perspective. Preventing the rejected electrons from delivering their accelerated energy to exposed, or even to an uncertain magnetically shielded surface before they decelerate as they mirror back away from the magrid high voltage electrode results in greater efficiency from an energy perspective. You are not only applying direct conversion schemes to to fusion ions, but also to escaping internal electrons (recirculation) and never inside electrons (always external electron recirculation if you will). The benifits of either or both approaches may make a net profound effect on the input energy picture.

The next question is the alternative Polywell configuration where the magrid is at ground, while the e- guns are at high voltage. I think when only electrons that are successfully injected into the Wiffleball are considered the two approaches are equivalent,or perhaps if the high voltage e- guns work better in terms of electron numbers injected (as a percentage of the total) it might be beneficial. But once the high(?) numbers of excluded electrons are considered the dynamics change considerably. A compromise where the e- guns are at modest voltage instead of low voltage, with the magrid providing most of the acceleration might be the best compromise.

Dan Tibbets
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happyjack27
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Re: Electron injection as an engineering issue

Post by happyjack27 »

from what i saw in my sims - far from the magrid, the b field is going axial from the cusp, and the electrons presumably are headed straight through it. this causes a radial lorentz force on the electrons.
then as they get closer to the magrid, the mag fields turns more towards straight through the magrid. but now the electron has picked up some decent radial inertia, and the cross produce of radial and linear is... axial. bad. this is the "tornado effect" i was seeing, in a bit more detail.

now as you increase the injection speed, well, that increases the lorentz force proportionally. so it seems to me the end result of adjusting the injection speed (i.e. voltage, whether it be a plate behind or magrid charge) will _not effect the axial spread of the electrons at the plane of the magrid_. i.e. will not effect injection efficiency.

now my thinking may be wrong, it's just a rough sketch. but it seems to imply that it all really hinges on the directional accuracy of the eguns (and distance from the magrid, and distance off center), and not so much the voltage gradient / injection velocity.

consequently then, one probably actually wants it injected as slow as possible, ke=0, since the ke in you drop it in at corresponds to the ke that it will "hit" the other side at. so then i guess what we're really looking for is an infinitesimal point exactly in the center of the plane, with zero KE, as close to the plane as possible without becoming too much of a loss target (due to exposed metal) comes to mind a very long and thin needle.

(and also that vortex effect is what got me thinking of shooting helixes or pinches at it, to counter-act the dispersion)

D Tibbets
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Re: Electron injection as an engineering issue

Post by D Tibbets »

Aiming, position, standoff ,and area of emmiter- especially as related to distance from line straight through the cusp. Also, the 'beam' from the e-gun will immediately start to disperse up to the point where the magnetic fields dominate the electrons motions. A complex problem. Oh and did I mention initial velocity? In your simulation are your electrons originating randomly outside the magrid, or from an ideal point source on axis with the cusp? The magrid needs to accelerate the electrons so I'm uncertain what complex arrangement could modify the picture in that regard. ie: by the time the electrons approach the midplane of the cusp between the magrid magnets, it has to be at full speed. You cannot accelerate it further within the machine, unless you involve alternate heating effects like microwaves, etc.

.
Dan Tibbets
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happyjack27
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Re: Electron injection as an engineering issue

Post by happyjack27 »

you can start it at any initial velocity you want. but i usually started it with zero. the parameters for particle sources in my sim are:

* x,y,z center of sphere of creation
* radius of sphere of creation
* dx,dy,dz average initial velocity
* radius of initial velocity

so e.g. if you had a dx of 1, dy and dz of 0, and a radius of velocity of 1, the initial velocity of a particle from that source would satisfy: 0^2<(dx-1)^2+dy^2+dz^2<1^2

thermalization, i believe; i.e. electrostatic forces, would help spread the energy levels of the electrons - though, true, as much up and down, and the center line of that up/down is going to be determined by initial energy, except for electron losses biasing that center line, and you want to avoid electron losses. anyways, presumably you want to set them up such that they reach zero KE exactly at the center, or as close to as possible.

D Tibbets
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Re: Electron injection as an engineering issue

Post by D Tibbets »

happyjack27 wrote:you can start it at any initial velocity you want. but i usually started it with zero. the parameters for particle sources in my sim are:

* x,y,z center of sphere of creation
* radius of sphere of creation
* dx,dy,dz average initial velocity
* radius of initial velocity

so e.g. if you had a dx of 1, dy and dz of 0, and a radius of velocity of 1, the initial velocity of a particle from that source would satisfy: 0^2<(dx-1)^2+dy^2+dz^2<1^2

thermalization, i believe; i.e. electrostatic forces, would help spread the energy levels of the electrons - though, true, as much up and down, and the center line of that up/down is going to be determined by initial energy, except for electron losses biasing that center line, and you want to avoid electron losses. anyways, presumably you want to set them up such that they reach zero KE exactly at the center, or as close to as possible.


From your variables I think you are only specifying radius and velocity from the center of the machine (and from the cusp midplane). The axial position relative to the cusp is random. So this would represent the worst case scenario for mirroring. It would be similar to electron confinement inside the machine at low Beta. According to the patent application the internal electrons will transit the interior volume ~ 60 times before escape, This number is consistent with my calculation that ~ 2% of the electrons from the E-Guns in WB6 were passing into the machine., While the remainder grounded on external surfaces (high voltage if the magrid proper or the nubs, low voltage if on distant external surfaces like the Faraday cage. That the input power was reported as ~ what would be expected for all electrons lost being at high voltage, I guess that the majority ground on Magrid structures (hit the high voltage electrode).
Your analysis considers the position and B field effects. The collisional effects and electrostatic field gradient complicates the picture, as mentioned in the paper.

http://www.askmar.com/Fusion_files/EMC2 ... eakage.pdf

I suspect your system is similar to the analysis in this paper. Simplistically, the only difference is that the paper discusses internal electrons and this discussion is concentrating on external electrons. The internal electrons can be modified by the high Beta condition, this is not the case for external electrons, otherwise the effects are possibly identical.

I have wondered at the 90% recirculation claims. I assumed that most of the remaining 10% was upscattered electrons. A portion of these though may be electrons that reach the outside and are mirrored before they can reenter the cusp. I suspect this represents the very best injection efficiency obtainable. The difference between 2 % and 90% (assuming not much upscattering loss- if upscattering contributes then the possible injection efficiency may be over 90%) is considerable. Improving the injection efficiency and/ or improved insulation of high voltage surfaces on the outside of the machine could result in profound gains. Perhaps gains of 10-30 X might be reasonable targets
As I've mentioned before, Pashin arc versus outside density may also be effected. If significant, the final Wiffleball trapped electrons (and thus ions) densities could be pushed a little further . If only a doubling in density (eg: 1*10^22 to 2*10^22/ M ^3) would quadruple the fusion rate in the same volume. As most of the input scaling is due to size, this could be a significant gain. This would probably be irrelevant for D-D fusion as I suspect engineering issues will limit the minimal size of the machine (heat loading concerns). But for P-B11 with direct conversion and the relatively lower Qs possible, the effects could again be profound.

Dan Tibbets
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happyjack27
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Re: Electron injection as an engineering issue

Post by happyjack27 »

D Tibbets wrote:
happyjack27 wrote:you can start it at any initial velocity you want. but i usually started it with zero. the parameters for particle sources in my sim are:

* x,y,z center of sphere of creation
* radius of sphere of creation
* dx,dy,dz average initial velocity
* radius of initial velocity

so e.g. if you had a dx of 1, dy and dz of 0, and a radius of velocity of 1, the initial velocity of a particle from that source would satisfy: 0^2<(dx-1)^2+dy^2+dz^2<1^2

thermalization, i believe; i.e. electrostatic forces, would help spread the energy levels of the electrons - though, true, as much up and down, and the center line of that up/down is going to be determined by initial energy, except for electron losses biasing that center line, and you want to avoid electron losses. anyways, presumably you want to set them up such that they reach zero KE exactly at the center, or as close to as possible.
From your variables I think you are only specifying radius and velocity from the center of the machine (and from the cusp midplane). The axial position relative to the cusp is random.
oh, that's just for a single particle source. one can have as many particle sources as they want. so e.g. if one was doing a 1-meter wb-6, one might have 8 particles sources: a pair of electron and proton sources at 0,0,0, radius=0.5 to simulate gas puff & ionization, and then 6 electron sources, say at 1,0,0; -1,0,0, 0,1,0; 0,-1,0; 0,0,1; & 0,0,-1, each of radius 0.01 (1 cm), to simulate electron guns at the coil mid-planes (err... actually closer to 1-sqrt(1/3) meters out from the coil midplane, since at radius=1, the midplanes lie at about x/y/z=+/- sqrt(1/3). particles spawn randomly (with a flat, as opposed to normal distribution) within each source sphere.
Your analysis considers the position and B field effects. The collisional effects and electrostatic field gradient complicates the picture
what i said above about the path of an electron during injection referred only to position, inertia, electrostatic, and b field effects of a single electron accellerated by the magrid, but my simulations also included both electric(coloumb) and magnetic forces both between each particle and between each particle and each grid segment.

and my single-particle analysis was an attempt to explain/understand my observations from the sims.

mattman
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Re: Electron injection as an engineering issue

Post by mattman »

The WB6 tank was a long tube. The numbers I have are: 3.5 meters in length and 2.5 meters in diameter. The cage/rings was a small portion of the volumn. There's no field outside the cage so I would assume any electron there would be gone.

KitemanSA
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Re: Electron injection as an engineering issue

Post by KitemanSA »

hanelyp wrote:We should consider under what conditions an injected electron makes it into a wiffleball.
Shoot it through the X-Cusp.

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