Well just humour me, it is not my problem that you cannot see the connection yet, (ever?) but we must take ever smaller steps to get there it seems.
So you agree basically that if there is 'small' spherical shell of cold (low KE) electrons the electric potential and first radial derivative of the potential in the very center will be zero. Good, you'll back me on that one I hope.
thread for segments files and parameters for simulation runs
Well, you seemed to claim there was no such connection. Is it a "purely theoretic logical argument" or does it have something to do with PWs? If so, are you claiming there are no potential wells?
Which is why I ask, yet again: are you going to acknowledge that wells have been measured and exist? I tried to think of a smaller step to help you. Maybe you could just acknowledge the concept of experiment and we can work from there?
Eh, it's late. I guess I'll let you argue with Bussard.
Which is why I ask, yet again: are you going to acknowledge that wells have been measured and exist? I tried to think of a smaller step to help you. Maybe you could just acknowledge the concept of experiment and we can work from there?
Yes... if that's everything that's happening.So you agree basically that if there is 'small' spherical shell of cold (low KE) electrons the electric potential and first radial derivative of the potential in the very center will be zero.
Eh, it's late. I guess I'll let you argue with Bussard.
The EMC2 device avoids these by using energetic electrons, trapped in a quasi-spherical polyhedral magnetic
field, to generate a spherical electric potential well.
...
If electrons live sufficiently long in the machine they could
become Maxwellianized (thermalized) and develop high
energy loss distributions. However, this has been found not
to be the case. The same arguments have been found for the
ions, as well. Detailed analyses show that Maxwellianization
of the electron population will not occur, during the lifetime
of the electrons within the system. This is because the
collisionality of the electrons varies so greatly across the
system, from edge to center. At the edge the electrons are all
at high energy where the Coulomb cross-sections are small,
while at the center they are at high cross-section but occupy
only a small volume for a short fractional time of their
transit life in the system. Without giving the details, analysis
shows that this variation is sufficient to prevent energy
spreading in the electron population before the electrons are
lost by collisions with walls and structures.
Last edited by TallDave on Thu Nov 25, 2010 6:29 am, edited 1 time in total.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
Not to worry, it just means they screen out forces.happyjack27 wrote: I don't know what a Debye sheath is. presumably its a thin layer of electrons, but beyond that it's greek to me.
http://en.wikipedia.org/wiki/Debye_shielding
http://en.wikipedia.org/wiki/Debye_length
IIRC Joel's simulation attempted to look at "Debye slices."
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
Would someone be so kind as to answer a quick question for me?
I am under the impression that Debye shielding occurs in quasi-neutral plasmas with LTE. Thus, the basic concept shouldn't apply to a functioning Polywell as the plasmas therein are NOT supposed to be under LTE. Now my question. In what way(s), if any, is that impression incorrect?
I am under the impression that Debye shielding occurs in quasi-neutral plasmas with LTE. Thus, the basic concept shouldn't apply to a functioning Polywell as the plasmas therein are NOT supposed to be under LTE. Now my question. In what way(s), if any, is that impression incorrect?
My understanding is it still applies, just not as strongly because the usual Debye length calculation assumes static conditions ("when the mobility of ions is negligible compared to the process's timescale") as opposed to the flows in a PW. Better informed opinions than mine appreciated.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
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happyjack27
- Posts: 1439
- Joined: Wed Jul 14, 2010 5:27 pm
well that makes sense. as a hollow sphere of charge, i suppose they'd act much like a hollow sphere of charge does. though if there's any non-uniformity in the efield they see i suppose they'd readjust to fill it in. so they'd leave the center free of electric fields. in that case any charged particles inside the sphere at relatively low velocity would act as if they were in a fieldless vaccum, and simply expand by their own mutual repulsion, until they reach a balance of forces. and hey, guess where that is, the debye sheath! (presumably, else how would it be there in the first place.)TallDave wrote:Not to worry, it just means they screen out forces.happyjack27 wrote: I don't know what a Debye sheath is. presumably its a thin layer of electrons, but beyond that it's greek to me.
curious, though would they be sheilding the mag field too, or just the e field? if they circle around the cusps they'd induce their own mag field. does that serve to cancel or transmit? i would presume cancel.
now i have a better idea of what i'm seeing and why.
on a different note, and this is for everyone:
i've had from the very begining the plan of adding "plasma diagnostics" to the sim. that is, it would show in real time charts describing different densities and what not at different radii. it seems i'm at the point now where to get any real valuable insight on different magrid configurations and parameters, i need to get a good idea of the well depth and how much energy it takes to maintain it. so that i have some quantitiave metric by which to compare different scenarios. this means i need at least a diagnostic on electrostatic potential (aka voltage). so that'll probably be the next major revision. calibrating the eguns will have to wait.
in computer speak, i'm going to be simply "binning" particles, into say 64 separate bins, each corresponding to a different 1/64th length of the radius of the magrid. i haven't settled on the resolution yet.
here are some measurements i'm thinking of for the diagnostics, we'll see how ambitious i get:
- these are measurements to be taken at different radii -
* electrostatic potential (definitely)
* electron/ion population density (measured separately)
* avg. electron/ion velocity
* avg. electron/ion thermalization (2nd statistical moment of velocity)
* avg. electron/ion radial velocity
* avg. electron/ion radial thermalization
* avg mag field strength
those are just possibilities i've thought of. listed roughly in order of priority. i'm open to suggestions.
My limited understanding is that the Debye length is an artificially defined number that is useful for predicting plasma behavior in very limited situations. Still it seems to be very useful. I once asked Art Carlson, when he was still hanging around here, to give a definition of the Debye length under non (near) static conditions. I got no response. From my reading it seams the calculation of the Debye length is done under very limited conditions. With no current it doesn't exist, and with more than extremely small currants it becomes incalculable (it is a moving target). To calculate, a nearly infinitely tiny current is assumed. Also,at least part of the calculation depends on the assumption of thermalization.
Dan Tibbets
Dan Tibbets
To error is human... and I'm very human.
Picturing the electron population as a stream of converging electrons towards the center, or as a shell nestled against the magnetic field are both symplistic. My convoluted picture is that both apply in part, and varies depending on conditions. I don't think anyone would argue against a single injected electron, focused through the cusp and with suffucuent kinetic energy (so that it does not 'stick' to the magnetic field) will fly through the center, bounce off the opposit magnetic wall, and continue this untill it again finds a cusp. In fact, Busard, etel. had to answer critisisms that the electron would only have one pass and exit at the opposite cusp. The magnetic focusing is not that percise, and once additional electrons are added, the central dispertion impeads this even more. The repulsive dispertion of the electrons from the center will assume random radial trajectories so the chances becomes purely dependant on the size of the cusp holes- thus the Wiffleball concept (without the subsequent arguments about shrinking the holes).
At the end of their life the old electrons (from a single pulse of electrons) tend to become trapped on magnetic field lines and accumulate in this periferal shield.
What is important is what happens in between and how long it takes to reach this end of life condition.
The radially injected electrons quickly begin mixing (thermalizing) into a bunch of randome electrons bouncing inside the Wiffleball, with a continous drain into the magnetic field or drain through the cusps. This transition takes a finite amount of time.
The important point is how long this process takes versus the lifetime of the electrons. In Fusors this is slow enough that a square potential well or perhaps even some some parabolic well can be maintained. This is done because the new injected electrons from the central grid keeps up with this thermalization time. In the fusors case, there is no life extending magnetic field, so the shell of electrons on the perifery does not form- the electrons fly straight to the walls. Of course this takes relative hug electron currents to maintain this picture (the trade off is small electron currents which produce measurable fusions, but only at feeble levels).
In the Polywell, the magnetic life extension process would greatly reduce the electron current needed, but not limit this thermalization and periferalization effect. In the Polywell a pulse of electrons would be expected to assume this condition, The conventional fusors would not as there is no limiting edge barrier- the electrons ground on the vacuum vessel wall. In the Polywell I think this would form a shell of electrons that maintains a spike of potential and because of Gauss Law, no potential inside.
A square potential would have enough electrons still bouncing around inside to maintain the edge potential clear to the center. Art Carlson (if I understood him correctly) suggested this. And Bussard also claimed this in his Google talk.
There have been arguments that this is the operational picture of the Polywell for the above reasons, but there are two modifiers. One is the confinement time of the electrons is not long enough for complete thermalization and entrapment on the magnetic field lines. This is only good if you can somehow cheat, and avoid the intolerable input electron currents needed to maintain this condition long enough for useful and profitable fusion. This is where recirculation comes in. Also, keep in mind, that this square potential well condition apparently will work, according to Nebel. Under these conditions the ions would have little or no central convergence, but you would still have the advantages of much higher densities due to the Wiffleball effect, and fusionability advantages due to a non thermalized distribution of the ions.
As Bussard said in his Google talk, and what I believe is the reason that parabolic wells have been seen in Fusors, is that there are other forces, dynamics involved. As the ions residing outside the majority of electrons- whether you consider the electrons to be located in a centrally converging (parabolic well), random (square well), or shell (periferal spike well) distribution are accelerated towards the center (thanks to the spherical nature of the system) they drag some of the light electrons with them. And this is what forms, at least in large part the parabolic well, just as it does in the spherical fusors. Even if my reasoning is flawed or my descriptions are confusing, the experimental evidence of these fusor parabolic wells measured by several labs would still be paramount.
It all boils down to Bussards insistence, that these systems need to be viewed as dynamic, not static systems.
Note: When I refer to the potential well being spiked due to the accumulation of the electrons on the magnetic border, the Gauss Law considerations still means that from the ions perspective it appears as a square potential well.
That is enough obtuse reasoning for now, I'm going to eat some turky
Dan Tibbets
At the end of their life the old electrons (from a single pulse of electrons) tend to become trapped on magnetic field lines and accumulate in this periferal shield.
What is important is what happens in between and how long it takes to reach this end of life condition.
The radially injected electrons quickly begin mixing (thermalizing) into a bunch of randome electrons bouncing inside the Wiffleball, with a continous drain into the magnetic field or drain through the cusps. This transition takes a finite amount of time.
The important point is how long this process takes versus the lifetime of the electrons. In Fusors this is slow enough that a square potential well or perhaps even some some parabolic well can be maintained. This is done because the new injected electrons from the central grid keeps up with this thermalization time. In the fusors case, there is no life extending magnetic field, so the shell of electrons on the perifery does not form- the electrons fly straight to the walls. Of course this takes relative hug electron currents to maintain this picture (the trade off is small electron currents which produce measurable fusions, but only at feeble levels).
In the Polywell, the magnetic life extension process would greatly reduce the electron current needed, but not limit this thermalization and periferalization effect. In the Polywell a pulse of electrons would be expected to assume this condition, The conventional fusors would not as there is no limiting edge barrier- the electrons ground on the vacuum vessel wall. In the Polywell I think this would form a shell of electrons that maintains a spike of potential and because of Gauss Law, no potential inside.
A square potential would have enough electrons still bouncing around inside to maintain the edge potential clear to the center. Art Carlson (if I understood him correctly) suggested this. And Bussard also claimed this in his Google talk.
There have been arguments that this is the operational picture of the Polywell for the above reasons, but there are two modifiers. One is the confinement time of the electrons is not long enough for complete thermalization and entrapment on the magnetic field lines. This is only good if you can somehow cheat, and avoid the intolerable input electron currents needed to maintain this condition long enough for useful and profitable fusion. This is where recirculation comes in. Also, keep in mind, that this square potential well condition apparently will work, according to Nebel. Under these conditions the ions would have little or no central convergence, but you would still have the advantages of much higher densities due to the Wiffleball effect, and fusionability advantages due to a non thermalized distribution of the ions.
As Bussard said in his Google talk, and what I believe is the reason that parabolic wells have been seen in Fusors, is that there are other forces, dynamics involved. As the ions residing outside the majority of electrons- whether you consider the electrons to be located in a centrally converging (parabolic well), random (square well), or shell (periferal spike well) distribution are accelerated towards the center (thanks to the spherical nature of the system) they drag some of the light electrons with them. And this is what forms, at least in large part the parabolic well, just as it does in the spherical fusors. Even if my reasoning is flawed or my descriptions are confusing, the experimental evidence of these fusor parabolic wells measured by several labs would still be paramount.
It all boils down to Bussards insistence, that these systems need to be viewed as dynamic, not static systems.
Note: When I refer to the potential well being spiked due to the accumulation of the electrons on the magnetic border, the Gauss Law considerations still means that from the ions perspective it appears as a square potential well.
That is enough obtuse reasoning for now, I'm going to eat some turky
Dan Tibbets
To error is human... and I'm very human.
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happyjack27
- Posts: 1439
- Joined: Wed Jul 14, 2010 5:27 pm
from my sims it seems the shape of the virtual anode (cathode? i can never get them straight), at least in the all electron runs, depends on 3 factors (besides the magrid, shape, ofcourse): grid current, grid charge, and electron count.
increasing electron count tends ofcourse to make it bigger, puffing it out, going from just an intersection of lines that follow the major cusps, to a spikey ball with spikes at all the cusps. (and on the wb-6 config at least it goes through a cube on its way) then as you increase it further it gets noisy around the outside, esp, at the spikes, and starts to leak more and more until it eventually breaks and scatters electrons all over the place. at which point i'd imagine your power gain/loss ratio drops dramatically. and these latter stages are where the well becomes a lot "fuzzier" / "softer".
http://www.youtube.com/user/happyjack27 ... GFmtQJrLq8
the mag field (current) tends to be the opposing force, to this. so presumably varying it is similiar to varying the electron count. (though inversely so).
the charge on the magrid -- i'm not certain of this yet, have to finally fix my efield from wire segments code, but -- seems to geometrically counter-act the mag field, making the anode more spherical. which i would guess makes the behavior at the cusps wrap the electrons more inward or in any case not so tornado-ey (you can tell i'm being precise when i use words like "tornado-ey"), which would probably serve to improve confinement. too high, ofcourse, and it goes towards the inverse of a spikey ball. in other words you just blow it open.
this is just from preliminary sims. i haven't really evaluated it systematically yet.
increasing electron count tends ofcourse to make it bigger, puffing it out, going from just an intersection of lines that follow the major cusps, to a spikey ball with spikes at all the cusps. (and on the wb-6 config at least it goes through a cube on its way) then as you increase it further it gets noisy around the outside, esp, at the spikes, and starts to leak more and more until it eventually breaks and scatters electrons all over the place. at which point i'd imagine your power gain/loss ratio drops dramatically. and these latter stages are where the well becomes a lot "fuzzier" / "softer".
http://www.youtube.com/user/happyjack27 ... GFmtQJrLq8
the mag field (current) tends to be the opposing force, to this. so presumably varying it is similiar to varying the electron count. (though inversely so).
the charge on the magrid -- i'm not certain of this yet, have to finally fix my efield from wire segments code, but -- seems to geometrically counter-act the mag field, making the anode more spherical. which i would guess makes the behavior at the cusps wrap the electrons more inward or in any case not so tornado-ey (you can tell i'm being precise when i use words like "tornado-ey"), which would probably serve to improve confinement. too high, ofcourse, and it goes towards the inverse of a spikey ball. in other words you just blow it open.
this is just from preliminary sims. i haven't really evaluated it systematically yet.
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happyjack27
- Posts: 1439
- Joined: Wed Jul 14, 2010 5:27 pm
also possibilities for diagnostics, some multi-dimensional / phase-space style diagonstics. possibilities for axis:
1 ) radius (distance from center)
2 ) electric potential energy
3 ) kinetic energy
4 ) total energy (KE+EPE)
5 ) radial kinetic energy
6 ) axial kinetic energy (KE - radial KE)
7 ) x coordinate absolute value (e.g. for mapping a quadrant)
8 ) y coordinate absolute value
also a profile of loss energies. (mv^2/2)
this would all require only one more quantity stored per particle and one more calculation per particle-particle interaction: in both cases, electric potential energy (coloumbs constant * charge of p0 * charge of p1 / (distance between p0 and p1) )
radius-kinetic-potential and it's 2-dimensional pairs are obvious combinations.
doing thermalization may be somewhat problematic because you're really looking at different parts of the space, which presumably _do_ have different KEs. to do that accurately / non-deceptively one'll probably have to do a slice.
1 ) radius (distance from center)
2 ) electric potential energy
3 ) kinetic energy
4 ) total energy (KE+EPE)
5 ) radial kinetic energy
6 ) axial kinetic energy (KE - radial KE)
7 ) x coordinate absolute value (e.g. for mapping a quadrant)
8 ) y coordinate absolute value
also a profile of loss energies. (mv^2/2)
this would all require only one more quantity stored per particle and one more calculation per particle-particle interaction: in both cases, electric potential energy (coloumbs constant * charge of p0 * charge of p1 / (distance between p0 and p1) )
radius-kinetic-potential and it's 2-dimensional pairs are obvious combinations.
doing thermalization may be somewhat problematic because you're really looking at different parts of the space, which presumably _do_ have different KEs. to do that accurately / non-deceptively one'll probably have to do a slice.
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happyjack27
- Posts: 1439
- Joined: Wed Jul 14, 2010 5:27 pm
added a spreadsheet to the svn, available for download here.
it calculates the coordinates for all the vertices of all the coils (32-gon approximated) of an icosododecahedron magrid (12 coils, 32 faces (12 explicit + 20 corner), bussard's original wb-8 plan).
it's in open document format (.ods), so you'll need open office to open it (which is free and open source). from there you can export it to .xls if you like.
it contains a sheet called "rotate" that does all the 3-d rotations. probably usefull for people who want to do stuff like that.
it calculates the coordinates for all the vertices of all the coils (32-gon approximated) of an icosododecahedron magrid (12 coils, 32 faces (12 explicit + 20 corner), bussard's original wb-8 plan).
it's in open document format (.ods), so you'll need open office to open it (which is free and open source). from there you can export it to .xls if you like.
it contains a sheet called "rotate" that does all the 3-d rotations. probably usefull for people who want to do stuff like that.
Yeah, as best I can recall I've never gotten a real satisfactory response on that question from anyone. We might ask Joel:DTibbets wrote:I once asked Art Carlson, when he was still hanging around here, to give a definition of the Debye length under non (near) static conditions. I got no response.
I may have asked him about this before and since lost the email to a drive crash.The simulation treats a 2d slab of some small thickness, approximately equal to the Debye length. The 3d (cubic) plasma volume was envisioned as a stack of square slabs of number sufficient to make the height of the ion plasma in the stack equal to the edge dimension of the simulated ion plasma in the slab. Substituting the slab thickness into the expression for Q = P_out/P_in yielded the following expression for the 3d power balance: Q = (3/32)(N^2)(L)(Sigma)(U)(Edd)/(P), where N is the 2d (areal) plasma density, L is the edge dimension of the confinement cube, U is the magnitude of the ions' velocity, and P is the power loss from ions hitting ONE corner of the tank.
Wonder what Rick's answer would be. Something that made a lot more sense than anything I'm thinking, if the past is any predictor.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
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happyjack27
- Posts: 1439
- Joined: Wed Jul 14, 2010 5:27 pm
i haven't gotten the phase space view up and running yet. i've got some things to work out with memory mapping from cuda to opengl. but in the meantime, to hold you over, i've got a new mixed-particle video.
this one has some green protons for better visual tracking. also the sliders for particle density have changed to be more practical: one is for net space charge (electron charge + ion charge), the other is for total space charge (abs(electron charge) + abs(ion charge)). so the parameters of the video are as follows:
3m radius.
~7 tesla mag field. (10E7.45 amp turns)
no coil charge
-10E-7 net space charge
10E-4 total (sum of absolute values) space charge
http://www.youtube.com/watch?v=8YLjwz3M9u0
something to note. the well depth is determined by the DIFFERENCE in charge concentrations, NOT the ratio. so at higher total charges, though you'll see a lower contrast ratio between electron density in the center vs. further away from the center, that doesn't mean that the well depth is any less. that's just because since the representation ratio is higher, it takes a smaller excess of electrons in the middle to account for the same charge differential.
so the picture really gets less clear as you up the particle density (representation ratio). something the phase space view will fix.
also i've notice that the video compression really reduces the clarity. so you still can't visually track very well. sorry about that. i've go to remember to keep the point size higher so the colors come out clearer on the video. in any case the phase space evolution view will most likely be much clearer since it will provide much greater particle segregation and uniformity of motion.
this one has some green protons for better visual tracking. also the sliders for particle density have changed to be more practical: one is for net space charge (electron charge + ion charge), the other is for total space charge (abs(electron charge) + abs(ion charge)). so the parameters of the video are as follows:
3m radius.
~7 tesla mag field. (10E7.45 amp turns)
no coil charge
-10E-7 net space charge
10E-4 total (sum of absolute values) space charge
http://www.youtube.com/watch?v=8YLjwz3M9u0
something to note. the well depth is determined by the DIFFERENCE in charge concentrations, NOT the ratio. so at higher total charges, though you'll see a lower contrast ratio between electron density in the center vs. further away from the center, that doesn't mean that the well depth is any less. that's just because since the representation ratio is higher, it takes a smaller excess of electrons in the middle to account for the same charge differential.
so the picture really gets less clear as you up the particle density (representation ratio). something the phase space view will fix.
also i've notice that the video compression really reduces the clarity. so you still can't visually track very well. sorry about that. i've go to remember to keep the point size higher so the colors come out clearer on the video. in any case the phase space evolution view will most likely be much clearer since it will provide much greater particle segregation and uniformity of motion.
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happyjack27
- Posts: 1439
- Joined: Wed Jul 14, 2010 5:27 pm
this one's clearer, and probably better parameters. i darkened everything but the greens so they stand out more, and made the electrons a little redder.
http://www.youtube.com/watch?v=dDa81EFRHjU
3m radius
-10E-7.972 net space charge
10E-6.024 total space charge
10E-14.055 coil charge (coloumbs/meter)
10E7.452 amp turms (~7 tesla)
i'm going to try using eguns outside the magrid now
http://www.youtube.com/watch?v=dDa81EFRHjU
3m radius
-10E-7.972 net space charge
10E-6.024 total space charge
10E-14.055 coil charge (coloumbs/meter)
10E7.452 amp turms (~7 tesla)
i'm going to try using eguns outside the magrid now
How do you model the Faraday cage that is encompassing the whole region?Is it grounded or held at set voltage?
Do the ions that make it tho the cage get removed from the sim.? Do the electrons that make it to the MaGrid get removed?
Can the rate at which those particles are removed be measured? (This would be a measure of loss rate)
Do the ions that make it tho the cage get removed from the sim.? Do the electrons that make it to the MaGrid get removed?
Can the rate at which those particles are removed be measured? (This would be a measure of loss rate)