videos of polywell phase space

[happyjack27]

any other thoughts about getting your sim projecting into a 1-3 second scale?

not at the moment. besides doing away with the idea of a per-particle method altogether, and going with something like field equations and/or a fourier-transformed space. i.e. an entirely different approach, which would reflect different priorities altogether. and if i understand the term correctly from context, a non-"Lagrangian" method. but like i said, that would reflect entirely different priorities. my priority choice was accuracy over practically simulable parameter range. with a fundamental switch like not-per-particle one'd probably be better off starting from scratch.

[happyjack27]

i suppose if you use a higher order derivative method (i.e. integrate over field _gradient_ over your time step) you might be able to get better accuracy at the cusps with a given time step. though in non-linear systems i believe john nash proved something to the effect that a locally linear approximation suffices in the limit if you use an infinitesimal time step. hence i was satisfied to do position = position + velocity *dt; velocity = velocity + acceleration * dt; and not consider jerk (not integrate over change in velocity). and i think it probably breaks down past then because past the first derivative it's no longer a hamiltonian system, i.e. the trajectory is unpredicatible so integral over jerk assuming a straight line is not an accurate approximation. though at this point i'm probably synthesizing/convoluting ideas so fast its incomprehensible.

the thing is though, esp. at equilibrium, it's far from nonlinear. so then you could perhaps simulate a certain equilibrium with, seeing as though its an equilibrium, a huge reduction in the number of variables. but then you still have to validate that that's the equilibrium; the "attractor" that it evolves into. which brings you back to square one.

[rcain]

any other thoughts about getting your sim projecting into a 1-3 second scale?

not at the moment. besides doing away with the idea of a per-particle method altogether, and going with something like field equations and/or a fourier-transformed space. i.e. an entirely different approach, which would reflect different priorities altogether. and if i understand the term correctly from context, a non-"Lagrangian" method. but like i said, that would reflect entirely different priorities. my priority choice was accuracy over practically simulable parameter range. with a fundamental switch like not-per-particle one'd probably be better off starting from scratch.

totally. thats why i was interested in z-transform space (essentially posh Fourier transforms happier with non-linearities). once in that orthogonal/partitioned space it is much easier to parcel stuff up into parallel jobs/accumulators (see diagram at end of the linked doc).

only transform back into rendering space when (and where) required.

it would be less efficient than what you have, and wouldnt build video in the same nice sequential way (in fact horribly expensive), but would be something we could just throw extra (community) hardware at to yield results by brute force.

good if we ever have to render/search a large number of multiple scenario's/configs perhaps. but i think you are right to focus where you are right now. great to get some realistic looking behaviours appearing at all.

in terms of real data to calibrate against (your're still after typical densities?) i wonder if the tiny WB1 was it? (permanent magnet based polywell), has any suitable data lying around we could use - it might just be small enough to make you particle (-group) counts manageable. (even Famulus's machine will be far too big to baseline i fancy).

[happyjack27]

in terms of real data to calibrate against (your're still after typical densities?) i wonder if the tiny WB1 was it? (permanent magnet based polywell), has any suitable data lying around we could use - it might just be small enough to make you particle (-group) counts manageable. (even Famulus's machine will be far too big to baseline i fancy).

that's just what i was thinking of this morning - my plan. e.g. whether to add coils to simulate image coils, or what have you. i've decided, from the considerations above, that i'm going to go for the gold. i.e. natural wiffleball formation.

so that means i'm going for a tiny magrid with a very weak mag field. that should greatly reduce the number of particles i need to get beta=1. and i'll run it all-electrons.

i can just start off scaling the mag field down linearly with the magrid radius, as i understand that's the reasoning they use for their r^5 power scaling law. (r^3*b^2 = r^5 thus r=b) in truth though i think that formula only works up to a point. once the core gets dense enough, and the potential well is easily in the peak fusion cross section range, well then as you increase it further, the point of peak fusion cross section moves out from the center. (inside it you're over the peak) and you see there, it's only the surface of a sphere that's at peek fusion velocities, not the volume of it. and eventually you push out that spherical surface to less and less dense area, and fusion rate is proportional to density squared so you're fusion rate is liable to start dropping off after a while.

EDIT: aye, but nevermind - potential well depth is a function of excess electrons not of total particle count. i suppose then the point of all that is there will be an amount of excess electrons where the product of that hollow sphere's surface area and the density squared of particles at that radius peaks. so i.e. you want to tune your well depth for maximum fusion rate by tuning the negative bias of your plasma. or does the n in beta=nE/B^2 refer to excess electrons? in that case my point stands because you also have to tune it w/the mag field strength to form a wiffleball. in any case for higher b fields you need more excess electrons so you'll get proportionally more electron loss. so it seems it would scale more like r^4. but in any case i'm probably way over my head at this point.

[happyjack27]

new display modes added. hope they actually work. here is the new list of modes:

-3: radius^3
-2: radius^2
-1: radius (i.e. radial displacement i.e. distance from center)
0: position.x (or y or z, depending on which axis this is)
1: electric potential energy
2: total momentum
3: radial momentum
4: axial momentum
5: x (or y or z) component of momentum <-NEW
6: total force
7: radial force
8: axial force
9: x (or y or z) component of force <-NEW

FROM HERE DOWN EVERYTHING IS NEW

10: total coloumb force
11: radial coloumb force
12: axial coloumb force
13: x (or y or z) component of coloumb force
14: total lorentz force
15: radial lorentz force
16: axial lorentz force
17: x (or y or z) component of lorentz force

EXCEPT THIS LAST ONE, WHICH IS NOT NEW

18: nuclear cross section (barns)

this pretty much doubles the number of display modes per axis.

should make for some interesting new videos.

[happyjack27]

it worked!

here's a video of cycling through the new modes as described, using the y-axis, electrons only.

http://www.youtube.com/watch?v=uZXBrakIEk4

one thing is quite clear: at these settings the mag field forces completely dominate the electron coloumb forces.

[krenshala]

one thing is quite clear: at these settings the mag field forces completely dominate the electron coloumb forces.

But is that good, or bad?

Interesting video as always.

[rcain]

i've decided, from the considerations above, that i'm going to go for the gold. i.e. natural wiffleball formation.

top man! just watching the vid now

[happyjack27]

one thing is quite clear: at these settings the mag field forces completely dominate the electron coloumb forces.

But is that good, or bad?

well it means one could pump in a lot more particles before confiment starts to break down. so it means i'm far from optimal parameters. so bad.

[ladajo]

Bad because the hardware won't support the particle count?

[happyjack27]

Bad because the hardware won't support the particle count?

for the given mag field. if i go smaller and weaker mag field i'll eventually run into a point where the situation reverses. it's mathematically inevitable. and i plan on doing that. i just mean that it's probably the wrong regime for wiffleball formation.

[happyjack27]

here's cycling through, but with x and z axis set to radius (distance from center).

http://www.youtube.com/watch?v=f4sLaSRz3DA

notice radius is on both sides sides now rather than just positive. i made every other thread flip the sign, so even number particles are on the right, odd on the left. much more visually intuitive.

my fav view is the radial momentum.

[D Tibbets]

One point that occurred to me with shrinking the magrid is that eventually you will reach the point where the gyroradius of the electron at some given energy will approach the radius of the magrid. This would scew everything up. The spacing between the magnets would need to be greater than the diameter of the coil. And the electrons would hit the facing magnet coil surfaces before they could complete a gyroradii turn. Decreasing the electrons energy would help, but how would that relate to decreasing the magnetic field strength so that a useful number of electrons could be used in the sim?
I wonder if cheating would work. IE: arbitrarily decrease the gyroradius of an electron at a given energy and magnetic field strengh. Say divide it by 10. The gyroradii is a constant determined by the electron energy and magnetic field strength so it might lend itself to such manipulation. The mathmatical calculations should (?) be consistent, so the proportions, etc should not change. So long as you multiplied at the end of the run, the results might be the same, or not . Unless this effected precision and accumulation of margins of error, etc.....

Would this be essentially the same as increasing the size of the machine? The limiting gyroradius would, I think. be the parameter that drives containment issues, and at least in part the edge Wiffleball properties. I'm guessing the pressure driven inflation of the Wiffleball is independant of the gyroradius within limits (gyroradii much less than radius of the machine).

Dan Tibbets

[happyjack27]

One point that occurred to me with shrinking the magrid is that eventually you will reach the point where the gyroradius of the electron at some given energy will approach the radius of the magrid. This would scew everything up. The spacing between the magnets would need to be greater than the diameter of the coil. And the electrons would hit the facing magnet coil surfaces before they could complete a gyroradii turn. Decreasing the electrons energy would help, but how would that relate to decreasing the magnetic field strength so that a useful number of electrons could be used in the sim?
I wonder if cheating would work. IE: arbitrarily decrease the gyroradius of an electron at a given energy and magnetic field strengh. Say divide it by 10. The gyroradii is a constant determined by the electron energy and magnetic field strength so it might lend itself to such manipulation. The mathmatical calculations should (?) be consistent, so the proportions, etc should not change. So long as you multiplied at the end of the run, the results might be the same, or not . Unless this effected precision and accumulation of margins of error, etc.....

Dan Tibbets

...and the mass of an electron. altering the gyroradii for a given mag field strength would be equivalent to altering the charge-to-mass ratio of the particle.

i'm just not modelling grid losses right now so that should take care of worrying about running into the grid. as for size, i think 1.5mm should do. that's what i'm running now. in them i'm "cheating" though by starting the electrons out in the center.

and for wb formation when i get tdown to some limiting size, i can just lower the mag field. but then again that gets to your point as lower mag field means larger gyroradii. (which is why i have to lower the time step as higher mag field strengths - cause the gyroradii are smaller)

anycase another:

electron-only momentum (1.5mm) axial-radial-density view:

http://www.youtube.com/watch?v=gZs9XulqJlU

and more coming.

[happyjack27]

i'm sorry, that should be 1.5cm - centimeters not millimeters. 1/10th the size of a wb-6. field strength is at 1E3.6 amp turns, whatever that turns out to be in teslas for that coil radius.

you'll notice i still have ions on, they're just at the minimum and i filtere them out from the display. i realized that at the population count i was doing, well there's about 1 ion for every electron, and i figure that's certainly not negligbly small, so i enabled display of them and it looked interesting. so anyways i ran it for a while, with a time step probably a little higher than i should, but i slowed down the electron time step relative to ion time step to compensate. so anyways this is what the radius-radial momentum-axial momentum view looks like, after some time:

http://www.youtube.com/watch?v=wAARwk7D_P4

remember i'm still "cheating". but in anycase this looks like a good range. i think i'm going to stick w/it and cheat less (turn on magrid losses, start electrons out uniformly, keep the time step small, etc.)

this looks like what one should be seeing in a functional polywell. notice you see deutrium and tritium in separate layers due to their different weights - swirling in slowly towards the center. as i've remarked earlier, since they start at different positions from the center, the energy levels are likewise distributed. and it looks like they do eventually tend to thermalize and dampen.

but as you can see, as they travel outwards, they lose outward radial momentum until they get to the end, where they reverse and start gaining inward radial momentum, until they get to the center and convert it to axial and back out the other side.

i messed up the params near the end of the video.
less cheating i'll have to do over the week, where i can just let it run while i'm at work and then time-lapse it.

it to test wb formation i'm going to have to vary the field strength / particle count and get some umbers on losses and electron lifetime and well depth and such, which means i'll have to make the sim generate some numbers. means more coding before i can properly do that.