thread for segments files and parameters for simulation runs

Discuss how polywell fusion works; share theoretical questions and answers.

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happyjack27
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Postby happyjack27 » Tue Nov 30, 2010 12:45 pm

rjaypeters wrote:Surely* you know the derivation of the pb&j shorthand?


actually, no.

BenTC
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Joined: Tue Jun 09, 2009 4:54 am

Postby BenTC » Tue Nov 30, 2010 12:48 pm

happyjack27 wrote:what's this about pb&j? i prefer ham, myself.

Protons, Boron-11 & Joules - in reference to the lack of neutron production (http://en.wikipedia.org/wiki/Aneutronic_fusion)
In theory there is no difference between theory and practice, but in practice there is.

happyjack27
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Postby happyjack27 » Tue Nov 30, 2010 2:09 pm

ah, well on that note i'm actually thinking of switching the sim to D-T fusion at 2m, 'cause i can get the theoretical numbers for that from here.

esp. in that it has the plasma density, a parameter that i've been looking for. then i have the added benefit of being able to compare theory with sim results. well, considering the sim doesn't model bremmstrag (whatever the spelling) and all that.

rjaypeters
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Location: Summerville SC, USA

Postby rjaypeters » Tue Nov 30, 2010 3:48 pm

happyjack27 wrote:
rjaypeters wrote:Surely* you know the derivation of the pb&j shorthand?

actually, no.

What?! You haven't read and remember everything that has been written on this forum? :)

On to business: Do you want 2m diameter or 3m diameter for the bent rings? And subsequent work?

Also, the inverted WB-6 implies (requires?) the current to run in the opposite direction (clockwise) from what I have used in the past (counterclockwise). Does the current direction matter?
"Aqaba! By Land!" T. E. Lawrence

R. Peters

happyjack27
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Joined: Wed Jul 14, 2010 5:27 pm

Postby happyjack27 » Tue Nov 30, 2010 4:15 pm

rjaypeters wrote:
On to business: Do you want 2m diameter or 3m diameter for the bent rings? And subsequent work?


i want 1m RADIUS circumscribed spherical volume. i.e. square root[(coil radius) squared + (distance from center of coil midplane to absolute center) squared] = 1 meter

Also, the inverted WB-6 implies (requires?) the current to run in the opposite direction (clockwise) from what I have used in the past (counterclockwise). Does the current direction matter?


doesn't matter. i can scale the current arbitrarily. and it doesn't make a difference for the polywell anyways. so long as the coils are all in the correct direction _relative to each other_, it's all good. and btw, you can flip the coil current direction just by appending ", -1.0" to the end of each line for that coil.

happyjack27
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Joined: Wed Jul 14, 2010 5:27 pm

Postby happyjack27 » Tue Nov 30, 2010 4:47 pm

a few numbers here.

using the numbers on page 8 of this paper. for a d-t fusion reactor scale polywell,

assuming that by "bulk density", they mean ions per cubic meter in the volume in the sphere circumscribed by the magrid.

volume of a sphere of radius r = v(r)=4/3*pi*r^3

volume = v(2 (listed)) = 33.510321638291127876934862754981 m^3
density (listed) = 2*10^20 / m^-3.
charge = 1 proton = 1.602176487*10^-19 coloumbs

volume * density = 6702064327658225575386.9725509963 total ions
volume * density * charge = 1073.7889880135472789027053347321 coloumbs total ion charge.

ion representation ratio = total ions / sim ion particle count(7168) =
934 997 813 568 390 844.780548625976

in other words, using those numbers, one colored dot in the simulation will represent about 934,997,813,568,390,845 particles.

that's a lot. thousand, million, billion, trillion, quadrillion, quintillion. 934 quintillion.

D Tibbets
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Postby D Tibbets » Tue Nov 30, 2010 5:25 pm

I had forgotten, or ignored the concise data in Table 2 of the above referenced paper.
Useful information, though keep in mind this is the pre recirculation epiphany of WB6. The confinement time of electrons of ~ 2 ms in the test machine, and 120 ms (?) in a reactor represents the lifetime of each electron, and the time available for thermalization processes to catch up. My understanding of recirculation is that the primary confinement time may be less, but recirculation more than makes up for this. Also, I believe the aviable thermalization time is limited by the primary confinement, while the recirculated electron is reset to initial conditions. A distinct advantage if electron thermalization time vs electron e-gun input costs is considered. At some point in the evolution of your modeling, this would have to be incorperated into the picture.

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

happyjack27
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Postby happyjack27 » Tue Nov 30, 2010 6:06 pm

D Tibbets wrote:I had forgotten, or ignored the concise data in Table 2 of the above referenced paper.
Useful information, though keep in mind this is the pre recirculation epiphany of WB6. The confinement time of electrons of ~ 2 ms in the test machine, and 120 ms (?) in a reactor represents the lifetime of each electron, and the time available for thermalization processes to catch up. My understanding of recirculation is that the primary confinement time may be less, but recirculation more than makes up for this. Also, I believe the aviable thermalization time is limited by the primary confinement, while the recirculated electron is reset to initial conditions. A distinct advantage if electron thermalization time vs electron e-gun input costs is considered. At some point in the evolution of your modeling, this would have to be incorperated into the picture.

Dan Tibbets


If, as it sounds, those are all consequences of the lorentz force, then they wouldn't require any code modifications; they are already modeled as the lorentz force. This is a _direct_ simulation of per-particle (well, with a representation ratio) classical (relativistic) electrodynamics. assuming the lorentz force and biot-savart equations are correct, and the time scale is fine enough, it logically follows that everything that follows from MHD is modeled correctly. (and likewise, if they are incorrect, everything is incorrect in the same way)

as far as i know, the only physical laws missing, besides being a classical approximation rather than a proper QED model, are the 3 other forces : strong nuclear, weak nuclear, and gravity. and gravity would be trivial to add in and the additional computation cost would be pretty negligible, but i presume so would be the effect at this scale. as regards the weak nuclear, well, the time scales are way below the half lives of any isotopes. as regards the strong nuclear force -- and here by extension a QED approximation -- in my phase space view you'll be able to see the fusion cross section for the KE of the ion, as stated on page 17 of this paper. I'm not aware of any other QED phenomena relevant at these scales and temperatures.

so with those caveats, anything that follows from the laws of physics as we know them should already be simulated correctly. to an approximation of the time increment, simulated particle count, and single precision floating point, of course. to put it succinctly, "this is not a model, it is a simulation."

the only questions that remain, then, would be accumulating and viewing the results (e.g. electron loss rate), and setting up the configuration correctly (e.g. current in coils, plasma density, etc.)

icarus
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Postby icarus » Tue Nov 30, 2010 6:27 pm

happyjack:
"this is not a model, it is a simulation."


What is the difference?

Usually the largest sources of error with numerical modelling of this sort comes from imperfect boundary conditions, spatial and temporal resolution; all limitations associated with availability of computing power. I don't think you are quite as far along as you seem to be expounding.

happyjack27
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Postby happyjack27 » Tue Nov 30, 2010 6:43 pm

icarus wrote:happyjack:
"this is not a model, it is a simulation."


What is the difference?


from merrian-webster:

model: a system of postulates, data, and inferences presented as a mathematical description of an entity or state of affairs

simulation: the imitative representation of the functioning of one system or process by means of the functioning of another

Usually the largest sources of error with numerical modelling of this sort comes from imperfect boundary conditions, spatial and temporal resolution; all limitations associated with availability of computing power. I don't think you are quite as far along as you seem to be expounding.


almost all those errors are actually "limitations associated with availability of computing power", which is just a catch-all really. i believe the largest source of error in my sim is the limited particle count ("spatial" approximation). as stated above. i'm counting on the MHD being what's important and being approximately "correct enough" to have a phase space evolution qualitatively and topologically identical (or very similiar) to a simulation with a 1:1 representation ratio.

i'm at the point in particle count where pretty much all the overhead (memory transfers, thread scheduling, etc.) is fully amortized, so the n^2 computation time scaling law is dominant. to increase the particle count much further (more than 2x), i'd have to go with an nlogn algorithm, such as a barnes-hut treecode. at that point, since n is >10,000, log n would be practically constant and thus nlogn is practically linear. meaning the frame rate will drop proportionally to the particle count, rather than the particle count squared. however, the frame rate is already pretty low, at about 15 fps. so it wouldn't be practical, i'd have to up the computing power, and in terms of Mhz they don't go much higher, so that means multi-gpu. and multi-gpu means memory transfers over the PCI bus, which would bottleneck the system, so it wouldn't really grow at nlogn 'cause it would be i/o limited now.

point being that without some elegant algorithmic solution to the i/o bottleneck (e.g. some kind of dynamic repartitioning), i'm pretty close to the current technological limit here. so if by "far along" you mean computational power, i'm about as "far along" as i can get.

if by "far along" you mean in the development of the computer code, then i don't think i am very far along. as mentioned there is much work on visualization, diagnostics, and control over the configuration i still have to do.

happyjack27
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Postby happyjack27 » Tue Nov 30, 2010 6:53 pm

i'm probably overstating the i/o bottleneck problem. i'm just not smart enough to figure out how to solve it.

rjaypeters
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Postby rjaypeters » Tue Nov 30, 2010 9:23 pm

We really must get better contractors!

Image Image

The reduction in radius has a large impact on this model. 15 degrees between coil centers wasn't much change from where the coil centers already were at close approach. I made the 15 degrees include the coil casings:

Casing close approach = 0.239m
Coil center close approach = 0.439m

The close approaches are at the ends of the deformation. Maximum separations at the center of the opening:

Casing: 0.278m
Coil: 0.478m

I think this is the model we want.
"Aqaba! By Land!" T. E. Lawrence

R. Peters

icarus
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Postby icarus » Wed Dec 01, 2010 12:56 am

happyjack:
i'm counting on the MHD being what's important and being approximately "correct enough"


Any idea (or effort) yet of the size of your errors that have been produced with the long train of assumptions and shortcuts that you have put into your 'simulation' to get around the lack of computing power?

Without an error estimate it is really little better than an animation, pretty but little to no relevance in the big scheme of modelling.

Just hope you are not feeling left like you have wasted your time, but I think you have had fair warning.

happyjack27
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Postby happyjack27 » Wed Dec 01, 2010 1:53 am

oh i have a good estimate of the error margin. i'm not worried.

just wish it was about 10x faster and had about 1,000x as many particles. but for that i'd need to witch to nlogn algorithm and have 10k the computing power. this is really about the lowest error margin available for the hardware i have, without a dramatic decrease in simulation speed, or adding assumptions. i choose this particular method because it had the least assumptions. i'm sticking with that. and the sim speed is slow enough as is. so like i said, my error margin is at a practical minimum for my hardware and simulation speed.

i know the weaknesses and approximations in the algorithm and i'm comfortable with them.

rjaypeters
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Location: Summerville SC, USA

Postby rjaypeters » Wed Dec 01, 2010 12:02 pm

Code: Select all

//Deformed coils, 15 deg. central angle, 1m central radius
//deformed coil perimeter (ideal and segmented) = 3.964m
//Unbent coil radius = 0.6305m; ideal unbent circumference = 3.962
//segmented unbent circumference = 3.968
//+x coil deformed begins
32
0.911, 0.572, 0.0, 0.903, 0.566, 0.113
0.903, 0.566, 0.113, 0.877, 0.877, 0.226
0.877, 0.877, 0.226, 0.830, 0.511, 0.341
0.830, 0.511, 0.341, 0.776, 0.446, 0.446
0.776, 0.446, 0.446, 0.776, 0.350, 0.524
0.776, 0.350, 0.524, 0.776, 0.241, 0.583
0.776, 0.241, 0.583, 0.776, 0.123, 0.618
0.776, 0.123, 0.618, 0.776, 0.0, 0.631
0.776, 0.0, 0.631, 0.776, -0.123, 0.618
0.776, -0.123, 0.618, 0.776, -0.241, 0.583
0.776, -0.241, 0.583, 0.776, -0.350, 0.524
0.776, -0.350, 0.524, 0.776, -0.446, 0.446
0.776, -0.446, 0.446, 0.776, -0.524, 0.350
0.776, -0.524, 0.350, 0.776, -0.583, 0.241
0.776, -0.583, 0.241, 0.776, -0.618, 0.123
0.776, -0.618, 0.123, 0.776, -0.631, 0.0
0.776, -0.631, 0.0, 0.776, -0.618, -0.123
0.776, -0.618, -0.123, 0.776, -0.583, -0.241
0.776, -0.583, -0.241, 0.776, -0.524, -0.350
0.776, -0.524, -0.350, 0.776, -0.446, -0.446
0.776, -0.446, -0.446, 0.776, -0.350, -0.524
0.776, -0.350, -0.524, 0.776, -0.241, -0.583
0.776, -0.241, -0.583, 0.776, -0.123, -0.618
0.776, -0.123, -0.618, 0.776, 0.0, -0.631
0.776, 0.0, -0.631, 0.776, 0.123, -0.618
0.776, 0.123, -0.618, 0.776, 0.241, -0.583
0.776, 0.241, -0.583, 0.776, 0.350, -0.524
0.776, 0.350, -0.524, 0.776, 0.446, -0.446
0.776, 0.446, -0.446, 0.830, 0.511, -0.341
0.830, 0.511, -0.341, 0.877, 0.547, -0.226
0.877, 0.547, -0.226, 0.903, 0.566, -0.113
0.903, 0.566, -0.113, 0.911, 0.572, 0.0
//+x coil deformed ends
//+y coil deformed begins
32
0.572, 0.911, 0.0, 0.566, 0.903, -0.113
0.566, 0.903, -0.113, 0.547, 0.877, -0.226
0.547, 0.877, -0.226, 0.511, 0.830, -0.341
0.511, 0.830, -0.341, 0.446, 0.776, -0.446
0.446, 0.776, -0.446, 0.350, 0.776, -0.524
0.350, 0.776, -0.524, 0.241, 0.776, -0.583
0.241, 0.776, -0.583, 0.123, 0.776, -0.618
0.123, 0.776, -0.618, 0.0, 0.776, -0.631
0.0, 0.776, -0.631, -0.123, 0.776, -0.618
-0.123, 0.776, -0.618, -0.241, 0.776, -0.583
-0.241, 0.776, -0.583, -0.350, 0.776, -0.524
-0.350, 0.776, -0.524, -0.446, 0.776, -0.446
-0.446, 0.776, -0.446, -0.524, 0.776, -0.350
-0.524, 0.776, -0.350, -0.583, 0.776, -0.241
-0.583, 0.776, -0.241, -0.618, 0.776, -0.123
-0.618, 0.776, -0.123, -0.631, 0.776, 0.0
-0.631, 0.776, 0.0, -0.618, 0.776, 0.123
-0.618, 0.776, 0.123, -0.583, 0.776, 0.241
-0.583, 0.776, 0.241, -0.524, 0.776, 0.350
-0.524, 0.776, 0.350, -0.446, 0.776, 0.446
-0.446, 0.776, 0.446, -0.350, 0.776, 0.524
-0.350, 0.776, 0.524, -0.241, 0.776, 0.583
-0.241, 0.776, 0.583, -0.123, 0.776, 0.618
-0.123, 0.776, 0.618, 0.0, 0.776, 0.631
0.0, 0.776, 0.631, 0.123, 0.776, 0.618
0.123, 0.776, 0.618, 0.241, 0.776, 0.583
0.241, 0.776, 0.583, 0.350, 0.776, 0.524
0.350, 0.776, 0.524, 0.446, 0.776, 0.446
0.446, 0.776, 0.446, 0.511, 0.830, 0.341
0.511, 0.830, 0.341, 0.547, 0.877, 0.226
0.547, 0.877, 0.226, 0.566, 0.903, 0.113
0.566, 0.903, 0.113, 0.572, 0.911, 0.0
//+y coil deformed ends
Last edited by rjaypeters on Fri Dec 03, 2010 9:57 pm, edited 1 time in total.
"Aqaba! By Land!" T. E. Lawrence

R. Peters


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