Progress in Fusor Plasma Simulations

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Nicolas Krause
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Re: Progress in Fusor Plasma Simulations

Post by Nicolas Krause » Sat Sep 11, 2021 10:03 pm

I'd contacted Matthew Lilley a few years back asking if I could see his code. He let me know he doesn't have it anymore, I believe it was written in Fortran and he indicated it was a poster for a conference, I don't know if he was trying to get funding for a project or look better on the job market but it's over a decade old at this point. I agree that the dynamics are very complex, I guess the reason I'm interested in the non-linear methods he was attempting is two fold. Firstly, it seems a good way to try and overcome some of the limitations amateurs like us have, buying a supercomputer to simulate some ungodly number of particles is a bit out of reach. Secondly, I think trying something different allows you to make different discoveries, I understand that PiC simulations are the standard for plasma modelling, and with very good reason, but I like the non-linear math and instead of trying to copy what everyone else is doing at least its a different tack.

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Liam David
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Re: Progress in Fusor Plasma Simulations

Post by Liam David » Sun Sep 12, 2021 12:34 am

I'm not trying to downplay a more analytic approach - quite the opposite. I think it complements simulations and can give some great insights, as Lilley's work demonstrates. It'd be interesting to see if I/we could replicate some of his results, and how well that lines up with his ODE... we could solve it numerically after all. To word what I meant earlier more carefully, it's important to recognize idealizations where they exist, and much work on fusors over the years has shown that they don't work quite like we thought, as in recirculation, beam-beam reactions, and all that. I'm quite the math-y guy and really do enjoy PDEs and the like....

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Richard Hull
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Re: Progress in Fusor Plasma Simulations

Post by Richard Hull » Sun Sep 12, 2021 6:20 pm

Agreed, any path to discovery and learning more about what we are doing to increase the yield is for the best, regardless of how it is arrived at, be it via simulation or in hardware. I have long believed there is no one explanation for how all fusion is done in the simple fusor.

Richard Hull
Progress may have been a good thing once, but it just went on too long. - Yogi Berra
Fusion is the energy of the future....and it always will be
Retired now...Doing only what I want and not what I should...every day is a saturday.

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Re: Progress in Fusor Plasma Simulations

Post by Nicolas Krause » Sun Sep 12, 2021 6:30 pm

Ah right, I see what you're saying Liam, yes I'd definitely agree with that. The whole art of simulating is picking the right simplifications so that the model captures the desired behaviour. I think the reason I'm interested in Lilley's work, is Richard talks a lot about how he has to condition his fusor to get good fusion numbers. The leading theory being that this is created by wall loading of the device with deuterium, this seems to be the furthest starting point for an orbit one could imagine. So the mechanism in my head is like so, a stable orbit leads to more chances to fuse, so an increase in the number of particles with stable orbits increases fusion, the best way to increase stable orbits is by starting the particles from their furthest possible point. The best way to do this is with wall loading. That's sort of the logical chain of thought I have regarding Lilley's work, no clue if people here would agree or disagree with it, but it seems to me plausible.

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Re: Progress in Fusor Plasma Simulations

Post by Richard Hull » Sun Sep 12, 2021 9:23 pm

I have always believed the walls on the long MFP in 6" and larger fusors was charged with neutral D molecules/atoms over time. Bombarding electrons at near full energy and even some neutrals of high energy pop imbedded D out at some X value of sufficient loading as Deuterons to undergo full acceleration towards the grid. Due to MFP few make it, fewer still circulate. Fusion occurs in velocity space within the spherical fusion reactor. This was pointed out by empirical experiment way back in 2004 by U of W. In 1999 Robert Hirsch told me he believed our fusion took placed in velocity space and not in a thermal environment. Velocity space includes inside the grid, but the grid represents near zero volume in the sphere related to the overall volume of the vessel.

Spheres offer only increased 360 degree volume of velocity space over a well done BOT type design. There are many other rare processes fast neutral/wall D fusions, neutral/neutral, neutral/deuteron, the list goes on and on. This is not to boost the sphere as a fusor, for I have already denigrated it for its well proven lower neutron and fusion production over other designs already extant and in use here. I work it more for aesthetics than any other reason now.

Richard Hull
Progress may have been a good thing once, but it just went on too long. - Yogi Berra
Fusion is the energy of the future....and it always will be
Retired now...Doing only what I want and not what I should...every day is a saturday.

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Liam David
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Re: Progress in Fusor Plasma Simulations

Post by Liam David » Sat Sep 25, 2021 5:59 am

Just a quick update as I work on a new and improved (read: much faster and with fewer bugs) iteration of the code. Some eye candy with ion optics:

https://youtu.be/XyJW5LpbuBE

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Nicolas Krause
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Re: Progress in Fusor Plasma Simulations

Post by Nicolas Krause » Sat Sep 25, 2021 9:37 pm

Lovely visualization Liam, are those level surfaces of ions in the video?

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Liam David
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Re: Progress in Fusor Plasma Simulations

Post by Liam David » Sat Sep 25, 2021 10:14 pm

It's the density of D2+ ions on the domain.

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Re: Progress in Fusor Plasma Simulations

Post by Liam David » Sun Oct 10, 2021 6:01 am

I've rewritten much of the code and have fundamentally changed the data storage architecture to reduce memory operations, resulting in about an order of magnitude speedup especially at large particle counts. The precision has also been reduced from double to single.

I have also focused on maximizing the performance of collisionless particle tracking, meaning simulations of several million particles evolving for several milliseconds are possible with an overnight run (with a timestep of 40ps). A common performance metric for PIC codes is particle push/boundary check operations per second, and mine achieves ~10^10/s on an RTX 3080, or very roughly 600 GFLOPS. It's a memory-limited application, so the raw FLOP performance does not come close to the maximum of about 30 TFLOPS.

Other changes include:
  • Implementing a 5-point stencil (instead of a 3-point) for the Laplacian in the electric field solver, and making it fully applicable to cylindrical coordinates by including the 1/r*df/dr term. It now accurately produces the logarithmic potentials found in cylindrical geometries.
  • Adding magnetic fields, which is accomplished by providing a magnetization density vector field M and solving a Poisson equation much like the electrostatic case. Some preliminary simulations indicate that a moderate axial magnetic field can enhance ion lifetime, as well as the phase space of stable and quasi-stable orbits. The Boris algorithm is used to push the particles.
  • Accounting for collision angle in the fusion rate calculation (work in progress).
laplacian.PNG
5-point Laplacian

magnetic.png
Magnetic field lines superimposed on electric potential

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Liam David
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Re: Progress in Fusor Plasma Simulations

Post by Liam David » Mon Oct 11, 2021 12:55 am

As I hinted at before, the simulation reproduces the color bands seen on cylindrical cathodes, as well as the off-axis beams and circumferential ring bisecting the inside. Due to all the code changes, I can now simulate steady state, which constitutes ~8e6 total particles. I'm also getting hints of what may be ion acoustic waves (or transit time resonance) at ~13 MHz... I'm slowly building confidence in the simulation, although the calculated locations of fusion reactions are not where expected, as in not within the cathode due to anomalous electron trapping. More results to come.

D2p Cathode Patterns.png
High density beamline obscured to enhance contrast

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