Jefimenko's Equations and Particle-in-Cell simulation

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

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93143
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Post by 93143 »

I'm not familiar with Jefimenko's equations specifically, but I do know that PIC methods with aggregate 'super-particles' are used in fluid spray modelling. They are much more computationally expensive than Eulerian methods that simply track moments of an assumed distribution, but they are more accurate (leaving aside newer Eulerian methods like DQMOM, which can narrow the gap considerably).

Properly done, PIC simulation with aggregate particles is probably significantly less expensive than a brute-force Maxwell+Boltzmann solution, which is why it's been used in plasma simulations before. The Williams spray equation is similar to the Boltzmann equation - except that it has an extra dimension (droplet size) and the collision term is way more complicated, but it's still a rough analogy... and PIC is greatly preferred to solving the Williams equation directly...

As far as quantum computers are concerned, it looks like they might be useful for this, since memory capacity doubles each time you add a qubit. Memory is just as important as computation speed; consider a relatively simple problem: you have a grid consisting of 100 cells in each spatial and velocity dimension. That's a trillion cells, or 7.3 terabytes just to store the cell-average value of the distribution function as a double precision float - and the resolution is awful. You'd never catch the behaviour of a Polywell plasma like that; the gyroradius of a boron-11 ion at 1 keV in a 10 tesla field is 300 µm... the Debye length for a 40 keV hydrogen plasma with a density of 1e22/m³ is about 10 µm...

Naturally there are simplifying assumptions you can make. EMC2's "1.5D" simulations are most assuredly not capturing the full physics of the problem, but it sounds like they're useful in their own way. My own 1.5D Boltzmann effort, if I ever finish it, should be useful too...

rcain
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Post by rcain »

cant we just get rid of the cells altogether? (nature doesn't use them after all). just particles. my point being we are only interested in 'actual' position, velocity, etc, at certain observation/measurement windows. (i admit to being a geometric algebra/quarternian/Clifford fan).

93143
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Post by 93143 »

Well, the cells in a spray simulation are necessary to track the continuous phase. Since in a discrete plasma simulation there is no continuous phase, you might as well not bother. I guess...?

Though now that I think about it, I doubt particle simulations of a high-density plasma would be all that accurate without a preposterous number of particles...

TallDave
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Post by TallDave »

EMC2's "1.5D" simulations are most assuredly not capturing the full physics of the problem, but it sounds like they're useful in their own way
NIF was modelled using VPIC at LANL.

http://www.iop.org/EJ/article/1742-6596 ... be4d66b67c

Maybe Rick can borrow some time on the petaflop machine. Meep meep!

EDIT: Haha, Raman scattering. Haven't seen that referenced in years. Brings back memories of Corvis Corp and Dr. Huber.

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