Jefimenko's Equations and Particle-in-Cell simulation

alexjrgreen · Post by **alexjrgreen** » Fri Dec 11, 2009 11:15 am

Has anyone tried Particle-in-Cell simulation using Jefimenko's Equations?

rcain · Post by **rcain** » Fri Dec 11, 2009 4:53 pm

.. but doesnt

...under the assumption that there is no electromagnetic field other than the one produced by those charges and currents...

make it slightly unsuitable for tackling a Polywell?

alexjrgreen · Post by **alexjrgreen** » Fri Dec 11, 2009 6:06 pm

rcain wrote:.. but doesnt
...under the assumption that there is no electromagnetic field other than the one produced by those charges and currents...
make it slightly unsuitable for tackling a Polywell?

Let's see: there are six static currents for the coils, a static distribution of charge for the magrid and dynamic point charges for the electrons and ions.

What more do you need?

rcain · Post by **rcain** » Sat Dec 12, 2009 12:07 am

... precisely that, static currents, or at least static B fields from the magrid. (a complement to Biot Savart model).

Just reading the wiki page, it suggested that it doesnt handle them easily - though, to be fair, it later says it can be extened in the case of dielectric/magnetic medium (plasma?).

i'm no expert, and i'm sure you are more qualified than me to say, but that suggests maybe its difficult to use it to model steady-state/arbitrary starting conditions in a Polywell, unless you trace the system all the way from power-up.

i certainly like the sound of his theoretical premis of 'no necessary causal link' between electric and magnetic fields.

so, back to your question i suppose, has anyone tried any code?

(Jefimenco certainly seems to have been touting his ideas for a long time. his website here - http://www.as.wvu.edu/phys/OJ/jefimenk.html)

alexjrgreen · Post by **alexjrgreen** » Sat Dec 12, 2009 11:41 pm

We need to know the charge density scalar rho (essentially the difference between the number of ions and the number of electrons) at any point and the current density vector J (the velocity of every ion and every electron multiplied by its unit charge represents a current) at any point.

We also need to know the rate of change of charge density at any point and the rate of change of current density at any point.

As well as this we need to be able to calculate each particle's retarded position - where it would have been if a beam of light from it arrives at a particular point now. For small devices and time slices of the order of 10ns (during which light travels 3m) we could use the previous position of a particle and interpolate.

From these we can calculate the E field and the B field, derive the forces on the particles and apply them.

We don't need to consider dielectric or magnetic media since we're running in a vacuum.

rcain · Post by **rcain** » Sun Dec 13, 2009 3:33 am

... so are you proposing we produce an iterative, interpolative Jefimenko model of a Polywell, using epxperimentally sampled charge density and current density at particular positions, then fold that data back into the model?

wouldnt it also be necessary to model the the surface shape/topology of the magrids as a 'fixed assembly' of point charges? (dont know how that constraint might work through the math).

(ps. found some background here - http://www.physics.princeton.edu/~mcdon ... imenko.pdf - havent read it all yet)

alexjrgreen · Post by **alexjrgreen** » Sun Dec 13, 2009 12:13 pm

rcain wrote:... so are you proposing we produce an iterative, interpolative Jefimenko model of a Polywell, using epxperimentally sampled charge density and current density at particular positions, then fold that data back into the model?

wouldnt it also be necessary to model the the surface shape/topology of the magrids as a 'fixed assembly' of point charges? (dont know how that constraint might work through the math).

(ps. found some background here - http://www.physics.princeton.edu/~mcdon ... imenko.pdf - havent read it all yet)

The static currents and charges just get added in. They're not varying and their retarded position is the same as their current one.

I would start with all the particles in the centre and see what happened.

The catch is that you need to model at least (10^20 + 10^15) electrons and 10^20 ions, so some aggregation mechanism is needed to make the simulation tractable.

rcain · Post by **rcain** » Mon Dec 14, 2009 8:05 pm

.. enormous sounding numbers, still.

agregation functions (blending perhaps), might make it more practical. but with the right sort of code/data architecture, it could be versatile.

i'm still a little concerned by the constraining assumption (wiki) quoted for the technique that

...that is no electromagnetic field coming from the infinite past

.. though willing to be guided by your greater knowlege and understanding.

as to starting things off in the centre - this seems to be a) not really what we are doing in practice, b) also contrary to the 'possible' proviso above.

how about injecting them, one by one, just like we do. it would also make it easier to verify/validate the model against othert models we already have.

if i take you reasoning correctly, i do see how the code might be pretty efficient to construct and run using this formulation.

alexjrgreen · Post by **alexjrgreen** » Mon Dec 14, 2009 8:34 pm

rcain wrote:.. enormous sounding numbers, still.

agregation functions (blending perhaps), might make it more practical. but with the right sort of code/data architecture, it could be versatile.

There are techniques for using "super-particles" - 10^10 electrons, say. As long as you can describe their spatial and velocity distributions you can calculate their contribution to J and rho and to the E and B fields.

Or you could simply define a 1nm grid and model the particles in each grid cell to achieve a comparable effect. Several people here have experience of using different sized cells depending on the local complexity of the behaviour.

rcain wrote:i'm still a little concerned by the constraining assumption (wiki) quoted for the technique that
...that is no electromagnetic field coming from the infinite past
.. though willing to be guided by your greater knowlege and understanding.

Given the size of the field we're applying through the coils, we don't really need to worry about this.

rcain wrote:as to starting things off in the centre - this seems to be a) not really what we are doing in practice, b) also contrary to the 'possible' proviso above.

how about injecting them, one by one, just like we do. it would also make it easier to verify/validate the model against othert models we already have.

Sounds good, as long as we can use "super-particles". Even if we inject one every microsecond, just 10^12 individual particles would take 12 days...

rcain wrote:if i take you reasoning correctly, i do see how the code might be pretty efficient to construct and run using this formulation.

I'll wait to see how efficient it would be, but it seems a straightforward approach.

rcain · Post by **rcain** » Mon Dec 14, 2009 8:58 pm

'super-particles' sounds interesting approach. (else grid computing perhaps - what were you thinking of running it on?). i take it this is a well provel technique/tool. if i understand it corerctly, we would be replacing 'real' populations with representative statistical objects/(assays).

can we be sure that the model will still be accessible to study, eg. electron/ion loss, thermalisation effects, fourier analysis?

alexjrgreen · Post by **alexjrgreen** » Mon Dec 14, 2009 9:56 pm

Some links:

Particle-in-cell codes

The Plasma Theory and Simulation Group

A massively parallel particle-in-cell code for the simulation of field-emitter based electron sources

DeltaV · Post by **DeltaV** » Tue Dec 15, 2009 5:59 am

Somewhat OT, but I just want to mention, in passing, Cellular Automata simulations. I'd prefer more "traditional" governing equations (if we knew what they were) for Polywell, but maybe the CA approach has something to offer for plasma dynamics...

http://www.wolframscience.com/nksonline/page-378

93143 · Post by **93143** » Tue Dec 15, 2009 6:56 pm

We know what the governing equations are for Polywell, and they're easy to implement.

http://en.wikipedia.org/wiki/Maxwell%27s_equations

http://en.wikipedia.org/wiki/Boltzmann_equation

Unfortunately modern supercomputers are not yet capable of obtaining a resolved solution...

alexjrgreen · Post by **alexjrgreen** » Tue Dec 15, 2009 8:08 pm

Hence the interest in Jefimenko's equations. Would you consider an implementation based on them likely to be more or less efficient?

Betruger · Post by **Betruger** » Tue Dec 15, 2009 10:24 pm

93143 wrote:We know what the governing equations are for Polywell, and they're easy to implement.

http://en.wikipedia.org/wiki/Maxwell%27s_equations

http://en.wikipedia.org/wiki/Boltzmann_equation

Unfortunately modern supercomputers are not yet capable of obtaining a resolved solution...

Would quantum computing in the near future be up to it?