well depth and electron counts

[bcglorf]

My background is comp sci rather than physics, so I've been wanting to write my own simulation of just the 'simple' E+M level stuff for potential well formation. Along the lines of Indrek's work. In that vein, I was wondering how one would go about calculating the electron count from the well potential. Specifically what order of electron count would WB6 have had, and what would a 15mm machine reduce that count to. 1E6 particles can be simulated in a sane time, but 1E16 not so much.

[Stefan]

I am no expert on this, but I have been trying to put something similar together for a while now, so I will write what I think I know.

For beta=1, electron density can be calculated from the energy density of the magnetic field and the kinetic energy of the electrons.

For WB6 this should be about right:

(0.13 Tesla)^2 / (2 * mu0) = e * (12500 Volt) * n
=> n = 3.4E12 electrons / cm^3

If you leave out the ions and only simulate the well formation, the electron density should be some orders lower, but since you want to simulate more than one cm^3, you still won't be able to simulate every single electron.
From the simulation I did so far, I'd estimate about E12 to E13 electrons for WB6 (on the whole, not per cubiccentimeter).

Since these are more particles than can be reasonably simulated, I'd suggest you use "macro electrons" with bigger mass and charge than real electrons have.
Until now I used constant factors of about E6 to E7, but I recently read about a similar simulation, where they specified a maximum particle count, and when that was reached they doubled the factor and removed half of the particles.

[pstudier]

For beta=1, electron density can be calculated from the energy density of the magnetic field and the kinetic energy of the electrons.

You can't assume beta=1. That is the absolute maximum pressure that excludes all the magnetic field, and is generally not achieved.

At http://www.mare.ee/indrek/ephi/ , there is a simulation of one electron which travels 11 meters before escaping. This is without collisions, that is, the machine contained only one electron. It would be very interesting to do this many times with a distribution of energies and starting locations. My suspicion is that the electrons will not cluster in the center as indicated in the logo.

Once this is done, one could calculate the electric field and see how much worse things get. Then add collisions with ions.

[bcglorf]

Thanks guys. It helps to know even a rough order, 1E12 and up particles is gonna put run time in months even for a few steps.
I know there are engineering limits that make going much smaller than WB6's 15cm diameter infeasible. If simulating just the electrons with the B field and the electric fields, how small a diameter can you go to without worrying about the physics becoming inaccurate? A .15mm device with 1E6 or 1E7 electrons might not get the electron density of WB6, but but would it be useful to at least show electron recirculation times?

A second more programing type question is for calculating/approximating the electric field of the electrons. If I take the electron density at increasing radii from the centre and calculate their contribution to the electric field that way will it mess with the physics? If there's any question I'll just have to use a standard particle density grid and bias the resolution on the centre. If this whole question is unclear I'll explain it terms less specific to simulations programming.

[drmike]

This sounds like a fun project. To make sure you get the basics, you might start with 100 electrons with a Maxwellian temperature distribution - one at each energy. Assume elastic collisions only and no walls. You can add fixed potentials at specific radius and see if particles with enough energy can penetrate that radius. This should give you a pretty interesting distribution over time.

Then increase dimensions, numbers of electrons and add complexity like wall collisions and finite structure to the magnetic coils. You can profile the code and find out where the longest computations are, then come up with better models for those sections. The process of tweaking will allow you to get to much larger numbers of electrons with some confidence that the code is telling you reasonable data.

Good luck - it really sounds like a neat problem to work on!

[bcglorf]

This sounds like a fun project. To make sure you get the basics, you might start with 100 electrons with a Maxwellian temperature distribution - one at each energy. Assume elastic collisions only and no walls. You can add fixed potentials at specific radius and see if particles with enough energy can penetrate that radius. This should give you a pretty interesting distribution over time.

Then increase dimensions, numbers of electrons and add complexity like wall collisions and finite structure to the magnetic coils. You can profile the code and find out where the longest computations are, then come up with better models for those sections. The process of tweaking will allow you to get to much larger numbers of electrons with some confidence that the code is telling you reasonable data.

Good luck - it really sounds like a neat problem to work on!

Elastic collisions and no walls would be pretty much a typical gravity simulation with slightly different force and mass calculations I think.
I'm thinking of only including collisions with the magrid and leaving out direct electron collisions. Adding electron-electron collisions moves immediately from O(N+Ng) to O(N^2) algorithms(with Ng being the electron density grid ). In practice that moves us from 1E6 particles to 1E3, in the same runtime. I'm also gonna assume the enclosing vacuum chamber is infinite.
If I simulate a .15mm diameter machine with 5keV electrons, are electron collisions gonna be significant to overall behaviour? Intuitively I figure that electron recirculation and order of magnitude life times should be alright when testing as few as 1E7 electrons. I'm thinking, even in a .15mm cubic polywell that should be a lowish electron density and overall electron collision rate.
Maybe a better question is what electron density do I need to start considering electron collisions at to remain order of magnitude accuracy?

[pstudier]

Thanks guys. It helps to know even a rough order, 1E12 and up particles is gonna put run time in months even for a few steps.
I know there are engineering limits that make going much smaller than WB6's 15cm diameter infeasible. If simulating just the electrons with the B field and the electric fields, how small a diameter can you go to without worrying about the physics becoming inaccurate? A .15mm device with 1E6 or 1E7 electrons might not get the electron density of WB6, but but would it be useful to at least show electron recirculation times?

Start simple. Just do a few electrons one at a time. That is, ignore collisions. Then average their density to calculate an electric field. One needs to know whether there is a loss cone like a mirror machine.

A second more programing type question is for calculating/approximating the electric field of the electrons. If I take the electron density at increasing radii from the centre and calculate their contribution to the electric field that way will it mess with the physics? If there's any question I'll just have to use a standard particle density grid and bias the resolution on the centre. If this whole question is unclear I'll explain it terms less specific to simulations programming.

Sounds like a good approach. One might have to do a few iterations. Calculate density from the trajectories, then calculate the electric field, then redo the trajectories to see how they change. My suspicion is that the electrons will not be confined in the center like the logo, but will resemble the levitated dipole. See http://en.wikipedia.org/wiki/Levitated_Dipole

[bcglorf]

Start simple. Just do a few electrons one at a time. That is, ignore collisions. Then average their density to calculate an electric field. One needs to know whether there is a loss cone like a mirror machine.
Sounds like how I was planning going at it. I was going to introduce electrons one at a time, injecting them at say 5keV along a cusp line. Then continuing to add them until there are a maximum of 1E6 or 7. Averaging their density for the electric field is what I was clumsily trying to get across. I wasn't sure about averaging the density by radius or just over a traditional square grid. Shouldn't take terribly long either way to put something that simple together, I just need to make the time(parenting can make that tricky).

[MSimon]

http://wwwsoc.nii.ac.jp/aesj/division/f ... hikawa.pdf

The above has actual experimental results.

[bcglorf]

http://wwwsoc.nii.ac.jp/aesj/division/f ... hikawa.pdf

The above has actual experimental results.

I found the same groups simulation work from 1997 that the above paper is a follow up to even more interesting. This from the summary:
The results strongly suggest that the high neutron production rate should be attributed to the unstable behaviour of the potential, i.e. the intermittent peaking of the density in the central region. The scaling of the neutron production versus the ion current is attractive in applications of IEC to a neutron source or a fusion reactor, even when there is a large spread of the ion energy distribution caused by the Coulomb collisions.

After reading Bussard's description of the 'correct' model of the physics inside the potential well, the above is very similar.
Yoshikawa actually got another paper published this month for applications of his IEC improvements for land mine detection. Looks like a funding move though with much bigger hopes than just neutron production reading the above.

[jlumartinez]

bcglorf,
Do you have any link to the new Yoshikawa paper?At lest to read the abstract

[bcglorf]

bcglorf,
Do you have any link to the new Yoshikawa paper?At lest to read the abstract

It's published in volume 261 of Nuclear Instruments and Methods in Physics Research Section B. The article is titled "Research and development of a compact discharge-driven D–D fusion neutron source for explosive detection". My uni has access to the full article through science direct, but I can't find any links with google to even the abstract. I'll chance posting it, I don't believe that's generally a problem? Hopefully the copyright mafia don't mind, I'm sure the researchers won't.

abstract:
Current results are described on the research and development of the advanced humanitarian landmine detection system by using a compact discharge-type fusion neutron source called IECF (Inertial-Electrostatic Confinement fusion) devices. With a 50 mm-thick water-jacketed IEC device (IEC20C) of a 200 mm inner diameter, it can produce 107 neutrons/s stably in CW mode for 80 kV and 80 mA. Ample 10.8 MeV γ-rays produced through (n, γ) reaction with nitrogen atoms in the melamine (C3H6N6) powder (explosive simulant) are clearly measured by a BGO-NaI-combined scintillation sensor with distinct difference in cases with and without melamine. This proves feasibility of the identification of the buried landmines.