The short answer would be: none of the above. Probably.
As I'm not really sure what ballistic ions or boltzmann
electrons are
![Wink ;)](./images/smilies/icon_wink.gif)
. I am a product of google and wikipedia
and I am an amateur so probably I did something unconventional,
probably something very wrong. For my dayjob I program
web pages and internet applications (mostly low level
big P2P applications - Skype).
But I do need someone telling me the truth about this so
please don't hold back. If you even bother to continue
from this point on.
I managed to reduce the calculation space using inherent
symmetries in the polywell:
http://www.mare.ee/indrek/ephi/symmetry/
http://www.mare.ee/indrek/ephi/symmetry2/
http://www.mare.ee/indrek/ephi/symmetry3/
The electric field of the coils and surrounding static
elements is calculated using this method:
http://www.mare.ee/indrek/ephi/pef2/
The magnetic field from the coils is precalculated using
the analytic equation for a ring of current (equation
given at the end of this document, seems the Dolan fusion
book is down):
http://www.mare.ee/indrek/ephi/efield_r ... charge.pdf
And during simulation through bicubic interpolation:
http://www.mare.ee/indrek/ephi/interpolate/
http://www.mare.ee/indrek/ephi/interpolate2/
I track individual electrons and at each step I recalculate
the magnetic and electric fields they see.
I calculate the fields from each individual moving charge,
summing them up. From a distance I use an aggregating grid
though (for charge and current approximations).
From close by I model individual moving electrons as
spheres of charge, and calculate the fields they generate
and their derivatives, as detailed here:
http://www.mare.ee/indrek/ephi/savart.pdf
http://www.mare.ee/indrek/ephi/vsphere.pdf
I put these calculated values into a grid so that I can apply
tricubic interpolation on them. The tricubic interpolation
algorithm I use is this:
http://www.lekien.com/~francois/papers/LeMa05/
Once I have this interpolation grid I move electrons ahead
by one step. For that I use the Runge-Kutta-Nystrom 4 with
adaptive step size:
http://www.mare.ee/indrek/ephi/nystrom.pdf
Additionally I keep the interpolation grids of two previous
steps and use them together with the latest to do Lagrange
extrapolation during the RK4 steps:
http://en.wikipedia.org/wiki/Lagrange_polynomial
Using my quad core 2.5GHz pentium I managed to calculate
one step in 5-10 seconds. One step is 1e-11 seconds (there
are up to 256 adaptive substeps done as well).
Getting anywhere like this took couple of days of calculation
so I didn't really get very far
One thing I failed to do was to check my model against
known plasma behaviour. Mainly cause I don't know much
about known plasma behaviour
![Wink ;)](./images/smilies/icon_wink.gif)
A beam of electrons
dispersed, that was about my only check for correctness.
I should probably go and try out PIC instead. But I kind
of got bored of all this for a moment there.
So here you are. For more information you can see
my ephi homepage:
http://www.mare.ee/indrek/ephi/
- Indrek