What approximations can be used for modelling?

[tomclarke]

This is going to be a not very informed post, so I apologise. And please bear with my sounding stupid!

One of the interesting issues to me seems to be the extent that ion-ion and ion-electron collisions transfer energy from radial direction to tangential

Could this usefully be modelled as follows (has it been)?

Assume system is spherically symmetric (!)

At each radius specify stochastic model for ion & electron population & velocity. For each species at given radius specify:
N0 (density)
vr (mean radial velocity)

The next part is a stochastic (spherically symmetric) description of velocity distribution,which in its most general form consists of a distribution:
p(vr, vt) where these are radial and tangential velocities respectively. Symmetry ensures that tangential veloity is uniformly distributed over angle.

The simplest non-trivial description would be to assume normal and independent radial and tangential distributions, but more complex models would perhaps be interesting?

So what this style of modelling does is to reduce the spatial modelling to one dimension while allowing arbitrarily complex stochastic models of non-thermal-equilibrium behaviour.


I realise it would not answer all those questions about non-symmetric B field it would perhaps allow discussion of speed at which thermal equilibria could be reached to be more informed.

So my question is:

a) What is known about this type of modelling generally (I guess it must be used elsewhere)
b) Has it been done for Polywell non-equilibrium system in an ideal spherically symmetric approximation?
c) Could it be used to provide some info about the real asymmetric system also, or is the approximation of symmetry so extreme that no useful info can be extracted? For example, it could perhaps provide best case measures, and maybe some of the assymmetry could be approximated as artificially increased tangential velocity variance at appropriate points.

Best wishes, Tom

[TallDave]

I know Bussard did PIC simulations; not sure what if anything Nebel is doing now. There's also a paper by Chacon, Miley and some others that did some bounce-averaged Fokker modelling of ion interactions in IEC devices.