Any Dense plasma focus scientists here? Could you explain the effects of having the anode: with less number of rods? hollow/non-hollow?
I am not an expert - but I have experience looking at these concepts.
The geometry of the rods would be compared to the geometry of the plasma. There are probably some dimensionless ratios that would come out of any analysis. For example, the distance between the rods and the mean free path of the plasma. Lets look at the geometry of a pinch device:
This is a simplification. The real device has a smooth shape, with curved electrodes (probably a pretty important detail). This diagram covers devices which are symmetric. If the rods were oddly spaced, then this would not cover the idea. Above are some equations you can write about the geometry. Now look at the "geometry" of plasmas:
It is worth pointing out what a few of these terms really mean.
The Columbic Logarithm: this is a measure of a plasma. It is connected to the distance that one ion can move before it smacks into another ion. It is normally a value from 15 to 25 [A].
The Mean Free Path: The average distance an ion can move before it smacks into another ion. How is it different from the columbic logarthim? IDK, I have been asking that for years.
The Debye Length: Beyond this distance, my particle cannot "see" your particle. I.e. the field made by your charge cannot effect my behavior if your beyond this length.
Quasi-nuetral: There are the same number of (+) and (-) charges in a space. This is not always true in plasmas and many people assume it too quickly. That said, when there is too much of one charge, instabilities can form.
There are probably dimensionless ratios here. Here are a few off the top of my head:
- Debye Length/Diameter = ?
- Debye Length/Space = ?
- Debye Length/Depth = ?
- Number of ions/Number of electrons = ?
What your getting into is a very common issue for all these fusion devices (fusors, the LDX, polywells, dynomaks, pinches): input variables and modes of operation. Any device has inputs. These are like knobs. You can adjust them. For example: you can have 4, 18 or 34 rods; you can have dense or light plasma. From these variables, arises the operating space. There are regions of the operating space (modes of operation). Say there are 4 modes of operation and 3 of them suck. You want to run your device in the region that does not suck.
It can take years to map out modes of operations in new machines. The ideal way to do it is with dimensionless numbers. This shrinks the operating space. It means you need to run fewer tests. This type of thinking is called Dimensional Analysis. It arose over 100 years ago [B]. Practicing this is not easy and frankly, dimensional analysis is more art than science.
A. Lyman J Spitzer Book "Physics of Fully ionized gases"