# Electron number density in fusion plasma

Hello everybody,

Is there a way to calculate/predict the electron number density of a plasma?

mfb
Mentor
Well, in thermonuclear fusion the plasma is fully ionized. I know in the ITER reactor they have an average electron density of 10^20 m-3. Is the Saha equation able to give me a fair approximation?

It depends on the context.

The Saha equation assumes that you have a uniform plasma in thermodynamic equilibrium. It really only takes into account the atomic processes. It's really not the right tool for understanding the density in the core of a magnetically confined plasma such as ITER. The Saha equation is more useful for colder partially ionized plasmas, such as those used in plasma processing. However, my understanding is that even here the Saha equation has limited utility.

The density is something that we can control in fusion experiments. We can fuel an experiment using gas puffing, neutral beams, and pellet injections.

The theoretical calculation of the density in magnetically confined plasmas is the subject of transport theory. This theory tries to calculate the density profile given the density sources and sinks. There are a number of different processes that give rise to different types of transport. For example there is turbulent transport, neoclassical transport, etc. In order to correctly calculate the density you have to correctly account for all the dominate types of transport. This is actually a very difficult problem with many open questions.

In current carrying devices there is also a hard stability boundary that limits the maximum density in a device. This is the Greenwald limit. The Greenwald limit is often used in design studies of tokamak reactors. Here is is assumed that the tokamak operates at some fraction of this limit.

Yes I understand. I know the Greenwald limit as a stability boundary and I thought of using this for my calculations. It is hard for an amateur to account for all the possible problems in a tokamak but at least it is fun learning new stuff. I've dealt with many of them in my research but they are so many and complicated in nature. Thank you all for your answers, they were really helpful! I appreciate it