# How is a plasma with only nuclei and electrons different?

How is a plasma with only bare nuclei and electrons, different from a plasma where the positive ions have some electrons attached?

I have looked in plasma physics books but never seen any mention of this. The behavior of a bare proton in a plasma must be different from that of, say an Argon atomic ion with charge +1.

• Recombination will increase with higher levels of ionization. Jul 16, 2019 at 20:14

There are a few different effects which will play a role, but they are usually related to ionization/recombination, and as you point out are often not treated in the literature.

I can't really claim to be an expert in ionization/recombination, but if the conditions are not such that the ions are fully ionized, then the plasma might contain a significant fraction of neutral atoms, which will affect the collision dynamics (diffusion, resistivity, etc.). This would especially be the case if you were talking about singly ionized ions such as Ar$$^{1+}$$.

A few things that I am more familiar with include:

• When ions get accelerated by some electric or magnetic force, the charge-to-mass ratio will come into play. The Lorentz force, $$\mathbf{F}_L=q(\mathbf{E}+\mathbf{v}\times\mathbf{B})$$, will generate an acceleration (non-relativistic) which is propotial to $$\mathbf{a}=\mathbf{F}_L/m\propto q/m$$.

• As an example, the gyro-radius of an ion in a magnetic field is $$r=\frac{mv_{\perp}}{qB}$$, where $$v_{\perp}$$ is the velocity component perpendicular to the magnetic field. If you go from Ar$$^{1+}$$ to Ar$$^{2+}$$, the mass will stay essentially unchanged but $$q$$ has just doubled, and hence the gyro-radius will shrink to half its size.

• Another effect can be found in laser-plasma based ion acceleration, where you want to use ultra-high intensity lasers to create a plasma and at the same time set up strong electric fields to accelerate ions with. There, the charge-to-mass ratio of the ions will govern how easy they are to accelerate. As seen in fig. 3 of this shameless plug of my own research, a much larger fraction of protons are accelerated compared to the Cs$${27+}$$ ions.

• It is also worth noting that the proton has the highest charge-to-mass ratio of all the ions. They have charge-to-mass ratio $$1e/1$$u, where $$e$$ is the elementary charge and u is the atomic mass unit, whereas other ions (even if they are fully ionized) carry with them about an equal number of protons and neutrons, giving a charge to mass ration of around $$\sim1e/2$$u.

• Then there are other exotic effects that ionization level will have on collisions between particles in the plasma. We usually treat the plasma as some form of continuous medium, but in reality they consist of individual particles. Usually when talking about collisions in plasma, we say that the effects of them scale as the ion charge squared (electron--ion collisions) or even to the forth power (ion--ion collisions). So for one, the charge state of the ion can quite significantly affect how big of an effects inter-particle collisions will have on the macroscopic plasma dynamics.

• Although you could argue that that's simply an effect of ion-charge, and not so much an effect of partial ionization. If you really want to dig deep into the difference between fully and partially ionized ions, then this shameless plug of my colleague's work (same paper but freely accessible) talks about how the collision dynamics between electrons ans ions are affected in partially ionized argon:
The basic idea is that the effects of collisions scale quadratically with ion charge (ionization level), but if you have really fast electrons, they can penetrate through the electron cloud of a partially ionized ion and effectively feel a higher ion charge in their collision than low energy electrons. In this way the fact that the ion is partially ionized affects the collision dynamics differently depending on the electron energy, in a way that would not happen with fully ionized ions.

There are probably more effects, but this is what I could think of off the top of my head.