I'm trying to do a simulation of many ions. In principle, the proper way to simulate a large quantity of plasma ions is by using a Particle-In-Cell approximation in order to avoid $O(n^2)$ interactions per timestep.

However, I was wondering about another idea that occurred to me. Imagine a plasma with $n$ ions per volume unit, each of mass $m_i$ and charge $q_i$. The idea was that another plasma simulation having $n'$ macrons per volume unit, with mass $ \frac{n}{n'} m_i$ and charge $ \frac{n}{n'} q_i$, would have

- mass-to-charge ratio equal to $\frac{m_i}{q_i}$

- about the same charge and mass density as the original plasma

- if $n' << n$, the reduced system has less degrees of freedom

I haven't seen this approximation anywhere on the literature, although probably could be under some different technical term/keyword that I'm not aware. So I'm unsure how valid would be the physics obtained from the reduced plasma simulation.

Thoughts? under what situation would the reduced plasma system be expected to behave significantly different than the original system?