# Validity of approximation of rescaled dense plasma

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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?
I'm trying to simulate interactions of a relatively low-energy beam < 500 KeV and densities of about $10^6$ nucleons/$m^3$, with low-density higher-energy beams (1 MeV-1 GeV) of densities in the range of $10^3$ nucleons/$m^3$. Basically I want to have a MonteCarlo estimation of deflection of one caused by the other
Are you meaning to simulate the "macron" plasma with a PIC method, or with the $n^2$ interactions between all macrons? If you mean using a PIC method, then this is just the normal PIC method (obviously we can't simulate every particle in any reasonably sized plasma). It is quite common to use macro-particles with finite size (often called shape factors) as this helps reduce the noise in the simulation.
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