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I am trying to make sense of the following Wikipedia page. Do you know what the charge state $Z$ is? Do you know if there is a table or list somewhere which lists these parameters but in SI units instead of Gaussian units?

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Do you know what the charge state $Z$ is?

$Z$ is the number of protons in the ions. The charge of each ion is $Ze$.

Do you know if there is a table or list somewhere which lists these parameters but in SI units instead of Gaussian units?

No, but this SI/Gaussian Formula Conversion Table should be helpful.

It is easy to find textbooks on plasma physics that use SI units. (The first one I found by web search did.)

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This may have what you're looking for: https://www.nrl.navy.mil/ppd/content/nrl-plasma-formulary

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