What you seen in literature about the use of fluid plasma model is correct.

I will try to give a complementary criterium allowing you to decide when fluid model can used for plasma modelling.

When considering a small volume (or elementary volume) in your plasma domain, the question is about the collision number or the mean free path number inside such a volume.

If the collision number (or the number of mean free path) is clearly high inside each elementary volume, therefore the fluid approximation is correct. For instance, if you have an electric field in your system, we consider the fluid model is applicable if the lightest plasma species (electron) can reach inside the elementary volume an time or spatial equilibrium between the energy lost through the collisions and the energy won from the electric field so that the known local electric field approximation becomes valid. You can also consider that you can use fluid model if the collision frequency is larger than the plasma frequency. It is generally the case of the plasmas generated at higher pressure.

However if there is only a very small number of collisions or mean free paths inside such volume, the fluid model is not recommended, you need to use to solve Boltzmann equation for each plasma species or to use PIC-MCC models. It is the case of the plasmas generated at low or very low pressure.

The intermediate pressures or the boundaries between high and low pressures cannot be simply defined and require pragmatic approaches for each considered plasma case.

I hope that this can help you to find the response to your question.

Kindest regards

I would go back to Francis F. Chen https://www.springer.com/us/book/9781475704617. He did work out most of the math you are looking for, if my memory serves me right. Especially when you are looking into fluid dynamics and when it does not apply anymore and becomes more of a QM effect, which I think has not been looked into deeply enough theoretically...

I agree with both of the above so I recommend both. I need, along the same line, emphasize how important the timescales are for the selection of your approach.! A criterion might be what is lost in each aproximation:

1. In single fluid MHD you cannot detect plasma oscillations at the characteristic frequency !!! So it is applicable when the assumption of quasineutrality is justified.!

2. In the Two fluid approximation, you have almost all waves (the whole zoo) minus kinetic effects (non Maxwellian electron Tails, Landau Dumping .. etc). So if you feel that the timescales are adequate for electrons and ions to relax to Maxwellians (of different T in the general case) you may try this approach.

3. In the kinetic theory everything gets a little complicated but it is needed when you are working on wave-particle interaction, or in the presence of non thermal populations etc....

Lastly in addition to Chen who provides a nice and rigorous (and pleasant) introduction to plasma, with a lot of exercises, I may recommend the books by Dwight Nicholson and Krall and Trivepiece once past Chen.

With Best Regards

Alexander

for electrons, this is discussed in our paper

Article Simulation of electron kinetics in gas discharges

For ions and neutrals, see

Article Towards adaptive kinetic-fluid simulations of weakly ionized plasmas

thank you everyone !! for improving my understanding

I agree with most answers, Dr. Purvi Kikani, the description using fluid dynamics serves to introduce a statistical description of plasmas and goes away from the single-particle picture.

In addition the fluid dynamics serves to introduce the physical kinetics formalism into plasmas, allowing to use of the Boltzmann equation.

Best Regards.

https://www.researchgate.net/post/Is_the_plasma_theory_consistent