A strongly coupled plasma is characterized by the following attributes:

  • higher number density
  • lower particle speeds (lower temperature)
  • smaller Debye length
  • continuous electrostatic influence throughout, stronger long range interaction
  • sparsely populated Debye sphere (lower Debye Number)

Likewise, weakly coupled plasmas are characterized by the inverse attributes:

  • lower number density
  • higher particle speeds
  • larger Debye length
  • only occasional electrostatic influence, weaker long range interaction
  • densely populated Debye sphere (higher Debye number)

The number density within the Debye sphere directly contrasts with the overall number density. Does this imply that a weakly coupled plasma has Debye-sphere-sized pockets of high density plasma within the greater, low-density plasma medium? Likewise, does this imply that a strongly coupled plasma has Debye-sphere-sized pockets of low density plasma within the greater, high-density plasma medium?

At first I thought it could be up to the size of the Debye sphere but sources clearly state density not just population.

Sources: https://farside.ph.utexas.edu/teaching/plasma/Plasma/node7.html



Similar question but without a direct answer: How is it possible that a collisionless plasma has a more densely populated Debye sphere?

  • $\begingroup$ I apologize but I do not understand what you are asking here. I have been working with plasmas for over a decade and am not sure I understand why those characteristics make a plasma "strongly coupled" or "weakly coupled." In fact, I am not sure what precisely is meant by "coupled." Coupled to what? It is perfectly okay to have huge (100s of meters) or tiny (sub-micron) Debye lengths in plasmas that are both fully ionized gases and fully described as plasmas. $\endgroup$ Aug 22, 2022 at 13:36
  • $\begingroup$ This is a concept from this online textbook I've been going through: farside.ph.utexas.edu/teaching/plasma/Plasma/node7.html It says that coupling has to do with how easily the plasma can be approximated as a neutral gas with a "modified boltzmann equation"... $\endgroup$ Aug 22, 2022 at 16:32

1 Answer 1


I would not go as far as you do in your conclusions. I think the confusion comes from the wording "densely populated" which does not mean "high density". The constraint on the populations of the Debye's sphere just add a compatible constraint onto the densities. Let's take:$ \rho _{s};\lambda _{s} $ for strongly coupled plasma and :$ \rho _{w};\lambda _{w} $ for a weakly coupled one.

The population of the Debye Sphere is given by: $$ N_{D}= \rho .V \sim \rho. \lambda _{D} ^{3}$$

And we are given: $$\begin{cases}\lambda _{s} << \lambda _{w}\\\rho_{s} >> \rho_{w}\\ N_{w} >> N_{s}\end{cases}$$

The question is to know if all these constraints are compatible. It comes:

$$ \frac{ N_{s} }{ N_{w} } = \frac{ \rho _{s} }{ \rho _{w} } \big( \frac{ \lambda _{s} }{ \lambda _{w} } \big)^{3}$$

But: $\begin{cases}\frac{ \rho _{s} }{ \rho _{w} } \gg 1\\\frac{ \lambda _{s} }{ \lambda _{w} } \ll 1\end{cases} $ is not incompatible with:$ N_{s} \ll N_{w} $

  • $\begingroup$ Ok I think I understand. Using the words "densely populated" is what threw me off. like you said. The real attribute of note there is that a weakly coupled plasma has a higher number density per unit of its Debye length than a strongly coupled plasma. Is that correct to say? $\endgroup$ Aug 23, 2022 at 21:20
  • $\begingroup$ weakly coupled= mean field approximation is good. Two particle interactions are rare and negligible. $ \lambda \gg 1$ $\endgroup$
    – Shaktyai
    Aug 23, 2022 at 21:32
  • $\begingroup$ Yes but my point is the wording is incorrect. The Debye sphere of a weakly coupled plasma is not more "densely populated" going by the typical usage of the term. E.G. a "densely populated" city is one that has a high number of inhabitants per unit area. It's like saying the entirety of Africa is more densely populated than New York City because there are more inhabitants in Africa. The wording should be more like: "a weakly coupled plasma has a HIGHLY POPULATED Debye sphere, whereas a strongly coupled plasma has a MOSTLY UNPOPULATED Debye sphere." $\endgroup$ Aug 23, 2022 at 21:51
  • $\begingroup$ Going by the same analogy, a weakly coupled plasma's Debye sphere would be analogous to the size of Africa, which has many more inhabitants than NYC and is therefore highly populated. Likewise a strongly coupled plasma's Debye sphere would be analogous to the size of an apartment building in NYC, which has many less inhabitants than Africa but still has a higher number density per unit area. $\endgroup$ Aug 23, 2022 at 21:57

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