The explanation is not complex. Higher the density, the charge in unit volume is higher, therefore a smaller displacement produces a larger screening field.

Assuming the Debye length a measure of the equilibrium displacement, you have the answer to your question.

@Gianpiero Colonna

Thank you.

I want some more information about it.

1). Does the 'screening field' means the field which screens the potential (produced due to local concentration of charges or due to the insertion test charge)?

2). What the statement ' Debye length a measure of the equilibrium displacement' means?

Thank you once again for your response.

1. The screening field is that produced by the charge separation around the test particles.

2. The debye length is the size of the non neutral region around the test particle. It is an equilibrium value, balancing the electrostatic force and the thermal diffusion of charges. For this reason i said that it is a measure of the displacement at equilibrium.

It is well known that,

The Debye length λD = (kT/4πne2)1/2 = 7.43 × 102T 1/2n-1/2 cm, which can be further simplified for an isothermal case as,

λD ~(n-1/2).

Thus, higher the constitutional population density (n) in a plasma configuration, lesser is the plasma Debye length (λD); and vice versa. I hope that this explanation is as per your desirability and expectation both.

Source Reference:

https://library.psfc.mit.edu/catalog/online_pubs/NRL_FORMULARY_13.pdf.

@Gianpiero Colonna

Now I got the point.

Thank you.

P.K. Karmakar

Thank you sir.

I know the relation between debye length and plasma density but, i did not understand that why the debye length is smaller in case of higher plasma density. But, now its clear from the explanation given by Gianpiero Colonna .

In continuation, it may be added further that the main criterion for plasma to exist is that the population of the constituent particles in the Debye sphere should be much "greater than unity (GTU)". Here, the Debye sphere represents the minimum volume needed for plasma existence. As the density increases, the electrostatic heteropolar interaction (inward, organizing) increases dominating over the thermal force (outward, randomizing) thereby resulting in the reduction in the Debye sphere, and hence, in its radius. It is of great interest that the GTU condition for plasma existence has to be fulfilled everywhere.

@P.K. Karmakar

Thank you,

I think, the condition "constituent particles in the Debye sphere should be much "greater than unity (GTU)" is because the plasma exhibits collective behavior. The explanation is below

1). Since the shielding effect is the result of the collective particle behavior inside a Debye sphere, it is also necessary that the number of electrons inside a Debye sphere be very large. (Fundamentals of Plasma Physics J. A. Bittencourt).

2). In addition to the condition, Debye length« L, "collective behavior" requires ND>>>1 (Francis F Chen).

Any further comments will be appreciated.

We assume have a plasma medium and perturb it with a potential. Since the medium is a plasma, the electrons screen the potential immediately and higher density causes the potential to be screen in lesser distance or lower Debye length.

@ Alireza Tanehkar

Thank you.

The screening of the perturbing electrostatic potential in a plasma system is performed in an existential coordination sphere (= Debye sphere) at the cost of the collective dynamics resulting from the constituent Coulombic species of opposite polarity in the system. It is the smallest 3-D volumetric zone for the plasma existence. Denser the plasma, more compact is this sphere; and vice versa. This is the physics behind the density-radius inverse relationship in the case of a Debye sphere in the plasma system.