Plasma and Debye Shielding

 

Plasma

Generally, we know three different states of matter i.e. solid, liquid and gas. But there is another fourth states of matter called plasma. Plasma is formed when the third state of matter i.e. gas is ionized by applying some energy(Heat energy at high temperature or electromagnetic field) to it. Every ionized gas will not be the plasma. To become a plasma, ionized gas must obey the two properties, They are quasi neutrality behavior and the collective behavior.

If the plasma density is very high it can block radiations like x-ray, Gamma ray etc.

Quasi neutrality behavior:

When the number of the positive charge density (ions) is equal to the negative charge density (electrons) then that behavior is called the Quasi neutrality behavior.

 Positive charge density (ions)is denoted by n_i and the  negative charge density (electrons ) is denoted by n_e.

Collective behavior:

Collective behavior in plasma means, each charge particle in plasma interact with other particles. so, to encounter the external stimulus, there is always response of many charge particles.

Debye Shielding :

Plasma has the ability to shield out the electric potential applied to it. When we apply the electric field to a single charge (positive charge or negative charge), that single charge attracts the opposite charge particle and makes a cloud(looks like a shield) of opposite charge particle around it, which is called the Debye shielding. Debye shielding is as shown in figure below. The length as indicated in the figure by red arrow line is known as the Debye length. Out of this Debye length there is no effect of the single charge. The shielding of the electrostatic field is a result of the collective behavior of the plasma particle.

Debye length is denoted by _d.

Here, to make the perfect shield thermal motion must be zero. If there is thermal motion then the charge particles around the single charge particle gets the kinetic energy and leaves the shield and then the shield is no more stronger. Thus, for the strong and perfect shielding thermal motion must be zero.

To find the Debye shielding formula we must have the two assumptions:

1.    The temperature must be finite

2.    The electron charge density i.e. n_e must be equal to the ion charge density i.e. n_i

The Debye length can be written as,

Where, Ꜫ₀ = permittivity of free space

k = Boltzmann constant

e = Charge of electron

From this relation we can see that the Debye length is inversely proportional to the square root of the number of electrons.

The number of electrons (N_d) inside a Debye sphere is given by

N_d = 4/3 π λ_d³n

Some Cases:

_d<<L  i.e. The Debye length must be lesser than the length of the container.

N_d>1 i.e The number of the particle inside the container must be greater than one because for the interaction and collision the particle must be equal to greater than one.