# Plasma Frequency And Its Meaning

When you throw a stone in a pond of calm water, what do you observe? Yes, you are right-ripples on the water surface that propagate outwards from the point where the stone had hit the water. The important highlight here is the ripples that are created have a sort of periodicity in their formation and the rate at which these ripples are formed is called the frequency. When perturbed, plasmas also form such ripples and the frequency associated with these periodic oscillations is plasma frequency. Today, I shall explain the expression of plasma frequency and the physical interpretation of its expression.

## Perturbation as the source of oscillation

To understand the concept of plasma frequency, let us consider a simple electron-ion plasma. Now, assume that a small perturbation displaces a bunch of electrons in the plasma, just as in the image below. Here, the darkened rectangles depict the alternately displaced elements of the electron fluid and the unshaded rectangles represent the elements of ion fluid in a plasma.

## The restoring force

Just as in the image, the bunching of electrons gives rise to an electric field that tries to restore the electrons to their neutral positions. However, due to their inertia, the electrons overshoot the equilibrium position and begin oscillating with a frequency. This is the electron plasma frequency.

Now, one might ask the question that why the same Coulomb's electric force generated due to charge separation acts only on the electrons? The restoring force also tries to pull the ions in a direction opposite to the electrons, but the oscillations are tremendously fast and the ions are much heavier than the electrons. Hence, the ions with greater inertia are unable to respond quickly to these oscillations and remain essentially fixed in the background.

## The Physical meaning of the Plasma expression

The plasma frequency has a different numerical value for the different species in a plasma. Its dependence on various plasma parameters is as follows:

• Inversely proportional to mass: It is inversely proportional to the mass of charged particles. This means that heavier charged species have a smaller value of the plasma frequency. Hence, electrons have a much greater value of plasma frequency as compared to ions.
• Directly proportional to number density: It is directly proportional to the number density of charged particles. This means that a charged species having a higher number density have a higher value of the plasma frequency.
• Direct proportionality to charge: Particles with a higher charge have a greater value of plasma frequency.

While studying waves and oscillatory motions, the temporal and spatial scales of study must be chosen carefully. To observe electron plasma oscillations, one must consider time scales greater than plasma time periods. In other words, the plasma system must be studied for time periods greater than the plasma period (inverse of plasma frequency).

A special type of plasma is a dusty plasma. A dusty plasma consists of the heavy and micron-sized charged dust-component along with electrons and ions. Due to their high mass, the dust species have the smallest plasma frequency followed by ions and electrons.

Previous in series: The Relativistic Doppler Effect And Its Importance In Astrophysics

## Author's Message

I have studied a number of different kinds of waves and oscillations in a plasma. While studying the different waves such as dust acoustic, ion-acoustic or electron acoustic waves, plasma physicists carefully chose the time periods of observations. This largely depends upon the dynamic plasma species in a particular wave mode. I hope you like and enjoy reading this article that highlights another important aspect of studying plasmas-the plasma frequency.

## One comment

1. Julius Anggot says:

Thank you very much!!!

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