# School of PhysicsLecture Demonstration Manual

## Ei-6 Plasma Frequency

Published: Tuesday 14 March 2006 - Updated: Tuesday 29 March 2011

### Aim

To demonstrate the cutoff frequency of electromagnetic waves in a plasma.

### Apparatus

•  3 cm Microwave apparatus
•  High pressure Mercury discharge tube
•  Sodium discharge tube
•  Apertures
•  Screen

### Diagrams

Click on pictures to enlarge.

 Plasma Frequency Pic

### Description

The plasma frequency is the natural frequency of oscillation of electrons in a plasma displaced relative to the ion background.

Electromagnetic waves propagating through an unmagnetised plasma obey the dispersion relation

where k is the wave number. Consequently, waves with frequency below the plasma frequency cannot propagate in the plasma. As a corollary, waves with

incident on the plasma from outside are reflected. This is the effect that causes short wave radio signals to bounce off the ionosphere. In this demonstration a beam of microwaves passes via an aperture through a High pressure Mercury or Sodium discharge tube to a microwave receiver. The microwaves are modulated so that an audible tone is heard if the electromagnetic waves are being transmitted to the receiver. Switching on the discharge tube causes the microwaves to reflect off the plasma, so that the tone (almost) disappears. In practice the discharge tube takes a few minutes to reach full strength so it is better to warm up the lamp before commencing the demonstration. The lamp will then light almost instantaneously, giving a more dramatic effect.

In this demonstration a beam of microwaves passes via an aperture through a High pressure Mercury(or Sodium) discharge tube to a microwave receiver. The microwaves are modulated so that an audible tone is heard if the electromagnetic waves are being transmitted to the receiver. Switching on the discharge tube causes the microwaves to reflect off the plasma, so that the tone(almost) disappears. In practice the discharge tube takes a few minutes to reach full strength so it is better to warm up the lamp before commencing the demonstration. The lamp will then light almost instantaneously giving a more dramatic effect.