Free Electron Refraction

Learning Objectives

 

Introduction

This page will describe how free electrons affect EM radiation. Free electrons exist in the ionosphere; they are important for HF and lower frequency EM radiation. More details on the characteristics of ionospheric refraction will be contained in the next module. Free electrons are also present in metals, which is the reason flat smooth metal surfaces tend to reflect all types of radio frequency waves. The presence of free electrons on the surface of a mirror has the same effect on light rays. This page provides some theoretical background on why free electrons affect radio transmissions the way they do.

 

How Free Electrons Respond to EM Radiation

Play the animation, figure 1, to see the effect of an EM wave on a free electron.

In this animation, a free electron responds to an EM wave. The important point is that the electron moves in opposite phase with the EM signal.

The next animation (Figure 2) shows the same effect, but now the EM radiation is shown in wave diagram form, with the free electron shown in red responding to an EM wave packet shown in blue.

 

The Reradiation from Free Electrons

Next we see the reradiation produced by bounded electrons (Animation 3). Reradiation due to movement of a free electron. This what happens when radio waves strike a flat metal surface at right angles to the rays. This also occurs in the ionosphere when the critical frequency of the free electrons is greater than the frequency of the EM radiation and the initial radiation is in the vertical direction. The critical frequency is in the HF range of frequencies and will be discussed in the next module. Note that the forward (actually upward in this figure) reradiation is exactly opposite the initial signal, it therefore cancels it. The backward (downward) reradiation radiates in the opposite direction, effectively causing a reflection. In reality, one electron will not totally reflect an incoming ray, but the effect of many electrons is to cause a reflection.

When the initial radiation is not exactly perpendicular to the layers of the ionosphere (or a metal), the ray will not be reflected backward, but instead will reflect at the same angle as the incoming ray. To get an idea of how this reflection actually works at the atomic level, examine the following figures. As with bounded electrons, the reradiation from free electrons occurs not just in the backward or forward directions, but there is also some spreading, as shown in animation 4. Note the reradiation waves and phase lines are 180 degrees out of phase with the initial EM field.

 

Final Implications: How the Spreading of Reradiation from Free Electrons Causes an Increase in Phase Speed

The resulting wave that is transmitted through a material such as the ionosphere or a metal is a combination of the original signal and the reradiation from the electrons. A single electron only absorbs and reradiates a minuscule fraction of the original signal, but many of them act to change the phase speed enough to cause significant refraction. In order to understand how this happens, spend some time carefully examining Animation 5. This is a complicated figure and you will need to spend some time understanding what is shown.

An interesting result of the effect or reradiation from free electrons is that the phase speed of the resultant signal is actually faster than the speed of light. How is this possible? Nothing can travel faster than the speed of light, right? Don't worry, no physical laws are being broken. Although the phases of the waves travel faster than the speed of light, the actual energy, represented by the wave packet and the leading yellow line in Figure 5, still travels at the same speed as the original signal. The individual waves within the wave packet move forward relative to the wave packet, but they lose magnitude and finally disappear as they approach the leading edge of the wave packet. The speed of the wave packet, which represents the energy propagation, is called the group velocity. The phase velocity (which determines the refractive characteristics) can be greater than the speed of light, but the group velocity cannot.

An example of waves that have a faster phase velocity than group velocity are water waves. Try throwing a rock into a flat (no wind) pond. Notice that as the wave disturbance travels outward from the rock entry point, the individual waves within that disturbance move forward and eventually disappear at the front of the disturbance (i.e. wave packet). The phase speed (speed of individual waves) is twice as fast as the group velocity (speed of the disturbance) for water waves, unless the water is shallow. In the ionosphere, free electrons cause a phase velocity that is only a minuscule amount faster than the group velocity, but it has enough of an effect over a distance to cause enough refraction to reflect lower frequency EM waves back toward the surface. The index of refraction in regions with free electrons is less than one and where a gradient in free electron density and index of refraction occurs, bending of the rays takes place.

 

Summary

We have shown that it is the interaction between an initial signal and the reradiation from free electrons that causes the phase speed to speed up compared to a signal with no free electrons present. The magnitude of this speeding up effect depends on how strong the reradiation is. The reradiation depends on the natural vibration speeds of the free electrons and this in turn is a function of the density of the free electrons. Therefore, the magnitude of the refractive index depends on the free electron density and on the incoming radiation frequency. This is different from the bound electron case in VHF, UHF and EHF frequencies, where the dependence of the refractive index on frequency is negligible. In the next module we will examine in more detail the factors that control the free electron density in the ionosphere.

Waves refract or bend toward regions of lower index of refraction (i.e. lower phase speeds). Waves striking a metal surface or the bottom of the ionosphere encounter a lower index of refraction (higher phase speed) and will therefore be refracted back. Sometimes, this bouncing back is referred to as a reflection, but we have shown that these reflections are actually refractions on a microscopic level.

 

Study Questions

  1. Do free electrons vibrate in phase with incoming EM radiation?
  2. In what way is a metal similar to the ionosphere?
  3. Explain how free electrons can negate the forward movement of an EM signal.
  4. How is it possible for phase speeds to be greater than the speed of light?