CMA diagram

The CMA diagram (Clemmow-Mullaly-Allis diagram) is a compact way of representing the solutions of the dispersion relation of an electromagnetic wave radiated into a plasma .

In 1953 PC Clemmow and RF Mullaly introduced a plot that WP Allis took over in a slightly modified form in 1959, which is why today we speak of the Clemmow-Mullaly-Allis or CMA diagram for short.

Basics

Two phenomena are important for the propagation of electromagnetic waves in the plasma: Without an external magnetic field , electromagnetic waves can only propagate in the plasma if their frequency is greater than the plasma frequency (therefore, for example, the terrestrial ionosphere is impermeable to radio waves in the medium wave and long wave short wave range ) . Waves of lower frequency only cause the electrons to "rock back and forth" on the surface of the plasma and are reflected. In the case of plasmas in an external magnetic field, it must also be taken into account that the electrons are deflected by the magnetic field. As a result, on the one hand, electromagnetic waves of a higher frequency can still pass through the plasma; On the other hand, the incident wave can also stimulate the cyclotron resonance of the electrons (i.e. the electrons are stimulated to form circular paths in the magnetic field) and are thereby strongly influenced ( resonance ). At high magnetic fields, the deflection of the positive ions in the magnetic field or their cyclotron resonance also has an effect .

The CMA diagram

The square of the ratio of the plasma frequency and the frequency of the incident wave is plotted on the x-axis ( abscissa ) of this diagram . The y-axis ( ordinate ) is the square of the ratio of the cyclotron frequency (gyration frequency) of the electrons and the frequency of the radiated wave. ${\ displaystyle \ omega _ {p}}$ ${\ displaystyle \ omega}$ ${\ displaystyle \ omega _ {c}}$

The points on the x-axis therefore correspond to a magnetic field of zero ( = 0), here you get wave propagation up to . Since the square of the plasma frequency is proportional to the electron density, the x-value increases with the density of the plasma (or the degree of ionization). ${\ displaystyle \ omega _ {c}}$ ${\ displaystyle \ omega _ {p} ^ {2} / \ omega ^ {2} = 1}$

As the y-value in the diagram increases, the external magnetic field increases; at the cyclotron frequency of the electrons is reached. ${\ displaystyle \ omega _ {c} ^ {2} / \ omega ^ {2} = 1}$

If the plasma density and the magnetic field are kept constant, then increasing distance from the origin corresponds to a decrease in the frequency of the incident wave.

The CMA diagram is divided into different zones, which correspond to different types of wave ( polarization , dependence of the speed of propagation on the direction between the magnetic field and the direction of propagation); and conditions for resonances in the plasma are shown. No wave propagation is possible to the right of a line that begins at , (cutoff). Therefore, in the CMA diagram it can be read whether or how an electromagnetic wave can propagate in the plasma under certain conditions and whether resonances occur. Conversely, by measuring the wave propagation as a function of the frequency, the plasma density, e.g. B. determine in the ionosphere. ${\ displaystyle x = 1}$ ${\ displaystyle y = 0}$

The CMA diagram applies to “cold” plasmas, ie plasmas in which the thermal movement of the particles is neglected. In addition, shocks in the plasma are neglected.

Web links

Masahisha Sugiura, Propagation of Hydromagnetic Waves in the Magnetosphere, NASA 1964 - Mathematical treatment of wave propagation in plasma (the ionosphere) and the CMA diagram (PDF, 1.9 MB)