Why is the adiabatic coefficient different for plasma waves and regular sound waves?

What is it about?

To find the speed of waves in gases and plasmas, a so-called adiabatic coefficient is needed. The adiabatic coefficient depends on how many different ways the wave can transfer energy to particles in the gas or plasma, known as the degrees of freedom. With D degrees of freedom, the adiabatic coefficient is (D+2)/D. For sound waves in regular gases, D is always at least three in three-dimensional space. However, for plasma waves a D-value of one is found in standard wave analyses ignoring particle collisions. We quantitatively show that the appropriate value of D is determined by the ratio of the particle collision frequency to the wave frequency. At low collision frequencies, relevant to plasma waves, the wave only interacts with the degree of freedom that it directly excites. At high particle collision frequencies, relevant to sound waves, collisions transfer the energy to all available degrees of freedom.

Featured Image

Photo by Yassine Ait Tahit on Unsplash

Photo by Yassine Ait Tahit on Unsplash

Why is it important?

We answer a basic question that has been the subject of much confusion in introductory plasma physics textbooks and beyond. Adiabatic coefficients are also critical for connecting detailed microscopic (kinetic) plasma models to the macroscopic (fluid) models needed to design practical devices, including fusion reactors. We characterise the conditions required for specific values of the adiabatic coefficients to apply, which is very important for ensuring correct modelling.

Perspectives