Ion acoustic wave

In plasma physics, an ion acoustic wave is one type of longitudinal oscillation of the ions and electrons in a plasma, much like acoustic waves traveling in neutral gas. However, because the waves propagate through positively charged ions, ion acoustic waves can interact with their electromagnetic fields, as well as simple collisions. In plasmas, ion acoustic waves are frequently referred to as acoustic waves or even just sound waves. They commonly govern the evolution of mass density, for instance due to pressure gradients, on time scales longer than the frequency corresponding to the relevant length scale. Ion acoustic waves can occur in an unmagnetized plasma or in a magnetized plasma parallel to the magnetic field. For a single ion species plasma and in the long wavelength limit, the waves are dispersionless (${\displaystyle \omega =v_{s}k}$) with a speed given by (see derivation below)

where ${\displaystyle K_{B}}$ is Boltzmann's constant, ${\displaystyle M}$ is the mass of the ion, ${\displaystyle Z}$ is its charge, ${\displaystyle T_{e}}$ is the temperature of the electrons and ${\displaystyle T_{i}}$ is the temperature of the ions. Normally γ_e is taken to be unity, on the grounds that the thermal conductivity of electrons is large enough to keep them isothermal on the time scale of ion acoustic waves, and γ_i is taken to be 3, corresponding to one-dimensional motion. In plasmas, the electrons are often much hotter than the ions, in which case the second term in the numerator can be ignored.

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