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Concept
Ion acoustic wave
Summary
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 () with a speed given by (see derivation below)
where is the Boltzmann constant, is the mass of the ion, is its charge, is the temperature of the electrons and is the temperature of the ions. Normally γe 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 γi is taken to be 3, corresponding to one-dimensional motion. In collisionless plasmas, the electrons are often much hotter than the ions, in which case the second term in the numerator can be ignored.
We derive the ion acoustic wave dispersion relation for a linearized fluid description of a plasma with electrons and ion species. We write each quantity as where subscript 0 denotes the "zero-order" constant equilibrium value, and 1 denotes the first-order perturbation. is an ordering parameter for linearization, and has the physical value 1. To linearize, we balance all terms in each equation of the same order in . The terms involving only subscript-0 quantities are all order and must balance, and terms with one subscript-1 quantity are all order and balance. We treat the electric field as order-1 () and neglect magnetic fields,
Each species is described by mass , charge , number density , flow velocity , and pressure .
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