Nonlinear Ion-Acoustic Waves

Abstract

Consider a plasma consisting of cold ions and hot electrons. Let us consider low-frequency waves in such a plasma. The electrons will then remain in thermodynamic equilibrium at a constant temperature T _e in these wave motions with a number density given by the Boltzmann distribution

$$ {n_e} = {n_0}{e^{{e\phi /K{T_e}}}} $$

(1)

where ø is the electrostatic potential associated with the wavemotions, and n₀ is the number density of electrons (or ions) in the unperturbed state. For low frequency waves we are considering, the underlying motion is that of the ions, with the electrons merely forming a screening cloud about the ions. Usually, the charge separation due to the ion-motion is immediately screened by the electrons so that the creation of ion-plasma waves is counteracted by the electrons. However, if the electron thermal speed is large enough, the electrons will not completely shield all electrostatic fields.