Propagation of sound in glow discharge plasma

Abstract

Propagation of sound in a medium where the rate of local heat addition is a function of gas density is analysed theoretically and the results are applied for modelling the experimentally observed effect of amplification of acoustic waves by an extended glow discharge in air. The model adequately describes the experimental dependences of the gain on the wave frequency and discharge power density and predicts that the amplification of sound by an unconfined glow discharge in air increases with discharge current density but does not change noticeably with gas pressure when the current density is kept constant. Quantitative estimates indicate that a gain of as high as 1 m−1 (or 9 dB for a 60 dB wave passing through 1 m of plasma) could be realized using a discharge in air with a current density of 100 mA cm−2.

Propagation of acoustic waves in a medium with the Rayleigh energy release mechanism

“…A hydrodynamic model of the plasma as the Ray leigh medium was studied in [14]. We remind that the essence of the Rayleigh mechanism lies in additional release or absorption of heat in a medium upon a change in its density.…”

“…We remind that the essence of the Rayleigh mechanism lies in additional release or absorption of heat in a medium upon a change in its density. A local relation between the amount of released Joule heat and the density of the medium was derived and the boundaries of its applica bility were determined in [14]. On the basis of this relation, the equation describing the propagation of acoustic waves in the plasma was derived, and its solu tion was obtained for the problem of evolution of the initial perturbation in the form of a plane harmonic wave.…”

“…2) and not the initial (problem no.1) conditions. Note that such analysis is carried out for the first time; in earlier theoretical studies devoted to the computations of the coefficient of the sound amplification in a plasma and to analysis of the plasma acoustic stability, the problem with the initial conditions was considered (see, for example [1,2,4,14]). …”

“…THEORETICAL ANALYSIS We will use the notation adopted in [14] and con sider the 1D case. The equation of propagation of monochromatic acoustic waves with frequency ω 0 and wavenumber k 0 in a weakly ionized plasma of a self sustained gas discharge, written in dimensionless coordinates, has the following form [14]: (1) where τ = ω 0 t and z = k 0 x are the dimensionless time and coordinate, respectively; u is the mass velocity of the gas;…”

“…(2) is the energy input parameter; g = Q/γP 0 ; ρ 0 is the gas density in the absence of the wave; P 0 is the pressure in the absence of perturbations; γ is the gas adiabatic index; and Q(x, t) is the power released in the plasma per unit of volume (see [14]). Using the expressions obtained for quantity Q in [14], we can estimate the ∂ ∂τ value of parameter b.…”