Linear ion acoustic waves in a density gradient

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Abstract
Both the experimental and theoretical behavior of linear ion acoustic waves in density gradients formed in a collisionless discharge plasma have been studied. The experiment and the theory both show a strong spatial growth of the density perturbation produced by the wave when the wave propagates in the direction of increasing density and a damping when the wave propagates in the direction of decreasing density. Theoretically, the growth and damping rates are found to be proportional to n01/2, where n0 is the local unperturbed density. By using the measured density profile, good agreement is found between experiment and the linearized fluid theory. Although the wave amplitude n1, itself, decreases as the wave propagates into a region of lower density, the relative amplitude n1/n0 increases. This can be expected to lead to wave steepening and shock-like behavior, as noted previously by others. The work reported here is mainly concerned with the range where the wavelength is smaller than the characteristic length of variation of the plasma density.