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Comment on ‘Effect of ionization on ion acoustic solitary waves in a collisional dusty plasma’ (J. Plasma Phys. 71, 519 (2005))
Published online by Cambridge University Press: 29 June 2006
Abstract
In a recent study [1] the effect of ionization and losses on the propagation of ion acoustic solitary waves is investigated. For that purpose the corresponding source and sink terms of the form $$\begin{equation} Q_{\rm i}- \nu_{\rm L}n_{\rm i}, \label{ss}\end{equation}$$ are included in the right-hand side of the ion continuity equation. The related contribution of the source–sink effects in the ion momentum equation is then given as the above source–sink term multiplied by the ion velocity, so that the ion momentum equation used in [1]becomes $$\begin{equation}n_{\rm i} \biggl(\frac{\partial v_{\rm i}}{\partial t} + v_{\rm i}\frac{\partial v_{\rm i}}{\partial x}\biggr)= - n_{\rm i}\frac{\partial \phi}{\partial x} - \sigma_{\rm i} \frac{\partial n_{\rm i}}{\partial x} - \nu_{\rm i} n_{\rm i} v_{\rm i} - (Q_{\rm i}- \nu_{\rm L} n_{\rm i}) v_{\rm i}.\end{equation}$$ The objective of this Comment is to show that the last term in (2) cancels out exactly, as will be shown in the further text, so that any effect originating from this term is spurious. In addition, this term implies that the velocity of the neutrals that become ions, before the impact ionization (or whatever the cause of its ionization may be), is equal to the velocity of ions that become neutrals, since this source–sink term is multiplied by the same velocity. A similar improper model has been used previously in the literature (see the references cited in [1]). It is remarked that the proper inclusion of the source–sink effects has been described in the literature before, although it seems to remain unnoticed. Therefore, it is timely to address this issue in order to provide a formally correct model for future studies.
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- 2006 Cambridge University Press