The method of matched asymptotic expansions is applied to the fluid model of the low-pressure positive column. The expansion of the eigenvalue in the plasma balance equation is obtained to second order in plane and in cylindrical geometry, and uniformly valid expressions for charged particle densities and fluid velocity in two separate regions are indicated.The free-fall model is also examined and the scales of the transition layer and sheath layer found. Comparison is made with the results of direct numerical integration of the equations involved for both models.
In this review an attempt is made to give a broad coverage of the problem of joining plasma and sheath over a wide range of physical conditions. We go back to the earliest works quoting them, where appropriate, to understand what those who introduced the various terms associated with the structure of the plasma-sheath had in mind. We try to bring out the essence of the insights that have been gained subsequently, by quoting from the literature selectively, indicating how misunderstandings have arisen. In order to make it accessible to the generality of those currently working in low temperature plasmas we have sought to avoid mathematical complexity but retain physical insight, quoting from published work where appropriate. Nevertheless, in clarifying my own ideas I have found it necessary to do additional original work in order to give a consistent picture. In this way I have sought to bring together work in the late 1920s, the 1960s, and now mindful of the commercial importance of plasma processing, work over the past 15 years that adds to the general understanding.
This paper seeks to summarize the work that has gone on over the past 20 years in plasmas that has become of great commercial importance but was not studied in depth previously. It points up the differences between conventional electropositive plasmas and those where negative ions dominate. It removes some of the errors and misunderstandings that have occurred and tries to bring the field into a coherent consistent whole
This paper builds on earlier work to give a consistent treatment of the positive column of discharges in electronegative gases covering the transition from collisionless to collisional. In particular it seeks to elucidate the conditions under which there is an ion-ion plasma core surrounded by an electron-ion plasma, and when there is not. The parameters which describe the processes of ionization, attachment, detachment and recombination are related to the central negative ion density relative to the electron density and, where appropriate, the size of the core. The use, by earlier workers, of the Boltzmann approximation to describe the negative ion distribution and to obtain ambipolar diffusion coefficients at higher pressures is shown not to be justified. This leads to the clarification of an inconsistency in the literature. Where possible, the work is related to other recent treatments of the same problem in order to begin to build a comprehensive picture of such discharges. The need to have results which combine both detachment and recombination as the negative ion loss processes is identified as outstanding. This, when rectified, should lead to a fully comprehensive treatment.
This paper brings together recent work in low-pressure plasmas dominated by negative ions, examining in detail the structure of the plasma-sheath boundary. The parallels between negative ion-electron plasmas and two-electron-species plasmas are drawn, as are those between probe-plasma and plasma-wall systems.Particular attention is given to the parameter region where, for the temperature ratio T e /T n greater than a critical value and a range of values of the density ratio n n /n e , there is a structure where two 'plasmas', one an ion-ion plasma and the other essentially an electron-ion plasma, are separated by a potential structure. It is shown that in neither the fluid model nor in the free-fall model is the structure a simple double layer.The results of analytical and computational treatments are brought together and it is suggested that experiment may be the only way to determine the relative merits of the two models, as well as demonstrating their general validity.
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