Contribution of surface-wave (SW) sustained plasma columns to the modeling of RF and microwave discharges with new insight into some of their features. A survey of other types of SW discharges

Abstract Plasma columns sustained by electromagnetic (EM) surface waves (SWs) not only yield stable and unambiguously reproducible gaseous discharges, but can also provide them over an unrivaled wide range of operating conditions. It means that the operating conditions of most existing radio-frequency (RF) and microwave discharges can be matched over their specific range by those of surface-wave discharges (SWDs). Such a unique attribute of SWDs allows parametric studies, i.e. the possibility of maintaining all but one of the operating conditions constant and scrutinizing the variation of that sole condition over a large enough range, such as to determine the actual influence of any given operating condition. The concept of power absorbed/lost per electron , which was initially introduced based on SWD properties, is herein developed to reveal new insightful aspects of the power balance, which can then be extended to all kinds of discharges. This approach emerged from the way that the EM SW expends its power flow P ( z ) as it propagates: it gets absorbed as d P ( z )/d z in the gas (plasma) slab delineated between the differential position z and z + d z , inducing, in that same axial interval (and not outside it), a corresponding electron density in the range of n , n + d n . In other words, the wave power is spent locally within the differential axial segments in which it is absorbed; because the plasma radius is most generally small with respect to the column length, the various phenomena occurring along the radius of the plasma column can be considered non-local and analyzed through radial averages. This distinct behavior of SWDs suggested setting θ A as the wave power absorbed per electron on average in a radial cross-section between z and z + d z from the EM E -field sustaining plasma, and θ L , the power lost in the discharge, expressed on a per electron basis, within the same corresponding axial segment. The power per electron quantities provide insight into the physical properties of DC, RF, and microwave discharges previously unknown, ignored, or misunderstood. Some corresponding examples are presented herein: (i) consider the case of the power absorbed from the EM E -field, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">A</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mover accent="true"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:mrow> <mml:mo stretchy="true">¯</mml:mo> </mml:mrow> </mml:mover> <mml:mspace width=".25em"/> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mo stretchy="true">/</mml:mo> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mi>ω</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:mrow> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , where ν is the electron collision frequency for the momentum transfer, ω , the wave angular frequency, e / m e , the electron charge to mass ratio, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:mrow> <mml:mo stretchy="true">¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>,</mml:mo> </mml:math> the mean squared value of the EM E - field. The θ A value is shown to adjust so as to compensate exactly for θ L , which is thus the dominant power parameter; as a result, the intensity of the maintenance E - field sustaining the discharge comes out as an internal parameter, i.e. it is operator independent, in contrast to what is generally believed whatever the kind of E -field sustained discharges; (ii) the smaller the volume in which power is absorbed with respect to the volume in whic

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