Concept of power absorbed and lost per electron in surface-wave plasma columns and its contribution to the advanced understanding and modeling of microwave discharges

Microwave (MW) sustained discharges have distinct advantages over other existing types of discharges in terms of the specific understanding they can provide regarding discharge phenomena and mechanisms. First, only electrons can pick up energy from the discharge E-field since ions cannot respond to rapid oscillations above approximate to 100 MHz. A second remarkable feature of MW discharges is that their plasma sheath is stationary, unlike in radiofrequency (rf) discharges. Furthermore, the sheath voltage is low, so that the electron energy expended to sustain them can be ignored as a first approximation. These characteristics favored the development of the concept of power per electron, which involves determining the respective roles of the power absorbed per electron I9A and the power lost on a per-electron basis I9L in the equilibrium relationship between them. This led to establishing the following: (i) In the equilibrium relation of the power per electron (I9A = I9L), the power lost has precedence over the power absorbed, the latter simply adjusting to compensate for the losses. (ii) The value of the power absorbed I9A, when conforming to compensate for the losses, determines the intensity of the high-frequency E-field in the discharge, the maintenance field, construing it as an internal parameter (as opposed to an operator-set). (iii) Ensuring a smaller volume within which power is absorbed (resulting from E-field confinement) compared to the loss volume (plasma) is a way to achieve higher maintenance E-field intensity, thus higher atomic (molecular) excitation and ionization rates, as is the case, for example, with microdischarges. (iv) In pulsed-operated discharges, the E-field intensity is maximum at the very beginning of the pulse and then decreases, eventually reaching stationarity as the pulse time elapses. (v) A significant and more comprehensive similarity law is procured than for direct-current (dc) discharges. (vi) The power per electron concept is valid for all MW discharges. In the case of dc and rf discharges, where ions are also accelerated in the E-field, I9A is no longer proportional to the E-field intensity: I9A is then the power necessary to maintain an electron-ion pair in the discharge. It can be used, taking into account the operating conditions (field frequency, gas nature and pressure, and discharge vessel properties), to optimize the power consumed for a given plasma-driven process.