Electron density profile inside a cylindrical plasma with elliptical cross section in a microwave discharge
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ORIGINAL PAPER
Electron density profile inside a cylindrical plasma with elliptical cross section in a microwave discharge Z Eghbali and A Abdoli Arani* Department of Laser and Photonics, Faculty of Physics, University of Kashan, Kashan, Islamic Republic of Iran Received: 15 October 2019 / Accepted: 02 March 2020
Abstract: In a microwave discharge, the profile of electron number density inside a cylindrical plasma with elliptic cross section is analytically calculated. Using separation of variables way for the electron continuity equation (as function of position and time) and so solving it, the electron number density profile is calculated. It is shown that the profile of electron number density in a cylindrical plasma with elliptical cross section is in the form of Mathieu functions. The characteristic diffusion length for the elliptical cylinder plasma is obtained, and it is seen that it is different with the characteristic diffusion length for the circular cylinder plasma. In the steady state, the normalized density profiles of lowest even and odd modes are plotted. Furthermore, the components of normalized electron number density gradient are plotted. In the limit that plasma cylinder with elliptical cross section being converted to plasma cylinder with circular cross section, the obtained results are confirmed. Keywords: Microwave discharge; Electron density profile; Elliptical cylinder plasma
1. Introduction Microwave discharges are widely used for generation of quasi-equilibrium and non-equilibrium plasma for different applications and are the electrical discharges generated by the electromagnetic waves with frequencies exceeding 300 MHz. Microwave discharges are operated with no internal electrodes, thus reducing sputtering and contamination of the plasma from electrode materials. Microwave discharges also can remain stable over a wide range of background gas pressures, relative to DC or low-frequency RF discharges [1]. Many researchers on the gas discharge experiments by high-power microwaves have been investigated [2–8]. One of these studies is attributed to the evergrowing power of the microwave radiation sources [9], and another researches are related to the potential applications of microwave-generated plasmas, including material processing [10], communication technology [11] and plasma propulsion [12]. Besides, the experimental investigations have been studied by some researchers [13–19]. A theoretical model has been developed by incorporating a chemistry reaction set and an energy partition module into
*Corresponding author, E-mail: [email protected]
the gas discharge plasma [20]. A study has proposed a formulation, in which the number of differential equations to prescribe microwave discharge is reduced as small as possible [21]. Furthermore, the methods of microwave plasma generation, general features of microwave plasma, and selected aspects of microwave plasma diagnostics have been presented [22]. Moreover, the atmospheric pressure microwave discharge methods and devices used for pr
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