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Electron density profile inside a cylindrical plasma with elliptical cross section in a microwave discharge

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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.

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Authors and Affiliations

  1. Department of Laser and Photonics, Faculty of Physics, University of Kashan, Kashan, Islamic Republic of Iran

    Z Eghbali & A Abdoli Arani

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  1. Z Eghbali
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  2. A Abdoli Arani
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Correspondence to A Abdoli Arani.

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Eghbali, Z., Abdoli Arani, A. Electron density profile inside a cylindrical plasma with elliptical cross section in a microwave discharge. Indian J Phys 95, 1557–1562 (2021). https://doi.org/10.1007/s12648-020-01828-x

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  • DOI: https://doi.org/10.1007/s12648-020-01828-x

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