Abstract
The boundary-value problem for diffusion-controlled breakdown of gases in microwave cavities is converted to a variational principle for the square of the reciprocal of the ``effective'' diffusion length. For a cylindrical cavity excited in the TM0n0 mode, the resultant variational principle was minimized by an iterative-variational procedure. This was done for an arbitrary functional dependence on the rms value of the electric field. The resultant hierarchy of approximations to the variational principle obtained by this iterative-variational procedure was applied to a cylindrical cavity excited in the TM010 and TM020 modes, respectively, using the high-frequency ionization coefficient of Herlin and Brown. Calculations were carried out and plots of the ratio of the effective to the characteristic diffusion length as a function of the Herlin and Brown parameter β are given for various ratios of cavity depth to radius. From this theoretical investigation, it is felt that the first ten approximations to the variational principle are sufficient to provide adequate convergence for any situation encountered in practice with regard to β as well as cavity dimensions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
