Excited State Distributions of Hydrogen Atoms in the Microwave Discharge Hydrogen Plasma and the Effect of Electron Energy Probabilistic Function

To understand the essentiality of the electron energy distribution function in a low-pressure discharge plasma, an experimental study is carried out on the diagnostics of microwave discharge hydrogen plasma with its discharge pressure ~1 torr in a cylindrical quartz tube. The electron kinetic temperature and density are measured by a Langmuir double probe. Number densities of electronically excited states of hydrogen atoms are experimentally examined by an optical emission spectroscopic (OES) measurement of line intensities of the Balmer series. The rotational and vibrational temperatures are observed for the Fulcher-α band spectrum of hydrogen molecule to understand the approximate value to the neutral gas temperature. The number density of the ground state of hydrogen atom is also experimentally estimated from the actinometry measurement. The electron energy probabilistic function (EEPF) is numerically calculated as a solution to the Boltzmann equation. Number densities of excited hydrogen atoms are calculated with the collisional-radiative (CR) model with experimentally measured data as input parameters. It is found that the population densities of excited states of hydrogen atoms become about one order or much larger than those determined by OES measurement if we assume Maxwellian EEPF. The CR model with the EEPF as a solution to the Boltzmann equation theoretically reproduce the experimentally measured values very well.