Average Electron Temperature Estimation Based on Rayleigh Scattering of Eletromagnetic Wave

As a critical parameter of plasmas, electron temperature usually differs from other temperatures for thermal nonequilibrium cases. Many diagnostic technologies have been developed such as Langmuir probe and Laser Thomson Scattering (LTS). However, Langmuir probe has a size limit to avoid changing the plasma, but the tiny probe is thus not strong enough and in risk to survive the current impact. LTS requires multiple pulses to avoid a dilemma of weak signal¹ or heating the plasma², especially for a low ionization degree situation. However, the multiple-pulse method requires or assumes that the plasma has no significant change during the measurement³. Therefore, we provide a supplemental method for electron temperature estimation. In the continuity equation of electron, the temporal derivative of electron density consists of diffusion current, drift current, and electron gain/loss events, such as ionizations, recombination, and attachments. The diffusion, drift and the rate coefficients of those events are functions of electron temperature and reduced electric field, while the temporal profile of electron density can be measured by Rayleigh scattering. Therefore, along with the electric field measured or estimated, the only unknown in the equation is the average electron temperature which can be solved numerically. An example of microwave scattering on cold atmospheric plasma jet⁴ is included for the demonstration. The plasma jet has an electron density around 10¹² cm-3 and keeps varying during its warm-up process.

As a critical parameter of plasmas, electron temperature usually differs from other temperatures for thermal nonequilibrium cases. Many diagnostic technologies have been developed such as Langmuir probe and Laser Thomson Scattering (LTS). However, Langmuir probe has a size limit to avoid changing the plasma, but the tiny probe is thus not strong enough and in risk to survive the current impact. LTS requires multiple pulses to avoid a dilemma of weak signal¹ or heating the plasma², especially for a low ionization degree situation. However, the multiple-pulse method requires or assumes that the plasma has no significant change during the measurement³. Therefore, we provide a supplemental method for electron temperature estimation. In the continuity equation of electron, the temporal derivative of electron density consists of diffusion current, drift current, and electron gain/loss events, such as ionizations, recombination, and attachments. The diffusion, drift and the rate coefficients of those events are functions of electron temperature and reduced electric field, while the temporal profile of electron density can be measured by Rayleigh scattering. Therefore, along with the electric field measured or estimated, the only unknown in the equation is the average electron temperature which can be solved numerically. An example of microwave scattering on cold atmospheric plasma jet⁴ is included for the demonstration. The plasma jet has an electron density around 10¹² cm-3 and keeps varying during its warm-up process.