Thomson microwave scattering for diagnostics of small plasma objects enclosed within glass tubes

In this work, coherent microwave scattering in the Thomson regime was demonstrated for small-scale plasmas enclosed within a glass tube and validated using a well-known hairpin resonator probe technique. The experiments were conducted in a DC discharge tube with a diameter of 1.5 cm and a length of 7 cm. Thomson microwave scattering (TMS) diagnostics yielded electron number densities of about 5.9 × 10¹⁰ cm^-3, 2.8 × 10¹⁰ cm^-3, and 1.8 × 10¹⁰ cm^-3 for air pressures in the discharge tube of 0.2, 0.5, and 2.5 Torr, respectively. Measurements using the TMS technique were consistent across the tested microwave frequencies of 3-3.9 GHz within the margin of error associated with non-idealities of the IQ mixer utilized in the circuit. The corresponding densities measured with the hairpin resonator probe were 4.8 × 10¹⁰, 3.8 × 10¹⁰, and 2.6 × 10¹⁰ cm^-3. Discrepancies between the two techniques were within 30% and can be attributed to inaccuracies in the sheath thickness estimation required for correct interpretation of the hairpin resonator probe results.