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the interface between the plasma and the surrounding dielectric, it is necessary to have an estimation of how the EM wave will interact with the flowing gas particles to creative chemically active species. The skin depth provides a basic calculation for describing penetration depth of the wave into the plasma. Skin depth is defined as: 2 5.03 δ = ωσμ = σ1/2(Ohm−1 · cm−1) · f1/2(MHz) (5.3) where ω/2π = f is the MW frequency, μ0 is the permitivity of free space, and σ is the plasma conductivity given in Equation 5.4. nee2 −4 ne(cm−3) σ=mν =2.82×10 ν (s−1) (5.4) e en en Here ne is the electron density, e is the electron charge, me is the electron mass, and νen is the electron-neutral collision frequency [61]. The collision frequency can be taken as νen = k(Te) · Ng, where k(Te) is the reaction rate coefficient as a function of electron temperature, and Ng is the neutral gas density [37]. Gas density can be calculated using the Ideal Gas Law, PV = nkBT, and k(Te) can be estimated for Te = 1 eV (chosen based on results shown in Figure 5.3a) from the electron impact cross section of CO2 for momentum transfer as 6 × 10−8 cm3/s. Using an estimation of electron density of 1013 cm−3 with a gas temperature range of Tg = 300 − 3000 K, the calculated skin depth layer has a range of 7.4 mm to 23.5 mm, corresponding to gas temperatures of 3000 K and 300 K, respectively. Given that it is expected the gas temperature will be closer to the higher end of that range due to melting of the quartz tube, the discharge tube diameter should remain close to 7.4 mm for the electric field to interact with gas particles radially across the tube. This calculation of conductivity uses the cold plasma approximation assuming ω << ωpe, νen [61]. This relation holds true for a wave oscillation frequency, ω, of 2.45 GHz and an electron density of 1013 cm−3 used to calculate the plasma frequency, ωpe, resulting in the 0 87PDF Image | CO2 Conversion in a Microwave Plasma Catalyst System
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