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where the scalar function ψ satisfies the wave equation as ∇ 2t + γ ψ = 0 (3.30) and γ, the propagation constant, is defined as γ2 = μεω2 − k2. (3.31) Here k is the wave number. For a given ω, k is determined for each solution, α, of the eigenvalue equations (3.29) [50]. kα2 = μεω2 − γα2 A cutoff frequency can be defined by setting kα = 0 in (3.32): (3.32) (3.33) (3.34) and k can be written as: γα ωα = √με kα = √μεω2 − ωα2 . An examination of (3.34) will determine if the wave will propagate in a given waveguide or not. For wave frequencies greater than the cutoff frequency (ω > ωα), kα is real and can propagate through the waveguide. For ω < ωα, kα is imaginary and thus the wave will decay exponentially in an evanescent field [50]. When an azimuthally symmetric (m = 0) surface wave is launched along the plasma column, a TM wave results with electric and magnetic field components Ez,Er,Hφ [10,65,67]. Figure 3.6 shows the radial and axial components of the electric field for the m = 0 wave. The electric field has a maximum at the plasma dielectric interface, and thus the wave is evanescent (exponentially decaying) in both directions 48PDF Image | CO2 Conversion in a Microwave Plasma Catalyst System
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