Three-dimensional modeling of microwave discharges in a waveguide-based plasma source with experimental comparison

This paper proposes a transient three-dimensional model to simulate microwave-induced discharges in a waveguide-based plasma source under intermediate pressures. A plane-symmetric simplification method is applied to simplify half of the microwave plasma source in the calculation domain, dramatically reducing the demand for computational resources and calculation time. Meanwhile, the numerical simulations remain in three dimensions without dimensionality reduction, which allows us to directly calculate the efficiency of power coupling from the incident microwave to the plasma. Besides, the computation decrease improves the convergence performance of the mathematical model, making it possible to model the entire discharge process from $1\times {10}^{-9}$ to $1\times {10}^4\mathrm{s}$. This period covers the instantaneous microwave breakdown to the formation of a stable plasma column near steady state. The results have revealed the electromagnetic waveguide structure change of the microwave plasma source during the discharge process. Several microwave power-coupling efficiencies of the waveguide-based plasma source with different thicknesses and permittivities of the glass tube are calculated and compared with the experimentally measured data. Furthermore, the effects of the glass tube on the electromagnetic modes of the traveling microwave propagating along the plasma column and the discharge properties are also investigated. The numerically obtained results generally agree with the theoretical analysis and the experimental data in our previous studies, demonstrating the validity of the proposed mathematical model and the plane-symmetric simplification method.

Figure 1

Schematic diagram of the MPS and its calculation domain: (a) structure chart, and (b) computational domain.

Figure 2

Calculation procedure.

Figure 3

Variation of the electron number density ($1/{\mathrm{m}}^3$) distribution at different times ($P=1000\mathrm{Pa};P_{\mathrm{in}}=200\mathrm{W};D_g=4\mathrm{mm};\mathrm{and}{\varepsilon }_g=3.5$).

Figure 4

Variation of the microwave electric field (V/m) distribution at different times ($P=1000\mathrm{Pa};P_{\mathrm{in}}=200\mathrm{W};D_g=4\mathrm{mm};\mathrm{and}{\varepsilon }_g=3.5$).

Figure 5

Variation of the $S_{11}$(dB) parameter at different times ($P=1000\mathrm{Pa};P_{\mathrm{in}}=200\mathrm{W};D_g=4\mathrm{mm};\mathrm{and}{\varepsilon }_g=3.5$).

Figure 6

Axisymmetric and nonaxisymmetric microwave electric fields (V/m) in the discharge tube. ($P=1000\mathrm{Pa};P_{\mathrm{in}}=200\mathrm{W};\mathrm{and}{\varepsilon }_g=3.5$).

Figure 7

Distributions of the microwave electric field (V/m) and the electron number density ($1/{\mathrm{m}}^3$) in the MPS ($P=1000\mathrm{Pa};P_{\mathrm{in}}=200\mathrm{W};D_g=6\mathrm{mm};\mathrm{and}{\varepsilon }_g=1.5$).

Figure 8

Effects of the thickness of the glass-tube wall on the microwave power-coupling efficiency and comparison between experimental and numerical results ($P=1000\mathrm{Pa};P_{\mathrm{in}}=200\mathrm{W};\mathrm{and}{\varepsilon }_g=3.5$).

Figure 9

Effects of the dielectric property of the glass-tube wall on the microwave power-coupling efficiency ($P=1000\mathrm{Pa};\mathrm{and}{P}_{\mathrm{in}}=200\mathrm{W}$).

Figure 10

Effects of the thickness of the glass-tube wall on the microwave power-coupling efficiency and comparison between experimental and numerical results ($P=500\mathrm{Pa};P_{\mathrm{in}}=200\mathrm{W};\mathrm{and}{\varepsilon }_g=3.5$).

Figure 11

Distributions of the plasma properties in the glass tubes with different wall thicknesses ($P=1000\mathrm{Pa};P_{\mathrm{in}}=200\mathrm{W};\mathrm{and}{\varepsilon }_g=3.5$).