Extended-field electromagnetic model for inductively coupled plasma

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Abstract
An extended-field (EF), two dimensional (2D) model formulation is proposed for inductively coupled plasma. By extending the calculating domain of the electromagnetic (EM) field outside of the plasma discharge region, the boundary conditions of vector potential used by the standard (ST) 2D model are replaced by simpler far field boundary conditions. The extended model converges faster than the standard formulation and gives rise to consistent solutions throughout the computational domain. Vector potential equations are solved with corresponding continuity, momentum, and energy transfer equations using the commercial code `FLUENT'. The computational domain for vector potential equations are extended well beyond the induction coil region, while for all the other equations, computations are limited to the discharge region inside the plasma confinement tube. The computational results are compared with those obtained using the ST 2D model. The difference between the results of the two models is noted mostly in the entrance regions of the flow, and close to the induction coil. To validate the EF model, a load with constant electric conductivity is placed centrally in the coil region and the calculated radial profile of the axial magnetic field is compared with existing analytical solutions. The results are in good agreement within an uncertainty of 1%.

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