**Topic/Type**:
1. Plasma Simulation, Invited

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R. ?lvarez
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Instituto de Ciencia de Materiales de Sevilla, CSIC, Sevilla, Spain IPFN, Instituto Superior T?cnico, Lisboa, Portugal
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The electromagnetic (EM) modeling of plasma reactors is an efficient engineering response to the optimization of devices, for example in view of ensuring a maximum power coupling. The plasma enters the model via the permittivity spatial distribution, which is related to the electron density and temperature. The modeling involves the solution to Maxwell\'s equations, subject to appropriated boundary conditions (Dirichlet, Neumann or mixed), whose definition usually depends on the nature of the physical device under study. In principle, the problem can be solved using standard techniques of computational electrodynamics, for example by combining a finite difference discretization scheme with a relaxation iterative algorithm (e.g. Gauss-Seidel), adopting either a time-dependent or a time-harmonic numerical resolution. However, the EM analysis of a plasma reactor generally involves its characterization for a given (applied) operating frequency, in which case Maxwell\'s equations are more adequately solved using a time-harmonic description (involving the previous Fourier expansion of the equations). This latter description leads to a boundary-value problem, whose solution should fulfill the (Neumann or Dirichlet) boundary conditions adopted, being unique for the particular operation mode considered. But using a time-harmonic description often leads to difficulties in the numerical completion of boundary conditions, particularly for field distributions with an oscillating pattern, in which case Neumann-type boundary conditions (upon the field derivatives) are difficult to meet over a multi-dimensional integration domain. In situations where convergence requires a more restrictive framework, these Neumann boundary conditions are better replaced by equivalent Dirichlet conditions, whose boundary values depend on the problem solution. Here, we use a simple numerical algorithm to manage these situations, by tailoring the Dirichlet boundary values to satisfy the physical Neumann conditions [1].

The algorithm is applied to a microwave-driven plasma torch coupled to a cylindrical metallic reactor [2], for which we have studied the dependence of the EM field distribution on the electron density and temperature profiles.

[1] R ?lvarez and L L Alves, J. Phys. D: Appl. Phys. 41(21) 215204 (2008).

[2] M. Moisan, G. Sauv?, Z. Zakrzewski and J. Hubert, Plasma Sources Sci. Technol. 3 584 (1994).