Finite difference calculations of electro-magnetic fields in arbitrary curvilinear coordinates for coaxial microwave plasma sources

We present a finite difference frequency domain (FDFD) algorithm for the vector wave equation. Employing covariant formulations, arbitrary curvilinear, non-orthogonal computational grids are mapped onto equidistant Cartesian coordinates. This provides an intrinsic method for a local increase of computational accuracy and application of standard finite difference expressions. As an example this technique is applied to the microwave plasma torch (MPT). It is shown that there is a high held plasma generating region on top of the inner conductor. The interior of this region is of comparably low electrical field strength and supposed to be responsible for the hollow structure of the plasma observed in this type of plasma source.