Consideration of DC space charge effects in the modal analysis of aperture-coupled cavities

The modal analysis of aperture-coupled cavities is frequently applied to the field theoretical analysis of high-power tube cavities and accelerating structures in high energy physics. Besides the RF electromagnetic field, DC space charge effects may also be important in such applications. Because there is no magnetic field related with DC space charges a straightforward application of the modal expansion method, which makes use of matching the aperture tangential magnetic field, to the investigation of DC space charge fields is not possible. In this contribution it is therefore demonstrated that the computation of the DC spectral component of the electric field due to space charges can also be included in the modal analysis of aperture-coupled cavities if instead of the aperture tangential magnetic field the corresponding normal electric field is matched. It is shown that even in this case the solenoidal electric eigenfunctions of the cavity have to be taken into account because of the waveguide coupling. Furthermore, the validity of the method is checked by applying it to a field problem for which a solution is already well-known from another analysis