Modes ofa Plasma-FilledWaveguideDeterminedby a Numerical hp Method

We present the application of the recent physics-conforming COOL method (2,4) to the eigenvalue problem of a cylindrical waveguide filled with unmagnetized plasma. Using the Fourier transform only along the waveguide and not in poloidal di- rection, this is a relevant test case for a numerical discretization method in two dimen- sions (radial and poloidal). Analytically, the frequency spectrum consists of discrete electromagnetic parts and, depending on the electron density profile of the plasma, of infinitely degenerate and/or continuous, essentially electrostatic parts. If the plasma is absent, the latter reduces to the infinitely degenerate zero eigenvalue of electrostat- ics. A good discretization method for the Maxwell equations must reproduce these properties. It is shown here that the COOL method meets this demand properly and to very high precision.