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Modes of a plasma-filled waveguide determined by a numerical $$hp$$ method. (English) Zbl 1364.82055
Summary: We present the application of the recent physics-conforming COOL method [M. Azaïez et al., Appl. Numer. Math. 58, No. 7, 985–998 (2008; Zbl 1143.65089)] to the eigenvalue problem of a cylindrical waveguide filled with unmagnetized plasma. Using the Fourier transform only along the waveguide and not in poloidal direction, this is a relevant test case for a numerical discretization method in two dimensions (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 electrostatics. 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.

##### MSC:
 82C80 Numerical methods of time-dependent statistical mechanics (MSC2010) 82D10 Statistical mechanics of plasmas 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 35P15 Estimates of eigenvalues in context of PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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