2019_EJRNL_PP_M__MIGLIORATI_1.pdf
Terbatas  Ratnasari
» Gedung UPT Perpustakaan
Terbatas  Ratnasari
» Gedung UPT Perpustakaan
Starting from the electric fields produced by a point charge and a dipole traveling inside a circular
vacuum chamber, in this paper we derive a formalism for a complete set of equations that describe the
electromagnetic fields and the longitudinal and transverse coupling impedances arising by the interaction
of a beam with a perfectly conducting pipe in the case of elliptic geometry. The expressions, which are
valid for any frequency and beam energy, are written in terms of expansions of Mathieu functions, allow
to range from a circular geometry to the parallel plates, and show an interesting parallelism with the
well-known expressions for a circular pipe. We also obtain that, under the approximation of low
frequency, the formalism allows us to derive the Laslett coefficients for parallel plates, circular and
elliptic beam pipe.