Canonical general Helmholtz equations for normally magnetized gyrotropic waveguides

From the general Helmholtz equations of hybrid HE- and EH- electromagnetic waves obtained in [1], containing all three components of electric and magnetic field strengths, the corresponding canonical general Helmholtz equations containing only longitudinal components of stresses are determined for gyrotropic waveguides with arbitrary orthogonally curved cross-sectional shapes under normal magnetization and taking into account heat losses. electric and magnetic fields. The obtained canonical general Helmholtz equations of hybrid HE- and EH- electromagnetic waves are necessary for the derivation of partial Helmholtz equations of hybrid HE- and EH-electromagnetic waves of gyrotropic waveguides with rectangular, round and elliptical cross-sectional shapes, taking into account thermal losses, which in turn allow us to pose and solve the corresponding boundary value problems.