  Microwave heating of a high-temperature plasma confined in a large-scale open
magnetic trap, including all important wave effects like diffraction,
absorption, dispersion and wave beam aberrations, is described for the first
time within the first-principle technique based on consistent Maxwell's
equations. With this purpose, the quasi-optical approach is generalized over
weakly inhomogeneous gyrotrotropic media with resonant absorption and spatial
dispersion, and a new form of the integral quasi-optical equation is proposed.
An effective numerical technique for this equation's solution is developed and
realized in a new code QOOT, which is verified with the simulations of
realistic electron cyclotron heating scenarios at the Gas Dynamic Trap at the
Budker Institute of Nuclear Physics (Novosibirsk, Russia).
