  Propagation of an extraordinary electromagnetic wave in the vicinity of
electron cyclotron resonance surface in an open linear trap is studied
analytically, taking into account inhomogeneity of the magnetic field in
paraxial approximation. Ray trajectories are derived from a reduced dispersion
equation that makes it possible to avoid the difficulty associated with a
transition from large propagation angles to the case of strictly longitudinal
propagation. Our approach is based on the theory, originally developed by the
Zvonkov and Timofeev [1], who used the paraxial approximation for the magnetic
field strength, but did not consider the slope of the magnetic field lines,
which led to considerable error, as has been recently noted by Gospodchikov and
Smolyakova [2]. We have found ray trajectories in analytic form and
demonstrated that the inhomogeneity of both the magnetic field strength and the
field direction can qualitatively change the picture of wave propagation and
significantly affect the efficiency of electron cyclotron heating of a plasma
in a linear magnetic trap. Analysis of the ray trajectories has revealed a
criterion for the resonance point on the axis of the trap to be an attractor
for the ray trajectories. It is also shown that a family of ray trajectories
can still reach the resonance point on the axis if the latter generally repels
the ray trajectories.
  As an example, results of general theory are applied to the electron
cyclotron resonance heating experiment which is under preparation on the Gas
Dynamic Trap in the Budker Institute of Nuclear Physics [3].
