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We present the results of Auroral Kilometric Radiation (AKR) measurements near the plasmapause on the ERG (Arase) satellite. The apogee of the satellite's orbit is located near the ecliptic plane, at latitudes ±30°. According to the generally accepted point of view, AKR observation is impossible in this region since it is shielded by the plasmasphere. Simultaneous measurements of AKR and local plasma density made it possible to determine that AKR in near-equatorial regions occur in plasma channels — density inhomogeneities elongated along magnetic field lines. AKR from sources located in the auroral magnetosphere is transferred by these channels to the equatorial region. This work analyzes the conditions for the capture and propagation of AKR in low plasma density channels. In the geometrical optics approximation, we have simulated the conditions for the radiation capture and propagation. The calculation results show that the proposed scheme for AKR capture into plasma channels can explain the measurement results — the radiation transfer from the auroral region to the near-equatorial region.