Theory of type III radio bursts in the interplanetary space: I. Derivation of permittivity tensor for the system consisting of electron beam and solar wind plasma

The tensor of permittivity for the system “electron beam - plasma of the interplanetary space” is derived in the approximation of geometrical optics. The problem is one-dimensional; all parameters such as density of the beam and of the solar wind plasma, and the induction of the interplanetary magnetic field are assumed to be dependent only on the distance to the Sun. The beam is generated by an active region during a solar flare, and it is a source of radio bursts of type III in the interplanetary space. The tensor of permittivity was obtained to close field equations by a material equation. On the basis of these equations it becomes possible to study theoretically the amplitude-frequency characteristics of the radio bursts as disturbances of the above-described beam-plasma system.