Theory of the diocotron and drift-beam instabilities of a relativistiic electron beam

In a joint study of diocotron and drift-beam instabilities of an annular beam, it is shown that the two instabilities can exist simultaneously but that the diocotron instability predominates because of its greater increment. The ion 'coat' of the beam leads to an increase in the drift-beam instability increment. In addition, it is found that the presence of ions inside the beam cavity leads to an increase in the diocotron-instability increment and facilitates the appearance of this instability.