Abstract :
The basic equations governing the small-signal oscillations in a cylindrical beam of electrons is studied, and it is shown that, in addition to the usual space-charge solution, there exists another, separate, infinite set of modes which are much more closely associated with the cyclotron angular frequency, ¿c, of the collimating magnetic field. It is found that the angular frequency associated with each of these `magnetic¿ modes always lies between ¿c and (¿c2+¿02)1/2, with the exception of one which equals ¿c. Here ¿0 is the Langmuir-Tonks characteristic angular frequency of the beam. A discussion of the amplitudes of these `magnetic¿ modes is included.
