Magnetodynamic Instabilities in a Plasma-Beam System

It is well known that Alfvén waves may be excited in a plasma-beam system. It is found in this investigation that such excitation is different for an ordinary (Alfvén-$O$) wave and for an extraordinary (Alfvén-$X$) wave. An Alfvén-$O$ wave is characterized by a nonisotropic velocity distribution. However, the instability behavior for such a wave is found to be isotropic, i.e., the excited frequency and the rate of growth are independent of the direction of propagation of the wave. On the other hand, an Alfvén-$X$ wave has an isotropic velocity distribution, but its instability behavior is found to be nonisotropic. Expressions are derived for the excited frequency and the rate of growth corresponding to any direction of an Alfvén-$O$ or Alfvén-$X$ wave. An analysis is made of an excited Alfvén wave aligned along the direction of the magnetic field and a relationship given between the instabilities of linearly and circularly polarized waves. A comparison is made of instabilities produced by an electron and by an ion beam.