Convective and absolute instabilities in beam−plasma systems

The linear theory of a mono−energetic electron beam interacting with a cylindrical, homogeneous, Maxwellian magnetoplasma is investigated numerically. Using standard criteria the instability of the upper branch (ω ≳ ωce; ω ∼ kzV) is shown to be either convective or absolute depending on the specific beam and plasma parameters. In the weak beam limit, nb ≪ np, a cubic dispersion equation is derived to describe the same system. The cubic equation is analyzed to show that the instability is convective when the group velocity of the plasma wave is positive. The instability is absolute when the group velocity of the plasma wave is negative and when the beam density exceeds a threshold density.