Janus modes of Hasegawa plasma waves in a streaming and tempestuous plasma pillar

Abstract

Janus modes of the damping and growing of Hasegawa plasma waves are studied in a plasma pillar containing the dissipation and the beam energy deposition caused by tempestuous electrons and streaming ions. We find that the Janus modes split into the upper- and the lower-modes. For the upper-mode, the imaginary part of the wave frequency is negative for any parameters so that the corresponding Hasegawa space-charge plasma wave is always damped away. We found that the damping rate of the upper-mode decreases with a reduction of the pillar radius and a raising of the degree of the harmonic-roots. However, for the lower-mode, called lower-Janus mode, the wave can be either damped away or growing, depending on the wave number, streaming velocity, and geometric factor. The lower-Janus mode can be a pure growing wave with a reduction of the pillar radius. Interestingly, this growing mode turns to damping as the wave number decreases.