Dissipative instability of negative energy wave of an intense E-beam

Dissipative instabilities in a flowing system have been widely discussed in the literature, and is being sought to be applied to explain various phenomena in fusion plasma. The instabilities are accompanied by plasma heating and diffusion and can also greatly enhance plasma transport across magnetic-field lines. Physical nature of these instabilities actually is coupled with that of resistive wall modes. Physics of instabilities in flowing systems is elaborated and it may seem that one fail to encounter a variety of that with new physics. This investigation presents new type of dissipative streaming instability. Strong dissipation changes physical nature of streaming instabilities. Instability becomes of dissipative type, caused by excitation of the beam wave of negative energy. Another type of streaming instability caused by excitation of the negative energy beam wave also is known in theory. With increase in beam intensity space charge fields set an upper limit on beam current that can be transmitted through given vacuum electrodynamic system. In systems of uniform transversal geometry overlimiting e-beam instability is due to modulation of the beam density in media with negative permittivity. Influence of dissipation on this instability was considered. But in no-uniform-cross-section plasma-filled systems overlimiting e-beam instability is also due to growing of the negative energy beam wave. Superposition of the two processes that lead to excitation of the beam wave with negative energy leads to new type of dissipative streaming instability. Its growth rate has previously unknown, inverse proportional dependence on dissipation. The influence of dissipation on excitation of the beam wave with negative energy is elaborated in detail as well as the transformation of the instability to that of dissipative type. Growth rate of the instability is obtained for arbitrary level of dissipation. An approach is developed that enables to investigate the dynamics of the instability development. The space-time evolution of the instability is governed by partial differential equation of second order independently on geometry and specific parameters. Basic parameters of the instability indicate that its role can be important for understanding of the processes in fusion plasma. (author)