The Formation of Dissipative Structures and Chaotic Beam Relaxation in the Strongly Dissipative Beam‐Plasma Instability

Abstract

Sumerical solutions of a nonlinear system of equations describing the evolution of the strongly dissipative beam-plasma instability are presented (time or space dependence of the unstable waves, the evolution of the beam distribution function and the corresponding phase space representations are given). Such an instability establishes if the linear growth rate of the unstable waves is small in comparison to the effective collision frequency of the electrons of the dissipative plasma. It is shown that after saturation of the instability there is a n efficient energy transfer from the directed motion of the beam electrona to the thermal motion of the plasma electrons. Arguments are given that the strongly disaipative beam-plasma instability is possibly the basic plasma heating mechanism which operates in the quasi-stationary state of the benm plasma discharge. Self-consistent initial conditions are used for the numerical calculations. Formation and evolution of dissipative structures (vortex structure, chaotic structure) were observed. -4 profound investigation of the chaotic or turbulent beam relaxation mechanism is presented. Such a relaxation mechanism develop in the case of the nonresonant dissipative instability (0.g. in resistive wall-electron beam amplifiers). The method of investigation of dissipative structures presented in this paper (application of Shannon's information theory and results of the theory of dynamical systems with chaotic behaviour) can be extended to studies of other beam-plasma systems within the framework of partial kinetic description.

Limits of the Physical Relevance of Numerical Investigations of the Chaotic Beam Relaxation in an Electron Beam‐Plasma System

“…On the other hand Fig. 6 shows that the evolution of a vortex structure (sin 8 = 0.9) which represents a higher order in shape (see [4]), in comparison with the chaotic relaxation, can be calculated for a long time t with a relatively low number of macroparticles.…”

“…[2][3][4][5][6][7][8]) and is of great advantage because the transition to the N-body dynamics does not change the form of the balance equations of the physical system. On the other hand we see from (1) and (6) that the usual N-body dynamics neglects that parts of the BPL which are placed between two neighbouring macroparticles.…”

“…The present paper can be considered therefore as a continuation of [4]. The non-linear evolution of an isolated mode remains an interesting problem, either for the study of short systems or as a relatively simple example of a fundamentally important non-Iinear process.…”