A system of nonlinear equations derived in a previous paper which describes the erolution of nonresonant waves in beam-plasma systems is solved numerically. It is given a physical interpretation of essential features of the nonresonant beom-plasma instability. The significant influence of higher harmonics on the evolution of a n electron beam in the plssma which is modulated on L nonresonant unstable frequency, is investigated. The interaction of unstable nonresonant and resonant waves in beam-plasma systems is examined. It is shown that the evolution of resonant waves can be essentially influenced by an initial modulation of the beam on an unstable nonresonant frequency. The role of a n initial velocity modulation of the beam for t h r influence of the wave spectrum is demonstrated.

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.

The chaotic relaxation mechanism of a monoenergetic electron beam in a strongly dissipative plasma is investigated in the framework of the single wave theory. An information theoretical quantity is introduced that describes the information loss of the beam system in course of time. It is shown that the numerical calcolation of a discrete macroparticle approximation of the continnous beam system loses its physical relevance if the information loss exceeds a critical value which is determined by the number of macroparticles. Moreover, a method is proposed in order to qumtify the degree of chaotic behaviour of the beam-plasma system with A minimum of additional numerical effort.

An information theoretical description is given of the action of ID maps on probability measures (e.g. on ergodic invariant measures of chaotic maps). On the basis of a detailed analysis of the elements of information flow the problem of optimum measuring of initial states for state predictions is discussed. Moreover, we give an information theoretical description of the relaxation, under the action of a map, of an initial probability distribution to any, not necessarily steady, final distribution. In this connection we formulate an H-theorem for ID maps.

The evolution of a resonant triplet of linearly stable electrostatic waves in a beam-plasma system is considered. A set of nonlinear ordinary differential equations is derived, which allow an investigation of the explosive instability with minimum numerical expense. Our model is different from the well known single wave model in taking into consideration the nonlinear susceptibility of the plasma and in making use of the ponderomotive force description. Maximum values of the wave amplitudes are obtained numerically and it is shown that the saturetion of the explosive instability is due to different trapping mechanisms of the beam electrons by the excited waves.