Resonant Wave‐Particle Interaction in an Explosively Unstable Beam‐Plasma System. I. Derivation of a System of Nonlinear Equations and Numerical Evaluation of the Saturation Field Strength

1987

Self Cite

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.

“…It should be mentioned that there are some advantages of the second approach (see sect. 3), however, generalIy the disadvantages in comparison to the usual approach (5) are predominant :…”

Section: (7)mentioning

confidence: 98%

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

1987

Self Cite

Resonant Wave‐Particle Interaction in an Explosively Unstable Beam‐Plasma System II. Investigation of the Relaxation Behaviour of the Electron Beam

Leven

1985

Three typical saturation mechanisms of the explosive instability (EI) in a beam-plasma system are investigated. It is shown that the maximum values of the electric field strengths of the erplosively unstable plasma waves can be of the same order ns the maximum wave amplitude of the linearly unstablc waves. Some conclusions with regard to the role played by the EI in the evolution of a r e d beam-plasma system are presented. The relaxation of a strongly modulated electron beam by the explosive wave coupling mechanism is examined in an appendix. A qualitative interpretation of the diversity of the EI saturation mechanisms found in this investigntion is given. Features of the Electron Beam RelaxationThe numerical investigations of [ 13 (Fig. 1.3) illustrate that the solutions of our systeiii of equations are physically significant almost only in the parameter range 0 5 5 (P > 1). In this range, however, the system of equations (1.37)-(1.42) (i.e. (37) of (13 is denoted by (1.37)) simplifies and obtains the form

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

Leven

1985

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.