An approach is presented that allows getting detailed information on the behavior of streaming instabilities (SI) from the dispersion relation (DR). The approach is based on general assumptions and does not refer to any particular model and/or type of the stream interaction with background system (Cherenkov, cyclotron, etc.). The basis of the approach is transformation of the DR to an equation for slowly varying amplitude of the developing waveform. The solution of the equation actually presents results of the important problem of time evolution of initial perturbation and gives detailed information on the instability behavior. Most of the information is unavailable by other methods. For particular SI, only two parameters should be specified. The expression for the fields’ structure shows that with increase in level of dissipation, SI gradually turns to dissipative streaming instability (DSI). Two new, previously unknown types of DSI are presented: DSI of overlimiting electron beam and DSI under weak beam-plasma coupling. Growth rates of these DSI depend on dissipation more critically than usual. Presented approach is valid for a large class of SI: beam-plasma instabilities of various types (Cherenkov, cyclotron, etc.) including over-limiting e-beam instabilities, the instability in spatially separated beam-plasma systems, Buneman instability, etc.
Part of the book: Plasma Science and Technology
Plasma is ionized gas (partially or fully). Overwhelming majority of matter in the universe is in plasma state (stars, Sun, etc.). Basic parameters of plasma state are given briefly as well as classification of plasma types: classic-quantum, ideal-nonideal, etc. Differences between plasma and neutral gas are presented. Plasma properties are determined by long distance electrostatic forces. If spatial dimensions of a system of charged particles exceed the so-called Debye radius, the system may be considered as plasma, that is, a medium with qualitatively new properties. The expressions for Debye radius for classical and quantum plasma are carried out. Basic principles of plasma description are presented. It is shown that plasma is a subject to specific electrostatic (or Langmuir) oscillations and instabilities. Simplest plasma models are given briefly: the model of “test” particle and model of two (electron and ion) fluids. As an example, Buneman instability is presented along with qualitative analysis of its complicate dispersion relation. Such analysis is typical in plasma theory. It allows to easily obtain the growth rate.
Part of the book: Selected Topics in Plasma Physics