Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma. V. Excitation of Waves in Strong Dissipative Plasmas by a Monoenergetic Beam

Abstract

A system of nonlinear equations derived in a previous paper which describes the evolution of the beam-plasma instability in strong diesipative plasmas is solved numerically. It is shown that there are three characteristic solutions of the system of equations: the resonant dissipative instability, the nonresonant instability with strong dissipation and the nonresonant dissipative instability. A physicel interpretation of essential features of these instabilities is given. The interaction of resonant nnd nonreaonant waves in the system electron beam-strong dissipative plasma is examined. Some conclusions for the transport problem of electron beams in strong dissipative plasmas are obtained in this paper. Characteristic Features of Waves in Strong Dissipative PlasmasThe present paper closes a series of investigations concerning the interaction 6 f "cold" niodulated low density electron beams with various plasmas [l-41. The numerical solutions of the system of nonlinear equations for the description of a strong dissipative instability derived in [3] is analyzed in the present paper. A strong dissipation of wave energy in the plasma ( D > 1) can be realized by various dissipation processes: collisions of the plasma electrons with ions, Landau-damping, Cyclotron-damping or turbulence. Because the growth rate of the beam-plasma instability y is a function of the beam density and the effective collision frequency v is a function of the plasma properties on principle, the relation y Q Y can he always realized. It must be accentuated, however, that the condition of strong dissipation ( D > 1) can be realized easier for the space-problem because iisuallv the group velocity of the excited wave is niuch sirialler than the beam velocity V,.Because C , < 1 it can be seen from a comparison of the systems of equations (3.61) to (3.86) and (3.901-(3.74) (the formula, e.g., (61) of [3] is denoted by (3.61)) that in the first approximation the time-and space-problems are described by the' same equations. Therefore the strong dissipative beam-plasma instability is investigated in this paper in the framework of the time-problem. The character of the investigated type of instability is demonstrated obviously by the balance equations (3.68), (3.69).