Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma IV. Excitation of Nonresonant Waves

Kruscha, K. J. G.; Kondratenko, A. N.

doi:10.1002/ctpp.19830230503

Cited by 6 publications

(6 citation statements)

References 6 publications

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“…When the beam is niodulated a t a nonresonant unstable frequency (Re E~ < 0, sin 0 w 1, nonresonant instability with strong dissipation) an instability is developed which in the first approximation does not essentially differ froin the nonresonant reactive instability investigated in [4] (for Y < ao). The loss of the mean beam velocity, however, is defined for the nonresonant instability with strong dissipation in distinction to the nonresonant reactive imtability by dissipative processes in the plasma.…”

Section: The Nonresonant Dissipative Instability and The Nonresonant mentioning

confidence: 98%

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

Kruscha

Kondratenko

1983

Contrib Plasma Phys

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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).

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Section: The Nonresonant Dissipative Instability and The Nonresonant mentioning

confidence: 98%

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

Kruscha

Kondratenko

1983

Contrib Plasma Phys

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“…Plasmaphys. 24 (1984) 6, 579 -592 the right hand sides of (14) and (15) can be reduced to 585 respect,ively. Within the framework of the ponderomotive force description it is advantageous to determine the right hand sides of (16)-( 19) with the aid of the relations 2nb, iv (n,(sin a1 + sin a2}) =sin (PI) cos (Pz), PI) cos (B,),…”

Section: The Ponderomotive Force Descriptionmentioning

confidence: 99%

“…The initial conditions (44), (45) are significant in order to obtain an explosive solution of our system of equations according to (1). It can be seen from (14) and (15) that the beam part of the nonlinear coupling term VbEOIEOP is realized if the initial modulation of the beam is given by (44), (45). The beam part of the coupling term ,VEolEm, however, is a significant supposition for the EI in the considered BPS.…”

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confidence: 99%

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

Kruscha

Leven

1984

Contrib Plasma Phys

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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.

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“…This wave is characterized by a maximum growth rate at the linear stage of plasma-beam instability. However, as it has been shown in [8][9][10], use of a preliminary modulation of the beam at a given frequency allows to control the plasma-beam instability dynamics. For example, it permits to suppress the modes with larger growth rates.…”

Section: Introductionmentioning

confidence: 99%

Influence of Azimuthal Structure of Surface Waves on Efficiency of their Excitation by Tubular Electron Beams

Akimov¹,

Olefir²,

Azarenkov³

2006

Contrib. Plasma Phys.

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The excitation of eigen surface waves by tubular electron beams in cylindrical discharge devices is studied. The influence of the wave-field azimuthal structure on the excitation efficiency and nonlinear stage of the plasmabeam instability is investigated both numerically and analytically. Analytical expressions for the saturation amplitude and excitation efficiency of the wave under study are derived. They are found to agree well with results obtained by numerical modelling of the plasma-beam interaction presented in this paper.

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Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma IV. Excitation of Nonresonant Waves

Cited by 6 publications

References 6 publications

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

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

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

Influence of Azimuthal Structure of Surface Waves on Efficiency of their Excitation by Tubular Electron Beams

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