linear wave amplification by beam-plasma interaction

2
_International Symposium on Beam-plasma Interactions This property could be used to improve the efficiency of electron bunching in a klystron-type amplifier by filling the drift space with a plasma of appropriate density. The beam behaviour is studied theoretically by computing in an exact, nonlinear manner, the trajectories of a disc model electron beam which traverses a linear, dielectric model plasma. The parameters varied are the beam space charge conditions (beam current), the degree of initial velocity modulation, and the ratio of modulation frequency to plasma frequency (co/cop). Com- putations show that it is possible to bunch the beam electrons to within 85~ of delta function bunching under some beam and plasma conditions. The electron beam behaviour is studied experimentally by observing the beam electron velocity phase distribution with a crossed-field velocity analyzer, and observing the beam current waveform (density-phase distribution) using a wide-band sampling oscilloscope. Experimental results show essentially the same beam be- haviour as predicted by the computations with some differences which are attributed to variation in the plasma density along the beam path. THEORY OF BEAM-PLASMA INTERACTIONS*) A. BERS Department of Electrical Engineering and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts, U.S.A. We present the results of our theoretical studies on beam-plasma interactions pertinent to experiments in which an unmodulated electron beam of finite cross-section is injected into a plasma confined by a uniform magnetic field. A new model, so-called "rigid beam model", is introduced for the electron beam in a plasma. This is particularly suitable for studying modes of wavelengths that are long compared to the beam cross-section, and in the presence of hot electron plasmas. It is shown that under suitable conditions strong oscillations of the ions may be excited. Beams with injection both along and across the magnetic field are considered, the latter being important in beam-plasma discharges at low-pressure. We also present the results of computer-model-calculations on the nonlinear aspects of beam-plasma interactions. The beam is modelled by "super-particle" disks of finite cross-section. Density gradients in the plasma along the beam flow direction are shown to have a profound effect on the nonlinear state of the inter- action. Results are compared with measurements of the velocity distribution on the beam that emerges from the plasma. LINEAR WAVE AMPLIFICATION BY BEAM-PLASMA INTERACTION S. BLIMAN, A. BOUCnOULE, M. WEINFELO Institut d'EIectronique Fondamentale -- Laboratoire Associd au CNRS -- Facultd des Sciences Bat. 220-91-Orsay -- France The electromagnetic interaction between a uniform beam and plasma, both having the same transverse dimension, in a uniform longitudinal magnetic field was studied. The dispersion relation was solved for two situations: *) This work was supported principally by the National Science Foundation (Grant GK-1i65). 686 Czech, J. Phys, B 18 (1968}

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Page 1: Linear wave amplification by beam-plasma interaction

_International Symposium on Beam-plasma Interactions

This property could be used to improve the efficiency of electron bunching in a klystron-type amplifier by filling the drift space with a plasma of appropriate density.

The beam behaviour is studied theoretically by computing in an exact, nonlinear manner, the trajectories of a disc model electron beam which traverses a linear, dielectric model plasma. The parameters varied are the beam space charge conditions (beam current), the degree of initial velocity modulat ion, and the ratio of modulat ion frequency to plasma frequency (co/cop). Com- putat ions show that it is possible to bunch the beam electrons to within 85~ of delta function bunching under some beam and plasma conditions. The electron beam behaviour is studied experimentally by observing the beam electron velocity phase distr ibution with a crossed-field velocity analyzer, and observing the beam current waveform (density-phase distribution) using a wide-band sampling oscilloscope. Experimental results show essentially the same beam be- haviour as predicted by the computations with some differences which are attr ibuted to variat ion in the plasma density along the beam path.

T H E O R Y O F B E A M - P L A S M A I N T E R A C T I O N S * )

A. BERS

Department of Electrical Engineering and Research Laboratory of Electronics, Massachusetts Institute o f Technology, Cambridge, Massachusetts, U.S.A.

We present the results of our theoretical studies on beam-plasma interactions pertinent to experiments in which an unmodulated electron beam of finite cross-section is injected into a plasma confined by a uniform magnetic field. A new model, so-called "rigid beam model" , is introduced for the electron beam in a plasma. This is particularly suitable for studying modes of wavelengths that are long compared to the beam cross-section, and in the presence of hot electron plasmas. It is shown that under suitable conditions strong oscillations of the ions may be excited. Beams with injection both along and across the magnetic field are considered, the latter being important in beam-plasma discharges at low-pressure. We also present the results of computer-model-calculations on the nonlinear aspects of beam-plasma interactions. The beam is modelled by "super-particle" disks of finite cross-section. Density gradients in the plasma along the beam flow direction are shown to have a profound effect on the nonlinear state of the inter- action. Results are compared with measurements of the velocity distribution on the beam that emerges from the plasma.

L I N E A R W A V E A M P L I F I C A T I O N B Y B E A M - P L A S M A I N T E R A C T I O N

S. BLIMAN, A. BOUCnOULE, M. WEINFELO

Institut d'EIectronique Fondamentale -- Laboratoire Associd au CNRS -- Facultd des Sciences Bat. 220-91-Orsay -- France

The electromagnetic interaction between a uniform beam and plasma, both having the same transverse dimension, in a uniform longitudinal magnetic field was studied. The dispersion relation was solved for two situations:

*) This work was supported principally by the Nat ional Science Foundat ion (Grant GK-1i65).

686 Czech, J. Phys, B 18 (1968}

Page 2: Linear wave amplification by beam-plasma interaction

International Symposium on Beam-plasma Interactions

a) Filled waveguide.

b) Beam-plasma system in vacuum.

The results were compared with the quasistatic predictions. Different couplings exist which may be used for amplification. Particular at tent ion is paid to

the amplification due to coupling between the beam slow space charge mode and the plasma mode existing below cop o r coce, whichever is smaller. I t is shown that for a given cote, cob, there exists a limiting beam velocity above which no amplification can exist. This velocity is studied as a function of cop. The authors deduce from this that in certain experiments, amplification should be interpreted as resulting from the coupling between the beam slow cyclotron mode with the plasma mode.

The authors have built a device in which they studied the amplification processes. The results show a fair agreement with the theoretical results.

O S C I L L A T I O N S O F B O U N D E D P L A S M A - B E A M S Y S T E M S

M. M. SHOUCRI, A. B. KITSENKO

Atomic Energy Establishment, Cairo, U.A.R.

Slow waves exist in a plasma which are not completely electrostatic. It is of some interest to study the excitation of these waves in beam-plasma systems. A method is presented for the in- vestigation of small oscillations in bounded plasma-beam systems with a distinct interface between the two media. The suggested method is a generalization of the Suhl and Walker method often used for the investigation of oscillations in bounded media. This made it possible to go beyond the quasi-static approximation. The beam of charged particles was assumed to be compensated. The thermal motion of the plasma and beam particles was neglected.

To illustrate the method the authors considered the problem of the excitation of oscillations in a cylindrical plasma waveguide by a paraxial low density beam. Oscillation frequencies and growth rates have been found for whistlers, for waves corresponding to the quasi-static approximation, and for low frequency magneto-hydrodynamic waves. The excitation of helical waves in a solid- state plasma has been also studied.

N E W R E S U L T S I N T H E A P P L I C A T I O N T O B E A M - P L A S M A S Y S T E M S

O F T H E T H E O R Y O F P U L S E P R O P A G A T I O N I N U N S T A B L E M E D I A * )

L. S. HALL, W. HECKROTTE, R. P. FREIS

Lawrence Radiation Laboratory, University of California, Livermore, California

The results of a new theory [1] o f the propagat ion and growth of an initial pulse disturbance in unstable media can be immediately applied to beam-plasma interactions. The determination of asymptot ic pulse shape (or asymptotic temporal response) has been carried out for a number of examples -- of particular importance being variations of the case of interaction between a plasma and a cold double-stream. Several new quanti tat ive results have been obtained, and some sug- gestions for experimental verification of certain of these results will be presented.

*) Work performed under the auspices of the U.S. Atomic Energy Commission.

Czech. J. Phys. B 18 (1968) 687