Particle Accelerators February 1980 [antikvár]

Particle Accelerators 1980, Vol. 10, pp. 73-81 0031 -2460/80/1001 -0073S04.50/0 © Gordon and Breach, Science Publishers, Inc. Printed in U.S.A. COHERENT INTERACTION BETWEEN WAVES AND PARTICLE STREAMS J. D. LAWSON Rutherford Laboratory, Chilton, Oxon, England (Received April 26, 1979) The interaction between beams of particles and traveling electromagnetic waves forms the basis of a large number of practical devices. Well-known examples are particle accelerators, microwave tubes, the cyclotron maser, and more recently, the free-electron laser. Such interaction is also responsible for the phenomenon of Landau damping which occurs in plasmas and intense accelerator beams. In this paper the basic characteristics of the wave-particle interaction are examined in a general way and illustrated with reference to the above examples. I. INTRODUCTION Many devices depend for their operation on the coherent interaction between traveling electromagnetic waves and streams of particles. Such an interaction forms the basis of linear particle accelerators, traveling-wave tube amplifiers and the free-electron laser. The spatial and temporal variation of such waves is characterized by the factor cos (uit — kz + 1In some devices, for example cyclic accelerators, magnetrons and the cyclotron maser, the wave has angular rather than linear velocity so that kz in the argument of the cosine is replaced by nd. Coherent interaction between waves in a plasma or intense accelerator beam and some of the particles that constitute it gives rise to the phenomenon of Landau damping. Detailed theories describing these devices tend to be complicated and specialized. The object of the present paper is to present a simple, general treatment of the interaction of particles with traveling waves in terms of a few characteristic parameters. These general parameters may then be expressed in particular form for particular applications. The objective is not to enable calculations of immediate practical value to be made, but rather to illustrate common features not always apparent in the conventional theories. Three regimes of operation may be distinguished; in the first of these, the particle density is sufficiently dilute that the amplitude of the external wave is not affected. In the second, the presence of the particles affects the wave amplitude, but direct interaction between particles can be neglected. In the third regime, interaction between the particles is significant; when this is so the ratio of frequencies associated with the collective effects to other characteristic frequencies of the system is not small. The analysis in this paper will be confined to the first regime. Extension to the second is relatively straightforward; the third, however, requires a more sophisticated approach. II. SINGLE PARTICLE IN A UNIFORM WAVE The simplest situation, to be considered first, is that of a particle and wave both traveling in the z direction, where the wave has an electric field of the form Ez — E0 sin (u)t—k.z) (1) and the particle velocity is z. Relativistic units will be used, so that z is written fi.c, and y. = (1 —/5.2)"K. If cf> represents the phase of the particle with respect to the zero of the wave, (Fig. 1) then