Electron dynamics and kinetics during the formation of a virtual cathode in different media
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Electron Dynamics and Kinetics during the Formation of a Virtual Cathode in Different Media S. V. Dergunov*, A. E. Dubinov*, I. Yu. Kornilova*, S. K. Saœkov*, V. D. Selemir*, and V. P. Tarakanov** *All-Russia Research Institute of Experimental Physics, Russian Federal Nuclear Center, Sarov, Nizhni Novgorod oblast, 607188 Russia **Institute for High Energy Densities, Associated Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya ul. 13/19, Moscow, 125412 Russia Received March 14, 2005
Abstract—Results are presented from the first systematic investigation of how various factors in material media influence electron kinetics during the formation of a virtual cathode in an overcritical-current electron beam. A study is made of such factors as the viscous frictional force acting on the electrons in the medium, the dielectric constant of the medium, and ionization processes induced by the electrons in the medium. The dynamics of formation of a virtual cathode and the kinetics of the so-called metastable electrons in the cathode are considered. PACS numbers: 52.59.Sa DOI: 10.1134/S1063780X06010028
1. INTRODUCTION
The next problem of practical interest is that of the distinctive features of the dynamics of formation of a VC in a beam propagating in an equipotential cavity filled with a material medium.
If an electron beam is injected into an equipotential vacuum chamber, then, at beam currents above a certain limiting value, the beam space charge creates a potential barrier that prevents further electron injection into the chamber. In this case, some of the beam electrons are decelerated and return to the place from which they were injected. The region where the beam electrons come to a stop and start to move backward is called a virtual cathode (VC), and the process of formation of a VC in vacuum is called the Bursian instability. Beams with currents above the vacuum limiting current, i.e., those with a VC, have found wide applications in highcurrent electronics, e.g., for the generation of microwaves and X radiation, for collective ion acceleration, and so on [1–3].
The presence of a medium can influence the dynamics of an electron beam with a VC in many ways. For instance, the permittivity ε of the medium can substantially alter the pattern of electric fields in the beam, the electron scattering by the particles of the medium can give rise to a viscous frictional force of specific type, and the beam dynamics can be significantly affected by the ability of the beam electrons to ionize the medium. Another interesting aspect of the problem is the dynamics and kinetics of the so-called metastable electrons, i.e., the electrons that remain within the VC (i.e., at the top of the potential barrier) and oscillate together with it for a long time [10]. In the present paper, the effect of the frictional force on the dynamics and kinetics of such electrons is studied for the first time.
At present, it is impossible to carry out a rigorous analysis of the general cases of formation and evolution
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