Equilibrium state of toroidal electron beam |
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Authors: | Milo? Seidl |
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Institution: | (1) Research Institute of Vacuum Electronics, Prague |
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Abstract: | The paper deals with the collective behaviour of electrons which rotate in a magnetic field used in a betatron. It is shown experimentally that there exists strong interaction between the electrons, which leads to the rapid formation of the equilibrium state with characteristic distribution of the charge density in the cross-section of the toroidal beam. The corresponding relaxation time is of the order of 1 sec. A statistical theory of the equilibrium beam is elaborated. Its main result is that the effective radius of the beam is a function of two parameters, one of which is proportional to the thermal energy of the electrons and the other to the perveance of the beam. The charge contained in a toroidal beam of given effective cross-section is equal to the product of the charge the beam would contain at zero temperature and a coefficient, which is a function of the temperature of the beam. Its value is unity at zero temperature and rapidly decreases with increasing temperature. The cause of cooling of the beam is shown.
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Now Institute of Vacuum Electronics, Czechosl. Acad. Sci., Prague. In conclusion the author thanks J. Luká and L. Hyttych for invaluable help in the experiments, A. Rajský for constructing the electronic apparatus and J. Sokol for preparing the miniature probe. |
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