Abstract
This paper presents a system of equations that describe the motion of charged particles in the electromagnetic field of a betatron. This system of equation was successfully used to study the behavior of the electron orbits and to determine the principal parameters of the electron beam in the electromagnetic field of a betatron during the electron acceleration and deceleration. The results of this study may find application in developing systems designed to accelerate electron beams. It has been shown that in the course of acceleration there is no damping of the betatron oscillations by the law B z –1/2 and, correspondingly, no decrease in beam cross section. In contrast to the existing belief, the initial departure of the kinetic energy (momentum) of the injected electrons from the energy (momentum) of the electrons following the equilibrium orbit is not preserved in the course of acceleration. In the betatron chamber, the electron beam, when accelerated, does not constrict to form a ring but occupies a broad zone, whose dimensions are determined by the initial double amplitudes of the vertical and horizontal oscillations. Despite the large double amplitude of the oscillations of the beam particles, the average energy of the electrons differs from the energy of the electrons following the equilibrium orbit only slightly, and the departure of the average energy from the energy of the equilibrium electrons varies proportionally to the (varying) field of the betatron.
Similar content being viewed by others
REFERENCES
A. A. Kolomenskii and A. N. Lebedev, Theory of Cyclic Accelerators [in Russian], Fizmatgiz, Moscow (1962).
A. A. Kolomenskii, Physical Foundations of the Methods for Acceleration of Charged Particles [in Russian], Moscow State Univ. Publishers, Moscow (1980).
A. A. Vorobjov, B. A. Kononov, and V. V. Evstigneev, Betatron Electron Beams [in Russian], Atomizdat, Moscow (1974).
V. V. Kashkovskii, Izv. Vyssh. Ucheb. Zaved., Fizika, 3, 29-35 (1998).
V. V. Kashkovskii, Ibid., Suppl., 4, 151-158 (2000).
L. D. Landau and E. M. Lifshits, The Field Theory [in Russian], Nauka, Moscow (1967).
B. N. Rodimov, Izv. Tomsk Polytekh. Inst., 87, 3-10 (1957).
B. N. Rodimov, Ibid., 30-40.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kashkovskii, V.V. The Dynamics of Electron Orbits during the Acceleration of Electrons in a Betatron. Russian Physics Journal 45, 601–608 (2002). https://doi.org/10.1023/A:1021155520312
Issue Date:
DOI: https://doi.org/10.1023/A:1021155520312