Dynamics of an electron beam in the magnetic field of a betatron

Expressions for the vector potential and magnetic induction vector components have been obtained for a vertically asymmetric magnetic field of a betatron. The dynamics of the electron beam in the process of injection and acceleration in the electromagnetic field of the betatron has been investigated. It has been shown that the asymmetry of the magnetic field decreases the efficiency of the electron involvement in acceleration. The mutually related radial-vertical asymmetric oscillations of the electron beam in the asymmetric field lead to considerable losses of the beam particles on the walls and injector of the acceleration chamber. The results of these investigations may be useful in developing and tuning electron beam acceleration systems.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 42–46, December, 2004.     

Parameters of the electron beam in a betatron with radial comb-type poles

Expressions for the vector potential and components of the magnetic field induction vector of a betatron with radial comb-type poles are derived. The dynamics of the electron beam in the electromagnetic betatron field is investigated in the process of electron injection and acceleration. It is demonstrated that the azimuthally varying field engender beam beats. However, the amplitudes of beam particle oscillations during acceleration do not exceed their values estimated from the symmetric azimuthal component of the betatron magnetic field induction. The energy spectrum of accelerated electrons is not described by a normal law. In the electron energy spectrum, the relative number of electrons whose energy exceeds the average value is large. Application of poles with radial combs improves the efficiency of electron capture in acceleration. Results of investigations can find application in the development and adjustment of electron beam accelerating systems. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 27–34, October, 2005.     

Effect of rate of current rise in the output windings on the space-time distribution of the electron beam in a betatron

This article reports results of a study of the effect of the rate of current rise in the output windings of a betatron on the parameters of the resultant electron beam. It is shown that the rate of current rise in the windings only changes the duration of the radiation pulse associated with the beam and its delay relative to the initiation of the current pulse in the windings. The spatial distribution of the beam is determined mainly by the distribution of the magnetic field of the betatron. The findings obtained from the study made it possible to simplify the current pulse generator in the output-winding supply circuit of the PMB-6E betatron, reduce its size, and make it more reliable.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 24–28, March, 1985.     

Selection of dimensions for the accelerating chamber of a betatron with extraction of an electron beam

This article reports results of refinement of the dynamics of particles of a beam extracted from a betatron. The refinement has made it possible to select the main dimensions of the accelerating chamber. Expressions were obtained which make it possible to determine the chamber dimensions and the profile of the extraction window from the distribution of the magnetic field of the betatron. It is shown that proper selection of the dimensions will increase the dose rate at the exit from the magnetic core of the accelerator.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 29–32, March, 1985.     

The Energy Spectrum of the Electron Beam of a Betatron

The process of extraction of an electron beam through the glass wall of a sealed-off acceleration chamber has been investigated. It has been shown that the electron beam extracted from the MIB-6E small-sized betatron has a nonuniform cross-sectional distribution of the particle flux density. This nonuniformity is due to the imperfection of the beam extraction devices and to the flaws in design of the extraction window of the accelerator chamber. The electrons extracted through the glass wall of the window lose a major portion of their energy. At the outlet of the chamber of the small-sized betatron, the spectrum of the electrons is not line. The half-width of the spectral line of the electron beam is, at best, 6% for a window glass thickness of 0.5 mm and about 15% for a glass thickness of 4 mm. The results of this study may find practical implementation in developing extracted electron beam formation systems.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 51–55, January, 2005.     

Simplified equations for investigation of charged-particle dynamics in magnetic fields

A system of motion equations presented for charged particles in betatron magnetic fields makes it possible to conduct all particle dynamics calculations in relative units because the particle velocity components are expressed in terms of trajectory geometry using comparatively simple notation, and the conversion from relative to absolute units is easily carried out in terms of the radius of a fixed orbit and the magnetic induction of the field on it. This equation system has been used successfully to investigate particle dynamics in an electron beam extracted from a betatron and to determine the principal parameters of the beam; the results were confirmed in practice. Tomsk Polytechnic University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 29–35, March, 1998.     

The Dynamics of Electron Orbits during the Acceleration of Electrons in a Betatron

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.     

Electret mechanism of electron beam capture by the magnetic field of a betatron

The mechanism of electron capture into acceleration that takes into account the electret properties of the accelerating chamber shell is described. The electron capture into acceleration is a self-consistent problem. It is demonstrated that the electron capture into acceleration is caused by the interaction of the injected electrons with the electric field of the charge created on the side interior wall of the chamber by electrons dropped out of the acceleration. The spectrum of the captured electrons is not normal. A large number of low-energy electrons are presented in the spectrum. Two and more peaks previously unknown are revealed in the dependence of the captured charge on the injected charge for large values of the injected charge. The results obtained are in agreement with the data of previous experimental studies. The captured charge and the dose rate of bremsstrahlung from a target correspond to their actual values for betatrons with accelerated electron energies of 6 and 10 MeV. Results of simulation can be used to design accelerating chambers and electron injection systems of betatrons and other cyclic accelerators. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 35–45, December, 2006.