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Telecommunications and Radio Engineering
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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v67.i13.50
pages 1177-1188

Calculation of Quasistatic Eigen-Field of a Charge, which Moves Arbitrarily in Cylindrical Drift Chamber

G. M. Gorbik
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine, 12, Academician Proskura Str., Kharkov 61085, Ukraine
K. V. Ilyenko
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine, 12, Academician Proskura St., Kharkov 61085, Ukraine
T. Yu. Yatsenko
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine 12, Academician Proskura St., Kharkiv 61085, Ukraine

RÉSUMÉ

In the Darwin approximation using the Green functions method, we found the solutions for the quasistatic (quasistationary) vector potential excited in cylindrical drift chamber with perfectly conducting walls by arbitrary charge and current densities (e.g., by a charged beam), which satisfy the continuity equation. The found Green functions are expressed as decomposition into the eigen functions of the Laplace operator within the cylindrical coordinate system with the Dirichlet and Neumann boundary conditions. Based on the obtained solutions for potentials, we find expressions for the induced magnetic field and relativistic correction to the electric field. Taking into account relativistic corrections to the order of field of radiation, we also found contribution from charges and currents being beam-induced on the drift chamber walls into the Lorentz force acting on the isolated charged particles of a beam. The method is proposed which enables the problem for vector potential to be reduced to a system of the scalar Poisson equation in cylindrical coordinate system.