TELECOMMUNICATIONS AND RADIO ENGINEERING - 2011 Vol. 70,
No 2 		 

 

 

 

AN ANALYTIC REPRESENTATION FOR THE ELECTRIC FIELD PRODUCED BY CHARGES WHICH ARE INDUCED BY A NON-RELATIVISTIC MOVING CHARGE ON THE WALLS OF A CYLINDRICAL DRIFT CHAMBER


K.V. Ilyenko & T. Yu. Yatsenko
A. Usikov Institute of Radio Physics and Electronics,
National Academy of Sciences of Ukraine
12, Academician Proskura St., Kharkiv 61085, Ukraine
Address all correspondence to K. Ilyenko at E-mail: kost@ire.kharkov.ua

Abstract
An analytic representation has been derived for the electric field produced by density distribution of a charge induced by a non-relativistic moving charge on a wall of the grounded perfectly conductive cylindrical drift chamber. Integration over the angular variable in the initial representation is reduced to two familiar quadratures (complete elliptic integrals of the first and second kind) and summation of two finite series whose coefficients represent functions of a single universal variable. A recurrence relation is proved which makes it possible to perform integration over the angular variable. Preliminary calculation of the finite sums for a specified mesh dividing the drift space allows considerably reducing the computation time required for completely 3D calculations of the charged beam transportation by the particle-in-cell method. As an example, an analytic representation has been found for the electric field on the system axis which is produced by a charge density distribution like that. The representation involves quickly convergent series only.

KEY WORDS:Kirchhoff scalar formula, Green’s function method, analytic representation

References

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pages 139-148

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