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Application of the finite-difference approximation to electrostatic problems in gaseous proportional counters

1975; Elsevier BV; Volume: 124; Issue: 2 Linguagem: Inglês

10.1016/0029-554x(75)90592-3

1878-3759

Kazimierz Urbańczyk, M.P.R. Waligórski,

Nuclear Physics and Applications

The basic principles of the finite-difference approximation applied to the solution of electrostatic field distributions in gaseous proportional counters are given with the aim of making this method more popular with authors dealing with electrostatic problems. When this method is used, complicated two-dimensional electrostatic problems may be solved, taking into account any number of anodes, each with its own radius, and any cathode shape. A general formula for introducing the anode radii into the calculations is derived and a method of obtaining extremely accurate (up to 0.1%) solutions developed. Several examples of potential and absolute field distributions for single rectangular and multiwire proportional counters are calculated and compared with exact results according to Tomitani, in order to discuss in detail errors of the finite-difference approximation.