TIME DETECTOR DESIGN FOR MEV PARTICLES I - THE ELECTRIC-FIELD IN A TRIANGULAR DOMAIN

We describe in this paper the methods used in the calculation of the e lectric potential and field in a triangular domain. These calculations are needed in the design of a time detector for high-energy particles . The electric field is created by three metal plates forming a triang ular prism with different voltage applied to each of the plates. An an alytical solution to the electric potential and field within the trian gle is introduced. The method is based on the conformal mapping princi ple. The discovery of the analytical mapping functions which convert a triangle to a parallel band is of key importance to the solution. Alt hough the methods described in this paper are given for right angled i sosceles triangle, which is used in the time detector design, the meth od is in fact applicable to any triangles. The same problem has also b een solved using the standard numerical method in which the electric p otential is calculated on a set of grid points. The accuracy of the nu merical solution depends on the size of the grid and the precision of iteration, which are generally limited by the computing resources. In comparison with the numerical method the analytical solution yields re quired information in a much more efficient and accurate way. (C) 1998 Elsevier Science B.V. All rights reserved.