Speaker
Dr
Nayana Majumdar
(Saha Institute of Nuclear Physics)
Description
The three dimensional electrostatic field configuration in a multiwire proportional
chamber (MWPC) has been simulated using an efficient boundary element method (BEM)
solver set up to solve an integral equation of the first kind. To compute the charge
densities over the bounding surfaces representing the system for known potentials,
the nearly exact formulation of BEM has been implemented such that the discretisation
of the integral equation leads to a set of linear algebraic equations. Since the
solver uses exact analytic integral of Green function [1,2] to compute the
electrostatic potential for a general charge distribution satisfying Poisson's
equation, extremely precise results have been obtained despite the use of relatively
coarse discretization. The surfaces of anode wires and cathode planes in the MWPC
have been segmented in small cylindrical and rectangular elements, carrying uniform
unknown surface charges distributed over the elements. The capacity coefficient
matrix for such a charge distribution has been set up using the exact expressions of
the new formulation. Finally, the surface charge densities have been computed by
satisfying the boundary conditions, i.e., potentials at the centroid of the elements
known from the given potential configuration. We have used a lower upper (LU)
decomposition routine incorporating Crout's method of partial pivoting to solve the
set of algebraic equations. From the computed surface charge densities, the potential
or electric field at any point in the computational domain can be obtained by
superposition of the contribution of the charge densities on the boundary elements.
Using the solver, we have performed a detailed study of the three dimensional field
configuration throughout the volume of the device. The solutions have been validated
by successfully comparing the computed field with analytical results available for
two-dimensional MWPCs. Significant deviations from this ideal mid-plane field have
been observed towards the edges of the detector. We have also studied the influence
of the edge configuration of the detector on these deviations. Utilizing the high
precision and three-dimensional capability of this solver, a study has been carried
out on the nature of the electrostatic forces acting on the anode wires and its
variation with the change in the wire position. Significant positional variations
have been observed which can have impact on future design and construction of MWPCs.
References
[1] N.Majumdar, S.Mukhopadhyay, Computation of Electrostatic Field near
Three-Dimensional Corners and Edges, accepted for presentation in the International
Conference on Computational and Experimental on Engineering and Sciences (ICCES05) to
be held at the Indian Institute of Technology, Madras (Chennai) from Dec 01 to 06, 2005.
[2] S.Mukhopadhyay, N.Majumdar, Development of a BEM Solver using Exact Expressions
for Computing the Influence of Singularity Distributions accepted for presentation in
ICCES05.
Authors
Dr
Nayana Majumdar
(Saha Institute of Nuclear Physics)
Prof.
Supratik Mukhopadhyay
(Saha Institute of Nuclear Physics)
