COMPUTATION OF NEARLY EXACT 3D ELECTROSTATIC FIELD IN GAS IONIZATION DETECTORS

N. Majumdar, S. Mukhopadhyay
Saha Institute of Nuclear Physics,
1/AF, Bidhannagar, Kolkata-700064, India
nayana.majumdar@saha.ac.in

\begin{abstract}
The three-dimensional electrostatic field configuration in gas ionization
detectors has been simulated using an efficient and precise 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 (NEBEM) [1]
has been implemented such that the discretization
of the integral equation leads to a set of linear algebraic equations. Since the
solver uses exact analytic integral of Green function to compute the
electrostatic potential for a general charge distribution satisfying Poisson's
equation, extremely precise results have been obatined despite the use of
relatively coarse discretization. The surface charge densities on the
discretized elements have been computed by satisfying the boundary conditions,
i.e., potentials at the centroid of the elements known from the given potential
configuration. From these charge densites, the potential or electric field at
any point in the computational domain has been obtained by superposition. 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 coparing 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 the
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.

Computation of the electrostatic field in certain detectors such as RPC, MSGC
and GEM is made complicated even more by the fact that materials with different
permittivity are used for the construction of these detectors. In addition, very
thin layers of materials are used in their design which has the possibility of
leading to degenerate surfaces. In order to illustrate the applicability of the
NEBEM solver for these detector geometries, it has been validated against
available FEM and BEM numerical solutions for geometries with multiple
dielectrics and degenerate surfaces.

References:
[1] S.Mukhopadhyay, N.Majumdar, "Development of a BEM Solver using Exact
Expressions for Computing the Influence of Singularity Distributions", ICCES05,
Chennai, December 2005.