Fig. 1 Position of the Spheres and the Contour points, Charge points and
Check points in the co-ordinate system used for Charge simulation method.
Boundary conditions are imposed at a set of co-location
points on the electrode surfaces, known as the Contour points
[5]. For each electrode as many contour points are chosen as
there are inner charge points. This condition leads to a set of
linear system of equations relating the unknown charges and
the known potential on the electrode. The equations are
solved by any standard method and the value of the charges is
thus calculated. In the next step, some points are selected on
the surface of the electrodes, other than the contour points,
where the calculated points are checked with the boundary
conditions, known as the Check points [5]. If the calculated
potentials at the check points satisfy the boundary conditions
then it is assumed that the selected charges successfully
simulated the electrodes. On the other hand, if the calculated
potentials at the check points does not satisfy the boundary
conditions then the location of the charge points and the types
of charges are changed and the entire process is repeated
again and again till the simulation ends successfully. The
accuracy of CSM largely depends upon the positioning and
the number of charges and the corresponding contour points
used in simulation. One of the measures of the accuracy is the
Potential error [5], defined as the difference between the
known potential and the computed potential at the electrode
surfaces at various check points. The permissible potential
error in this work has been kept less than 1%. A guideline to
keep the potential error within limit is to keep the
Displacement ratio [5], defined as the ratio of the distance
between two successive contour points and that between a
contour point and a charge point, between 0.7 to 1.5. A
number of literatures [9]-[13] have been published which
deals various applications of CSM.
III. OUTLINE OF CHARACTERIZING THE SYMMETRICAL
ELECTRODE SYSTEM
The flow chart of simulating symmetrical electrod system
to estimate the degree of uniformaty in terms of
symmetrically and aymetrically applied high voltage is
shown in fig. 2.