pdf file - Saha Institute of Nuclear Physics

Field Solver for MPGDs
GEM
Typical dimensions:
Electrodes (5 μm thick)
Insulator (50 μm thick)
Hole size D ~ 60 μm
Pitch p ~ 140 μm
Induction gap: 1.0 mm,
Transfer gap: 1.5 mm
Micromegas
Typical dimensions:
Mesh size: 50 μm
micromesh sustained
by 50 μm pillars
Some of the expected features are as follows
1. Handle large variation in length scales (a
micron to a meter)
2. Make available, on demand, properties at
arbitrary locations (near- and far-field)
3. Model intricate geometrical features using
triangular elements as and when needed
4. Model multiple dielectric devices
5. Model nearly degenerate (closely packed)
surfaces
6. Model space charge effects
7. Model dynamic charging processes
8. Compute field for the same geometry, but
with different electric configuration,
repeatedly
The de‐facto standard FEM is unsatisfactory in
dealing with 1., 2., 5., 6., 7. and 8. Hence, the
search for a new tool.

Field Solver
Solution of 3D Poisson's Equation using a recently proposed BEM - neBEM
• Numerical implementation of boundary integral equations (BIE) based on Green’s
function by discretization of boundary.
• Boundary elements endowed with distribution of sources, doublets, dipoles, vortices.
Potential at r
Electrostatics BIE
Φ( r)
= ∫ G(
r,
r′
) ρ ( r′
) dS ′
S
Green’s function
G ( r , r ′)
=
4 πε
1
r
−
r
′
Charge density at r’
Influence
Coefficient
Matrix
discretization
[ A]{ ρ} = { Φ}
{ρ} = [A] -1 {Φ}
ε - permittivity of medium
Accuracy depends critically on the
estimation of [A], in turn, the
integration of G, which involves
singularities when r → r'.
Most conventional BEM solvers fail
here leading to large numerical errors.

Contrast of approaches
Conventional BEM (nodal) versus nearly exact BEM (distributed)
We have derived exact expressions for
the integration of G and its derivative
for uniform charge distributions over
triangular and rectangular elements
Conventionally, charges are assumed to be
concentrated at nodes. This is convenient
since the preceding integration is avoided.
Introduces large errors in the near field.

Micromegas
Electrostatics of MPGDs
Micro‐Wire
200
180
160
neBEM
FEM
Theoretical considerations
imply better performance by
the neBEM solver which
solves for the charge density
on boundary elements rather
than potential at a pre‐fixed
set of nodal points.
140
E (kV/cm)
140
120
100
80
60
40
20
0
20 40 60 80 100 120 140
Y (µm)
FEM: gap = 32µm
gap = 40µm
gap = 65µm
gap = 75µm
gap = 85µm
neBEM: gap = 32µm
gap = 40µm
gap = 65µm
gap = 75µm
gap = 85µm
E (kV/cm)
Total E field (kV/cm)
120
100
80
60
40
20
0
-100 0 100 200 300 400 500 600 700
Y (µm)
300
280
260
240
220
200
180
160
140
120
100
80
neBEM Segmented
FEM Segmented
neBEM Mesh
FEM Mesh
60
0 100 200 300 400 500 600
Distance * 10 micron
Numerical comparisons
1) neBEM results are as
accurate as FEM results in the
far‐field
2) In the near‐field, neBEM
performs better than FEM
3) No artificial truncation of
open domain is necessary
while using neBEM

Plans for the near future
‣ Development of an interface to ROOT so that devices built using ROOT
can be directly imported to neBEM and solved for
‣ Study dynamic charging
‣ Improve upon Particles‐on‐Surface – a model to represent space charge
‣ Simulate problems related to magnetostatics
‣ A working interface to garfield and the new detailed detector simulation
framework is expected to be complete by the middle of 2009
‣ We will also try to set up an experimental laboratory for the development
of MPGD as soon as possible
Supratik Mukhopadhay, Nayana Majumdar, Sudeb Bhattacharya
Saha Institute of Nuclear Physics, Kolkata, India
E‐mails: supratik.mukhopadhyay@saha.ac.in, nayana.majumdar@saha.ac.in, sudeb.bhattacharya@saha.ac.in