1. Diego González-Díaz (GSI-Darmstadt)
Santiago, 05-02-09

2. This is a talk about how to deal with signal coupling
in highly inhomogeneous HF environments,
electrically long and very long, not properly matched
and with an arbitrary number of parallel conductors.
This topic generally takes a full book, so I will try to
focus on theoretical results that may be of
immediate applicability and on experimental results
from non-optimized and optimized detectors.

3. definitions used
mirror electrode
not counting
Pad: set of 1+1(ref) conductors electrically small
Multi-Pad: set of N+1(ref) conductors electrically small
Strip: set of 1+1(ref) conductors electrically large
Double-Strip: set of 2+1(ref) conductors electrically large
Multi-Strip: set of N+1(ref) conductors electrically large
For narrow-gap RPCs this definition leads to:
pad strip
vp c t rise vpc t rise
D< = < 5 cm D≥ = ≥ 5 cm
f c 2 0.35 f c 2 0.35

4. Some of the geometries chosen by the creative RPC developers
HADES-SIS FOPI-SIS ALICE-LHC
-V -V
V
V
-V -V
STAR-RHIC
-V -V
V
V
V ! all these schemes are equivalent
-V regarding the underlying avalanche
dynamics... but the RPC is also a strip-
V
line, a fact that is manifested after the
-V avalanche current has been induced. And
all these strip-lines have a completely
V
different electrical behavior.
S. An et al., NIM A 594(2008)39
HV filtering scheme is omitted

5. pad
pad structure
taking the average signal and neglecting edge effects
induction signal collection
t '−t
t
1 Cg α *v 1
iind (t ) = imeas (t ) = vdrift q ∫ exp[ + α * vdrift t ' ] dt '
t
vdrift q e drift
g C gap gC gap 0
RinC g
if RinCg << 1/(α*vdrift)
imeas (t ) ≅ iind (t )
reasonable for
Rin typical narrow-
iind (t ) gap RPCs at 1cm2
scale
D
h Cg Cg Rin
w imeas (t )

6. How to create a simple avalanche model
We follow the following 'popular' model
• The stochastic solution of the avalanche Raether limit 8.7
equation is given by a simple Furry law (non-
space-charge
equilibrium effects are not included). regime ~7.5
• Avalanche evolution under strong space-
log10 Ne(t)
~7
charge regime is characterized by no
exponential-growth threshold
effective multiplication. The growth stops regime
when the avalanche reaches a certain number
of carriers called here ne,sat that is left as a
~2
free parameter.
exponential-fluctuation
regime
• The amplifier is assumed to be slow enough 0
to be sensitive to the signal charge and not to
to tmeas t
its amplitude. We work, for convenience, with
a threshold in charge units Qth. avalanche Furry-type
fluctuations
the parameters of the mixture are derived from recent measurements
of Urquijo et al (see poster session) and HEED for the initial ionization

7. MC results. Prompt charge distributions
for 'pad-type' detectors
4-gap 0.3 mm RPC standard mixture 1-gap 0.3 mm RPC standard mixture
Eff = 74%
Eff = 60%
Eff = 38%
simulated
simulated
measured
qinduced, prompt [pC]
qinduced, prompt [pC] measured
assuming space-charge saturation at
ne,sat= 4.0 107 (for E=100 kV/cm)
Data from:
P. Fonte, V. Peskov, NIM A, 477(2002)17.
P. Fonte et al., NIM A, 449(2000)295. qinduced, total [pC]

8. MC results. Efficiency and resolution for
'pad-type' detectors

9. fine so far
till here one can find more than a handful of similar
simulations by various different groups, always able to
capture the experimental observations.
to the authors knowledge nobody has ever attempted a
MC simulation of an 'electrically long RPC'
why?

10. strip
single-strip (loss-less)
induction transmission and
signal collection
1 Cg 1 Τ Cg y
iind (t ) ≅ vd q N e ( t ) imeas (t ) ≅ vd q N e (t − av ) + ∑
g C gap g 2 C gap v reflections
L0,L 1 2Z c
Zc = v= T=
C g ,L L0,L ⋅ C g ,L Z c + Rin
iind (t ) imeas (t )
Lo,L
D
Cg,L
h
Rin
w z
y
x − iind (t )

11. strip
single-strip (with losses)
At a given frequency signals attenuate in a transmission
line as: D
− have little effect for glass and Cu
Λ( f )
≈e electrodes as long as tan(δ)<=0.001 equivalent threshold !
?
1 R (f)
≈ L + Z c GL ( f )
Λ( f ) Zc ~ x 2/Texp(D/Λ)
log Ne(t)
threshold
iind (t )
Lo,L RL imeas (t )
to t
Cg,L GL
Rin
− iind (t )

12. strip
single-strip (HADES TOF-wall)
- area 8m2, end-cap, 2244 channels
- cell lengths D = 13-80 cm
Zc = 5 - 12Ω (depending on the cell width)
T = 0.2 - 0.4
v = 0.57c
- disturbing reflections dumped within 50ns
built-in electronic dead-time
- average time resolution: 70-75 ps
- average efficiency: 95-99%
- cluster size: 1.023
D. Belver et al., NIM A 602(2009)687
A. Blanco et al., NIM A 602(2009)691
A. Blanco, talk at this workshop

13. double-strip
double-strip (signal induction)
strip cross-section for HADES-like geometry
wide-strip E ≅
1 Cg
limit h << w z
iind (t ) = E z vdrift N e (t )
g C gap
same polarity
this yields signal induction
even for an avalanche
produced in the neighbor
strip (charge sharing)
opposite polarity!
D
We use formulas from:
T. Heubrandtner et al. NIM A 489(2002)439
h z
y
w extrapolated analytically to
an N-gap situation
x

15. double-strip
double-strip (transmission and signal collection)
0
Τ iind,v+ (t )+iind,v− (t ) Z m Rin iind,v− (t )−iind,v+ (t )
itr,meas(t )= + + ∑
2 2 ( Zc + Rin )2
2 reflections
y0
iind,v+ (t ) = iind (t − )
Z m Rin iind ,v − (t )+iind ,v + (t ) Τ iind ,v − (t ) −iind ,v + (t ) v + ∆v
ict,meas (t ) = + + ∑
( Z c + Rin ) 2
2 2 2 reflections y
iind,v− (t ) = iind (t − 0 )
v − ∆v
low frequency high frequency
term / 'double pad'-limit dispersive term
1 −1 ∆v Lm,L C m, L
v= v = L0,L (C g ,L +Cm,L ) , = −
L0,L ⋅ C g ,L v L0,L C g ,L + Cm,L 2Z c
T=
L0,L Z m 1 ⎡ Lm,L C m, L ⎤ Z c + Rin
L0,L Zc = , = ⎢ + ⎥
Zc = C g , L + C m, L Z c 2 ⎢ L0,L C g ,L + Cm,L ⎥
⎣ ⎦
C g ,L
It can be proved with some
single strip double strip parameters simple algebra that ict has
parameters zero charge when integrated
over all reflections

16. double-strip
double-strip (simulations)
input:
signal induced from an
avalanche produced at the signal transmitted
cathode + FEE response normalized to
signal induced
A. Blanco et al. NIM A 485(2002)328
cross-talk signal normalized
to signal transmitted in main
strip

17. double-strip
double-strip (measurements)
unfortunately very little information is published
on detector cross-talk. In practice this work of
2002 is the only one so far performing a
systematic study of cross-talk in narrow-gap RPCs
80-90% cross-talk
levels
cluster size:
1.8-1.9
!!!

18. double-strip
double-strip (optimization)
fraction of cross-talk Fct:
-continuous lines: APLAC
-dashed-lines: 'literal' formula
for the 2-strip case.
a) original structure
b) 10 mm inter-strip
separation
c) PCB cage
d) PCB
e) differential
f) bipolar
g) BW/10, optimized inter-
strip separation, glass
thickness and strip width.
h) 0.5 mm glass. Shielding
walls ideally grounded +
optimized PCB

19. double-strip
double-strip (optimization)

20. multi-strip
multi-strip
A literal solution to the TL equations
in an N-conductor MTL is of questionable
interest, although is a 'mere' algebraic problem. It is known
that in general N modes travel in the structure at the same
time.
For the remaining part of the talk we have relied on the
exact solution of the TL equations by APLAC (FDTD method)
and little effort is done in an analytical understanding

21. multi-strip
but how can we know if the TL theory works after all?
A comparison simulation-data for the cross-talk levels
extracted from RPC performance is a very indirect way
to evaluate cross-talk.
comparison at wave-form level was also done!

22. multi-strip
Far-end cross-talk in mockup RPC (23cm)
signal injected
with:
trise~1ns
tfall~20ns
50 anode 1 50
50 cathode 1 50
50 anode 2 50
50 cathode 2 50
50 anode 3 50
50 cathode 3 50
50 anode 4 50
50 cathode 4 50
50 anode 5 50
50 cathode 5 50

23. multi-strip
Near-end cross-talk in FOPI 'mini'
multi-strip RPC (20cm)
HV HV cathode
Glass
z
Spacers
signal injected
with:
trise~0.35ns
tfall~0.35ns cathode
Multistrip anode
M. Kis, talk at this workshop
50 anode 0 50
Y
50 anode 1 50
50 .......... 50
50 anode 11 50
50 anode 12 50
50 anode 13 50
50 anode 14 50
50 anode 15 50

24. multi-strip
most prominent examples of an a
priori cross-talk optimization
procedure as obtained in a recent
beam-time at GSI

25. multi-strip
30cm-long differential and ~matched
multi-strip
experimental conditions:
~mips from p-Pb reactions at 3.1 GeV, low rates,
high resolution (~0.1 mm) tracking
8 gaps Cm=20 pF/m
... ...
Cdiff=23 pF/m
Zdiff=80 Ω
intrinsic strip profile is
accessible!
probability of pure cross-talk:
1-3%
I. Deppner, talk at this
workshop

26. multi-strip
100cm-long shielded multi-strip
experimental conditions:
~mips from p-Pb reactions at 3.1 GeV, low
rates, trigger width = 2 cm (< strip width)
long run. Very high statistics.
... ...
5x2 gaps

27. multi-strip
100cm-long shielded multi-strip
time resolution for double-hits
double-hit no any of 3rdneighbors
double-hit in double 2st neighbors
hit
in any of 1 nd neighbors

28. multi-strip
100cm-long shielded multi-strip
time resolution for double-hits
tails

29. summary
• We performed various simulations and in-beam measurements of Timing
RPCs in multi-strip configuration. Contrary to previous very discouraging
experience (Blanco, 2002) multi-strip configuration appear to be well
suited for a multi-hit environment, if adequate 'a priori' optimization is
provided. Cross-talk levels below 3% and cluster sizes of the order of 1
have been obtained, with a modest degradation of the time resolution
down to 110 ps, affecting mainly the first neighbor. This resolution is
partly affected by the poor statistics of multiple hits in the physics
environment studied.
• There is yet room for further optimization.

30. acknowledgements
A. Berezutskiy (SPSPU-Saint Petersburg)
G. Kornakov (USC-Santiago de Compostela),
M. Ciobanu (GSI-Darmstadt),
J. Wang (Tsinghua U.-Beijing)
and the CBM-TOF collaboration