D Gonzalez Diaz Optimization Mstip Rp Cs
-
Upload
miguel-morales -
Category
Documents
-
view
2.987 -
download
0
Transcript of D Gonzalez Diaz Optimization Mstip Rp Cs
Diego González-Díaz (GSI-Darmstadt)
Santiago, 05-02-09
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.
definitions used
mirror electrodenot 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
cm535.02
≥=≥ rise
c
p tcfv
Dcm535.02
<=< rise
c
p tcfv
D
Some of the geometries chosen by the creative RPC developers
ALICE-LHC
V
-V
-V
STAR-RHIC
V
-V
V
HADES-SIS
-V
-V
FOPI-SIS
-V
V
all these schemes are equivalent regarding the underlying avalanche dynamics... but the RPC is also a strip-line, a fact that is manifested after the avalanche current has been induced. And all these strip-lines have a completely different electrical behavior.
-V
V
V
-V
V
S. An et al., NIM A 594(2008)39
!
HV filtering scheme is omitted
padpad structure
taking the average signal and neglecting edge effects
induction signal collection
D
w
h
tvdrift
gap
gind
drifteqvCC
gti *1)( α=
Cg RinCg
)(tiind
)(timeas
']'*'exp[1)(0
dttvCRttqv
gCti
t
driftgin
driftgap
meas ∫ +−
= α
)()( titi indmeas ≅
if RinCg << 1/(α*vdrift)
reasonable for typical narrow-gap RPCs at 1cm2
scale
Rin
How to create a simple avalanche model
We follow the following 'popular' model
• The stochastic solution of the avalanche equation is given by a simple Furry law (non-equilibrium effects are not included).
• Avalanche evolution under strong space-charge regime is characterized by no effective multiplication. The growth stopswhen the avalanche reaches a certain number of carriers called here ne,sat that is left as a free parameter.
• The amplifier is assumed to be slow enough to be sensitive to the signal charge and not to its amplitude. We work, for convenience, with a threshold in charge units Qth.
8.7Raether limit
~7
log 1
0N
e(t)
to
space-charge regime
exponential-growthregime
~7.5
~2
exponential-fluctuationregime
threshold
0
tmeas tavalanche 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
qinduced, prompt [pC]
qinduced, total [pC]
1-gap 0.3 mm RPC standard mixture
simulated
measured
Eff = 74%Eff = 60%Eff = 38%
measured
simulated
qinduced, prompt [pC]
assuming space-charge saturation atne,sat= 4.0 107 (for E=100 kV/cm)
4-gap 0.3 mm RPC standard mixture
Data from:P. Fonte, V. Peskov, NIM A, 477(2002)17.P. Fonte et al., NIM A, 449(2000)295.
MC results. Prompt charge distributions for 'pad-type' detectors
MC results. Efficiency and resolution for 'pad-type' detectors
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?
stripsingle-strip (loss-less)
transmission and signal collection
induction
)(1)( tNqvCC
gti ed
gap
gind ≅ ∑+−
Τ≅
sreflection
aved
gap
gmeas v
ytNqvCC
gti )(
21)(
LgL CLv
,,0
1⋅
=Lg
Lc C
LZ
,
,0=inc
c
RZZT+
=2
)(tiind
D
hw Rin
)(tiind−
)(timeasLo,L
Cg,L
x
zy
stripsingle-strip (with losses)
At a given frequency signals attenuate in a transmissionline as:
)( fD
e Λ−
≈have little effect for glass and Cu electrodes as long as tan(δ)<=0.001 equivalent threshold !
)(tiind
Rin
)(tiind−
Lo,L
Cg,L
)(timeas
log
Ne(
t)
to t
threshold
?)()(
)(1 fGZ
ZfR
f Lcc
L +≈Λ ~ x 2/Texp(D/Λ)
RL
GL
stripsingle-strip (HADES TOF-wall)
- cell lengths D = 13-80 cm
- average time resolution: 70-75 ps- average efficiency: 95-99%- cluster size: 1.023
D. Belver et al., NIM A 602(2009)687A. Blanco et al., NIM A 602(2009)691
- area 8m2, end-cap, 2244 channels
A. Blanco, talk at this workshop
Zc = 5 - 12Ω (depending on the cell width)T = 0.2 - 0.4v = 0.57c
- disturbing reflections dumped within 50ns built-in electronic dead-time
)()( tNvEti edriftzind =
T. Heubrandtner et al. NIM A 489(2002)439
wide-strip limit h << w gap
gz C
Cg
E 1≅
strip cross-section for HADES-like geometry
double-stripdouble-strip (signal induction)
same polarity
We use formulas from:
extrapolated analytically to an N-gap situation
this yields signal induction even for an avalanche produced in the neighbor strip (charge sharing)
opposite polarity!
D
w
x
zy
h
double-stripdouble-strip (transmission and signal collection)
∑+−
++
+Τ= +−−+
sreflection
vindvind
inc
inmvindvindmeastr
titiRZRZtiti
ti2
)()()(2
)()(2
)( ,,2
,,,
∑+−Τ
++
+= +−+−
sreflection
vindvindvindvind
inc
inmmeasct
titititiRZRZti
2)()(
22)()(
)()( ,,,,
2,
⎥⎥⎦
⎤
⎢⎢⎣
⎡
++=
+=
+−=
∆+=
−
LmLg
Lm
L
Lm
c
m
LmLg
Lc
LmLg
Lm
L
LmLmLgL
CCC
LL
ZZ
CCL
Z
CCC
LL
vvCCLv
,,
,
,0
,
,,
,0
,,
,
,0
,1
,,,0
21,
,)(
)()(
)()(
0,
0,
vvytiti
vvytiti
indvind
indvind
∆−−=
∆+−=
−
+
inc
c
RZZT+
=2LgL CL
v,,0
1⋅
=
Lg
Lc C
LZ
,
,0=
0
single stripparameters
double strip parameters
high frequencydispersive term
low frequencyterm / 'double pad'-limit
It can be proved with some simple algebra that ict has zero charge when integrated over all reflections
double-stripdouble-strip (simulations)
input:signal induced from an avalanche produced at the cathode + FEE response
signal transmitted normalized to signal induced
cross-talk signal normalized to signal transmitted in main strip
A. Blanco et al. NIM A 485(2002)328
double-stripdouble-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-talklevels
cluster size: 1.8-1.9
!!!
double-stripdouble-strip (optimization)
fraction of cross-talk Fct:-continuous lines: APLAC-dashed-lines: 'literal' formulafor the 2-strip case.
a) original structureb) 10 mm inter-strip separationc) PCB caged) PCBe) differentialf) bipolarg) BW/10, optimized inter-strip separation, glass thickness and strip width.h) 0.5 mm glass. Shielding walls ideally grounded + optimized PCB
double-stripdouble-strip (optimization)
multi-stripmulti-strip
A literal solution to the TL equationsin an N-conductor MTL is of questionableinterest, 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 theexact solution of the TL equations by APLAC (FDTD method)and little effort is done in an analytical understanding
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!
cathode 150 anode 1
5050
50
cathode 250 anode 2
5050
50
cathode 350 anode 3
5050
50
cathode 450 anode 4
5050
50
cathode 550 anode 5
5050
50
Far-end cross-talk in mockup RPC (23cm)multi-strip
signal injectedwith:trise~1nstfall~20ns
50 anode 0 50
50 anode 1 50
50 .......... 50
anode 11 50
50 anode 12 50
50
cathode
50 anode 13 50
50 anode 14 50
50 50anode 15
Y
z
Multistrip anode
HV cathodeHV
Spacers
Glass
Near-end cross-talk in FOPI 'mini' multi-strip RPC (20cm)
multi-strip
M. Kis, talk at this workshop
signal injectedwith:trise~0.35nstfall~0.35ns
multi-strip
most prominent examples of an a priori cross-talk optimization procedure as obtained in a recent beam-time at GSI
30cm-long differential and ~matched multi-strip
... ...
Cm=20 pF/m
Cdiff=23 pF/m
experimental conditions:~mips from p-Pb reactions at 3.1 GeV, low rates, high resolution (~0.1 mm) tracking
8 gaps
multi-strip
intrinsic strip profile is accessible!
probability of pure cross-talk:1-3%
Zdiff=80 Ω
I. Deppner, talk at this workshop
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.
100cm-long shielded multi-strip
5x2 gaps
no double hitdouble-hit in any of 1st neighborsdouble-hit in any of 2nd neighborsdouble-hit in any of 3rd neighbors
100cm-long shielded multi-stripmulti-strip
time resolution for double-hits
tails
100cm-long shielded multi-stripmulti-strip
time resolution for double-hits
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.
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