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