Diego González-Díaz (GSI-Darmstadt)

GSI, 10-02-09

acknowledgements

A. Berezutskiy (SPSPU-Saint Petersburg) G. Kornakov (USC-Santiago de Compostela),

J. Wang (Tsinghua U.-Beijing)

and the CBM-TOF collaboration

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.

why?

Dipolemagnet

The Compressed Baryonic Matter Experiment

Ring ImagingCherenkovDetector

Transition Radiation Detectors

Resistive Plate Chambers(TOF), more than 150m2, more than 100m2 require of strip-based coverage

Electro-magneticCalorimeter

SiliconTrackingStations

Projectile SpectatorDetector(Calorimeter)

VertexDetector

huge cross-talk observed for timing RPCs with double-strip read-out

80-90% cross-talklevels

cluster size: 1.8-1.9

!!!

A. Blanco et al. NIM A 485(2002)328

but really...why?

definitions used here

cm535.02

rise

c

p tc

f

vD

Pad: set of 1+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

This definition leads to:

cm535.02

rise

c

p tc

f

vD

pad strip

mirror electrodenot counting

Multi-Pad: set of N+1(ref) conductors electrically small

narrow-gapRPCs

cm6035.02

rise

c

p tc

f

vD cm60

35.02 rise

c

p tc

f

vDwide-gap

RPCs

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

pad readoutpad

D

w

h

tvdrift

gap

gind

drifteqvC

C

gti

*1)(

Cg

induction signal collection

RinCg

)(tiind

)(timeas

']'*'

exp[1

)(0

dttvCR

ttqv

gCti

t

driftgin

driftgap

meas

)()( titi indmeas

if RinCg << 1/(α*vdrift)

reasonable for typical narrow-gap RPCs at 1cm2 scale

Rin

taking the average signal and neglecting edge effects

how to create a simple avalanche 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 stops when 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.

log 1

0 N

e(t) ~7

to t

space-charge regime

exponential-growthregime

~7.5

tmeas

avalanche Furry-typefluctuations

~2

Raether limit 8.7

exponential-fluctuationregime

threshold

0

We use the following 'popular' model

the parameters of the mixture are derived from recent measurements of Urquijo et al. (see poster session) and HEED for the initial ionization

pad

qinduced, prompt [pC]

qinduced, total [pC]

simulated

measured

Eff = 74%

Eff = 60%

Eff = 38%

measured

simulated

ne,sat= 4.0 107 (for E=100 kV/cm)

qinduced, prompt [pC]

assuming space-charge saturation at

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

pad

1-gap 0.3 mm RPC standard mixture

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

to the authors knowledge nobody has ever attempted a MC simulation of an 'electrically long RPC'

fine so far

why?

till here one can find more than a handful of similar simulations by various different groups, always able to capture the experimental observations.

single-strip readoutstrip

)(1

)( tNqvC

C

gti ed

gap

gind

D

hw

inc

c

RZ

ZT

2

transmission and signal collection

)(tiind

induction

Rin

)(tiind

Cg,L

Lo,L

LgL CLv

,,0

1

Lg

Lc C

LZ

,

,0

sreflection

aved

gap

gmeas v

ytNqv

C

C

gti )(

1

2)(

)(timeas

x

zy

single-strip readout (with losses)strip

)(tiind

Rin

)(tiind

Cg,L

Lo,L )(timeas

log

Ne(

t)

to t

threshold

~ x 2/Texp(D/Λ)

GL

RL

)()(

)(

1fGZ

Z

fR

f Lcc

L

At a given frequency signals attenuate in a transmissionline as:

)( f

D

e

?

equivalent threshold !they have little effect for glass and Cu electrodes as long as tan(δ)<=0.001

)()( tNvEti edriftzind

T. Heubrandtner et al. NIM A 489(2002)439

We use formulas from:

extrapolated analytically to an N-gap situation and based on the Ramo theorem

wide-strip limit h << w gap

gz C

C

gE

1

strip cross-section for HADES-like geometry

this yields signal induction even for an avalanche produced in the neighbor strip (charge sharing)

double-strip

double-strip readout (signal induction)

same polarity

opposite polarity!

D

hw

x

zy

double-stripdouble-strip readout (transmission and signal collection)

sreflection

vindvind

inc

inmvindvindmeastr

titi

RZ

RZtititi

2

)()(

)(2

)()(

2)( ,,

2,,

,

sreflection

vindvindvindvind

inc

inmmeasct

titititi

RZ

RZti

2

)()(

22

)()(

)()( ,,,,

2,

LmLg

Lm

L

Lm

c

m

LmLg

Lc

LmLg

Lm

L

LmLmLgL

CC

C

L

L

Z

Z

CC

LZ

CC

C

L

L

v

vCCLv

,,

,

,0

,

,,

,0

,,

,

,0

,1

,,,0

2

1,

,)(

)()(

)()(

0,

0,

vv

ytiti

vv

ytiti

indvind

indvind

inc

c

RZ

ZT

2LgL CLv

,,0

1

Lg

Lc C

LZ

,

,0

single-stripparameters

double-strip parameters

0

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-strip

double-strip (simulations)

input:signal induced from an avalanche produced at the cathode + FEE response

signal transmitted normalized to the induced signal

cross-talk signal normalized to the signal transmitted in the main strip

A. Blanco et al. NIM A 485(2002)328

prototype 2002!

double-strip

double-strip (comparison with data)

multi-stripmulti-strip

A literal solution to the Transmission Line equationsin an N-conductor Multi-TL 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 rest 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

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

50

50

50

cathode 250 anode 2

50

50

50

cathode 350 anode 3

50

50

50

cathode 450 anode 4

50

50

50

cathode 550 anode 5

50

50

50

far-end cross-talk in mockup RPC (23cm)

signal injectedwith:trise~1nstfall~20ns

multi-strip

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

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

selected example of an optimized read-out structure as obtained in a recent beam-time at GSI

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

RHV~10MΩ/

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

seems to be well suited for a multi-hit environment, if adequate 'a

priori' optimization is provided. Cross-talk levels below 3% 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

environment studied.

• There is yet room for further optimization.

Appendix

double-strip

double-strip (optimization)

fraction of cross-talk Fct:-continuous lines: APLAC-dashed-lines: 'literal' formulafor 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

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

probability of pure cross-talk:1-3%

intrinsic strip profile is accessible!

Zdiff=80 Ω

I. Deppner, talk at this workshop

8 gaps

multi-strip

35-cm long wide-strip, mirrored and shielded

... ...

Zc~18 Ω

BW=260 MHzRin=100 Ω

Fct=11%little dispersive

experimental conditions:~mips from p-Pb reactions at 3.1 GeV, low rates, trigger width = 2 cm (< strip width)

Fct=19%

'fine-tunning'inter-strip regiondominated by trigger width

probability of pure cross-talk:1-3%

Analysis with high resolution tracking on-going.

transverse scan

Cg

Cm

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

continuous line: data from Basurto et al.

in pure Freon [5]

α extrapolated to mixture by using Freon's partial pressure:

αmixture = αFreon(E/fFreon) fFreon

vd directly taken from Freon (inspired on microscopic codes)

vd,mixture = vd,Freon

Parameters of the gas used for input: α* (effective Townsend coefficient), vd (drift velocity), no (ionization

density)

HEED(from Lippmann[4])

n o [m

m-1]

little dependencewith mixture!

*purely phenomenological!

strip

single-strip (HADES TOF-wall)

- average time resolution: 70-75 ps

- average efficiency: 95-99%

- cluster size: 1.023

- cell lengths D = 13-80 cm

D. Belver et al., NIM A 602(2009)687

A. 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