Development of Advanced Gaseous Detectors for Muon ... · layer of high resistive sheet directly on...

Development of Advanced Gaseous Detectors for Muon

Tracking and Triggering in Collider Experiments

Liang Guan 1,2

16-10-2014 Dissertation Defense

Supervised byProf. Xiaolian Wang1, Prof. Zhengguo Zhao1 and Prof. Junjie Zhu2

1 University of Science and Technology of China2 University of Michigan

Outline

Introduction

Thermo-bonded MICRO-MEsh GAseous Structure (Micromegas)

Thin gap Resistive Plate Chamber (RPC)

Small-strip Thin Gap Chamber (sTGC)

Summary

Liang Guan ([email protected]) Dissertation Defense 16 October 2014

mailto:[email protected]

Outline

Introduction

Thermo-bonded Micromegas (Micromegas)



Summary

Liang Guan ([email protected]) Dissertation Defense 16 October 2014 1


Physics of Collider Experiments

…

Standard model Dark matter Super symmetryLiang Guan ([email protected]) Dissertation Defense 16 October 2014 2

• Collider experiments, utilizing high energy accelerators and large spectrometers, are unique to discover new particles, resonances, phenomena … Changing our understanding of fundamental building blocks of the nature and their interactions

• Very broad physics topics: Standard Model, SUSY, Extra dimension etc…

• Hunting for heavy new particles relies on capturing high momentum secondary particles from their decays via different channels. (decay to muons is one of the important channel. e.g. H ZZ* 4µ)

New!


Muon tracking and trigger in collider experiments


ATLAS CMS

• Examples:

Drift tube (DT), Resistive plate chamber (RPC), Cathode Strip Chamber (CSC)

Monitored drift tube (MDT), Resistive plate chamber (RPC), Thin gap chamber (TGC) and Cathode Strip Chamber (CSC)

• Muon trigger and tracking based on large scale gaseous detectors. • Trigger and tracking are performed with separate detectors


Challenges of muon tracking and triggering in future experiments


• Take ATLAS as an example

• High backgrounds environment (expected ~ 15 kHz/cm2 at the hottest region at end-cap @ lumi. 7x1034 cm-2s-1) results in

» Low detector efficiency» Higher probability of generate fake trigger» Reduced tracking accuracy (space charge effect)

• Stringent requirements on rate capability, timing and localization precision simultaneously for on-line trigger and off-line muon reconstruction!

Rate vs. radius


R&D of Three Advanced Gaseous Detectors


• In the context of ATLAS muon upgrade program, we performed extensive studies on three advanced gaseous detectors for muon tracking and trigger in future collider experiments.

• Studies are carried out on Micro-mesh gaseous structure (Micromegas) (Part I), Resistive plate chamber (RPC) (Part II) and Thin gap multi-wire chamber (TGC) (Part III).

• Researches are focused on addressing critical issues of applying these detectors for muon detection in harsh high rate environment and understanding their basic characteristics which affect the timing and tracking.

• Research approaches: simulation, calculation, lab and beam tests …

Garfield, Magboltz, HEED: electron transportation ...Ansys Maxwell 3D, neBEM: electric field


Outline

Introduction

Part I Thermo-bonded MICRO-MEsh GAseous Structure (Micromegas)



Summary


• Thermo-bonded Micromegas

• Basic performance parameters

• Simulation

• High resistivity anode Micromegas

• Parallel ionization multiplier (PIM)



Introduction

• bulk-Micromegas* photolithography• microbulk-Micromegas** Kapton etching

* Giomataris et al. NIMA 560.2 (2006): 405-408.1.** Andriamonje et al. JINST 5.02 (2010): P02001.

• Fabrication• Micromegas structures

• Key advantages:• High rate capability: 105 Hz/mm2 *

• Spatial resolution: < 100 µm

• Present challenging • Scale to large size• Spark resistance in hadron

environment * Y. Giomataris, NIMA 419 (1998) 239



Thermo-bonded Micromegas

• Thermo-bond film: excellent insulating spacer

• Fabrication of thermo-bonded Micromegas

• An novel approach to construct avalanche gap: thermally bond woven meshes to anode PCB using thermo-bond film spacers

°C

No photolithography process Easier to build small prototyped in Univ. labs. with simple tools.

Potential to go to at least a few hundreds of cm2 size.


Measurement of Basic Performance Parameters

4.5 cm x 4.5 cm Thermo-bonded Micromegas

9 cm x 9 cm Bulk Micromegas

• Energy resolution for 5.9 keV X-rays

• Gas gain and energy resolution in Ar/iC4H10


I. Giomataris et al. NIM A560 (2006) 405


Measurement of Basic Performance Parameters

• Uniformity:

• Gain non-uniformity due to:

» PCB warping

» Avalanche gap non-uniformity

» Mesh sagging


• ± 20% across ~ 4.5 x 4.5 cm2

unsupported active area

Sufficiently for tracking and triggering applications


Simulation optimization

• Optimizing gas to improve uniformity• Electron transparency optimization

> 50% optically transparent woven wire meshes should be used


Various simulations studies on operational mechanism, among them are:


Micromegas with High Resistivity Anode

Micromesh

PCB Anode Pads

Thermo-bond film

Resistive sheet

Resistive adhesive film

Cathode

Signals1 MΩ

collimator

X-ray source• Attempting an alternative ways to make Micromegas spark-tolerant: attaching a thick layer of high resistive sheet directly on the anode

• Standard Micromegas is vulnerable to discharge when highly ionizing particles are present. Coating a thin resistive layer on the metal anode (separated by thin insulating layer and grounded at its periphery).

• High resistive materials studied

» High gain» Lateral charge spread in thick

resistive layer» Spark-protection


13


Micromegas with High Resistivity Anode (cont.)• Basic performance measurements

Gas Gain Charge up

Polycarbonate anode

Fe-55 spectra

Energy resolution

Rate capability

Illuminated area:2 mm x 0.3 mm

Semi-condu. glass

Polycarbonate

105

Regular glass


Semi-conductive

glass


Micromegas with High Resistivity Anode (cont.)

~ 2 x 104 ~ 3 x 104 ~ 4 x 104

• “Spark” signals recorded directly using 50 Ω terminated oscilloscope:

Gain

• Spark amplitudes: mostly < 100 mV; up to 0.5 V at high gain, rate less than ~10-4

per detected photon count • Spark signal duration : < 200 ns• Charge released: less than few nC; mostly at few tens of pC effective to protect front-end

electronics



Parallel Ionization Multiplier

• Parallel ionization multiplier (PIM): multiple mesh layers and multi-stage of avalanches. Originally intended to be used for tracking low energy beta rays.

• Attempt to design a structure and operate PIM at GEM-mode: only electrons extracted to the bottom induction gap. fast signal, fast timing!

• Prompt electron signal component:


Fast signal: 50% Fast signal: 17%


Parallel Ionization Multiplier

• Can we extract enough electrons from the bottom mesh to the induction gap?

• Fast signal is preferable, but …

E2

E1



Parallel Ionization Multiplier (cont.)

• Experimental study

Prototype photo Signals

Fe-55 spectrum Effective gain on anode

~ 15 % of amplitude on mesh(Sim: 10%)



Part I Summary

Development of a novel method to fabrication Micromegas: thermal bonding. Good energy resolution, basic performances parameters comparable to bulk Micromegas. Reasonable gain uniformity (< 20%).

Many simulation studies for optimizing thermo-bonded Micromegas with woven wire mesh.

Attempts made to develop high resistivity anode Micromegas for spark tolerance High resistivity material significantly reduce discharge amplitude.

Attempts made to develop fast timing parallel ionization multiplier (PIM) Analysis of prompt charge concentration; experimentally assesses the viability to operate PIM at “GEM-mode”.



Outline

Introduction


Part II Thin gap Resistive Plate Chamber (RPC)


Summary

• Introduction

• Beam test setup

• Beam test results (spatial resolution … )

• Rate capability measurements



Introduction - RPC for muon triggering

Aielli et al., NIM A 456.1 (2000): 77-81.

ATLAS CMS

Carrillo, NIMA 661 (2012): S19-S22.

• RPC in muon spectrometers of present experiments» Timing: 1-2 ns» Spatial resolution: a few mm to a few cm » Rate capabilities: up to 1 kHz/cm2



Introduction – Benefit of good timing for trigger



Introduction- Proposed fast tracking trigger system based on RPC

• Thin gap RPCs for excellent timing, fine pitch readout strips for precision coordinate measurements, dual end readout to make RPCs as mean-timers and also for second coordinate measurement

• Ideas need to be assessed Beam tests



• Glass electrode RPC» ~ 1 mm glass electrodes» 1.15 mm gas gap» Resistive paint: 1-5 MΩ/» Size: 96 cm x 32 cm» 1.27-mm-pitch readout strips at the

ground side

• Bakelite RPC» 2-mm-thick Bakelite electrodes,

1010 Ω∙cm bulk resistivity (same as used for ATLAS RPC)

» 1mm gas gap» Size: 20 cm x 20 cm» 1.27-mm-pitch readout strips at

the ground side • Gas mixture : Ar (94.7%):iC4H10(0.5%):SF6 (0.3%)

96 cm

20 cm

Thin gap Resistive Plate Chamber



• CERN SPS H8 beam line (180 GeV/c muon beam)

Reference for spatial resolution measurements: small-diameter (15 mm) Monitored Drift Tube Chamber (sMDT)

• Glass RPCs: horizontal strips reading from both ends

• Bakelite RPC: with vertical readout strips provide reference hit position along glass RPC r/o strips.

Beam Test Setup



Bakelite RPC

Glass RPC

180 GeV/c muon

180 GeV/c muon TGC Quad.

sMDT

Glass RPC

Beam Test Setup (cont.)



ATLAS MDT Front-end

Low noise electronics with Amplifier, Shaper and Discriminator (ASD)Zin=120 Ω. ENC = 6000 e- rms

Bipolar shaping, 15ns shaper peaking time

Sensitivity: 8.9 mV/fC

ALICE NINO Front-end

Fast electronics with differential in/out puts

40 Ω<Zin<75 Ω. ENC = 5000 e- rms

1 ns peaking time

Threshold: 10fC to 100fC

F. Anghinolfi et al., IEEE TNS 51(2004)Yasuo Arai et al., IEEE TNS 51 (2004)

• TDC chips with 0.78 ns least countused

• 100 ps resolution VME TDC modules (CAEN v1190A)used

Precision coordinate measurements Timing and 2nd coordinate measurements

Readout Electronics



• With MDT readout electronics

• With NINO readout electronics

HV @6.5 kV

HV @6.8 kV

1.15 mm gap glass RPC

1.15 mm gap glass RPC

Efficiency and Cluster Size



• Charge centroid (1.27-mm-pitch):- Resolutions: ~ 200 µm (Best) and ~ 220 µm (Average)- Limited by the nonlinear charge representation and small cluster size (~2.3)

• Using timing information only (1.27-mm-pitch): - Hit position determined to be the average center of strips in the cluster- Resolutions < 290 µm Useful for fast tracking at trigger level. (ATLAS NSW requires 300 µm online resolution per detector layer)

Precision Coordinate Spatial Resolution



• Over all time jitter from RPC and Scintillator

• Overall time jitter after time walk correction

After de-convolution:𝜎𝜎𝑅𝑅𝑅𝑅𝑅𝑅 ≅ 453 ±15 ps

𝜎𝜎 ≅ 613 ±16 ps

𝜎𝜎𝑅𝑅𝑅𝑅𝑅𝑅 ≅ 562 ±18 ps

𝜎𝜎 ≅ 697 ±18 ps

After de-convolution:

time jitter of reference scintillator: 413 ps

Time Resolution -1.0 mm gap RPC



• Over all time jitter from RPC and Scintillator

• Overall time jitter after time walk correction

After de-convolution:


𝜎𝜎 ≅ 656 ±14 ps


𝜎𝜎 ≅ 707 ±16 ps

After de-convolution:time jitter of reference scintillator: 413 ps

Time Resolution -1.15 mm gap RPC



Bonus of excellent timing


• Maximum charge strip off-line time jitter

Time

Strip ID

σ = 400 ps

• Good timing after off-line corrections Trigger RPC act as Time of flight detector. Could be used for searching slow exotic particles.


• 2nd Coordinate measurements• Hit position determine from signal arrival time difference from two ends of a strip• Resolution: ~1 cm (w/ 100 ps resolution TDCs) and ~ 7 mm if averaging the

reconstructed positions from multiple strips.

Mean-time and 2nd Coordinate

v ~15 cm/ns

• Mean-time: Average signal arrival time from two ends of a strip measured to be independent of hit position



Bakelite RPC Rate Capability Measurements

• Critical issue with RPC: rate capability limitations due to voltage drop across the high resistive electrodes.

Rate

Charge per countElectrode bulk resistivity

Electrode thickness

• A bi-gap Bakelite RPC (constructed by Univ. of Rome II) tested under intense 137Cs source at CERN GIF.

• RPC basic parameters: 2 x 1 mm gaps, 2 x 1010 Ω∙cm and 2 mm thick Bakelite plates as electrodes


filters


Bakelite RPC Rate Capability Measurements (cont.)

• Results: » fully efficient to muons @ > 18 kHz/cm2 detected photon rate. » charge per count: ~ 2 pC (compared with 30 pC for present ATLAS 2 mm

gap RPCs)

Current, charge per count vs. HVEfficiency vs. HV



Part II Summary

We proposed a fast tracking trigger scheme based on thin gap RPCs.

Several beam tests to study thin gap RPC on-line/off-line spatial resolution, timing etc. possibility to construct (sub-ns x sub-mm x sub-cm) trigger logic cells. It will be very powerful to handle muon triggering in an unexpected high rate environment.

Rate capability tests: critical to reduce delivered charge per count. RPC with 1 mm gaps and 1010 Ω∙cm resistive electrodes can be fully efficient to muons at > 18 kHz/cm2.



Outline

Introduction



Part III Small-strip Thin Gap Chamber (sTGC)

Summary • Introduction: ATLAS NSW upgrade

• sTGC Simulation – basic parameters

• sTGC Simulation – timing

• sTGC Simulation – charge production and sharing



Motivations for upgrading present muon Small Wheel:• Remove the “fakes”• Improve muon pT resolution and sharpen the trigger “turn-on” curve after the

Phase-II upgrade when the BW segment angle resolution is improved to ~ 1 mrad

New Small Wheel (NSW) structure: 2 x 4 planes of Micromegas (Primary tracking) sandwiched by 2 sTGC quadruplets (Primary trigger)

Introduction – ATLAS New Small Wheel



Similar structure as TGC in the present end-cap muon system except:

• Strip readout (3.2 mm x 1-2 m): precision measurement of track position in η• Pad segmentation (8 cm x 8 cm): fast pattern recognition for selecting readout strips• Lower cathode resistivity (~1 MΩ/ 100 kΩ/)

Introduction – sTGC for NSW



Introduction – sTGC Trigger Logic



Understand sTGC operational parameters • Electric field, Electron transportation coefficients

Evaluate sTGC timing capability for LHC bunch crossing identification • Impact of particle incident angle, magnetic field and HV

Estimate total amount of charges collected on strips, pads and wires

Understand the charge sharing among readout strips

Motivations for the simulation studies

Strips, pads, wires from sTGC detectors are all read out and used for on-line trigger or off-line muon reconstructions. Key requirements:

Timing LHC BX discrimination

Tracking 1 mrad on-line angular resolution trigger

~ 100 µm off-line resolution

Rate Up to 15 kHz/cm2

It is essential to:



• Electric field simulated using neBEM and FEM methods consistent with analytical calculation

• Strong (>1 kV/cm) electric field over 97% of the detector volume @ 2.85 kV

sTGC Electric Field



• Motions of electrons under E, B fields governed by

• Lorentz angle: the angle between the drift direction and the electric field

• Simulation of electron transport parameters: Magboltz package

Lorentz angleDrift velocity

Long. DiffusionTrans. Diffusion

Electron transportation in sTGC



• Timing performance: mainly determined by earliest cluster arrival time (high gas amplification factor)

• B-field at Small Wheel: < 1 T

Earliest cluster arrival time under different HV

2.8 kV, 0 degree0 degree

Earliest cluster arrival time under B field

Timing – Impact of HV and B-field

• Non-degraded timing performance in NSW B-field and with reduced HV.



• The earliest cluster arrival time: related to the track angle in the plane orthogonal to the wire plane.

• 16 sectors in the NSW φ direction. The track incident angle in the plane normal to wire plane: 0~11 degree.

• The simulation suggests an improved timing capability for inclined tracks.

Earliest cluster arrival time under different angles

Timing - Impact of Incident Angle



• Full simulation of single-layer time spectrum: take into account the gain fluctuation, electronics and reference detector time jitters > 95% events within 25 ns

• Multiplayer timing performance improves by shifting wire positions wrt. adjacent layers minimize the probability of passing low eclectic field region

0 degree

(With arbitrary offset)

2.85 kV

Single layer time spectrum Time spectrum from 3/4 coincident

with shifted wires

Timing – Fully Simulated Time Spectrum



• Avalanches develop within ~20 µm above the wire surface (Garfield sim.)

• Charge proportional to the logarithm of integration time

• Only ~ 20% of total charge will be collected within 25 ns int. gate

sTGC Charge Production



<<Raw charge spread on the cathode>>

<<Point charge dispersion>>

• R: resistance of cathode resistive paint per unit length

• C: capacitance between cathode and readout strip layer per unit length

• σ: width of raw charge spread (from Garfield simulation)

wire

wire

<<Charge development with time>>

• C: normalization factor • t0: average arrival time of earliest cluster

wire

sTGC Charge Sharing


(τ = RC)


• The charge density at position x and time t

𝜌𝜌′ 𝑥𝑥, 𝑡𝑡 = 𝐷𝐷(𝑥𝑥) ⊗𝜌𝜌(𝑥𝑥, 𝑡𝑡) ⊗𝑇𝑇(𝑡𝑡)

• The charge density at certain strip:

𝜌𝜌′ 𝑡𝑡 = 𝑥𝑥1

𝑥𝑥2𝜌𝜌′ 𝑥𝑥, 𝑡𝑡 𝑑𝑑𝑥𝑥

Strip charge density evolution

• Integration over time gives the collected charge on each strip

Important parameters to determine the charge spread:Resistive paint (cathode) resistivityStrip-cathode coupling capacitor (distance, dielectric constant)Electronics integration timeStrip width and pitch

sTGC Charge Sharing (cont.)



Distributions of the ratios of charges induced on various strips to the maximum charge

position charge

Maximum strip -x0 QC

2nd maximum strip p-x0 QR

3rd maximum strip -p-x0 QL

• Simulation procedures:» Vary hit position: (strip center,

half strip pitch).» Integrate charge density func.

between strip boundaries

sTGC Charge Sharing (cont.)

• Result: 2nd and 3rd max. charge strips get 60% and 20% of the charge on max. strip High dynamic front-end electronics required.


Data from beam test



Part III summary

Various simulations of sTGC electric field, electron transportation etc.

sTGC timing capability full-fills ATLAS NSW LV-1 trigger requirement (LHC 25 ns BX discrimination). Does not degrade with reduced HV, mag. field in NSW.

We have built an analytic model to describe charge dispersion in resistive layer and charge sharing among strips (still in developing):

• Could be implemented in ATLAS main software framework for sTGC digitization

• Very crucial to understand the impact of resistive paint non-uniformity to off-line muon reconstruction accuracy



Outline

Introduction




Summary



Summary

• Extensive R&D on three gaseous detectors are carried out to explore theircapabilities for muon tracking and triggering in collider experiments.

• We developed a novel way of constructing Micromegas. Detailed simulation andexperimental studies are performed. Attempts are made to construct highresistivity anode Micromegas and parallel ionization multiplier to address sparkissues and to improve parallel mesh structure detector timing capability.

• Our studies indicate RPCs are capable of providing (sub-ns x sub-mm x sub-cm) high granularity logic trigger cells Powerful for rejecting backgrounds and improving muon selectively

• Simulation study suggest sTGC is capable to preform LHC BX discrimination inNSW environment. We developed an analytical charge sharing model for betterunderstanding the detector characteristics.


Thank you!

感谢各位评审老师的聆听！

不积跬步无以至千里，不积小流无以成江海

List of publications

(5 in total. 4 as primary author or contact person)

Contact person. Drafted the paper

Contact person. Drafted the paper

Primary author. Drafted the paper


Second author

List of publications

(4 in total. 3 as primary author)




Important contributor

NSW TDR 2013: sTGC simulation subsection

List of conferences and talks

• IEEE NSS , 2010, Knoxville, USA• RD51 mini week meeting, 2010, CERN• 第八届全国高能物理年会，2010 南昌• 第一届中国微结构气体探测器会议，2010，庐江• 第二届中国微结构气体探测器会议，2012，高能所

• “Studies on Fast Trigger and High Precision Tracking with Resistive Plate Chamber”, 2013 CPAD and Instrumentation Frontier Community meeting, Argonne, IL, USA （口头报告）

• “Development of 1 mm low resistivity Bakelite Plate for thin-gap Resistive Plate Chamber”, RPC 2012 Conference, Frascati, Italy （会议海报）

• “Simulation Studies of Characteristics and Performances of sTGC for ATLAS Muon New Small Wheel”, 2013 US ATLAS Workshop Upgrade Session, Argonne, IL, USA （口头报告）

8 oral talks in total in national and international conferences

Backup slides

hardware based trigger that searches for high transverse momentum leptons, photons, jets and large missing and total transverse energy. Reduce 40MHz rate to 75kHz.

ATLAS Level -1 Trigger

dN_mu vs PT

Hot roll and hot press

Hot roll and hot press

Trans. diffu. coefficient

• Typical Fe-55 spectrum

Characteristics of Mmegas in Argon based mixture Ar/CO2 93:7

• Gas Gain

• Electron transparency • (Fe-55) Energy resolution vs. Gain

Gain ~104

Vm [V]

Gai

nFW

HM[%

]

Ea/Ed Vm [V]

“knee” @80

Uniformity correction

PIM fast signal calculation

PIM bottom mesh electron extraction coefficient

Prompt charge signal from 1.15 m gap

Beam test (w/ NINO) trigger logic

RPC time resolution (w. MRPC as reference)

Magnetic field around the SW

Earliest Cluster Arrival Time Distributions

Degree 0 Degree 5 Degree 10 Degree 15


Degree 40 Degree 45 Degree 50

Earliest Cluster Arrival Time vs. Track Hit Position



Degree 40 Degree 45 Degree 50

Algorithm for timing determination

• Trigger: n out of 4 coincidence

• Timing tag is given after nth latest response of a layer

Layer 1

Layer 2

Layer 3

Layer 4

Time Trigger!

Layer 1

Layer 2

Layer 3

Layer 4

Time Trigger!

3/4 coincidence time spectrum – single layer efficiency effect

• For instance, wire displacement = 0.5 mm

Tail disappears as efficiency approaches 100%

From J. Dubbert’s Talk @ ATLAS muon week 27th,March,2013

sTGC big sector layout

• sTGC big sector is subdivided into 4detection areas in azimuthal direction.

• Maximum wire length ~1 m

• Signal propagation velocity: 27ns/cm 3.7 ns arrival time difference for 1m

3/4 coincidence time spectrum – including additional jitters

• Signal propagation jitter

• Electronics jitter

• Single layer time spectrum measured with SonyASD/VMM+TDC well reproduced assuming a total external time jitter of 3 ns

• The subtracting ~2ns jitter from largereference scintillator : ~2.3 ns

𝜌𝜌(𝑥𝑥, 𝑡𝑡) = 𝑅𝑅𝑅𝑅/4𝜋𝜋𝑡𝑡𝑒𝑒(−𝑅𝑅𝑅𝑅4𝑡𝑡 𝑥𝑥2)𝐷𝐷 𝑥𝑥 =

𝑄𝑄2𝜋𝜋𝜎𝜎

𝑒𝑒(− 𝑥𝑥22𝜎𝜎2)

𝜌𝜌′ 𝑥𝑥, 𝑡𝑡 = 𝐷𝐷(𝑥𝑥) ⊗𝜌𝜌(𝑥𝑥, 𝑡𝑡) =𝑄𝑄

2𝜋𝜋(2 𝑡𝑡𝑅𝑅𝑅𝑅 + 𝜎𝜎2)

𝑒𝑒(− 𝑥𝑥2

4 𝑡𝑡𝑅𝑅𝑅𝑅+2𝜎𝜎

2)

⇒ Charge density on readout strip

Initial charge spread Dispersion on resistive layer

Induced charge distribution on strip

Charge sharing

𝜌𝜌 𝑡𝑡 = 𝑤𝑤1

𝑤𝑤2𝜌𝜌′ 𝑥𝑥, 𝑡𝑡 𝑑𝑑𝑥𝑥 =

𝑄𝑄2

[𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅

4𝑡𝑡 + 2𝑅𝑅𝑅𝑅𝜎𝜎2𝑤𝑤2 − 𝐸𝐸𝐸𝐸𝐸𝐸(

𝑅𝑅𝑅𝑅4𝑡𝑡 + 2𝑅𝑅𝑅𝑅𝜎𝜎2

𝑤𝑤1)]

Charge density of strip (w1,w2) vs. time

Strip width/pitch: 2.7/3.2mm

RC: 25 ns

σ: 1.12 mm

The charge sharing among strips depends on:• Dispersion time constant RC

• Charge integration time

Charge sharing

Validation: Garfield + Psipice

Initial charge spread:• Built wire chamber model and segmented

cathode to 1.5 mm pitch strips. Charge on cathode is the superimposition from each strip

Charge diffusion through resistive layer:• Built equielent1D RC network in Pspice

R47

rv arC47cv ar

R48

rv arC48cv ar

R49

rv arC49cv ar

C50cv ar

Charge sharing

Time

0s 5ns 10ns 15ns 20ns 25ns 30ns-I(Cstr1) -I(Cstr2) -I(Cstr3) -I(Cstr4) -I(Cstr5)

-20uA

-10uA

0A

Central strip

Neighbor to neighboring strip

Neighboring strip

Simulated current signals

RC=10ns

R(kΩ/mm) C (pF/mm) RC (ns) Calculation Garfield+Psipce

50 0.2 10 30.4% 31.8%

100 0.43 43 13.5% 16.8%

Q2nd/Qmax (muon hit in the center of the strip with Qmax charge)

Charge sharing

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