MP-TPC TESTS at KEK-PS
and
Analytic Formulation of Spatial Resolution
fora MPGD-Readout TPC
The ILC CDC group
(T. Matsuda/IPNS/KEK)
09/01/2008
ILC TPC School at Tsinghua Univ.
Toward the LC TPC
LC Detector Concept
Reconstruct final states in terms of partons (q, l, gb)
z
z
z
Identify 2ndary & 3tiary Vertex ID
Jet invariant mass --> W/Z/t ID and angular analysis -Æ Energy flow
Missing momentum --> neutrinos Æ Hermetic Detector
Æ Visualize Events as viewing Feynman Diagrams
Æ Require A State-of-the-art Detector
Requirements for the Central Trucker
z Momentum Resolution
z Two Hit Separation
z Truck Cluster (Cal) Matching
z Time Stamping
≦ 0.5 x 10-4 PT
≦ 2 mm (rΦ) x 5 mm (z)
≦ 1 mm (rΦ, ｒz)
O( 1ns)
Momentum Resolution:
What We Need to Acheive?
1.
e+e- → ZH → (Z→ μμ/ee) + X:
If δM（ μμ/ee） ＜＜ Γｚ、
then the beam energy spraed dominate.
→ Most probabaly δ(1/pt） ~ 1.0 - 0.5 x 10-4
2.
Slepton and the LSP masses though the end point measurement:
σM (Momentum Resolution) ~ σM (Parent Mass)
Only @ 1 ab-1 when δ(1/pt） ~ 0.5 x 10-4
3.
Rare decay: e+e- → ZH → Z + (H → μμ):
→
→
δ(1/pt) ~ 0.5 x 10-4 sufficinet？
Still need study one more time?
R&D for LC TPC
1 Demonstration Phase ：
With small TPC prototypes on mapping
out MPGD operation parameters and understanding spatial
resolution etc, to prove feasibility of MPGD TPC. Still need to work
for the best gas and the ion feed back and gating scheme. For MOSbased pixel digital TPC, still to complete the proof-of-principle tests.
2 Consolidation Phase:
The world-wide LC TPC collaboration and
EUDET build and operate the Large TPC Prototype (LP), φ ~ 80cm,
drift length ~ 60cm, with EUDET infrastructure as basis, to
establish a proof for the target momentum resolution (in nonuniform magnetic field), as well as basic designs and manufacturing
techniques of MPGD endplates, field cage and advanced electronics
in next 3 – 5 years. This phase corresponds to the term of the
Japanese Grant-in-Aid (“Gakujyutu Sosei”).
3 Design Phase:
During phase 2, a conclusion as to which endplate
technology to be the best for the LC TPC would be approached, and
final design would start as the real experimental collaboration is to
be formed.
Demonstration Phase
(1) Studies of New Gas Amplification System: MPGD
GEM, MicroMEGAS (MM)
* Basic characteristics of MPGD: Gain, electron
transmission, ion feedback, signal time structure,
signal spread, stabilities, gas, operation etc.
* New structures and new fabrication methods of
MPGD: Laser etching GEM, larger MPGD (up to 30
cm x 30cm), thicker GEM, MM with pillars, Bulk
MM structure,
Examples of Prototype TPCs
Carleton, Aachen,
Cornell/Purdue,Desy(n.s.)
for B=0or1T studies
Saclay, Victoria, Desy (fit
in 2-5T magnets)
Karlsruhe, MPI/Asia,
Aachen built test TPCs for
magnets (not shown),
other groups built small
special-study chambers
Settles
Demonstration Phase
(2) Performance Tests with Small TPC Prototypes
Various cosmic ray tests and beam tests of GEM and MicroMEGAS for
different gases with or without magnetic field (up to 5T) provided
data of spatial resolution and track separation.
In 2004-2006, the MP-TPC collaboration (Saclay/Orsay, MPI/DESY,
Carleton university and the CDC group including MSU group)
performed a series of performance tests at KEK π2 beam line for:
(1) MWPC with 2mm wide normal pads,
(2) 3-layer GEM (CERN) with 1mm wide normal pads,
(3) MicroMEGAS with normal pads (2 mm), and
(4) MiroMEGAS with the restive anode.
The tests utilized a small MP-TPC prototype, a thin-coil PermanentCurrent superconducting MAGnet; (PCMAG), and the ALEPH TPC
electronics at LEP.
A new analytic calculation of the spatial resolution was made to
understand the results.
KEK Beam Tests w/ MP-TPC
Use the same small prototype (MP-TPC) as a test
bench to compare different readout planes:
MWPC (1mm wire-pad gap)
Cathode plane:
typically at -6kV
GEM
Field cage:
maximum drift distance = 26 cm
MM (MicroMEGAS)
A Question Arises!
From the old Slide by A. Sugiyama in Nov. 2004
Analytic Formulation of
Spatial Resolution for
a MPGD-Readout TPC
-- Fundamental Limits on Spatial Resolution --
Achievement with KEK Beam Tests
Two Mysteries
Generic behaviors of resolution data
σx2
w2
if σP RF ! w
12
hodoscope limit
2
σx
=
Why
diffusion
dominant
2
σ0
+
2
Cd z/Nef f
Nef f < !N "
?
What is the origin
of σ0 ≡ σx (z = 0) ?
σ02
z
Fundamental Processes
Beam
Ionizations
Liberation of Electrons
PI (N ; N̄ )
Normal incidence
(no angle effect)
No δ-ray
Drift and Diffusion
Drift Volume
!
"
1
x2i
PD (xi ; σd ) = √
exp − 2
2σd
2πσd
Amplification and
further Diffusion
Amplification Gap
Readout Pads
(θ + 1)θ+1
PG (G/Ḡ; θ) =
Γ(θ + 1)
!
G
Ḡ
"θ
!
! ""
G
exp −(θ + 1)
Ḡ
Pad Response
x
Coordinate
Ionization Statistics
Ideal Readout Plane: Coordinate = Simple C.O.G.
PDF for Center of gravity of N electrons
&
'
%
#
$
∞
N
N
!
"
1 !
dxi PD (xi ; σd ) δ x̄ −
P (x̄) =
PI (N ; N̄ )
xi
N
i=1
N =1
i=1
Ideal readout plane
Gaussian diffusion
!
"
2
1
xi
PD (xi ; σd ) = √
exp − 2
2σd
2πσd
x
√
√
σd = Cd z
σx̄2
≡
!
2
dx̄ P (x̄) x̄ =
σd2
"1#
N
xi
1
≡ σd2 Nef
f
Nef f ≡ 1/ "1/N # < "N #
σd = Cd z
Gas Gain Fluctuation
Coordinate = Gain-Weighted Mean
PDF for Gain-Weighted Mean of N electrons
P (x̄) =
∞
!
PI (N ; N̄ )
N #$
"
dxi PD (xi ; σd )
i=1
N =1
$
(
'N
% &
i=1 Gi xi
d(Gi /Ḡ) PG (Gi /Ḡ; θ) δ x̄ − '
N
i=1 Gi
Gain-weighted mean
Gaussian diffusion as before
Gas gain fluctuation (Polya) θ = 0 : exp.
∞ : δ-fun
!
! ""
! "θ
G
(θ + 1)θ+1 G
exp −(θ + 1)
PG (G/Ḡ; θ) =
Γ(θ + 1)
Ḡ
Ḡ
!
σx̄2
≡
!
2
dx̄ P (x̄) x̄ =
Nef f =
!"
1
N
σd2
"
# $%
1
N
G
Ḡ
# $%
G
Ḡ
&2 '(−1
&2 '
≡
σd2
1
)
= 1*
%
N
x
Gi
1
Nef f
1+θ
2+θ
xi
&
< !N "
Sample Calc. for Neff
For 4 GeV pion and pad pitch of 6mm in pure Ar
M.Kobayashi
θ = 0.5
K=
Distribution of N
(<N> = 71)
Distribution of 1/N
(<1/N> = 0.028)
Distribution of Q
(K = 0.67)
!"
Nef f =
!"
1
N
# $%
G
Ḡ
&2 '(−1
1
1+θ
G
Ḡ
#2 $
=1+
% σ &2
G
Ḡ
= 21 < !N " = 71
≡1+K
Finite Size Pads
Coordinate = Charge Centroid
Charge on Pad j
Qj =
N
!
Electronic
!
"noise
2
∆Q2 = σE
Gi · fj (x̃ + ∆xi ) + ∆Qj ,
i=1
Normalized response fun. for pad j
!
j
Charge Centroid
track position
xi = x̃ + ∆xi
diffusion
!
"
∆x2 = σd2 = Cd2 z
x
fj (x̃ + ∆xi ) = 1
Pad pitch
!
!
Qj
Qj (wj)/
x̄ =
xi
Gi
j
j
PDF for Charge Centroid
P (x̄; x̃)
=
%
$
"N #$
d∆x
P
(N
;
N̄
)
P
(∆x
;
σ
)
d(G
/
Ḡ)
P
(G
/
Ḡ;
θ)
I
i
D
i
d
i
G
i
N =1
&
''
$
" &$i=1
!N
× j
d∆Qj PE (∆Qj ; σE ) dQj δ Qj − i=1 Gi · fj (x̃ + ∆xi ) − ∆Qj
!
)
(
Qj (wj)
j
× δ x̄ − !
Q
!∞
j
j
Full Analytic Formula
σx̄2 ≡
!
+1/2
−1/2
%
" #!
! +1/2 " # $
1
x̃
x̃
dx̄ P (x̄; x̃) (x̄−x̃)2 =
[A] +
d
[B] +[C]
d
w
w
Nef f
−1/2
Purely geometric term

[A] = 
#
j
2
(jw) !fj (x̃ + ∆x)" − x̃
Diffusion, gas gain fluctuation & finite
pad pitch term

2
[B] =
!
j,k
2
jkw !fj (x̃ + ∆x)fk (x̃ + ∆x)" − 
!fj (x̃ + ∆x)fk (x̃ + ∆x)" ≡
Electronic noise term
! σ "2 # 1 $ %
E
2
(jw)
[C] =
N2
Ḡ
j
!
!
j
jw !fj (x̃ + ∆x)"
d∆xPD (∆x; σd ) fj (x̃ + ∆x) fk (x̃ + ∆x)
!
!fj (x̃ + ∆x)" ≡ d∆xPD (∆x; σd ) fj (x̃ + ∆x)
Interpretation
σx2
2
[A]
Purely geometric term
(S-shape systematics
from finite pad pitch):
rapidly disappears as Z
increases
[B]
Diffusion, gas gain
fluctuation & finite pad
pitch term: scales
as 1/Nef f, for delta-fun
like PRF asymptotically:
w
if σP RF ! w
12
1
!
[A]
[B]
Nef f
!
w2
+ Cd2 z
12
"
if σP RF ! w
[C]
z
σx̄2
[C]
1
!
Nef f
!
2
w
+ Cd2 z
12
"
Electronic noise term:
Z-independent,
scales
!
"
as 1/N 2
Application√ to MM
For delta-function like
PRF, σx /w depends only
on σd /w and Nef f
(0, 1/ 12) : hodoscope limit
Full formula
√ has a fixed
point (0, 1/ 12)
Full formula enters
asymptotic region at
σd /w ! 0.4
Full formula has a minimum
of σx /w ! 0.1 at
σd /w ! 0.3
0.3
N eff =18.5
0.25
Full Theory
0.2
0.15
Asymptotic Formula
0.1
No Noise
0.05
0
!
σ0 /w = 1/ 12 Nef f
0
0.5
1
C d √z/w
Comparison with MC
Theory reproduces the
Monte Carlo simulation
very well !
0.8
Analytical Theory Neff=21.3
0.7
Monte Carlo Simulation
MP-TPC Micromegas
ArIso(95:5)
0.6
B=0T
0.5
0.4
B=0.5T
0.3
B=1T
drift distance
σx = σx (z; w, Cd , Nef f , [fj ])
pad pitch
0.2
Edrif t = 220V/cm
0.1
0
We can estimate the
resolution analytically
w = 2.3mm
0
100
200
drift distance (mm)
diffusion const.
pad response function
δ-fun. for MM: σP RF ! 12µm
gauss. for GEM: σP RF ! 350µm
Comparison with
Measurements
0.8
Analytical Theory Neff=18.5
0.7
c)
Global Likelihood
χ2
0.6
MP-TPC Micromegas
ArIso(95:5), B=1T
0.5
0.4
0.3
0.2
Edrif t = 220V/cm
0.1
0
w = 2.3mm
0
100
200
drift distance (mm)
Theory reproduces the
data well
Underestimation in the
data of σx at short
drift distance due to
track bias
Global likelihood method
eliminates S-shape
systematics at short
distance when possible
A Preliminary Result
TU–TPC Cosmic Ray Test at KEK
(Dec. 2007)
A Preliminary Result
TU–TPC Cosmic Ray Test at KEK
(Dec. 2007)
A Preliminary Result
TU–TPC Cosmic Ray Test at KEK
Dec. 2007
3 Layers of GEM
Pads: 1 x 10 mm
Extrapolation to LC TPC
0.8
Need to reduce pa Defocusing
+ narrow (1mm) pad for GEM d
size relative to PRF
Analytical Theory N eff =21.3
ArIsoCF 4(95:2:3), B=4T
0.7
0.6
0.5
Defocusing + narrow (1mm)
pad for GEM
2.3 mm pitch
0.4
Resistive anode for MM
0.3
0.2
1.0 mm pitch
0.1
0
0
500
1000
1500
2000
drift distance (mm)
Digital pixel readout? ideal
to avoid effect of gain
fluctuation if possible
Future R&D
Extrapolation to LC TPC
Sample calculation for GEM with Ar/CF4
0.8
0.7
Ar/CF4
0.6
E=200[V/cm ]
w=1.27[mm]
σ PRF=0.35[mm]
Neff =22
B=0[T ]
0.5
0.5[T ]
0.4
0.3
1[T ]
0.2
4[T]
0.1
0
0
500
1000
1500
2000
2500
Drift Distance [mm]
promising GEM in Ar/CF4 needs R&D
Summary
Efforts to understand KEK beam test data crystalized
as an analytic formula for the spatial resolution of a
MPGD readout TPC.
We can now analytically estimate the spatial resolution
drift distance
σx = σx (z; w, Cd , Nef f , [fj ])
pad pitch
diffusion const.
pad response function
Effective No. track electrons
Theoretical basis for how to
improve the spatial resolution!
Possible improvement of theory: angle effects