Transcript No Slide Title

Spectrometer design
Alain Blondel UniGe,
Patrick Janot CERN-EP
OUTLINE
•
Summary of requirements on
resolutions in space, time, energy
material budget multiple scattering
 ID
•
Open questions and how to answer them?
field homogeneity requirements
electron identification
background combinatorial
rates
•
Discussion
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
1
Cooling box
Tracking devices:
Measurement of momentum angles and position
Tracking devices
T.O.F. III
Precise timing
T.O.F. I & II
Pion /muon ID and precise timing
MICE collab. meting
5-8 Feb. 2002
Electron ID
Spectrometer designEliminate muons that decay
2
DWARF4.0 What’s in it?
 Particle transport in magnetic field and in RF; homogeneous field.
 Multiple Scattering in matter;
 tracker: 4 sets of three layers of 500 micron scintillating fibers
 Energy Loss (average and Landau fluctuations) in matter;
 Bremsstrahlung in matter; no showering
 Beam contamination with pions, pion decay in flight;
 Muon decay in flight (with any polarization), electron transport;
 Poor-Man Cooling Simulation (only Bz and EZ) to quantify
particle and correlation losses with cooling;
 Gaussian errors on measured quantities (x, y, t).
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
3
tracking detectors simulated
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
4
DWARF4.0: What’s not in ?
 Imperfections of magnetic fields; heating at solenoid exits;
(A field map and step tracking will be needed here…
Might be the source of important bias and systematic uncertainty
 Dead channels;
 Misalignment of detector elements;
 Background of any origin (RF, beam, …)
(Could well spoil the measurement. Need redundancy in case…)
track fit in presence of noise and dead channels (pattern recognition)
 electron ID detector
(definitely needs a geant4 type simulation for showers)
Fortran 77 + PAW
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
5
From Bob Palmer (after workshop in october 2001). See also J.-M. Rey
Such a realistic field map has not yet been implemented. Working on it.
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
6
Initial Beam:
Incoming beam
• Negligible transverse dimensions
• <pT> = 3 MeV/c;
• <pz> = 290 MeV/c, Spread  10%;
transverse
momentum
•After diffusion on Pb:
•Transverse dimensions: 15 cm RMS
• <pT> = 30 MeV/c;
• <pz> = 260 MeV/c, 10%;
ein = 110 mrad X 150 mm = 16 500 mm mrad
4% of these accepted
longitudinal momentum
The beam must “fill”
entirely the solenoid
acceptance to allow
the 6D-emittance to
be conserved without
cooling in the channel
MICE collab. meting
5-8 Feb. 2002
10,000 Muons
Spectrometer design
7
Emittance measurement
Each spectrometer measures 6 parameters per particle
x y t
x’ = dx/dz = Px/Pz
y’ = dy/dz = Py/Pz t’ = dt/dz =E/Pz
Determines, for an ensemble (sample) of N particles, the moments:
Averages <x> <y> etc…
Second moments: variance(x) sx2 = < x2 - <x>2 > etc…
covariance(x) sxy = < x.y - <x><y> >
Covariance matrix
 s 2x

 ...

M =  ...
 ...

 ...
 ...

s xy
s xt
s xx '
s xy '
s 2y
...
...
...
...
s t2
...
...
...
...
s 2x'
...
...
...
...
s 2y '
...
...
...
...
s xt ' 

s yt ' 

s tt ' 
s x't ' 

s y 't ' 
s t2' 
6D
e
 det( M xytx 'y 't ' )
Evaluate emittance with:
e 4 D  det( M xyx 'y ' )  e 2
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
Getting at e.g. sx’t’
is essentially impossible
with multiparticle bunch
measurements
Compare ein with eout
8
Statistics
Measure a sample with N particles
Statistical error on <x> is D<x>  sx / N
Where sx is the width of the measured distribution
Stat error on width of distribution is also Dsx sx / N
Stat error on emittance is De6D= e6D 6/N
Verify by generating M samples of N muons, that the spread of results
obeys the above laws.
Input and output particles are the same!
The emittances measured before and after the cooling channel are strongly
correlated. The variation of a muon transverse momentum going
through a short channel is smaller than the spread of transverse momenta
of the muons.
This explains that D ( ein / eout ) << Dein / ein
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
9
Resolution, bias, systematics
The width of measured distribution is the result of the convolution of
the true width with the measurement resolution
( s xmeas)2 = ( s xtrue)2 + ( s xdet)2
The detector resolution generates a BIAS on the evaluation of the width of the
true distribution. This bias must be corrected for.
sxmeas = s xtrue ( 1 + ½ ( s xdet)2/ ( s xtrue)2 )
For the bias to be less than 1%, the detector resolution must be (much)
better than 1/7 of the width of the distribution to be measured,
i.e. the beam size at equilibrium emittance. Say 1/10.
The systematic errors result from uncertainties in the bias corrections.
Rule of experience says that the biases can be corrected with a precision
of 10% of its value (must be demonstrated in each case).
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
10
MICE: what will it measure?
Equilibrium emittance = 4200 mm. mrad(here)
Cooling
Performance
= 16%
Figure V.4: Cooling channel efficiency, measured as the increase of the
number of muons inside an acceptance of 0.1 eV.s and 1.5  cm rad
(normalized), corresponding to that of the Neutrino Factory muon
accelerator, as a function of the input emittance [31].
MICE collab. meting
5-8 Feb. 2002
28 MeV cooling experiment (kinetic energy Ei=200 MeV)
Spectrometer design
11
Requirements on detectors
Equilibrium emittance: 3000 mm.mrad = 75 mm X 40 mrad
1. Spatial resolution must be better than 10 mm
VERY EASY,
The resolution with a 500 micron fiber is 500/12 =144 mm
2. Angular resolution must be better than 6 mrad…
s2x’ = ( s2x1 + s2x1 )/D + (sx’ (m.s.) )2
( s2x1 + s2x1 )/D < 1mrad for D = 30 cm.
sx’ (m.s.) = 13.6/ bP  x/X°
x = detector thickness X° = rad. Length of material
x = 1.5 mm of scintillating fiber (3 layers of 500 microns) X° = 40 cm
=> sx’ (m.s.) = 6 mrad….
JUST MAKE IT!
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
12
Requirements on detectors (ctd)
3. Time resolution
Must be better than 1/7 of the rms width of the particles contained
in the RF bucket.
200 MHz => 5 ns period, 2.5 ns ½ period, rms = 700 ps approx.
Need 70 ps or better.
Fast timing with scintillators gives 50 ps (with work) OK.
(This also provides pi/mu separation of incoming particles)
4. t’ = E/Pz resolution. Trickier, needs reconstruction. * ->
OK
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
13
Spectrometer principle
Need to determine, for each muon, x,y,t, and x’,y’,t’ (=px/pz, py/pz, E/pz)
at entrance and exit of the cooling channel:
Solenoid, B = 5 T, R = 15 cm, L > 3d (to keep B uniform on the plates)
z
d
T.O.F.
Measure t
With st  70 ps
MICE collab. meting
5-8 Feb. 2002
Note: To avoid heating
exit of the solenoid
due to radial fields, the
cooling channel has to
either start with the
same solenoid, or be
matched to it as well as
Possible.
d
Three plates of, e.g.,
three layers of sc. fibres
(diameter 0.5 mm)
Measure x1, y1, x2, y2, x3, y3
with precision 0.5mm/12
Extrapolate x,y,t,px,py,pz,
at entrance of the channel.
Make it symmetric at exit.
Spectrometer design
14
Tracker performance
Resolution on pT:
• Same for all particles; (4 plates)
• s(pT)  0.8 MeV/c.
Resolution on pZ:
• Strong dependence on pT;
• Varies from 1 to 50 MeV/c.
20%
10,000 muons
MICE collab. meting
5-8 Feb. 2002
10,000 muons
Spectrometer design
15
Emittance Measurement
Transverse variable Resolution
(  pT/pZ)
s(pT/pZ)  2.5%
MICE collab. meting
5-8 Feb. 2002
Longitudinal variable Resolution
(  E/pZ)
s(E/pZ)  0.25%
Spectrometer design
16
Emittance Measurement: Results
e1
mes
ein
ein
Cooling channel without cooling
No  contamination, no m decay
eout
With 1000 samples of 1000 accepted muons each:
ein
eout
Ratio meas/gen
Ratio meas/gen
e inmes  e1 (1   )
MICE collab. meting
5-8 Feb. 2002
mes
eout
Generated
Measured
Generated
Measured
e in  e1 (1   )
e4
0.5%
0.6%
with 1000 m
with 1000 m
e inmes  e in
(1   )
(1   )
mes
e out
 e out (1   )(1   )
Spectrometer design
e 4  e out (1   )
mes
e out
 e 4 (1   )
17
Emittance Reduction: Results
R = eout/ ein
Each entry is the ratio of
emittances (out/in) from
a sample of 1000 muons.
Biases and resolutions are
determined from this kind
of plots in the following.
Generated
RGEN,  1.
A 0.9% measurement
with 1000 single m’s
(No cooling)
(corresponding to
• 25,000 single m’s produced
• 70,000 “20 ns bunches” sent
Measured
RMEAS,  (1.+)2
Bias  1%
(No cooling)
MICE collab. meting
5-8 Feb. 2002
Note:  is purely instrumental
(mostly due to multiple scatt.
in the detectors). It can be
predicted and corrected for,
if not too large.
Spectrometer design
18
Emittance Reduction: Optimization (I)
(1000 m’s, No cooling, Perfect /e Identification)
Optimization with respect to the distance between the 1st and the last plates
e6D reduction: Resolution
e6D reduction: Bias
e4D reduction: Resolution
e4D reduction: Bias
No clear minimum, but the resolution and bias on the long. emittance reduction become
(slightly) worse when the average muon cannot do a full turn between 1st and last plates…
(possibly alleviated with reconstruction tuning ?)
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
19
Emittance Reduction: Optimization (II)
(1000 m’s, No cooling, Perfect /e Identification)
Optimization with respect to the scintillating fibre diameter
Measured
Perfect detectors
6D bias
4D bias
6D resolution
4D resolution
The smaller the better… Keeping the 6D bias and resolution at the % level requires a
diameter of 0.5 mm. Still acceptable with 1 mm, though. (2% bias, 1.2% resolution)
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
20
Pion Rejection: Principle
-34 MeV ()
-31 MeV (m)
z1
z0

Beam
10 metres
0.1 X0
(Pb)
Measure
t0
Measure
x0, y0
t1  t0
z1  z0

E
pz
x1 , y1 , x0 , y0  tan 
z
E

p
1.11 for ’s
1.06 for m’s
(p = 290 Mev/c)
m
4 X0
(Pb)
Measure
x1, y1
Measure
t1
Compare with

With st = 70 ps
1.08 for
’s and m’s
Em
p
Measured in solenoid
MICE collab. meting
5-8 Feb. 2002
Cut
Spectrometer design
21
Pion contamination in a solenoid muon beam line
(muE1 or muE4)
set B1 to 200 MeV/c
/m ratio in beam is less than 1% if
P(B2)/P(B1) < 0.8
TOF monitors contamination and
reduces it to <10-4.
=> No effect on emittance
or acceptance measurements.
MICE collab. meting
5-8 Feb. 2002
This is the pion and muon yield
as a function of B2 setting
Spectrometer design
22
Poor-Man Electron Identification (I)
 At the end of the cooling channel, a few electrons from muon decays (up to 0.4%
of the particles for a 15 m-long channel) are detected in the diagnostic device.
 These electrons have very different momenta and directions from the parent
muons, and they spoil the measurement of the RMS emittance (6D and 4D)
 About 80% of them can be rejected with kinematics, without effect on muons

2
pZ
Large pZ difference (pin-pout)
Poor fits for electrons (Brems)
m
e
e
m
MICE collab. meting
5-8 Feb. 2002
 p2
T
Spectrometer design
23
status & next steps
 A measurement(stat) of 6D/4D cooling can be achieved with reasonable detectors
10-3 stat error requires a few 105 muons
1% systematic bias on 6D cooling and and 0.5% bias on transverse cooling
Three time measurements with a 50-100 ps precision
 Two 1.5 to 2 m long, 5 T solenoids (1m useful length)
 Ten (twelve?) 0.5 mm diameter scintillating fibre plates (three layers each)
 One Cerenkov detector and/or one electromagnetic calorimeter (10 X0 Pb)
 However, systematic effects to be addressed with further
and/more detailed simulation
 Effect of magnetic field (longitudinal and radial) imperfections
 Effect of backgrounds
 Effect of dead channels and misalignment
 Multiple scattering dominates resolution, biases and systematics
we achieve 1% bias for nominal emittance,
will this be the case for equilibrium emittance?
 Other possibilities should be studied to evaluate their potential/feasibility
 Thin silicon detectors instead of scintillating fibres ?
MICE collab. meting
Spectrometer design
5-8 Feb.
 2002
TPC-GEM ?
24
(Obsolete) Experimental Layout (I)
Pb, 0.1X0
Pb, 4X0
10 m
About 5% of the
muons arrive here
88 MHz
88 MHz
88 MHz
88 MHz
Channel with or without cooling
B = 5 T, R = 15 cm, L = 15 m
Measure x, y
px, py, pz
Measure t, x, y
For pion rejection
Determine, with many m’s:
• Initial RMS 6D-Emittance ei
• Final RMS 6D-Emittance ef
MICE collab. meting
5-8 Feb. 2002
• Emittance Reduction R
Spectrometer design
ef
R
ei
25
TOF II
Electron ID
Experimental
Solenoid II
Spectrometer
trackers II
2m
2m
4-cell RF cavities
6m
Coupling coil
Focusing coils
Experimental
Solenoid I
Liquid Hydrogen
absorbers
Spectrometer
trackers I
2m
Diffusers
10 m
TOF I & II
MICE collab. meting Incoming
5-8 Feb. 2002
muon beam
Spectrometer design
26
Emittance Measurement: Principle (II)
In the transverse view, determine a circle
from the three measured points:
x2, y2
Df12
Df23
C
x1, y1
R
x3, y3
 Compute the transverse momentum
from the circle radius:
pT = 0.3 B R
px = pT sinf
py = -pT cosf
 Compute the longitudinal momentum
from the number of turns
pZ = 0.3 B d / Df12
= 0.3 B d / Df23
= 0.3 B 2d / Df13
(provides constraints for alignment)
d = pz/E  cDt
RDf12 = pT/E  cDt
 Adjust d to make 1/3 of a turn between
pz/d = pT/ RDf12
two plates
(d = 40 cm for B = 5 T and
pZ = 260 MeV/c) on average
 Determine E from (p2 + m2)1/2
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
27
Emittance Measurement: Improvement (I)
 The previous (minimal) design leads to reconstruction ambiguities for particle which
make  a full turn between the two plates (only two points to determine a circle)
 It also leads to reconstruction efficiencies and momentum resolutions dependent
on the longitudinal momentum, which bias the emittance measurements.
Solution: Add one plate, make the plates not equidistant
z
30 cm
35 cm
(optimal for 5 T)
40 cm
To find pT and pZ, minimize:
 p2
T
 x  x  R cos f  2  y  y  R sin f  2 
i
0
i
   i
  and
   i 0
si
si
i 1 
 
 

4
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
 p2
Z
pT


R
D
f

D
z

ij
ij 
p
Z

 


s RDfij
i j




2
28
Emittance Measurement: Improvement (II)?
 The previous design is optimal for muons between 150 and 450 MeV/c (or any
dynamic range [x,3x].
 Decay electrons have a momentum spectrum centred a smaller values and some
of them may make many turns between plates. The reconstructed momentum
is between 150 and 450 MeV anyway. Very low momentum electrons cannot be
rejected later on…
5 cm
z
 Possible cure: Add a fifth plate close to35
the
cmfourth one
40 in
cmthe exit diagnostic
30 cm
device. First try in the simulation (yesterday) looks not too good, but the
reconstruction needs to be tuned to this new configuration. (The rest of the
presentation uses the design with four plates.)
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
29
Emittance Reduction: Optimization (III)
(1000 m’s, No cooling, Perfect /e Identification)
Optimization with respect to the TOF resolution
 time resolution is almost irrelevant (up to 500 ps) for the emittance
measurement: no effect on the transverse emittance, and
marginal effect on the 6D emittance (resolution 0.9%  1.1%);
 Quite useful to determine the timing with respect to the RF, so
as to select those muons in phase with the acceleration crest
1/10th of a period (i.e., 1.1 ns for 88 MHz and 0.5 ns for 200 MHz).
Resolution must be 10% of it, i.e., 100 ps for 88 MHz and
50 ps for 200 MHz.
 Essential to identify pions at the entrance of the channel: Indeed
the presence of pions in the muon sample would spoil the longitudinal.
emittance measurement (E is not properly determined for pions,
and part of these pions decay in the cooling channel).
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
30
Pion Rejection: Optimization (II)
(1000 m’s, No cooling, Perfect e Identification)
Beam Purity Requirement (confirmed with cooling)
Measured
Perfect detectors
6D bias
4D bias
6D resolution
4D resolution
Need to keep the pion contamination below 0.1% (resp 0.5%) to have a negligible
effect on the 6D (resp. 4D) emittance reduction resolution and bias. It corresponds
to a beam contamination smaller than 10% (50%) when entering the experiment.
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
31
Pion Rejection: Optimization (III)
(1000 m’s, Perfect e Identification)
Beam Purity Requirement with Cooling
1) 6D-Cooling and Resolution
Pion cut at 1.00
Pion cut at 0.99
(Four 88 MHZ cavities)
2) Statistical significance with 1000 m’s
6D Cooling
No
Effect
Resolution
MICE collab. meting
5-8 Feb. 2002
(in the beam)
Spectrometer design
32
Pion Rejection: Optimization (IV)
(1000 m’s, Perfect e Identification)
Beam Purity Requirement with Cooling
1) Transverse-Cooling and Resolution
Pion cut at 1.00
Pion cut at 0.99
(Four 88 MHZ cavities)
2) Statistical significance with 1000 m’s
4D Cooling
No Effect
Resolution
MICE collab. meting
5-8 Feb. 2002
(in the beam)
Spectrometer design
33
Pion Rejection: Optimization (I)
(1000 m’s, No cooling, Perfect e Identification)
Optimization with respect to the TOF resolution
 Assume an initial beam formed
with 50% muons and 50% pions
(same momentum spectrum)
Remaining pion fraction
 Vary the T.O.F. resolution
 Apply the previous pion cut
(E/p)/(Em/p) < 1.00 and check
the remaining pion fraction
in a 10,000 muon sample.
Because of the beam momentum spread and of the additional spread
introduced by the 4X0 Pb plate, the m/ separation does not improve
for a resolution better than 100-150 ps (for a path length of 10 m)
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
34
Poor-Man Electron Identification (II)
(1000 m’s, with cooling, 0 to 20 RF cavities)
1) 6D-Cooling and Resolution
• Generated
• Measured, perfect e-Id
• Measured, poor man e-Id
2) Statistical significance with 1000 m’s
Remaining electron fraction
3 10-4
6 10-4
8 10-4
6D Cooling
Need better e-Id to get
back to the red curve!
• Cerenkov detector (1/1000)
• El’mgt calorimeter (?)
Resolution
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
35
Poor-Man Electron Identification (III)
(1000 m’s, with cooling, 0 to 20 RF cavities)
1) Transverse Cooling and Resolution
• Generated
• Measured, perfect e-Id
• Measured, poor man e-Id
2) Statistical significance with 1000 m’s
Remaining electron fraction
3 10-4
6 10-4
8 10-4
4D Cooling
No need for more e Id
For the transverse
cooling measurement
Resolution
MICE collab. meting
5-8 Feb. 2002
Spectrometer design
36