MICE collab. meting

1
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

2
Cooling box
Tracking devices
Tracking devices Measurement of momentum angles
and position
T.O.F. III Precise timing
T.O.F. I II Pion /muon ID and precise timing
Electron ID Eliminate muons that decay
3
DWARF4.0 Whats 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).

4
tracking detectors simulated
5
DWARF4.0 Whats 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
6
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.
7
Incoming beam

• Initial Beam
• Negligible transverse dimensions
• ltpTgt 3 MeV/c
• ltpzgt 290 MeV/c, Spread ? ?10
• After diffusion on Pb
• Transverse dimensions ?15 cm RMS
• ltpTgt 30 MeV/c
• ltpzgt 260 MeV/c, ?10

transverse momentum
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
10,000 Muons
8
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 ltxgt ltygt etc Second moments
variance(x) sx2 lt x2 - ltxgt2 gt etc
covariance(x) sxy lt x.y - ltxgtltygt gt
Covariance matrix
M
Getting at e.g. sxt is essentially
impossible with multiparticle bunch
measurements
Compare ein with eout
Evaluate emittance with
9
Statistics
Measure a sample with N particles Statistical
error on ltxgt is Dltxgt 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 ) ltlt Dein / ein
10
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.
• xmeas 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).

11
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 p cm rad
(normalized), corresponding to that of the
Neutrino Factory muon accelerator, as a function
of the input emittance 31. 28 MeV cooling
experiment (kinetic energy Ei200 MeV)
12
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 lt 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 gt sx (m.s.) 6
mrad. JUST MAKE IT!
13
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 gt 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.
-gt OK
14
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
(to keep B uniform on the plates)
Solenoid, B 5 T, R 15 cm, L gt 3d
z
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
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
T.O.F. Measure t With st ? 70 ps
Extrapolate x,y,t,px,py,pz, at entrance of the
channel. Make it symmetric at exit.
15
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
10,000 muons
16
Emittance Measurement
Transverse variable Resolution ( ? pT/pZ)
s(pT/pZ) ? 2.5
Longitudinal variable Resolution ( ? E/pZ)
s(E/pZ) ? 0.25
17
Emittance Measurement Results
Cooling channel without cooling No p
contamination, no m decay
?1
?in
?out
?4
mes
mes
With 1000 samples of 1000 accepted muons each
?in
?out
Generated Measured
Generated Measured
?in
?out
Ratio meas/gen
Ratio meas/gen
0.6
0.5
with 1000 m
with 1000 m
18
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 ms
(No cooling)

• (corresponding to
• 25,000 single ms produced
• 70,000 20 ns bunches sent

Measured
RMEAS, ? (1.?)2
Note ? is purely instrumental (mostly due to
multiple scatt. in the detectors). It can be
predicted and corrected for, if not too large.
Bias ? 1
(No cooling)
19
Emittance Reduction Optimization (I)
(1000 ms, No cooling, Perfect p/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 ?)
20
Emittance Reduction Optimization (II)
(1000 ms, No cooling, Perfect p/e Identification)
Optimization with respect to the scintillating
fibre diameter
6D bias
4D bias
Measured Perfect detectors
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)
21
Pion Rejection Principle
-34 MeV (?) -31 MeV (?)
z1
z0
?
Beam
10 metres
z
0.1 X0 (Pb)
?
4 X0 (Pb)
Measure x0, y0
Measure t0
Measure x1, y1
1.11 for ps 1.06 for ms
Measure t1
(p 290 Mev/c)
m
p
Compare with
With st 70 ps
1.08 for ps and ms
Measured in solenoid
Cut
22
Pion contamination in a solenoid muon beam line
(muE1 or muE4)
set B1 to 200 MeV/c
p/m ratio in beam is less than 1 if P(B2)/P(B1)
lt 0.8 TOF monitors contamination and reduces it
to lt10-4. gt No effect on emittance or
acceptance measurements.
This is the pion and muon yield as a function of
B2 setting
23
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

Large pZ difference (pin-pout)
Poor fits for electrons (Brems)
m
e
e
m
24
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 ?

25
(Obsolete) Experimental Layout (I)
About 5 of the muons arrive here
Pb, 0.1X0
Pb, 4X0
88 MHz
88 MHz
88 MHz
88 MHz
10 m
Channel with or without cooling B 5 T, R 15
cm, L 15 m
Measure x, y px, py, pz

• Determine, with many ?s
• Initial RMS 6D-Emittance ?i
• Final RMS 6D-Emittance ?f
• Emittance Reduction R

Measure t, x, y For pion rejection
26
TOF II
Electron ID
Experimental Solenoid II
2 m
Spectrometer trackers II
2 m
4-cell RF cavities
6 m
Coupling coil
Liquid Hydrogen absorbers
Focusing coils
Experimental Solenoid I
Spectrometer trackers I
2 m
Diffusers
10 m
TOF I II
Incoming muon beam
27
Emittance Measurement Principle (II)
In the transverse view, determine a circle from
the three measured points

• 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)
• Adjust d to make 1/3 of a turn between
• two plates (d 40 cm for B 5 T and
• pZ 260 MeV/c) on average
• Determine E from (p2 m2)1/2

x2, y2
Df12
Df23
R
C
x1, y1
x3, y3
d pz/E ? cDt RDf12 pT/E ? cDt
pz/d pT/ RDf12
28
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
(optimal for 5 T)
35 cm
40 cm
30 cm
To find pT and pZ, minimize
29
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
• Possible cure Add a fifth plate close to the
  fourth one in the exit diagnostic
• 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

5 cm
z
35 cm
40 cm
30 cm
30
Emittance Reduction Optimization (III)
(1000 ms, No cooling, Perfect p/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).

31
Pion Rejection Optimization (II)
(1000 ms, 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.
32
Pion Rejection Optimization (III)
(1000 ms, Perfect e Identification)
Beam Purity Requirement with Cooling
(Four 88 MHZ cavities)
1) 6D-Cooling and Resolution
2) Statistical significance with 1000
ms
6D Cooling
Pion cut at 1.00 Pion cut at 0.99
No Effect
Resolution
(in the beam)
33
Pion Rejection Optimization (IV)
(1000 ms, Perfect e Identification)
Beam Purity Requirement with Cooling
(Four 88 MHZ cavities)
1) Transverse-Cooling and Resolution
2) Statistical significance with 1000 ms
4D Cooling
Pion cut at 1.00 Pion cut at 0.99
No Effect
Resolution
(in the beam)
34
Pion Rejection Optimization (I)
(1000 ms, 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)
• Vary the T.O.F. resolution
• Apply the previous pion cut
• (E/p)/(Em/p) lt 1.00 and check
• the remaining pion fraction
• in a 10,000 muon sample.

Remaining pion fraction
Because of the beam momentum spread and of the
additional spread introduced by the 4X0 Pb plate,
the m/p separation does not improve for a
resolution better than 100-150 ps (for a path
length of 10 m)
35
Poor-Man Electron Identification (II)
(1000 ms, with cooling, 0 to 20 RF cavities)
1) 6D-Cooling and Resolution
2) Statistical significance with 1000
ms

• Generated
• Measured, perfect e-Id
• Measured, poor man e-Id

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)
• Elmgt calorimeter (?)

Resolution
36
Poor-Man Electron Identification (III)
(1000 ms, with cooling, 0 to 20 RF cavities)
1) Transverse Cooling and Resolution
2) Statistical significance with 1000 ms

• Generated
• Measured, perfect e-Id
• Measured, poor man e-Id

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