Workshop on MICE

1
Emittance Reduction MeasurementResults of
simulations, Beam requirements
Patrick Janot, CERN EP

• OUTLINE
• (Obsolete) Experimental Layout Detectors and
  Cooling Channel
• Fast Simulation Whats simulated and what is not
  ?
• Emittance Reduction measurement Principle and
  Design
• Emittance Reduction measurement Results and
  Optimization
• Pion Rejection and Beam Requirements
• Electron Identification
• Perspectives and Outlook

2
(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
3
(Obsolete) Experimental Layout (II)

• 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, Spread ? ?10

The beam must fill entirely the
solenoid acceptance to allow the 6D-emittance
to be conserved without cooling in the channel
10,000 Muons
4
Fast Simulation Whats in ?

• Particle transport in magnetic field and in RF
• Multiple Scattering in matter
• Energy Loss (average and Landau fluctuations) in
  matter
• Bremsstrahlung in matter
• 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).

5
Fast Simulation Whats not in ?

• Imperfections of magnetic fields heating at
  solenoid exits
• (A full simulation would be needed here
  Volunteers needed!
• Might be the source of important systematic
  biasses and uncertainties)
• Dead channels
• (Act as a global ineffiency, mostly
  irrelevant if independent of
• muon initial momentum and direction to be
  checked)
• Misalignment of detector elements
• (Easy to align in absence of background with
  a few thousand muons
• To be done in practice.)
• Background of any origin (RF, beam, )
• (Could well spoil the measurement. Need
  redundancy in case)
• ?

6
Emittance Measurement Principle (I)
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.
7
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
8
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
9
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
35 cm
40 cm
30 cm
10
Emittance Measurement Results (I)

• 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
11
Emittance Measurement Results (II)
Transverse Emittance Resolution ( ? pT/pZ)
s(pT/pZ) ? 2.5
Longitudinal Emittance Resolution ( ? E/pZ)
s(E/pZ) ? 0.25
12
Emittance Measurement Results (III)
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
13
Emittance Reduction Results (IV)
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 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)
14
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 ?)
15
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)
16
Emittance Reduction Optimization (III)
(1000 ms, No cooling, Perfect p/e Identification)
Optimization with respect to the TOF resolution

• Almost irrelevant (between 0 and 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
  accelerating 1/10th of
• a period (i.e., 1.1 ns for 88 MHz and 0.5 ns
  for 200 MHz). The
• resolution ought to 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).

17
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
18
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)
19
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.
20
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)
21
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)
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

Large pZ difference (pin-pout)
Poor fits for electrons (Brems)
m
e
e
m
23
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
24
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
25
Perspectives and Outlook

• A 1 measurement of 6D cooling and a 0.5
  measurement of transverse cooling
• can be achieved with ?1,000 detected muons
  (i.e., ?100,000 muon bunches) and
• reasonable detectors (typical transverse size
  30 cm)
• Three time measurements with a 50-100 ps
  precision
• Two 1.5 to 2 m long, 5 T solenoids
• Ten (twelve?) 0.5 mm diameter scintillating
  fibre plates (three layers each)
• One Cerenkov detector and/or one electromagnetic
  calorimeter (10 X0 Pb)
• However, some systematic effects have to be
  addressed with a detailed full
• simulation (to be written) to make this
  estimate rock-solid
• Effect of magnetic field (longitudinal and
  radial) imperfections
• Effect of background (any)
• Effect of dead channels and misalignment
• Other possibilities should be studied to
  evaluate their potential/feasibility
• Thin silicon detectors instead of scintillating
  fibres ?
• Detector design with a 200 MHz cooling channel ?