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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

Spectrometer design

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

Electron ID

Eliminate muons that decay

Spectrometer design

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).

Spectrometer design

tracking detectors simulated

Spectrometer design

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

Spectrometer design

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.

Spectrometer design

Incoming beam

- Initial Beam:
- Negligible transverse dimensions
- <pT> = 3 MeV/c;
- <pz> = 290 MeV/c, Spread 10%;
- After diffusion on Pb:
- Transverse dimensions: 15 cm RMS
- <pT> = 30 MeV/c;
- <pz> = 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

Spectrometer design

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

M =

Getting at e.g. sx’t’

is essentially impossible

with multiparticle bunch

measurements

Compare ein with eout

Evaluate emittance with:

Spectrometer design

Statistics

Measure a sample with N particles

Statistical error on <x> is D<x> = sx / N

Where sxis 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

Spectrometer design

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).

Spectrometer design

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 Ei=200 MeV)

Spectrometer design

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!

Spectrometer design

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

Spectrometer design

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 > 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.

Spectrometer design

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

Spectrometer design

Emittance Measurement

Transverse variable Resolution

( pT/pZ)

s(pT/pZ) 2.5%

Longitudinal variable Resolution

( E/pZ)

s(E/pZ) 0.25%

Spectrometer design

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

Spectrometer design

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

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)

Spectrometer design

Emittance Reduction: Optimization(I)

(1000 m’s, 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 ?)

Spectrometer design

Emittance Reduction: Optimization(II)

(1000 m’s, No cooling, Perfect p/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)

Spectrometer design

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 p’s

1.06 for m’s

Measure

t1

(p = 290 Mev/c)

m

p

Compare with

With st = 70 ps

1.08 for

p’s and m’s

Measured in solenoid

Cut

Spectrometer design

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) < 0.8

TOF monitors contamination and

reduces it to <10-4.

=> No effect on emittance

or acceptance measurements.

This is the pion and muon yield

as a function of B2 setting

Spectrometer design

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

Spectrometer design

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 ?
- TPC-GEM ?

Spectrometer design

(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

Spectrometer design

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

Spectrometer design

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

Spectrometer design

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:

Spectrometer design

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

presentation uses the design with four plates.)

5 cm

z

35 cm

40 cm

30 cm

Spectrometer design

Emittance Reduction: Optimization(III)

(1000 m’s, 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).

Spectrometer design

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.

Spectrometer design

Pion Rejection: Optimization (III)

(1000 m’s, Perfect e Identification)

Beam Purity Requirement with Cooling

(Four 88 MHZ cavities)

1) 6D-Cooling and Resolution 2) Statistical significance with 1000 m’s

6D Cooling

Pion cut at 1.00

Pion cut at 0.99

No

Effect

Resolution

(in the beam)

Spectrometer design

Pion Rejection: Optimization (IV)

(1000 m’s, Perfect e Identification)

Beam Purity Requirement with Cooling

(Four 88 MHZ cavities)

1) Transverse-Cooling and Resolution 2) Statistical significance with 1000 m’s

4D Cooling

Pion cut at 1.00

Pion cut at 0.99

No Effect

Resolution

(in the beam)

Spectrometer design

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)

- 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.

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)

Spectrometer design

Poor-Man Electron Identification (II)

(1000 m’s, with cooling, 0 to 20 RF cavities)

1) 6D-Cooling and Resolution 2) Statistical significance with 1000 m’s

- 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)
- El’mgt calorimeter (?)

Resolution

Spectrometer design

Poor-Man Electron Identification (III)

(1000 m’s, with cooling, 0 to 20 RF cavities)

1) Transverse Cooling and Resolution 2) Statistical significance with 1000 m’s

- 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

Spectrometer design

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