Diagnostic for the Decay Ring :
Energy Monitoring
m. apollonio – Imperial College London
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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the lattice of the DK racetrack ring
G4beamline 3D model
the method of spin depolarisation
resolution in ideal case
detector issues (location, …)
conclusions
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
Track DK Ring lattice
[C. Prior, IDS baseline]
Pm = 25 GeV/c
eN = 4.8 mm rad
e = 0.02 mm rad
aN = 30 mm rad (accept)
a = 0.127 mm rad
Twiss Parameters
(MADX)
straights:
sx = 51 mm
sx’ = 0.4 mrad
arcs:
sx = 16 mm
sx’ = 0.13 mrad
1/g = 4 mrad
sx’ * g ~ 0.1
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
G4beamline MODEL
spin depolarisation
ideal case
detector issues
conclusions
straight section
matching section
main open issues
on diagnostics
- measurement of divergence
- measurement of energy
via beam (de)polarisation
location for the device?
arc section
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
MAGNET
eff.
length
(mm)
width
(mm)
gap
(mm)
pole tip
radius
(mm)
field/gradient
(T/Tm-1)
QF
1500
-
-
200
+0.454
QD
1500
-
-
200
-0.464
1st Bend
4000
1000
200
-
-0.64
QD
800
-
-
200
-9.2
QF
1600
-
-
200
+11.6
MATCHING QD
1600
-
-
200
-7.66
2nd bend
600
1000
200
-
-1.9
QF
800
-
-
200
+4.1
3rd bend
2300
1000
200
-
+0.35
bend
2000
1000
200
-
-4.27
QF
500
-
-
200
+24.18
QD
500
-
-
200
-23.77
STRAIGHT
ARC
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
- Energy can be measured using the Polarisation of the Muon Beam
[ Raja-Tollestrup – FERMILAB-Pub-97 / 402] IF some P is saved after
all the massage in the machines ...
turn0 - I assume P = 27% is left when filling the DK ring
turn1
- Spin precesses in a ring due to coupling with magnetic fields
(bending magnets). NB: the trick does NOT work in a bow-tie shape
turn2
Sz(1)
Sz(0)
Sz(2)
- At every turn spin precession is determined by the SPIN TUNE:
w=2pga
a = 1.16E-3
This determines a modulation in P
- NB: if DE/E =0  g same for all muons  P keeps oscillating
if DE/E !=0  P goes to 0 after n turns
e+ spectrum from m-decay is a function of P :
d2N/dx dcosq = N0[(3-2x)x2 – P(1-x)x2 cosq]
(CM)
- I modelled the behaviour of a beam made of 100000 muons, all with
their spin and energy (DE/E =[0.01-0.05])
- Lorentz Boost
- Modulation in P produces a modulation in E(e+)
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
Centre of Mass frame: P=+100%
x=2Ee/mm
cosq
cosqLAB ~ 1
13/10/2009
0.99996
IDS-NF - TIFR Mumbai
- Joint Session
E (MeV)
X=2Ee/mm (CM)
Cos (qLAB)
LAB frame after
Lorentz boost
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g4beamline model
POL (%)
lattice
spin depolarisation
ideal case
detector issues
conclusions
DP/P = 3%
Pol=27%
fine mesh = 10 samples / turn
TURN
P modulation (spin precession)
and damping (DE/E !=0)
turn #
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
MEASURABLE SIGNAL
collect electrons at three different energy bins
[0,5] GeV
[5,10] GeV
[10,25] GeV
measure the TOTAL energy deposited
(e.g. in a calorimeter)
Energy resolution modeled as: sE/E=SQRT(1.03…/Ne)
[Raja-Tollestrup]
obtain a signal which shows:
- an oscillation due to Polarisation
- a decay slope due to continuous muon decays
- a modulation/damping due to DE/E
fit the signal at every TURN with a function:
2
f(T) = A e-BT (C exp-(G T ) cos(D+E T) + F)
G: contains DP/P
E: is the SPIN tune from which g can be inferred
B: describes muon decay slope
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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Ee (GeV)
g4beamline model
100000 initial muon decays
lattice
spin depolarisation
ideal case
detector issues
conclusions
31% in [0,5] GeV/c
turn #
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
28% in [5,10] GeV/c
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
41% in [10,25] GeV/c
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
This is somewhat ideal ... we need to collect the electrons!
How do we turn it into a realistic device for our case?
It has been suggested [Blondel – ECFA 99-197(1999)] to use the first bending magnet
after the decay straight section to SELECT electron energy bins: what does that mean
today with a realistic lattice (25 GeV)?
In fact electron is emitted ~parallel to m (due to the high g)
The spectral power of the 1st magnet depends on its FIELD and LENGTH
A G4Beamline simulation can tell us where electrons impinge after decaying somewhere
along the orbit
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
use a “realistic” beam of m+ from Zgoubi [C. Prior]
- Pm = 25 GeV/c DP/P = 1%
- eN = 30 mm rad
m at mid - straight
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
m at end of straight
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
elmon5
e from m decays
…
B2
B= -4.27T/L=2.0m
B1
B= -4.27T/L=2.0m
M3
B=+0.35T/L=2.3m
M2
B=-1.9T/L=0.6m
M1
B=-0.64T /L=4.0m
elmon3
elmon2
elmon1
force m decay
13/10/2009
elmon4
IDS-NF - TIFR Mumbai - Joint Session
m beam
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lattice
g4beamline model
First Dipole
of the Arc section
B= -4.27T / L=2.0m
spin depolarisation
ideal case
detector issues
conclusions
First Dipole of
the matching section
B= -0.64T / L=4.0m
elmon2
low P e-
elmon1
elmon5
elmon4
force m decay
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
elmon5 sensible plane
ideal case
detector issues
conclusions
aperture-x
R=200 mm pole tip radius
R>200 mm
R>200 mm
e+ out of
the aperture
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
elmon4 sensible plane
magnet gap
Dipole Length = 2m
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
elmon3
long drift for higher momenta
force m decay
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
Elmon3 – DS of M2  consider Ee = [2.5-7.5]
R=200 mm pole tip radius
R>200 mm
e+ out of
the aperture
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
How does TOT Ee changes turn by turn?
OUT OF detector acceptance
TOT Ee in [12.5,25] GeV/c bin
fit on 40 turns
TOT Ee in [12.5,25] GeV/c bin
fit on 80 turns
TOT Ee in [2.5,7.5] GeV/c bin
fit on 40 turns
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
TOT Ee in [2.5,7.5] GeV/c bin
fit on 80 turns
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lattice
g4beamline model
spin depolarisation
ideal case
[12.5,25] GeV/c – Energy Bias
= (E-25)/25
detector issues
conclusions
[12.5,25] GeV/c – DE/E
OUT OF detector acceptance
[2.5,7.5] GeV/c – Energy Bias
[2.5,7.5] GeV/c – DE/E
consider an initial sample of ~100000 e- [0,25]
bin [2.5,7.5] = 30%
measure E (DE/E) with (de)polarisation after n turn
E
= 25009+/-44 after 40 turns (24986+/-23, 100 turns)
DE/E = 0.89+/-0.36 after 40 turns (0.93+/-0.07, 100 turns)
Q.: how many electrons can I collect at turn=0?
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
1021 n/yr (1yr = 200 days) = 5.8x1013n/s
- 50 Hz (proton) rep. rate = 20 ms (fill) 
- 1.16 x 1012 n per fill
- NB: every fill = 3 bunch trains (L=440ns / S=1200ns)
- how many e+ (say) in a 10m section before the bending element?
2ns
- 10/1608 * 1.16 * 1012 = 7*109
- 30% [2.5-7.5GeV/c]  2*109
88 B
440ns
1200ns
(T)
(S)
3ns
1640ns
Tperiod = 5.36 msec
tm=520 msec
2x104 msec = 50Hz rep.rate
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
Open issues:
- which electrons are relevant for the measurement? i.e. which decay points
upstream of the bending dipole?
ideal decay point
- 1m? 10m? 100m upstream?
decay region >10m
B
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
A
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
to do list:
a- force the decay over a continuous volume (length) = some
technicalities with g4bl to be solved
b- build the e+spectrum at elmon(i)
c- introduce polarisation (verify if P is taken into account in
g4bl)
d- perform fit and evaluate precision/biases
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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lattice
g4beamline model
spin depolarisation
ideal case
detector issues
conclusions
Conclusions
• method of Energy Monitoring via depolarisation
revived for the IDS Race Track Decay Ring
• Use of G4Beamline for a more realistic rendering of
the events
• detail study on how distributed decays (upstream of
a dipole) change an e+ spectrum
• think of a better geometry/technology for a possible
detector
• evaluate e+ rate in interested areas
13/10/2009
IDS-NF - TIFR Mumbai - Joint Session
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