2-4/june/20102nd euronu meeting - strasbourg1 muon beam polarimeter for the nf decay rings m....
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2-4/June/2010 2nd EUROnu meeting - Strasbourg 1
Muon Beam Polarimeter for the NF Decay Rings
m. apollonio – Imperial College (London)a. blondel – Universite de Geneve
d. kelliher – ASTeC (RAL)
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• the lattice of the DK racetrack ring• G4beamline 3D model• the method of spin precession• resolution in ideal case• detector issues (location, …)• conclusions
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Track DK Ring lattice[C. Prior, IDS baseline]
P = 25 GeV/cN = 4.8 mm rad = 0.02 mm radaN = 30 mm rad (accept)a= 0.127 mm rad
Twiss Parameters (MADX)straights:x = 51 mmx’ = 0.4 mradarcs:x = 16 mmx’ = 0.13 mrad
1/ = 4 mrad x’ * ~ 0.1
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MAGNET eff. length (mm)
width(mm)
gap (mm)
pole tip radius (mm)
field/gradient (T/Tm-1)
STRAIGHTQF 1500 - - 200 +0.454
QD 1500 - - 200 -0.464
MATCHING
1st Bend 4000 1000 200 - -0.64
QD 800 - - 200 -9.2
QF 1600 - - 200 +11.6
QD 1600 - - 200 -7.66
2nd bend 600 1000 200 - -1.9
QF 800 - - 200 +4.1
3rd bend 2300 1000 200 - +0.35
ARC
bend 2000 1000 200 - -4.27
QF 500 - - 200 +24.18
QD 500 - - 200 -23.77
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main open issues on diagnostics
- measurement of divergence
- measurement of energy/polarization
via spin precession
location for the device?
G4beamline MODEL straight section
matching section
arc section
- measurement beam current
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- Spin precesses in a ring due to coupling with magnetic fields (bending magnets).
- At every turn spin precession is determined by the SPIN TUNE: = 2 a a = 1.16E-3
-Every muon spin evolves independently:- if ∆E/E = 0, P oscillates between two extremes (± |Pmax|)- if ΔE/E ≠ 0, P decoheres (polarization damping)
- modelled behaviour of a beam (1E6 muons) all with their spin and energy (E/E =[0.01-0.05])
- Lorentz Boost - Modulation in P produces a modulation in E(e+)
- I assume P = 18% is left when filling the DK ring
Sz(0)Sz(1)
turn0turn1
Sz(2)
turn2
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B
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d. k
ellih
er –
AS
TeC
(R
AL)
, m
.a.
(IC
)
-Check polarization vs turn pattern: model vs Zgoubi
0
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P e
cos
P = 1 -c.o.m.
cos(Θ) x=2E/m
Ee (MeV)
cos(
Θ)
Lab-FramePe LAB
cosLAB ~ 1
-Ee spectrum in the muon c.o.m.- function of P
1
2
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[0,5] GeV[0,5] GeV [15,18]GeV
[15,18]GeV
- What does it happen when we sample a fraction of the Ee spectrum? - How we parametrize the Beam Energy spread?
3
2-4/June/2010
Ee spectrum
We sample [a,b]:- [0,5] or,- [15,18]…
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NOsensitivity
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MEASURABLE SIGNAL
- collect electrons at different energy bins, [a,b] GeV
- try to maximize A (enhanced oscillatory pattern)
- measure the TOTAL energy deposited (e.g. in a Cherenkov+calorimeter) -Energy resolution modeled as: E/E=√(1.03…/Ne) [Raja-Tollestrup]
Signal fitted to Eq. (3)
f(T) = A e-T/ (1+/7*exp(-(E/E)2/2) * P * cos (+T))
: is the SPIN tune from which can be inferred: muon decay slope [in n. of turns]P: polarisation of the beam
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[0,5] GeV/cN0=30% (1E6)
fit (80 turns)
E = 24999 ± 40 MeV
E/E = 2.6 ± 0.1 %
= 97.5 ± 0.15
P = (22. ± 0.7)%[15,18] GeV/cN0=30% (1E6)
fit (80 turns)
E = 25040 ± 38 MeV
E/E = 2.57 ± 0.15 %
= 97.6 ± 0.16
P = (10.8 ± 0.7)%
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-18% P0
E/E=2.5% (hw)
derive actual P from MAX-min excursions
[0, 5] GeV
[15, 18] GeV
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-18% P0
E/E=2.5% (hw)
[0.0,2.5] GeV/cN0=16.0% (1E6)
fit (80 turns)
E = 24998 ± 37 MeV
E/E = 2.55 ± 0.09 %
= 97.56 ± 0.14
P = (25.9 ± 0.7)%
Statistic Precision of Fit (w.r.t. # of turns)
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High A
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-18% P0
E/E=2.5% (hw)
[2.5,5.0] GeV/cN0=15.5% (1E6)
fit (80 turns)
E = 24999 ± 49 MeV
E/E = 2.57 ± 0.12 %
= 97.47 ± 0.14
P = (20.8 ± 0.7)%
Statistic Precision of Fit (w.r.t. # of turns)
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-18% P0
E/E=2.5% (hw)
[5.0,7.5] GeV/cN0=14.7% (1E6)
fit (80 turns)
E = 24876 ± 68 MeV
E/E = 2.66 ± 0.15 %
= 97.52 ± 0.14
P = (15.5 ± 0.7)%
Statistic Precision of Fit (w.r.t. # of turns)
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-18% P0
E/E=2.5% (hw)
[7.5,10.] GeV/cN0=13.4% (1E6)
fit (80 turns)
E = 25069 ± 126 MeV
E/E = 2.33 ± 0.35 %
= 97.65 ± 0.15
P = ( 7.5 ± 0.8)%
Statistic Precision of Fit (w.r.t. # of turns)
Low A
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This is somewhat ideal ... we need to collect the electrons!
How do we turn it into a realistic device for our case?
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 (due to the high)
The spectral power of the 1st magnet depends on its FIELD and LENGTH
A G4Beamline simulation used to determine downstream electron distributions
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use finite size beams of from Zgoubi [C. Prior, D. Kelliher]- P = 25 GeV/c P/P = 1% , P/P = 2.5% (*)
- N = 30 mm rad at mid - straight at end of straight(*) half width
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Device location and Naming Convention
beamlow E e+
high E e+
longitudinal monitor
tran
sver
se m
onito
r
“good” decay
“bad” HE decay
Bending Magnet
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…B3B2B= -4.27T/L=2.0mB1B= -4.27T/L=2.0mM3B=+0.35T/L=2.3mM2B=-1.9T/L=0.6m M1B=-0.64T /L=4.0m beam
e from decays
elmon6-L
elmon5-T
elmon4-Lelmon3.1-Lelmon3-T
elmon2-T
elmon1-L
force decay
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Choice of location compromise among several factors- spectral power of magnet (determines covered energy range)- upstream free decay path (ideally “magnet free”)
some cases here considered:
Naming convention: HE>10 GeV, ME=[5,10] GeV, LE<5GeV Possible Cases (PRO, CON)- elmon1-L: 1st bending after long straight, small SP selects LE e+ mostly swept
away by previous q-poles
-elmon2-T: small SP, cannot separate HE component
-elmon3-T: long decay path, decent SP separate LE,ME
-elmon3.1-L: inside the last bend of the matching section, small SP (E<0.7 GeV)
-elmon4-L: need to review the study -elmon5-T: need to review the study
-elmon6-L: between two arc-bending magnets, very good SP
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80m100m120m
180m
260m324
300m1730
0 m
160m 140m
240m156
280m734
200m
220m
300 m
elmon1-L
.64T/4m
.64T/4m
- only e+ at <20m generate a clear pattern which is disturbed by e+ decayed far away- also the low bending E<4 GeV- need further investigation
P (GeV/c)
L (m)
P (GeV/c)
L (m
)lattice g4beamline model spin precession ideal case detector issues conclusions
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drift path ~ 13 m
elmon3-T long drift for higher momenta
force decay
1.9T/0.6m1.9T/0.6m
13 m
-2200 mm
0 mm
lattice g4beamline model spin precession ideal case detector issues conclusions
2-4/June/2010 2nd EUROnu meeting - Strasbourg 23Impact Point (m)
25
20
15
10
5
0
GeV/c
-0.2 0 0.2 0.4 0.6 0.8 1.0 1.2
<x>
RMS-x
<P>
RMS-P
RMS-P
beam
siz
e=
30 m
mra
d
dispersion
[15,18] GeV
unifo
rmity
ch
eck
for
upst
ream
dec
ays
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- study the decay of 10K muons along the line from B2 to B3 included (step 200mm)- check the effect on P vs detected position on the B3-monitor
B2
An interesting location for a detector: sideway in an ARC-DIPOLE
elmon6-L
-4.3m
-2.3m0m
+2.m
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-4300 mm
-3900 mm
-3500 mm
-3100 mm
-2700 mm-2500 mm
-4100 mm
-3700 mm
-3300 mm
-2900 mm
P (GeV/c)
Impa
ct P
oint
(m
)
Decays in B2
e+ start falling in the acceptance of the channel only at the exit ofthe bending magnet
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US-B2
DS-B2
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0mm
-2400mm
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L=a+bEc
Decays in the gap between B2 and B3e+ are almost all in the acceptance
DS-drift
US-drift
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100 mm
Decays in B3
1300 mm
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DS-B2
US-B3
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Uniformity Zone: P vs ImpactPoint unchanged in B3
67%
of
tot
colle
cted
e+
this component can distort the spectrum
-4.3m 0m
uniformity check for upstream decays
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5x1020 /yr (1yr = 200 days) = 2.9x1013/s- 50 Hz (proton) rep. rate = 20 ms (fill)
- 0.6 x 1012 per fill- NB: every fill = 3 bunch trains (L=440ns / S=1200ns)
- how many e+ (say) in a 10m section before the bending element?- 10/1608 * 0.6 * 1012 = 3.5*109 - 30% [2.5-7.5GeV/c] 109 (15% [2.5-5.0] 0.5x109)
- in 2.5m 1.2x108 /100 (# of turns = ): ≈106 per turn per 2.5GeV-bin achievable
2x104 sec = 50Hz rep.rate
t=520 sec
2ns
3ns
88 B
440ns 1200ns (T) (S)
Tperiod = 5.36 sec
1640ns
Nx1012 / …= ?E=[2.5,5] then
…some back-of-the-envelope calculations
Buy eggs
milk,
tomato
es ..
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# of decays over the ring
electrons detectable in a 2.5 GeV binFrom a device with 2.5 m U.S. acceptance
1.2E+61.2E+6
0.5E+60.5E+6
It should not be a problem of statistics …… rather an issue of very high intensity
turn #
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challenging?Special magnet?C-dipole?
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how close can we get?
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• method of Energy/Polarization Monitoring via spin precession revived for the IDS Race Track Decay Ring
• Use of G4Beamline for a more realistic rendering of the events• Zgoubi to realistically describe P
– Need to introduce a proper 3-body decay …
• detailed 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• Clarify some key issues:
– What is the degree of Polarisation?– which realistic signal in a realistic detector?– How to analyze the polarisation pattern? (fit, Fourier …) and which precision
obtainable?– Best Location? – Special Magnet and Hi-Rad detector
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IPAC10 - Kyoto
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End / Spares
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elmon5
elmon4
First Dipole ofthe matching sectionB= -0.64T / L=4.0m First Dipole
of the Arc sectionB= -4.27T / L=2.0m
elmon2
elmon1
low P e-
force decay
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lattice g4beamline model spin depolarisation ideal case detector issues conclusions
[7.0,8.0] GeV/c [8.0,9.0] GeV/c [9,10] GeV/c [10,11] GeV/c
[11,12] GeV/c [12,13] GeV/c [13,14] GeV/c [14,15] GeV/c
0 0.2 0.4 0.6 0.8 1.0 1.2
0 0.2 0.4 0.6 0.8 1.0 1.2
0 0.2 0.4 0.6 0.8 1.0 1.2
0 0.2 0.4 0.6 0.8 1.0 1.2
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1021 /yr (1yr = 200 days) = 5.8x1013/s- 50 Hz (proton) rep. rate = 20 ms (fill)
- 1.16 x 1012 per fill- NB: every fill = 3 bunch trains (L=440ns / S=1200ns)
- how many e+ (say) in a 10m section before the bending element?- 10/1608 * 1.16 * 1012 = 7*109 - 30% [2.5-7.5GeV/c] 2*109 (15% [2.5-5.0] 109)
- in 1m 108 /100 (# of turns = tm): 106 per turn per 2.5GeV-bin is achievable
2x104 sec = 50Hz rep.rate
t=520 sec
2ns
3ns
88 B
440ns 1200ns (T) (S)
Tperiod = 5.36 sec
1640ns
Nx1012 / …= ?E=[2.5,5] then
…some back-of-the-envelope calculations
Take th
e flight
to C
hicago
lattice g4beamline model spin precession ideal case detector issues conclusions