8-9/June/2010UKNF - RAL1 Muon Beam Polarimeter for the NF Decay Rings m. apollonio – Imperial College (London) a. blondel – Universite de Geneve d. kelliher

8-9/June/2010 UKNF - RAL 1

Muon Beam Polarimeter for the NF Decay Rings

m. apollonio – Imperial College (London)a. blondel – Universite de Geneve

d. kelliher – ASTeC (RAL)


• the lattice of the DK racetrack ring• G4beamline 3D model• the method of spin precession• resolution in ideal case• detector issues (location, …)• conclusions


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’ = 1.3 mrad

1/ = 4 mrad x’ * ~ 0.1

lattice g4beamline model spin precession ideal case detector issues conclusions


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



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



- 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


B


d. k

ellih

er –

AS

TeC

(R

AL)

, m

.a.

(IC

)

-Check polarization vs turn pattern: model vs Zgoubi

0


UKNF - RAL 8

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

8-9/June/2010


8-9/June/2010

UKNF - RAL 9

[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]…


NOsensitivity


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



[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)%


-18% P0

E/E=2.5% (hw)

derive actual P from MAX-min excursions

[0, 5] GeV

[15, 18] GeV


-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)


High A


-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)%




-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)%




-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)%


Low A



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



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



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



…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



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



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


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


8-9/June/2010 UKNF - RAL 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



- 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



-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


US-B2

DS-B2


0mm

-2400mm


L=a+bEc

Decays in the gap between B2 and B3e+ are almost all in the acceptance

DS-drift

US-drift


100 mm

Decays in B3

1300 mm


DS-B2

US-B3


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



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 ..



# 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 #



challenging?Special magnet?C-dipole?


how close can we get?


• 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


IPAC10 - Kyoto


End / Spares

lattice g4beamline model spin depolarisation ideal case detector issues conclusions


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




[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


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


Documents

8-9/June/2010UKNF - RAL1 Muon Beam Polarimeter for the NF Decay Rings m. apollonio – Imperial College (London) a. blondel – Universite de Geneve d. kelliher