7-8/1/2010UKNF - Imperial College London1 Diagnostic for the Decay Ring : Energy Monitoring m. apollonio – Imperial College London

7-8/1/2010 UKNF - Imperial College London 1

Diagnostic for the Decay Ring : Energy Monitoring

m. apollonio – Imperial College London


• the lattice of the DK racetrack ring• G4beamline 3D model• the method of spin depolarisation• 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’ = 0.13 mrad

1/ = 4 mrad x’ * ~ 0.1

lattice g4beamline model spin depolarisation ideal case detector issues conclusions


main open issues on diagnostics

- measurement of divergence

- measurement of energy

via beam (de)polarisation

location for the device?

G4beamline MODEL


straight section

matching section

arc section

- measurement beam current


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



- 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 ...

- I assume P = 27% is left when filling the DK ring

- Spin precesses in a ring due to coupling with magnetic fields (bending magnets). NB: the trick does NOT work in a bow-tie shape

- At every turn spin precession is determined by the SPIN TUNE: = 2 a a = 1.16E-3

This determines a modulation in P- NB: ifE/E =0 same for all muons P keeps oscillating if E/E !=0 P goes to 0 after n turns

e+ spectrum from -decay is a function of P : d2N/dx dcos = N0[(3-2x)x2 – P(1-x)x2 cos] (CM)- I have modelled the behaviour of a beam made of 100000 muons, all with their spin and energy (E/E =[0.01-0.05])

- Lorentz Boost

- Modulation in P produces a modulation in E(e+)

Sz(0)Sz(1)

turn0turn1

Sz(2)

turn2


7-8/1/2010 UKNF - Imperial College London 7E (MeV)

Cos

(LA

B)

Centre of Mass frame: P=+100%

LAB frame after Lorentz boost

X=2E

e/m

(C

M)

x=2Ee/m

P e

cos

Pe LAB

cosLAB ~ 1 0.99996



DP/P = 3%Pol=27%

fine mesh = 10 samples / turnTURN

P modulation (spin precession)and damping (E/E !=0)


PO

L (%

)

turn #


MEASURABLE SIGNAL

collect electrons at three different energy bins[0,5] GeV[5,10] GeV[10,25] GeVmeasure the TOTAL energy deposited (e.g. in a calorimeter)Energy resolution modeled as: E/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 E/Efit the signal at every TURN with a function:

f(T) = A e-BT (C exp-(G T2) cos(D+E T) + F)

G: contains P/P E: is the SPIN tune from which can be inferredB: describes muon decay slope



31% in [0,5] GeV/c

1000

00 i

nit

ial

mu

on

dec

ays


turn #

Ee

(Ge

V)


28% in [5,10] GeV/c



41% in [10,25] GeV/c



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 (due to the high)

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



use a “realistic” beam of from Zgoubi [C. Prior]- P = 25 GeV/c P/P = 1% - N = 30 mm rad


at mid - straight at end of straight


…B2B= -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

elmon5

elmon4

elmon3

elmon2

elmon1

force decay



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



elmon5 sensible plane




elmon4 sensible plane

Dipole Length = 2m

magnet gap


drift path ~ 13 m

elmon3long drift for higher momenta

force decay



Elmon3 – DS of M2 consider Ee = [2.5-7.5]

e+ out of the aperture



OUT OF detector acceptance

How does TOT Ee changes turn by turn? lattice g4beamline model spin depolarisation ideal case detector issues conclusions

TOT Ee in [2.5,7.5] GeV/c bin fit on 40 turns

TOT Ee in [2.5,7.5] GeV/c bin fit on 80 turns

TOT Ee in [12.5,25] GeV/c bin fit on 80 turns

TOT Ee in [12.5,25] GeV/c bin fit on 40 turns


consider an initial sample of ~100000 e- [0,25]bin [2.5,7.5] = 30% measure E (E/E) with (de)polarisation after n turnE = 25009+/-44 after 40 turns (24986+/-23, 100 turns)E/E = 0.89+/-0.36 after 40 turns (0.93+/-0.07, 100 turns)Q.: how many electrons can I collect at turn=0?

[2.5,7.5] GeV/c – Energy Bias [2.5,7.5] GeV/c – DE/E


[12.5,25] GeV/c – Energy Bias= (E-25)/25

[12.5,25] GeV/c – DE/E

OUT OF detector acceptance


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

2x104 sec = 50Hz rep.rate

t=520 sec

2ns

3ns

88 B


440ns 1200ns (T) (S)

Tperiod = 5.36 sec

1640ns


decay region >10m


ideal decay point

Open issues: - which electrons are relevant for the measurement? i.e. which decay pointsupstream of the bending dipole? - 1m? 10m? 100m upstream?

AB


to do list: a- introduce polarisation(*) of the beam Zgoubib- use Zgoubi-generated files as input for G4beamlinec- force the decay over a continuous volume (length) = some technicalities with g4bl to be solved

d- build the e+spectrum at elmon(i)e- perform fit and evaluate precision/biases


(*) so far a self made model


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

• Zgoubi to realistically describe P

• 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



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


Documents

7-8/1/2010UKNF - Imperial College London1 Diagnostic for the Decay Ring : Energy Monitoring m. apollonio – Imperial College London