7-8/1/2010 UKNF - Imperial College London 1
Diagnostic for the Decay Ring : Energy Monitoring
m. apollonio – Imperial College London
7-8/1/2010 UKNF - Imperial College London 2
• the lattice of the DK racetrack ring• G4beamline 3D model• the method of spin depolarisation• resolution in ideal case• detector issues (location, …)• conclusions
7-8/1/2010 UKNF - Imperial College London 3
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
7-8/1/2010 UKNF - Imperial College London 4
main open issues on diagnostics
- measurement of divergence
- measurement of energy
via beam (de)polarisation
location for the device?
G4beamline MODEL
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
straight section
matching section
arc section
- measurement beam current
7-8/1/2010 UKNF - Imperial College London 5
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
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
7-8/1/2010 UKNF - Imperial College London 6
- 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
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
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
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
7-8/1/2010 UKNF - Imperial College London 8
DP/P = 3%Pol=27%
fine mesh = 10 samples / turnTURN
P modulation (spin precession)and damping (E/E !=0)
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
PO
L (%
)
turn #
7-8/1/2010 UKNF - Imperial College London 9
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
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
7-8/1/2010 UKNF - Imperial College London 10
31% in [0,5] GeV/c
1000
00 i
nit
ial
mu
on
dec
ays
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
turn #
Ee
(Ge
V)
7-8/1/2010 UKNF - Imperial College London 11
28% in [5,10] GeV/c
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
7-8/1/2010 UKNF - Imperial College London 12
41% in [10,25] GeV/c
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
7-8/1/2010 UKNF - Imperial College London 13
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
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
7-8/1/2010 UKNF - Imperial College London 14
use a “realistic” beam of from Zgoubi [C. Prior]- P = 25 GeV/c P/P = 1% - N = 30 mm rad
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
at mid - straight at end of straight
7-8/1/2010 UKNF - Imperial College London 15
…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
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
7-8/1/2010 UKNF - Imperial College London 16
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
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
7-8/1/2010 UKNF - Imperial College London 17
elmon5 sensible plane
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
7-8/1/2010 UKNF - Imperial College London 18
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
elmon4 sensible plane
Dipole Length = 2m
magnet gap
7-8/1/2010 UKNF - Imperial College London 19
drift path ~ 13 m
elmon3long drift for higher momenta
force decay
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
7-8/1/2010 UKNF - Imperial College London 20
Elmon3 – DS of M2 consider Ee = [2.5-7.5]
e+ out of the aperture
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
7-8/1/2010 UKNF - Imperial College London 21
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
7-8/1/2010 UKNF - Imperial College London 22
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
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
[12.5,25] GeV/c – Energy Bias= (E-25)/25
[12.5,25] GeV/c – DE/E
OUT OF detector acceptance
7-8/1/2010 UKNF - Imperial College London 23
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
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
440ns 1200ns (T) (S)
Tperiod = 5.36 sec
1640ns
7-8/1/2010 UKNF - Imperial College London 24
decay region >10m
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
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
7-8/1/2010 UKNF - Imperial College London 25
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
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
(*) so far a self made model
7-8/1/2010 UKNF - Imperial College London 26
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
lattice g4beamline model spin depolarisation ideal case detector issues conclusions
7-8/1/2010 UKNF - Imperial College London 27
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
lattice g4beamline model spin depolarisation ideal case detector issues conclusions