MICE analysis meeting - (01/06/2006)
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few words on emittance growth in step III
M. Apollonio – University of Oxford
MICE analysis meeting - (01/06/2006)
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Investigate emittance growth
effort on understanding its origin vacuum
Is <emittance> the only quantity we want to use to characterize cooling?
Or rather we want to use all the information we can get
from the SPE distribution?
MICE analysis meeting - (01/06/2006)
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parameters used in simulation (ICOOL) Pz=207 MeV/c with 3% gaussian spread initial emittances ranging from 0.1 to 1.0 (cm rad) 40000 generated muons per initial emittance 40 positions along Z to study the amplitudes of the
beam (Single Particle Emittance)
MICE analysis meeting - (01/06/2006)
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Vacuum: 0=1.0 cm rad
BETA function in a.u.
Fit to SPE:
dN/d1=N0/4 1/2 exp(-1/2)
(m)
(Ge
V/c
)
(m rad)
(GeV/c)
(m) (m)(G
eV
/c)
(Ge
V/c
)
Z (m)
MICE analysis meeting - (01/06/2006)
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MICE analysis meeting - (01/06/2006)
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MICE analysis meeting - (01/06/2006)
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ecalc9
Fit to SPE
/d
of
Z (m)
warming in vacuum … why?
MICE analysis meeting - (01/06/2006)
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G. Penn’s note 71: p.10, eq. (15)
Can be derived from the general expression of normalized emittance (4D)
xqByP
xPxqBPqBxxPxPP
qB
xPP
qBxP
P
PxPP
P
xPcm
xx
xyxyxyz
z
xz
zy
z
xxx
z
xNN
2
2222
Predicts an emittance growth in vacuum Ideally if Bz=const+uniform and Pz=const the
emittance growth is zero: this is fairly true in the solenoid regions where infact ~const
When you cross the flip region you have a rapid change in Bz Bx, By components: emittance grows up
MICE analysis meeting - (01/06/2006)
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Z (m)
(m
rad
)
ecalc9
Penn’s prediction
Most of the effect explained
MICE analysis meeting - (01/06/2006)
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Is emittance growth uniform over the SPE spectrum or specific, i.e. some values more affected?
Look at SPE distributions in different Z planes along the channel
MICE analysis meeting - (01/06/2006)
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Intermediate region: specific warming
E(reg2) vs E(reg1, Z=0m)
E(reg2) - E(reg1, Z=0m) vs E(reg1, Z=0m)
MICE analysis meeting - (01/06/2006)
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MICE analysis meeting - (01/06/2006)
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SPE(Z=0)
SPE(Z=5m)
MICE analysis meeting - (01/06/2006)
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MICE analysis meeting - (01/06/2006)
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Cooling soon after 1st LiH absorber
Intermediate region: specific warming
MICE analysis meeting - (01/06/2006)
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Intermediate region: cooling is spoiled (specially for high values of SPE)
MICE analysis meeting - (01/06/2006)
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Cooling soon after 2nd LiH absorber: more effective on low SPEs
MICE analysis meeting - (01/06/2006)
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SPE(Z=0)
SPE(Z=5m)
MICE analysis meeting - (01/06/2006)
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Integral of events with emi<et
Blue=cooled
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