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