A (short) history of MICE – step III

MICE CM - Fermilab, Chicago - (11/06/2006)

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A (short) history of MICE – step IIIM. Apollonio – University of Oxford


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Motivations:

can we observe an effect of cooling at an earlier stage ?

First Results:

they showed how emittance is not reduced as expected

cooling not so effective. Why?

What happens to emittance in vacuum?

It grows. Why?

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?


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Parameters used in simulation (ICOOL)

Pz = 207 MeV/c Gaussian Beams

10000 muons per configuration

selected sigma_pz=10%

several emittances

lost muons < 4%

ERROR spotted: actual sigma_pz=3%


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Step III: two back to back tracker solenoids and no RF cavities

Step VI

Step III

This operation requires some attention in redefining the currents of the coupling coils (matching)

Tried several techniques MINUIT+evbeta (beta evolution equation in

paraxial approximation) MINUIT+ICOOL

They give approximately the same results for the optimised currents

[MICE-CM-Osaka,28/2/2006]

just so currents

optimised currents


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FLIP mode (LiH)Initial

emittances:

=0.2 cm rad

=0.25 cm rad

=0.3 cm rad

=0.6 cm rad

Points taken at several initial emittance values

Emittance ‘measured’ at the end of the II tracker


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LiH, Li, Be, CH, C

0.22, 0.26, 0.38, 0.41, 0.57 (cm rad) 0.22, 0.25, 0.35, 0.4, 0.6 (cm rad)

Non-flip modeFlip mode

equilibrium emittances

/

(%

)

/

(%

) (cm rad) (cm rad)

currents optimization: evbeta + MINUIT (in vacuum)simulation: ICOOL + ecalc9


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Fli

p m

od

e: 2

ab

sorb

ers

LiH, Li, Be, CH, C

2x7cm absorbers = 13% pz reduction

0.22, 0.26, 0.39, 0.4, 0.57 (cm rad)

Op

tim

isat

ion

: IC

OO

L+

Min

uit

wit

h n

on

si

mm

. cu

rren

ts


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… and what do we get?

What do we expect ?


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current optimizationschemes:

evbeta+MINUIT

ICOOL+MINUIT

ICOOL+MINUITwith 2 absorbers

equilibrium

asymptoticcooling


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1st observation: something is happening in the region between the two solenoids which spoils the emittance causing an undesired growth

What is the cause of this growth? Is it due to the presence of material? Does it happen in vacuum?

Investigate a channel without absorbers


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i=0.1 cm radi=0.2 cm rad

Em

ittan

ce g

row

th in

vac

uum

:N

O A

BS

OR

BE

RS

i=0.3 cm radi=0.6 cm radi=1.0 cm rad


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(%)

Non Flip Mode

Flip Mode

(cm rad)

(cm rad)

2.3 %

2.8 %


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Investigate emittance growth

effort on understanding its origin vacuum

Follow the beam along the channel at different Z

Calculate the amplitude (single particle emittance) for

each Z-planeNB if the beam is gaussian you can prove SPE follows a

simple function [John’s note, in preparation]

yyxx

,,,x

xVxεεT

1T1

d.o.f. 4 with χ 2

If V is the covariance of a multivariate gaussian distribution

4 Vdetε


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Vacuum: 0=1.0 cm rad

eta 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)

2 contributions


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ecalc9

Fit to SPE

/d

of

warming in vacuum … why?


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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


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Z (m)

(m

rad

)

ecalc9

Penn’s prediction

Most of the effect explained


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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

Start with the vacuum case...


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Intermediate region: specific warmingE(reg2) vs E(reg1, Z=0m)

E(reg2) - E(reg1, Z=0m) vs E(reg1, Z=0m)

vacuum

4

5

4

5

12

13

1213

Z=0.61m

Z=1.025m

Z=1.925m

Z=2.025m


22vacuum

20 21

Z=2.95m

Z=3.25m Z=3.45m

Z=3.45m

24

20

21

24

25

25


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SPE(Z=0)

SPE(Z=5.5m)

vacu

um

40

40

Z=5.5m


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...co

ntin

ue

with

LiH

(2

ab

sorb

ers)

LiH

abs

orbe

rs

4

4

5

5

Z=0.61m

Z=1.025m


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Cooling soon after 1st LiH absorber Intermediate region: specific warming

LiH absorbers

6

7

12

13

Z=1.025m

Z=1.125m Z=2.025m

Z=1.925m

612

13

7


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Intermediate region: cooling is spoiled (specially for high values of SPE)

LiH absorbers

20 22

2321

Z=2.95m

Z=3.25m Z=3.35m

Z=3.25m

2021 22 23


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Cooling soon after 2nd LiH absorber: more effective on low SPEs

LiH absorbers

24 26

2725

Z=3.45m

Z=3.45m Z=4.25m

Z=3.85m

24 25 26 27


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SPE(Z=0)

SPE(Z=5.5m)

LiH

abs

orbe

rs

40

40


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• The effect of warming up of overall emittance can be partly explained with the considerations seen in the vacuum case

• Yet the emittance growth in vacuum is just a fraction of the effect as seen with absorbers

• Emittance can be evaluated:• as an average quantity (with some cautious cut): ecalc9• as a result of a fit on SPE distributions (seems to work well when world is gaussian)• or considering the density of phase space for low values of 1

• after all we want to INCREASE the phase space density, possibly without caring about the tails of the SPE distribution


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220

20

02

202

22

20

8bin-first

8/ :NB

2 2

exp8

/

///

1 2

exp4

/

Aε

Nn

ε

NdAdn

ε

A

ε

NdAdn

dAdAdAdndAdn

ε

A

ε

ANdAdn

112

1

1

2

n

n


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Emi=1.0 cm rad

beginning of channel

end of channel

end - beginning

Emi=0.6 cm rad


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Emi=0.4 cm radEmi=0.5 cm rad


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Emi=0.3 cm rad Emi=0.2 cm rad

Emi=0.1 cm rad


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current optimizationschemes:

evbeta+MINUIT

ICOOL+MINUIT

ICOOL+MINUITwith 2 absorbers

equilibrium

asymptoticcooling

phase space densityfor low SPE regions


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Integral of events with emi<et

Blue=cooled


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Conclusions: a review of step III has been shown some better understanding of the emittance growth effect has been

gained (Penn’s fmla) a suggestion about a different definition of cooling based on SPE

distribution has been introduced: this produces emittances in good agreement with the simple model

Future things ... What happens when beam is not gaussian (real beam)? Repeat studies with higher spread in Pz Non-flip mode?

Documents

A (short) history of MICE – step III