MICE analysis meeting - (01/06/2006) 1 few words on emittance growth in step III M. Apollonio – University of Oxford.

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MICE analysis meeting - (01/06/2006) 1 few words on emittance growth in step III M. Apollonio – University of Oxford

MICE analysis meeting - (01/06/2006) 2 Investigate emittance growth effort on understanding its origin vacuum Is 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) 3  parameters used in simulation (ICOOL)  Pz=207 MeV/c with 3% gaussian spread  initial emittances ranging from 0.1 to 1.0 (cm rad)  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) 4 Vacuum:  0 =1.0 cm rad BETA function in a.u. Fit to SPE: dN/d  1 =N 0 /4  1 /  2 exp(-  1 /2  ) (m) (GeV/c) (m rad) (GeV/c) (m) (GeV/c) Z (m)

MICE analysis meeting - (01/06/2006) 5

6

7 ecalc9 Fit to SPE   /dof Z (m) warming in vacuum … why?

MICE analysis meeting - (01/06/2006) 8  G. Penn’s note 71: p.10, eq. (15)  Can be derived from the general expression of normalized emittance (4D)  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) 9 Z (m)  (m rad) ecalc9 Penn’s prediction Most of the effect explained

MICE analysis meeting - (01/06/2006) 10 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) 11 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) 12

MICE analysis meeting - (01/06/2006) 13 SPE(Z=0) SPE(Z=5m)

MICE analysis meeting - (01/06/2006) 14

MICE analysis meeting - (01/06/2006) 15 Cooling soon after 1 st LiH absorber Intermediate region: specific warming

MICE analysis meeting - (01/06/2006) 16 Intermediate region: cooling is spoiled (specially for high values of SPE)

MICE analysis meeting - (01/06/2006) 17 Cooling soon after 2 nd LiH absorber: more effective on low SPEs

MICE analysis meeting - (01/06/2006) 18 SPE(Z=0) SPE(Z=5m)

MICE analysis meeting - (01/06/2006) 19 Integral of events with emi<et Blue=cooled