marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 1 Transmittance, scraping and maximum radii for MICE STEPVI M. Apollonio – University of Oxford

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 2 Amplitude – a single particle concept Amplitude – also known as ‘single particle emittance’ = SPE Focussing magnetic field  Particle (muon) performs oscillations about beam axis x’’ + k 2 (s) x = 0 (Hill’s eqn) k 2 (s) = focussing strength A = amplitude of betatron oscillations A is constant of motion in linear system Particle moves on ellipse of fixed area =  A in x, x’ space x x’

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 3 Amplitude (single particle property) A =  x  xx’ +  x’ 2  are optical (Twiss) parameters Emittance (many particle description)   rms amplitude of beam Normalise by multiplying by p/mc Optical parameters from covariance matrix of a set of muons or from magnetic field At focus or in uniform field: A = x 2 /  +  x’ 2 A n = (p/mc) A = p x 2 /(  mc) + p t 2  / (p mc)  = p / (150 [MeV ] B [T] ) in uniform field x x’ x max = sqrt (  A) (ECALC9 does all this) MICE can measure single muon amplitudes

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 4 Scattering HEATS on average COOL by reducing p t  Increase central phase space density, i.e. increase density at low amplitudes x ptpt

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 5 Abs RF Abs RF Abs Absorbers & RF cavities in channel scrape beam Scraping can be described in terms of normalised amplitude A n = (p/m) R 2 /  p = 200 MeV/c R (cm)  (cm) A n max (cm) Absorber RF Tracker Tracker is ‘bigger’ than channel – good! 2.Note: Full scraping will be seen only in a long channel (1 betatron oscillation)

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 6  parameters used in simulation (ICOOL)  TRANSMITTANCE  Define a VACUUM channel (NO ABS, NO RF) and a large aperture upstream/downstream trackers  40cm + vacuum channel + 40cm + 90cm  Evaluate amplitude upstream/downstream and do the ratio=transmission/amplitude  Max radius (effect of scraping) and cooling  Use the realistic channel (real radii)  Select throughoing muons  Record the max radius for every z-slice  Parameters used in ICOOL simulation  Pz=240, 200, (170) MeV/c with no gaussian spread  initial emittances: 0.1, 0.3, 0.6, 1.0, 2.0, 3.0 (cm rad)  generated muons per initial emittance  128 positions along Z to study the amplitudes of the beam (Single Particle Emittance)

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 7 NuNu NdNd T=N d /N u Scheme for transmission study: No selection on muons Ratio between downstream and upstream particles Scheme for max radius and cooling study: selection on muons  only throughgoing accepted Search for max value of radial distribution R=40 cm R=90 cm Z u =-5.2 mZ d =-5.2 m

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 8 RF ABS Tracker TRANSMISSION Amplitude ICOOL NO material or RF Soft edge Compare with long channel

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 9 the case of a LONG channel (a la NF), ~90 m of MICE repeated cells Bz (T) Pz (GeV/c) Beta (m)m

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 10 P Z =200 MeV/c,  abs =42 cm e=2.0cm rad e=3.0cm rad Long channel  Harder edge as expected

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 11 MICE STEP VI ~90m of MICE Channel

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 12 CAVEAT: The RF is designed to work with a beam of ~200 MeV/c When working with 240/170 MeV/c the RF config should be changed properly I did it “by hand” changing the phase and the peak voltage Discovered recently (last analysis PC) COOLING USING AMPLITUDE

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 13 N.B.  200 MeV/c: 8.74 MV/m – 90 deg P (GeV/c) Z (m) Still not perfect … 9.1 MV/m – ph.shift=30 deg Pz=170 MeV/c emi=1 mm rad Z (m) P (GeV/c) 8.74 MV/m – ph.shift=130 deg Pz=240 MeV/c emi=1 mm rad 8.74 MV/m ph.shift=90

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 14 beam maximum radius + cooling

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) cm rad 0.3 cm rad 0.6 cm rad 1.0 cm rad 2.0 cm rad 3.0 cm rad P Z =200 MeV/c,  abs =42 cm MICE profile in ICOOL sim

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 16  =0.1cm rad  =0.3cm rad downstream P Z =200 MeV/c,  abs =42 cm ratio 40K  heating cooling

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 17  =1.0 cm rad  =0.6cm rad P Z =200 MeV/c,  abs =42 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 18  =2.0 cm rad  =3.0 cm rad P Z =200 MeV/c,  abs =42 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) cm rad 0.3 cm rad 0.6 cm rad 1.0 cm rad 2.0 cm rad 3.0 cm rad P Z =240 MeV/c,  abs =42 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 20  =0.1cm rad downstream  =0.3cm rad P Z =240 MeV/c,  abs =42 cm 40K 

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 21 e=0.6cm rad e=1.0cm rad P Z =240 MeV/c,  abs =42 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 22 e=3.0cm rad e=2.0cm rad P Z =240 MeV/c,  abs =42 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) cm rad 0.3 cm rad 0.6 cm rad 1.0 cm rad 2.0 cm rad 3.0 cm rad P Z =170 MeV/c,  abs =15 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 24  =0.1cm rad downstream  =0.3cm rad P Z =170 MeV/c,  abs =15 cm 40K 

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 25  =0.6cm rad downstream  =1.0cm rad P Z =170 MeV/c,  abs =15 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 26  =2.0 cm rad downstream  =3.0 cm rad P Z =170 MeV/c,  abs =15 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 27 transmittance

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 28 P Z =200 MeV/c,  abs =42 cm  =0.1cm rad  =0.3cm rad

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 29 P Z =200 MeV/c,  abs =42 cm e=0.6cm rad e=1.0cm rad

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 30 P Z =200 MeV/c,  abs =42 cm e=2.0cm rad e=3.0cm rad

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 31 P Z =170 MeV/c,  abs =15 cm !!!! 4K  !!!!

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 32 P Z =170 MeV/c,  abs =15 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 33 P Z =170 MeV/c,  abs =15 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 34 P Z =240 MeV/c,  abs =42 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 35 P Z =240 MeV/c,  abs =42 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 36 P Z =240 MeV/c,  abs =42 cm

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 37 the case of a LONG channel (a la NF), ~90 m of MICE repeated cells Bz (T) Pz (GeV/c) Beta (m)m

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 38 P Z =200 MeV/c,  abs =42 cm  =0.1cm rad  =0.3cm rad

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 39 P Z =200 MeV/c,  abs =42 cm e=0.6cm rad e=1.0cm rad

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 40 P Z =200 MeV/c,  abs =42 cm e=2.0cm rad e=3.0cm rad

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 41

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 42

marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 43