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Transmittance, scraping and maximum radii for MICE STEPVI

Transmittance, scraping and maximum radii for MICE STEPVI. M. Apollonio – University of Oxford. Amplitude – a single particle concept. x’. Amplitude – also known as ‘single particle emittance’ = SPE Focussing magnetic field  Particle (muon) performs oscillations about beam axis

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Transmittance, scraping and maximum radii for MICE STEPVI

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

  2. Amplitude – a single particle concept x’ Amplitude – also known as ‘single particle emittance’ = SPE Focussing magnetic field  Particle (muon) performs oscillations about beam axis x’’ + k2(s) x = 0 (Hill’s eqn) k2(s) = focussing strength A = amplitude of betatron oscillations A is constant of motion in linear system Particle moves on ellipse of fixed area = pA in x, x’ space x MICE coll. meeting 16- RAL - (10/10/2006)

  3. Amplitude(single particle property) A = gx2 + 2 axx’ + bx’2 a, b, gare optical (Twiss) parameters Emittance(many particle description) e = rmsamplitude 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 = x2/b+ bx’2 An = (p/mc) A = p x2 /(b mc) + pt2b / (p mc) b = p / (150 [MeV ] B [T] ) in uniform field x’ x xmax = sqrt (b A) MICE can measure single muon amplitudes (ECALC9 does all this) MICE coll. meeting 16- RAL - (10/10/2006)

  4. pt x Scattering HEATS on average COOL by reducing pt  Increase central phase space density, i.e. increase density at low amplitudes MICE 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 An = (p/m) R2/b • Tracker is ‘bigger’ than channel – good! • Note: Full scraping will be seen only in a long channel (1 betatron oscillation) MICE 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) 40000 generated muons per initial emittance 128 positions along Z to study the amplitudes of the beam (Single Particle Emittance) MICE coll. meeting 16- RAL - (10/10/2006)

  7. Scheme for transmission study: No selection on muons Ratio between downstream and upstream particles R=40 cm R=40 cm R=90 cm Zu=-5.2 m Zd=-5.2 m T=Nd/Nu Nd Nu Scheme for max radius and cooling study: selection on muons  only throughgoing accepted Search for max value of radial distribution MICE coll. meeting 16- RAL - (10/10/2006)

  8. RF ABSTracker ICOOL NO material or RF TRANSMISSION Soft edge Compare with long channel Amplitude MICE 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 MICE coll. meeting 16- RAL - (10/10/2006)

  10. PZ=200 MeV/c, babs=42 cm e=2.0cm rad e=3.0cm rad Long channel  Harder edge as expected MICE coll. meeting 16- RAL - (10/10/2006)

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

  12. CAVEAT: COOLING USING AMPLITUDE • 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) MICE coll. meeting 16- RAL - (10/10/2006)

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

  14. beam maximum radius + cooling MICE coll. meeting 16- RAL - (10/10/2006)

  15. 0.1 cm rad 0.3 cm rad 0.6 cm rad 1.0 cm rad 2.0 cm rad 3.0 cm rad PZ=200 MeV/c, babs=42 cm MICE profile in ICOOL sim MICE coll. meeting 16- RAL - (10/10/2006)

  16. 40K m e=0.1cm rad PZ=200 MeV/c, babs=42 cm downstream e=0.3cm rad ratio heating cooling ratio MICE coll. meeting 16- RAL - (10/10/2006)

  17. e=0.6cm rad PZ=200 MeV/c, babs=42 cm e=1.0 cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  18. e=2.0 cm rad PZ=200 MeV/c, babs=42 cm e=3.0 cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  19. 0.1 cm rad 0.3 cm rad 0.6 cm rad 1.0 cm rad 2.0 cm rad 3.0 cm rad PZ=240 MeV/c, babs=42 cm MICE coll. meeting 16- RAL - (10/10/2006)

  20. 40K m e=0.1cm rad PZ=240 MeV/c, babs=42 cm downstream e=0.3cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  21. e=0.6cm rad PZ=240 MeV/c, babs=42 cm e=1.0cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  22. e=2.0cm rad PZ=240 MeV/c, babs=42 cm e=3.0cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  23. 0.1 cm rad 0.3 cm rad 0.6 cm rad 1.0 cm rad 2.0 cm rad 3.0 cm rad PZ=170 MeV/c, babs=15 cm MICE coll. meeting 16- RAL - (10/10/2006)

  24. 40K m e=0.1cm rad PZ=170 MeV/c, babs=15 cm downstream e=0.3cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  25. e=0.6cm rad PZ=170 MeV/c, babs=15 cm downstream e=1.0cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  26. e=2.0 cm rad PZ=170 MeV/c, babs=15 cm downstream e=3.0 cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  27. transmittance MICE coll. meeting 16- RAL - (10/10/2006)

  28. PZ=200 MeV/c, babs=42 cm e=0.1cm rad e=0.3cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  29. e=0.6cm rad PZ=200 MeV/c, babs=42 cm e=1.0cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  30. PZ=200 MeV/c, babs=42 cm e=2.0cm rad e=3.0cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  31. !!!! 4K m !!!! PZ=170 MeV/c, babs=15 cm MICE coll. meeting 16- RAL - (10/10/2006)

  32. PZ=170 MeV/c, babs=15 cm MICE coll. meeting 16- RAL - (10/10/2006)

  33. PZ=170 MeV/c, babs=15 cm MICE coll. meeting 16- RAL - (10/10/2006)

  34. PZ=240 MeV/c, babs=42 cm MICE coll. meeting 16- RAL - (10/10/2006)

  35. PZ=240 MeV/c, babs=42 cm MICE coll. meeting 16- RAL - (10/10/2006)

  36. PZ=240 MeV/c, babs=42 cm MICE 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 MICE coll. meeting 16- RAL - (10/10/2006)

  38. PZ=200 MeV/c, babs=42 cm e=0.1cm rad e=0.3cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  39. e=0.6cm rad PZ=200 MeV/c, babs=42 cm e=1.0cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  40. PZ=200 MeV/c, babs=42 cm e=2.0cm rad e=3.0cm rad MICE coll. meeting 16- RAL - (10/10/2006)

  41. MICE coll. meeting 16- RAL - (10/10/2006)

  42. MICE coll. meeting 16- RAL - (10/10/2006)

  43. MICE coll. meeting 16- RAL - (10/10/2006)

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