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Angular Momentum from diffuser

Angular Momentum from diffuser. Beam picks up kinetic angular momentum (L kin ) when it sits in a field Canonical angular momentum (L can ) is conserved in the absence of material In material L kin is damped leading to non-conservation of L can

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Angular Momentum from diffuser

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  1. Angular Momentum from diffuser • Beam picks up kinetic angular momentum (Lkin) when it sits in a field • Canonical angular momentum (Lcan) is conserved in the absence of material • In material Lkin is damped leading to non-conservation of Lcan • At higher fields we have more Lkin and so the change in Lcan is greater • This leads to a mismatch • Stronger Bz => bigger mismatch • Motivates pulling the diffuser out of the solenoid • Two questions: • Does this seriously effect the amount of cooling? • Does this require serious amounts of reweighting to get a beam distribution with no mismatch? • Additionally consider an alternative matching condition

  2. Change in Angular Momentum • Kinetic angular momentum given by Lkin = <xpy - ypx> • In a material change in angular momentum given by dLkin/Lkin ~ dpz/pz • Thin foil approximation • Monte Carlo (ICOOL) shows this is reasonably accurate • dLkin/Lkin in black, dpz/pz in grey • The usual 4 T, 333 mm, 200 MeV, 6 pi beam

  3. DLkin from MICE diffuser • Without knowing the precise beamline design we can make an estimate for the diffuser thicknesses • Assume beamline produces roughly 2 p beam • Expect this to be good to ~10% • Gives lead thicknesses: • Gives dLkin/Lkin:

  4. Effect on beta function • Introducing angular momentum will knock the beta function off • 10,000 muons, no energy spread/absorbers/rf/windows/scifi in these plots • Black plot shows beam with “normal” beta function • Red plot shows beam with mismatch that would be induced by a material • So take dLkin/Lkin=0.1 but keep s(x), s(x’) the same • Blue plot shows a slightly different beam matched with the Lcantaken into account • Take out some of the transverse momentum spread

  5. “Rematching” • Define matched covariance matrix by • And use • When I go through a diffuser g doesn’t change • If I want a beam with s(x) constant I have to be careful to choose s(px) with this L dependence • L is basically the canonical angular momentum i.e. • L = 0 w/o diffuser, <~ 0.1 with diffuser (depending on thickness)

  6. Angular Momentum • Kinetic angular momentum varies wildly • The three plots that vary between +/- 3000 mm MeV/c are kinetic angular momentum • Canonical angular momentum is really conserved very well • Blue and red plots have non-zero canonical angular momentum • Again blue plot has been rematched to account for the Lcan • Black plot is again for standard solution with Lcan= 0 Lcan Lkin

  7. Full Cooling Channel • Go on to consider MICE VI with absorbers and RF • No SciFi/detectors, still 10,000 events • Energy looks spot on • Slight mismatch induced by the momentum change even in case of Lcan=0 • Black is Lcan= 0 • Red has Lcan~0.1Lkin in the tracker • Blue has Lcan~0.1Lkin but rematched

  8. Effect on Cooling • Slightly worse performance from the matched channel with angular momentum vs standard channel • Slightly better performance from the unmatched channel with angular momentum • But higher initial emittance • Regardless, the change in cooling performance from this effect (i.e. de/e) ~ 5% • This is well within specification (Perhaps beyond limits of statistics)

  9. Phase Space Density • Phase space density contours in x-py phase space • 6 p beams but density scales • Looks like any reduction in phase space density will be a tweak

  10. Underdensity Due to Lkin • This is [nLkin=0.1(mu) - ndesign(mu)]/ndesign(mu) in x-py phase space • Left is for unmatched beam • Right is for rematched beam • Black contours are phase space density contours for the ideal beam • Only underdensities are shown • Depletion in the fringes • Low statistics in this region (1000000 mu total) • Compared to the gain in rate through quad aperture, this is not an issue

  11. Effect of Energy Spread on Cooling • Beta function for several different beams • Black has 1 MeV energy spread • Red has 25 MeV energy spread • Blue has 25 MeV energy spread and tracking in ICOOL • Green has 25 MeV energy spread and RF is at 40 degrees • Left hand plot has no RF/Absorbers, RH has full cooling

  12. Transverse Emittance 25 MeV/RF 40o • Non-linear effects dominate with a small NuFact energy spread • Typical NuFact dE ~ 25-100 MeV • No cooling!? • Note blue & red have input beam but with different scaping (~1-5%) • In ICOOL I killed particles at r>250 mm • Did it properly in G4MICE 25 MeV/G4MICE 25 MeV/ICOOL 25 MeV/RF 0o 1 MeV 1 MeV

  13. Longitudinal Phase Space Running on-crest Running at 400 • Longitudinal phase space at z = 2020.5 (centre of RF-8) • Note energy scale of RF bucket/Contours of Hamiltonian

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