Post on 18-Jan-2016
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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
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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
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Lkin from MICE diffuser• Without knowing the precise beamline design we can
make an estimate for the diffuser thicknesses– Assume beamline produces roughly 2 beam
– Expect this to be good to ~10%
– Gives lead thicknesses:
– Gives dLkin/Lkin:
2pi 6pi 10pi
140 0 4.2 7.4
200 0 7.6 12.9
240 0 8.2 14
2pi 6pi 10pi
140 0 0.048 0.079
200 0 0.055 0.092
240 0 0.048 0.080
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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 Lkin/Lkin=0.1 but keep (x), (x’) the same
– Blue plot shows a slightly different beam matched with the Lcantaken into account
– Take out some of the transverse momentum spread
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• Define matched covariance matrix by
– And use
• When I go through a diffuser doesn’t change
• If I want a beam with (x) constant I have to be careful to choose (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)
“Rematching”
"
0"
0~
~00/
Lp
Lp
m z
z
n
2)~
(1 L
n
can
m
LL
~
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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
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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
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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. /) ~ 5%
• This is well within specification (Perhaps beyond limits of statistics)
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Phase Space Density
• Phase space density contours in x-py phase space– 6 beams but density scales
– Looks like any reduction in phase space density will be a tweak
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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
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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
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Transverse Emittance
• 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
1 MeV
25 MeV/G4MICE
25 MeV/ICOOL 25 MeV/RF 0o
25 MeV/RF 40o
1 MeV
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Longitudinal Phase Space
• Longitudinal phase space at z = 2020.5 (centre of RF-8)– Note energy scale of RF bucket/Contours of Hamiltonian
Running on-crest Running at 400