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PID Detector Size & Acceptance Chris Rogers Analysis PC 04-05-06

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Overview The MICE PID detectors should be large enough that they accommodate any muons that are not scraped by the cooling channel How large is this acceptance? Transversely this is defined by the size of the scraping aperture Longitudinally this is defined by the RF bucket Also defined by the resonance structure of the solenoids Additionally worry about “halo” outside this due to multiple scattering, energy straggling and muons that scatter off the apertures How do we measure the acceptance? How accurately do we need to measure it? I only consider the 200 MeV/c magnets Is this sufficient?

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Scraping Aperture 1 TransportAperture 2 I show a 2D cartoon of the sort of analysis I would do to figure out the acceptance There is a closed region in phase space that is not scraped I want to measure the size of this region Aperture 1TransportAperture 2 x px

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Physical Model 842 4303040 230 15 150630 No Detector Apertures No absorbers or windows No Detector Apertures Hard edge - Kill muons that scrape

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Transverse Acceptance - 200 MeV/c Appeal to cylindrical symmetry s.t. each particle is parametrised by 3 variables, x, p x, L can (canonical angular momentum) I consider muons on a grid in x and p x X = 0, 10, 20 … mm; px = 0, 10, 20, 30… MeV/c Choose p y so canonical angular momentum is 0 on this slide radius z Radius of MICE acceptance vs z

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Trans Acceptance with spread in L can Repeat the exercise but now use a spread in L can Should I extend the plot to larger values of L can ? Nb slight difference is that I plot particles that lose energy in the right hand plot, not in the left hand plot So include muons that hit the edge of the channel and then scatter back in radius z Radius of MICE acceptance vs z with L can L can r Radius of accepted particles: Z=diffuser end: shown as a function of L can NEED TO FIX PLOT

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Longitudinal Acceptance - RF Cavities What is the longitudinal acceptance of MICE? Two factors, RF bucket and solenoid resonance structure RF Cavities A muon which is off-phase from the cavities will not gain enough momentum or gain to much momentum and become more out of phase from the cavity A muon which is off-momentum from the cavities will soon become off-phase and be lost from the cooling channel Define “RF bucket” as the stable region in longitudinal phase space Inside RF bucket muons are contained within the cooling channel

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RF Bucket Hamiltonian H = Total Energy = Kinetic Energy + Potential Energy Plot contour of H=0 in longitudinal phase space Means total energy=0 so particles are contained Hamiltonian given in e.g. S.Y.Lee pp 220 & 372 But in a single pass, quite short linac how important is this? H=0 ~ Neutrino Factory RF 0 =40 ~ MICE RF 0 =90

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Single muon in RF bucket Take a single muon and fire it through a toy cooling channel (Periodic 2.75 m SFoFo lattice at 200 MeV/c, =420) See it gradually spiral out and get lost when RF at 40 o Energy-time phase space relative to the reference particle Spiralling out due to aberrations? See it lost very quickly when RF at 90 o Basically though muons follow contours in the Hamiltonian ~ Neutrino Factory RF 0 =40 ~ MICE RF 0 =90 z=0 m z=200 m z=0 m z=100 m

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Longitudinal Acceptance - Resonances Solenoid lattice is only focusing for certain momenta Outside of these momenta, magnets are not focusing Outside of these momenta, emittance grows and muons are expelled from the cooling channel Consider transmission for many MICE cells in two cases At resonances transmission is low Full MICE lattice But can’t just take field periodic about any point due to Maxwell I think centre of tracker solenoid should be reasonable MICE SFoFo lattice only Repeating cells consisting of Focus coil - RF coil - Focus coil I only look at the 200 MeV/c case Should I look at other cases?

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MICE Resonance Structure Transmission of repeating MICE lattice from -5.201 to +5.201 metres Regions with no muons indicate edge of MICE momentum acceptance Initial beam After 10 10.4 m cells After 20 10.4 m cells Pz [MeV/c] transmission ~ RF acceptance

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SFoFo Resonance Structure Initial beam After 10 2.75 m cells After 20 2.75 m cells Surprisingly similar to the full MICE lattice I expected these to be different Need to cross-check but no time Pz [MeV/c] transmission ~ RF acceptance

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Radius of MICE acceptance vs z with spread in pz Trans Acceptance with spread in Pz Now introduce a spread in Pz well into resonance regions Overlap for “safety” Take L can = 0 Radius of accepted particles: z=diffuser end: shown as a function of pz NEED TO FIX PLOT radius z pz ~ RF acceptance, SFoFo acceptance

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Effect of Losing Muons What is the effect of losing muons? How does it effect emittance measurement Is the standard criterion (0.999 efficiency) sufficient? Quantify the argument that “losing signal muons (because the TOF is too small) at larger amplitude will bias the measurement more” How does a mis-measurement effect the measurement of cooling channel efficiency? “Surely muons on the edge of the beam will never make it into an accelerating structure anyway” Consider the “acceptance measurement” (number of muons within a certain acceptance)

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Effect on Emittance Measurement Measured x variance ( meas ) is related to true x variance, ( true ) from rejected signal by: N meas meas = N true true - N rs rs Ref: Analysis PC Aug 19 2005 N is number of muons rs is Rejected signal Assume that the scraping aperture is at > 2 x and 2 px Then after some algebra emittance is given by meas >~ true [1 - (2 2 -1) N rs /N true ] Losing signal at high emittance will bias the measurement more This means that for a 1e-3 emittance requirement the efficiency requirement is much tougher than 0.999 More like 0.9995-0.9998 The emittance measurement is very sensitive to transmission Consider this for a large emittance beam => worst case

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10 beam Amplitude of rejected signal A 2 of rejected signal TOF width N rs N rs /N true [%] 4801050.120.50 600450.0520.33 800220.0230.15 100040.0050.06 Consider the example of a 10 beam, hard edged MICE The beam was generated carefully so that the divergence and width of the beam is well controlled by the magnets Carefully choose the angular momentum and ratio (p x )/ (x) See that the standard criterion is out by factor >~ 5 in this case NOTE: this looks worse than in reality - the rejected signal for this were all at the edge of the momentum acceptance TOF II placed at z=6.5 metres

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High Emittance Particles Particles of high emittance won’t make it into a downstream accelerating structure anyway? So we shouldn’t take so much notice? Histogram initial vs final amplitude for a single 350 mm LH2 absorber (20 beam to populate high amplitude region) After one absorber not much reduction in emittance A in 2 =A fin 2 Initial vs final amplitude for 350 mm LH 2 Scraping region

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Toy Cooling Channel Return to the toy cooling channel Made up of repeating 2.75 metre MICE cells The particles near the scraping aperture do make it into the aperture of some accelerator We really do need to worry about them for the cooling measurement Working on quantifying this at the moment A in 2 =A fin 2 Typical accelerator acceptance

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