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

2. 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?

3. Scraping Aperture 1 TransportAperture 2 I show a 2D cartoon of the sort of analysis I would do to figure out the acceptance Note that 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

4. Physical Model 842 4303040 230 15 150630 No Detector Apertures No absorbers or windows No Detector Apertures All materials are copper No Detector Apertures

5. 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

6. 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

7. 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

8. 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

9. 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?

10. MICE Resonance Structure Transmission of full MICE lattice from -5.401 to +5.401 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

11. SFoFo Resonance Structure Initial beam After 10 10.4 m cells After 20 10.4 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

12. 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 Take L can = 0 Radius of accepted particles: z=diffuser end: shown as a function of pz radius z pz

13. Other issues No time to figure this out Worry about the halo of muons around the central acceptance of the MICE beam Caused by multiple scattering and energy straggling How do we measure the acceptance? How accurately do we need to measure it? How accurately can we measure it?