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

2. 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

3. 3 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 It is independent of the particular beam going through MICE Aperture 1TransportAperture 2 x px

4. 4 Physical Model 842 4303040 230 15 150630 No Detector Apertures No absorbers or windows No Detector Apertures Hard edge - Kill muons that scrape

5. 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 Max radius 251 mm at z=6611 mm radius z Radius of MICE acceptance vs z

6. 6 Trans Acceptance with spread in L can Repeat the exercise but now use a spread in L can Slightly larger maximum radius r=260 mm at z=6611 mm 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. 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. 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. 9 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

10. 10 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 See that r=287mm at z=6611mm Radius of accepted particles: z=diffuser end: shown as a function of pz radius z pz ~ RF acceptance

11. 11 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)

12. 12 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 Examine “Amplitude 2 ”, the contribution each muon makes to emittance

13. 13 10  beam Amplitude of rejected signal A 2 of rejected signal TOF width N rs N rs /N true [%]  4801150.150.30 600190.0260.11 80090.0120.06 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 >~ 3 in this case The efficiency is a highly beam-dependent quantity => bad Not clear that this is the correct question to answer TOF II placed at z=6.611 metres ? High L can, high pz  ?

14. 14 High Emittance Particles How many “high emittance” particles are cooled? Look at “amplitude” of each particle - how far it is from the beam centre/what “emittance” each particle has Plot change in amplitude between the input and output Here I look at the change over a single absorber A in 2 =A fin 2 Initial vs final amplitude for 350 mm LH 2 Scraping region

15. 15 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 I use an input beam of 10  here - NuFact input beam more like 20  A in 2 =A fin 2 Typical accelerator acceptance

16. 16 Halo So far considered walls of accelerator as hard No muons get through So far ignored effects of material/RF in the cooling channel In reality of course this isn’t the case Multiple scattering off material kicks muons into the scraping region Multiple scattering off scraping region kicks muons back into the channel How significant is this effect? We have no analysis framework for answering such a question But this is an important thing to understand I have not found the time to examine this problem “Reality” So far

17. 17 Amplitude with Materials I repeat the plot from before But now include LH2 and RF Still no Tracker Only 10000 muons (10% of slide 13) See ~ 20 x the number of muons missing TOF II

18. 18 Summary Further work is still required by the analysis group to create robust criteria for measurement of acceptance/scraping This is important if we are to understand the cooling of the ~20  beam which comes out of a neutrino factory In the meantime, a pragmatic approach to TOF design is probably sensible It should be bigger… 600 mm seems a reasonable full width This may well get larger when the “halo” is fully studied I have not devoted enough attention to this so far I do not worry about trcker apertures at all This work is important but takes time