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PID Detector Size & Acceptance

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

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PID Detector Size & Acceptance

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  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 • 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. Scraping in a Neutrino Factory FS2A FS2 • In a Neutrino Factory cooling channel, scraping is a first order effect • Typical input emittances ~ 15 p transverse (FS2A) vs scraping aperture ~ 20 p • We should be aiming to measure it to the same high precision as we aim to measure emittance • Standard 1e-3 efficiency requirement is not appropriate for scraping effects

  4. Scraping Aperture 1 Transport Aperture 2 px • 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 1 Transport Aperture 2 x

  5. Physical Model 430 30 40 15 842 No Detector Apertures No Detector Apertures 150 630 230 No absorbers or windows No Detector Apertures No Detector Apertures Hard edge - Kill muons that scrape

  6. Transverse Acceptance - 200 MeV/c Radius of MICE acceptance vs z radius • Appeal to cylindrical symmetry s.t. each particle is parametrised by 3 variables, x, px, Lcan (canonical angular momentum) • I consider muons on a grid in x and px • X = 0, 10, 20 … mm; px = 0, 10, 20, 30… MeV/c • Choose py so canonical angular momentum is 0 on this slide • Max radius 251 mm at z=6611 mm z

  7. Trans Acceptance with spread in Lcan Radius of MICE acceptance vs z with Lcan Radius of accepted particles: Z=diffuser end: shown as a function of Lcan r radius • Repeat the exercise but now use a spread in Lcan • Slightly larger maximum radius r=260 mm at z=6611 mm z Lcan

  8. 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

  9. RF Bucket H=0 • 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? ~ Neutrino Factory RF f0=40 ~ MICE RF f0=90

  10. Single muon in RF bucket z=0 m ~ MICE RF f0=90 ~ Neutrino Factory RF f0=40 z=200 m z=0 m z=100 m • Take a single muon and fire it through a toy cooling channel • (Periodic 2.75 m SFoFo lattice at 200 MeV/c, b=420) • See it gradually spiral out and get lost when RF at 40o • Energy-time phase space relative to the reference particle • Spiralling out due to aberrations? • See it lost very quickly when RF at 90o • Basically though muons follow contours in the Hamiltonian

  11. Trans Acceptance with spread in Pz ~ RF acceptance Radius of MICE acceptance vs z with spread in pz Radius of accepted particles: z=diffuser end: shown as a function of pz radius radius • Now introduce a spread in Pz well into resonance regions • Take Lcan = 0 • See that r=287mm at z=6611mm z pz

  12. 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)

  13. Effect on Emittance Measurement • Measured x variance (<x2>meas) is related to true x variance, (<x2>true ) from rejected signal by: • Nmeas<x2>meas = Ntrue<x2>true - Nrs<x2>rs • Ref: Analysis PC Aug 19 2005 • N is number of muons • rs is Rejected signal • Assume that the scraping aperture is at > 2sxand 2spx • Then after some algebra emittance e is given by • emeas >~ etrue [1 - (22-1) Nrs/Ntrue] • 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 “Amplitude2”, the contribution each muon makes to emittance

  14. 10 p beam Amplitude of rejected signal ? High Lcan, high pz m? • Consider the example of a 10 p 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 s(px)/s(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 A2 of rejected signal

  15. High Emittance Particles Initial vs final amplitude for 350 mm LH2 Ain2=Afin2 • 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 Scraping region

  16. Toy Cooling Channel Ain2=Afin2 Ain2=Afin2 Typical accelerator acceptance • 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 p here - NuFact input beam more like 20 p

  17. Halo So far “Reality” • 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

  18. 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

  19. Effect of Other Momenta 200 MeV/c, 4T (and other momenta scale) • s(x) for MICE baseline 200 MeV/c case • Calculated assuming linear optics • This is the same for MICE baseline 140 MeV/c and 170 MeV/c cases • Field scales with momentum to ensure s(x) is constant

  20. Effect of Other Momenta (2) 240 MeV/c, 4T 140 MeV/c, 4T • 240 MeV/c case the field stays at 4 T and s(x) is smaller • There are rumours of a 140 MeV/c case with the field at 4T • Better resolution in tracker? • In this case s(x) is larger and more muons will miss the TOF • s140(x) /s200(x) = 1.22

  21. 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 p 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 • Also difficulties if the tracker folks want to run at 4T/140 MeV/c • I have not devoted enough attention to this so far • I do not worry about tracker apertures at all • This work is important but takes time

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