1. PID Detector Requirements for Emittance Measurement Chris Rogers, MICE PID Review, Thursday Oct 12

2. Overview Emittance definition & MICE aims Longitudinal and transverse phase space Trade-off between longitudinal heating and transverse cooling Emittance calculation method Longitudinal emittance measurement using TOF I PID Effects on longitudinal and transverse emittance Pi mis-ID Mu mis-ID e mis-ID But the effects of the PID Detectors on emittance has barely been studied The effort should come from the PID group Needs someone on it full time

3. Emittance Definition Reminder: emittance is defined according to the covariance matrix of the phase space variables Phase space vector U 6D =(t,E,x,p x,y,p y ) Transverse phase space vector U 4D =(x,p x,y,p y ) Longitudinal phase space vector U 2D =(t,E) To a good approximation longitudinal and transverse phase space are independent Then we want to measure at least the following quantities: Where V(U) is the determinant of a matrix with elements which is the covariance and

4. MICE Aims MICE decreases transverse emittance  4D And MICE increases longitudinal emittance  2D Energy straggling increase  (E) An accelerator has a maximum 2D and 4D emittance which it can accept If we are to show that MICE really cools, i.e. increases the number of muons we can fit into an accelerator, we need to measure both longitudinal emittance and transverse emittance This means we need to measure the time to calculate 6D emittance This is in the RAL proposal Time measurement is a responsibility of TOF1 and TOF2 i.e. the PID group

5. Emittance Calculation The baseline emittance calculation (upstream): 1. Particle passes through upstream detectors 2. Particle is identified 3. Throw away particles identified as background There may be a better way 4. Particles have some measured distribution in E,x,P x,y,P y and a ~ flat distribution in time (on scale of RF) 5. Particles are given a statistical weight to tweak the distribution from the beamline so that particles have a chosen distribution that corresponds to a known emittance E.g. give particles a gaussian distribution in momentum and position The distribution of measured variables should be chosen to be the “convolution” of the desired true distribution and the distribution of errors 6. (This set of particles is then measured downstream and the new, cooler emittance is calculated)

6. (1) Time measurement Measure time of each muon at the TOF Extrapolate the measured time at the TOF to the tracker using measured (x,y,p x,p y p z ) in the tracker Uncertainty due to presence of diffuser/materials stochastic processs ~ 40 ps RMS (+ ~25 ps mean time offset due to Multiple Scattering effects) Uncertainty due to tracker resolution ~ 25 ps RMS Uncertainty due to TOF resolution ~ 70 ps RMS Total uncertainty ~ 90 ps RMS for 70 ps TOF

7. (2) Deconvolution Beam RMS width is ~ 500 ps We want to measure this RMS to ~ 1% accuracy (5 ps) TOF resolution is ~70 ps IF the error on t is independent of the phase space variables If we know  2 (dt) to <10% then we can get the desired accuracy In practice this “deconvolution” will be more complicated But a careful calibration is crucial to perform the emittance calculation Calibration resolution is more important than the absolute resolution

8. Effect of mis-ID on emittance This timing measurement is probably as important/more important than the PID measurement But on to PID! Measured emittance is related to true emittance via: N meas meas =N true true +N bg bg - N mis mis Subscript “meas” is measured, subscript “true” is true, subscript “bg” is background identified as muons, subscript “mis” are muons identified as background A 2 is amplitude squared is “emittance” of a particle wrt beam ~ beam emittance (with some constant terms) We select our beam to have the distribution with meas The actual beam will be a distribution with true Fine… but really we want to know what will happen to the change in emittance…

9. Effect of mu mis-ID Muon mis-ID as something else If we lose muons upstream, this will not effect the emittance change at all The only effect is the damage to muon rate Don’t want to lose all muons in some region of phase space! E.g. if we lose a large number of muons with a particular momentum that are mis-ID’d by the Cerenkov then we may find trouble Require that the mis-ID of muons is not sufficient to reduce the phase space density by > 10 % in any region of phase space I.e. for any values of U 6D =(t,E,x,p x,y,p y )

10. Effect of pi/e mis-ID Pion mis-ID as muon Pions that are mis-identified will typically decay somewhere in the cooling channel to muons Many decay muons will be lost and we will see an excess of scraping/muon decay Other decay muons will typically have a higher transverse momentum than the incoming pions RMS distribution of the decay Any Multiple Scattering the pion sees in material This will look like beam heating With what significance? Needs quantitative study Electrons mis-ID as muon If electrons are mis-ID’d as muons upstream, we will see an excess of scraping/muon decay downstream Not a problem I think

11. Cooling measurement bias I hesitate to give even an estimate of the bias in the cooling measurement I will try but forgive me for my lack of physics Say that ~1/2 of muon decays from mis-ID’d pions are captured in the channel Say that the decay muons have ~double the single particle emittance of decayed pions Then use Emittance  = so that  =N bg /N true bg Then  = N bg /N true For  << 10e-3 require N bg /N true << 10e-3 BUT this needs a serious quantitative study

12. Conclusions The effects of the PID Detectors on emittance has barely been studied This is essential and the effort should come from the PID group Needs someone on it full time The PID group must sail their own ship For me the timing measurement is probably as important/more important than the PID measurement Calibration resolution is more important than the absolute resolution In general pi mis-ID is what we worry about Require ~10 -3 purity Require muon density is not heavily depleted in a particular region But it all needs a quantitative study There is no manpower on this effort We are close to running