PID Detector Requirements for Emittance Measurement

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 U6D=(t,E,x,px,y,py) • Transverse phase space vector U4D=(x,px,y,py) • Longitudinal phase space vector U2D=(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 <uiuj> which is the covariance and

4. MICE Aims • MICE decreases transverse emittance e4D • And MICE increases longitudinal emittance e2D • Energy straggling increase s(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): • Particle passes through upstream detectors • Particle is identified • Throw away particles identified as background • There may be a better way • Particles have some measured distribution in E,x,Px,y,Py and a ~ flat distribution in time (on scale of RF) • 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 • (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,px,pypz) 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 s2(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: • Nmeas<A2>meas=Ntrue<A2>true+Nbg<A2>bg- Nmis<A2>mis • Subscript “meas” is measured, subscript “true” is true, subscript “bg” is background identified as muons, subscript “mis” are muons identified as background • A2 is amplitude squared is “emittance” of a particle wrt beam • <A2> ~ beam emittance (with some constant terms) • We select our beam to have the distribution with <A2>meas • The actual beam will be a distribution with <A2>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 U6D=(t,E,x,px,y,py)

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 e=<A2> so that de=Nbg/Ntrue<A2>bg • Then de/e = Nbg/Ntrue • For de/e << 10e-3 require Nbg/Ntrue << 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