1

PID Detector Size & Acceptance

Chris RogersAnalysis PC04-05-06

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

3

Scraping

Aperture 1 Transport Aperture

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 1

Transport Aperture 2

x

px

4

Physical Model842 430 30 40

230

15

150 630

No Detector Apertures

No absorbers or windows

No Detector Apertures

No Detector Apertures

No Detector Apertures

Hard edge -Kill muons that scrape

5

Transverse Acceptance - 200 MeV/c

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

radiu

s

z

Radius of MICE acceptance vs z

6

Trans Acceptance with spread in Lcan

Repeat the exercise but now use a spread in Lcan

Slightly larger maximum radius r=260 mm at z=6611 mm

rad

ius

z

Radius of MICE acceptance vs zwith Lcan

Lcan

rRadius of accepted particles:Z=diffuser end: shown as a function of Lcan

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

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 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

~ Neutrino Factory RF 0=40 ~ MICE RF 0=90

z=0 mz=200 m

z=0 m

z=100 m

10

Radius of MICE acceptance vs zwith spread in pz

Trans Acceptance with spread in Pz

Now introduce a spread in Pz well into resonance regions

Take Lcan = 0 See that r=287mm at z=6611mm

Radius of accepted particles:z=diffuser end: shown as a function of pz

radiu

s

zra

diu

spz

~ RF acceptance

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

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 > 2x and 2px

Then after some algebra emittance is given by meas >~ true [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

13

10 beamAmplitude of rejected signal

A2 of rejected signal

TOF widt

h

Nrs Nrs/Ntrue

[%]

480 115 0.15 0.30

600 19 0.026 0.11

800 9 0.012 0.06

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 (px)/(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 Lcan, high pz ?

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 in2 =A fin

2

Initial vs final amplitude for 350 mm LH2

Scraping region

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 in2 =A fin

2

A in2 =A fin

2

Typical accelerator acceptance

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

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

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