PID Detector Size & Acceptance

Chris RogersAnalysis PC04-05-06

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? 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 Is this sufficient?

Scraping

Aperture 1 Transport Aperture

2

I show a 2D cartoon of the sort of analysis I would do to figure out the acceptance

Note that there is a closed region in phase space that is not scraped

I want to measure the size of this region

Aperture 1

Transport Aperture 2

x

px

Physical Model842 430 30 40

230

15

150 630

No Detector Apertures

No absorbers or windows

No Detector Apertures

No Detector Apertures

All materials are copper

No Detector Apertures

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

radiu

s

z

Radius of MICE acceptance vs z

Trans Acceptance with spread in Lcan

Repeat the exercise but now use a spread in Lcan

Should I extend the plot to larger values of Lcan? Nb slight difference is that I plot particles that lose

energy in the right hand plot, not in the left hand plot So include muons that hit the edge of the channel and then

scatter back in

rad

ius

z

Radius of MICE acceptance vs zwith Lcan

Lcan

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

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

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

Longitudinal Acceptance - Resonances

Solenoid lattice is only focusing for certain momenta

Outside of these momenta, magnets are not focusing Outside of these momenta, emittance grows and muons

are expelled from the cooling channel Consider transmission for many MICE cells in two

cases At resonances transmission is low Full MICE lattice

But can’t just take field periodic about any point due to Maxwell

I think centre of tracker solenoid should be reasonable MICE SFoFo lattice only

Repeating cells consisting of Focus coil - RF coil - Focus coil

I only look at the 200 MeV/c case Should I look at other cases?

MICE Resonance Structure

Transmission of full MICE lattice from -5.401 to +5.401 metres Regions with no muons indicate edge of MICE momentum

acceptance

Initial beamAfter 10 10.4 m cellsAfter 20 10.4 m cells

Pz [MeV/c]

tran

smis

sion

SFoFo Resonance Structure

Initial beamAfter 10 10.4 m cellsAfter 20 10.4 m cells

Surprisingly similar to the full MICE lattice I expected these to be different

Need to cross-check but no time

Pz [MeV/c]

tran

smis

sion

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

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

radiu

s

zra

diu

spz

Other issues

No time to figure this out Worry about the halo of muons around the

central acceptance of the MICE beam Caused by multiple scattering and energy straggling

How do we measure the acceptance? How accurately do we need to measure it? How accurately can we measure it?