Transcript 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.

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?





How do we measure the 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 accurately do we need to measure it?
I only consider the 200 MeV/c magnets

Is this sufficient?
Scraping
Aperture 1
Transport
Aperture 2
px
Aperture 1
Transport
Aperture 2
x



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
Physical Model
842
430 30
40
15
No Detector
Apertures
No Detector
Apertures
150
No Detector
Apertures
All
materials
are copper
630
230
No absorbers or windows
No Detector
Apertures
Transverse Acceptance - 200 MeV/c
radius
Radius of MICE acceptance vs z
z


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
Trans Acceptance with spread in Lcan
radius
Radius of MICE acceptance vs z
with Lcan



r
Radius of accepted particles:
Z=diffuser end: shown as a
function of Lcan
z
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
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
H=0
~ Neutrino Factory RF f0=40


Hamiltonian H = Total Energy = Kinetic Energy + Potential Energy
Plot contour of H=0 in longitudinal phase space



~ MICE RF f0=90
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?
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



MICE SFoFo lattice only


But can’t just take field periodic about any point due to Maxwell
I think centre of tracker solenoid should be reasonable
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
Initial beam
After 10 10.4 m cells
After 20 10.4 m cells
Pz [MeV/c]


Transmission of full MICE lattice from -5.401 to +5.401 metres
Regions with no muons indicate edge of MICE momentum
acceptance
SFoFo Resonance Structure
transmission
Initial beam
After 10 10.4 m cells
After 20 10.4 m cells

Pz [MeV/c]
Surprisingly similar to the full MICE lattice


I expected these to be different
Need to cross-check but no time
Trans Acceptance with spread in Pz
radius
radius
Radius of MICE acceptance vs z
with spread in pz


Radius of accepted particles:
z=diffuser end: shown as a
function of pz
z
Now introduce a spread in Pz well into resonance
regions
Take Lcan = 0
pz
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?