Analysis of MICE
Chris Rogers1
Imperial College/RAL
Thursday 28 October, 2004
1With
thanks to John Cobb
This talk
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Comparison of G4MICE transport/Analysis against
ICOOL - not full channel yet
Start trying to understand how we analyse MICE
1.
2.
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Case study: no rf/absorbers
Full cooling channel
Scope:
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work only in the transverse plane for now s(E)= s(t)=0
Assume we have pid; x,y,t; px,py,E of all particles at some
plane in the upstream and downstream trackers
Not thinking about experimental errors
Assume we have a Gaussian input beam
G4MICE Analysis Package
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We can get:
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Phase space emittance
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Trace space emittance
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Beta function
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Transmission, <E>, <Pz>, z
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Single Particle Emittance
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Holzer Acceptance
We can:
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Cut on transmission, position, momentum
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Apply statistical weights
We can take inputs from:
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For003
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For009
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G4beamline
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G4MICE simulation
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G4MICE reconstruction
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in 2, 4, 6 dimensions
Status of Analysis using
G4MICE
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G4MICE Simulation still has some issues
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Virtual planes not reliable
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Emittance growth in absorbers
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Need to fill entire MICE volume
Cause problems in G4 transport for low beta
Effect materials in the cooling channel
Needs virtual planes first
Mostly events from ICOOL but Analysis from
G4MICE
Try to be explicit about which one I’m using
Emittance (no RF/absorbers)
G4MICE
ICOOL +
Ecalc9f
Heating
Emittance (no RF/absorbers)
Low beta regions near Absorbers
G4MICE
ICOOL +
Ecalc9f
On-Axis Bz
- G4MICE
- ICOOL
What needs doing in MICE’s
Analysis before data taking?
Aims of MICE:
1.
Prove that we can achieve cooling
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Do we have a robust measurement of “cooling”?
Is it good to ~10-3?
Is 10-3 appropriate?
Show how to achieve the best cooling
2.
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Different input beams
Input beta function, Lcan …
It would be nice to know where to look…
Emittance not constant?
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Emittance is not constant in empty channel
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Depending on what you want to know…
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Emittance grows and shrinks - is this cooling/heating?
Systematic Error? ~ 10-1
“What is the increase in the number of muons I can get into
my acceptance?”
“What is the increase in the number of muons I can get into
my acceptance beyond any magnetic field effects?”
(Liouville)
We should at least know where the boundaries of our
understanding lie
Case study for emittance analysis
Emittance Growth
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We see emittance growth (cf also
Bravar). Perhaps this is to be expected
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Equation of motion in drift is non-linear1:
px
dx
x( z )  x(0)  z  x(0)  z
2
2
2
dz
E  ( px  p y  m 2 )
1Berg;
Gallardo
Pz in terms of phase space variables
Emittance Growth 2
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Solution - use normalised trace space?
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Equation of motion in drift
dx
x( z )  x(0)  z
dz
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Take x’, y’ instead of px, py - then normalise
(From now on we get events from ICOOL,
analysis/plots from G4MICE Analysis)
Trace space emittance
(magnets only)
?
4D Phase Space
Emittance
4D Trace Space
Emittance
Low emittance beam - Phase
Space
Phase Space
Emittance
(p mm rad x
10-2)
4D Phase Space Emittance
Low emittance beam - Trace
Space
Trace Space
Emittance
(p mm rad x
10-2)
Same scale as
previous slide
4D Trace Space Emittance
Single Particle Emittance (SPE)
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We can see the heating as a function of
emittance without using many beams of
different emittance
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Define Single Particle Emittance (SPE) by
Rms Emittance=
Area (2D)
Our particle
SPE=
Area (2D)
Phase space density contour at 1 s
SPE - Math
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Or mathematically1 (in 4 Dimensions):
Single Particle
Emittance
 sp   rms1/ 4
Rms Emittance
1
 U C U
T
Beam Covariance
Matrix
1Holzer
Particle Phase Space
Coordinate Vector
uses a slightly different definition but I want to keep units consistent
SPE (magnets only)
Why no particles
in beam centre?
Nevts
4D SPE (pi mm rad)
SPE - Upstream
SPE - Downstream
Why so few low Emittance
Particles?
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In 1 s we have ~ 60 % of particles:
0.6
Why so few low Emittance
Particles?
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In 1 s we have ~ 60 % of particles:
0.6
0.6
Why so few low Emittance
Particles?
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In 1 s we have ~ 60 % of particles:
0.6
2D: 0.36
0.6
Why so few low Emittance
Particles?
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In 1 s we have ~ 60 % of particles:
0.6
2D: 0.36
0.6
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In 4D we have O.362~15% of particles in 1 s
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(Conclusion - we need beams with different emittance)
“Heating” as a function of
emittance - SPE
Constant heating across the
beam???
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It looks like there is constant heating
across the beam!
But we assumed this was only a fringe
effect
Further investigation…
Heating as a function of
acceptance - Holzer
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Alternatively use Holzer Acceptance
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Measure the number of particles in a (4D)
hyper-ellipsiodal phase space volume
Plot Nin(V)/Nout(V)
I assume Gaussian distributions
Holzer Acceptance Upstream
and Downstream
Consistently have
more particles upstream
than downstream
Holzer - Upstream
Holzer - Downstream
Holzer Acceptance Upstream
vs Downstream - Heating
Goes up to 12
Holzerout
Holzerin
Cooling performance
Transverse Phase
Space Emittance
Transverse Trace
Space Emittance
Single Particle Emittance
SPE - Upstream
SPE - Downstream
Nevts
Single Particle Emittance 2
Holzer Acceptance
Holzer - Upstream
Holzer - Downstream
Holzer Acceptance 2
Holzerout
Holzerin
Not enough statistics for
low emittance particles wanted to see centre heating
Slight “heating”
due to beam
loss in fringe
Conclusions
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We need to understand what causes
“heating” and “cooling” in the magnets
only channel
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It appears to be constrained to the fringes
?Guess due to non-linear fields?
We can plot emittance as a function of
phase space volume
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Shouldn’t assume a Gaussian beam
Needs more code!
Conclusions 2
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A lot I haven’t touched
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Longitudinal emittance/dynamics
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I expect it to be more difficult than transverse
How many events do we need to select the
desired beam? What beams do we need to
get full coverage of our phase space?
Much more…