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Analysis of MICE
Chris Rogers1
Imperial College/RALThursday 28 October, 2004
1With thanks to John Cobb
This talk Comparison of G4MICE transport/Analysis against
ICOOL - not full channel yet Start trying to understand how we analyse MICE
1. Case study: no rf/absorbers2. Full cooling channel
Scope: work only in the transverse plane for now (E)= (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 We can get:
Phase space emittance Trace space emittance
in 2, 4, 6 dimensions Beta function Transmission, <E>, <Pz>, z Single Particle Emittance Holzer Acceptance
We can: Cut on transmission, position, momentum Apply statistical weights
We can take inputs from: For003 For009 G4beamline G4MICE simulation G4MICE reconstruction
Status of Analysis using G4MICE G4MICE Simulation still has some issues
Virtual planes not reliable Need to fill entire MICE volume Cause problems in G4 transport for low beta Effect materials in the cooling channel
Emittance growth in absorbers Needs virtual planes first
Mostly events from ICOOL but Analysis from G4MICE
Try to be explicit about which one I’m using
What needs doing in MICE’s Analysis before data taking?Aims of MICE:1. Prove that we can achieve cooling
Do we have a robust measurement of “cooling”?
Is it good to ~10-3? Is 10-3 appropriate?
2. Show how to achieve the best cooling Different input beams Input beta function, Lcan … It would be nice to know where to look…
Emittance not constant? Emittance is not constant in empty
channel Emittance grows and shrinks - is this cooling/heating? Systematic Error? ~ 10-1
Depending on what you want to know… “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 We see emittance growth (cf also
Bravar). Perhaps this is to be expected Equation of motion in drift is non-
linear1:
)()0()0()(
2222 mppE
pzxz
dz
dxxzx
yx
x
Pz in terms of phase space variables
1Berg; Gallardo
Emittance Growth 2 Solution - use normalised trace space?
Equation of motion in drift
Take x’, y’ instead of px, py - then normalise
(From now on we get events from ICOOL, analysis/plots from G4MICE Analysis)
zdz
dxxzx )0()(
Low emittance beam - Trace Space
4D Trace Space EmittanceTrace Space Emittance ( mm rad x 10-2)Same scale as previous slide
Single Particle Emittance (SPE) We can see the heating as a
function of emittance without using many beams of different emittance Define Single Particle Emittance (SPE)
by
Phase space density contour at 1
Our particle
SPE=Area (2D)
Rms Emittance=Area (2D)
SPE - Math Or mathematically1 (in 4
Dimensions): 4/1 rmssp
1Holzer uses a slightly different definition but I want to keep units consistent
UCU T 1
Particle Phase Space Coordinate VectorBeam Covariance
Matrix
Rms EmittanceSingle ParticleEmittance
SPE (magnets only)
Why no particles in beam centre?
4D SPE (pi mm rad)
Nevts
SPE - UpstreamSPE - Downstream
Why so few low Emittance Particles?
In 1 we have ~ 60 % of particles:
In 4D we have O.362~15% of particles in 1 (Conclusion - we need beams with different
emittance)
0.6
0.6
2D: 0.36
Constant heating across the beam??? 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 Alternatively use Holzer
Acceptance 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
Holzer - UpstreamHolzer - Downstream
Consistently have more particles upstream than downstream
Holzer Acceptance 2
in
out
Holzer
Holzer
Not enough statistics for low emittance particles - wanted to see centre heating
Slight “heating” due to beamloss in fringe
Conclusions We need to understand what
causes “heating” and “cooling” in the magnets only channel 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 Shouldn’t assume a Gaussian beam Needs more code!