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

Emittance (no RF/absorbers)

G4MICEICOOL +Ecalc9f

Heating

Emittance (no RF/absorbers)

G4MICEICOOL +Ecalc9fLow beta regions near Absorbers

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

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()(

Trace space emittance (magnets only)

4D Phase Space Emittance4D Trace Space Emittance

?

Low emittance beam - Phase Space

4D Phase Space Emittance

Phase Space Emittance ( mm rad x 10-2)

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:

0.6

Why so few low Emittance Particles? In 1 we have ~ 60 % of particles:

0.6

0.6

Why so few low Emittance Particles? In 1 we have ~ 60 % of particles:

0.6

0.6

2D: 0.36

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

“Heating” as a function of emittance - SPE

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 Upstream vs Downstream - Heating

in

out

Holzer

Holzer

Goes up to 12

Cooling performance

Transverse Phase Space EmittanceTransverse Trace Space Emittance

Single Particle Emittance

SPE - UpstreamSPE - Downstream

Nevts

Single Particle Emittance 2

Holzer Acceptance

Holzer - UpstreamHolzer - 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!

Conclusions 2

A lot I haven’t touched Longitudinal emittance/dynamics

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…