marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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Transmittance, scraping and maximum radii for MICE STEPVI

M. Apollonio – University of Oxford

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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Amplitude – a single particle concept

Amplitude – also known as ‘single particle emittance’ = SPE

Focussing magnetic field

Particle (muon) performs oscillations about beam axis

x’’ + k2(s) x = 0 (Hill’s eqn)

k2(s) = focussing strength

A = amplitude of betatron oscillations

A is constant of motion in linear system

Particle moves on ellipse of fixed area = A in x, x’ space

x

x’

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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Amplitude (single particle property)

A = x2 + 2 xx’ + x’2

are optical (Twiss) parameters

Emittance (many particle description)

rms amplitude of beam

Normalise by multiplying by p/mc

Optical parameters from covariance matrix of a set of muons or from magnetic field

At focus or in uniform field:

A = x2/+ x’2

An = (p/mc) A = p x2 /( mc) + pt2 / (p mc)

= p / (150 [MeV ] B [T] ) in uniform field

x

x’

xmax = sqrt ( A)

(ECALC9 does all this)

MICE can measure single muon amplitudes

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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Scattering HEATS on average

COOL by reducing pt

Increase central phase space density, i.e. increase density at low amplitudes

x

pt

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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Abs RF Abs RF Abs

Absorbers & RF cavities in channel scrape beam

Scraping can be described in terms of normalised amplitude

An = (p/m) R2/

p = 200

MeV/c R (cm) (cm) Anmax (cm)

Absorber 15 42 10.1

RF 21 110 7.6

Tracker 15 33 12.9

1. Tracker is ‘bigger’ than channel – good!

2. Note: Full scraping will be seen only in a long channel (1 betatron oscillation)

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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parameters used in simulation (ICOOL) TRANSMITTANCE

Define a VACUUM channel (NO ABS, NO RF) and a large aperture upstream/downstream trackers

40cm + vacuum channel + 40cm + 90cm Evaluate amplitude upstream/downstream and do the

ratio=transmission/amplitude Max radius (effect of scraping) and cooling

Use the realistic channel (real radii) Select throughoing muons Record the max radius for every z-slice

Parameters used in ICOOL simulation Pz=240, 200, (170) MeV/c with no gaussian spread initial emittances: 0.1, 0.3, 0.6, 1.0, 2.0, 3.0 (cm rad) 40000 generated muons per initial emittance 128 positions along Z to study the amplitudes of the beam (Single

Particle Emittance)

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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NuNdT=Nd/Nu

Scheme for transmission study:No selection on muonsRatio between downstream and upstream particles

Scheme for max radius and cooling study:selection on muons only throughgoing acceptedSearch for max value of radial distribution

R=40 cm R=40 cm

R=90 cm

Zu=-5.2 m Zd=-5.2 m

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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RF ABS Tracker

TRANSMISSION

Amplitude

ICOOL

NO material or RF

Soft edge

Compare with long channel

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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the case of a LONG channel (a la NF),~90 m of MICE repeated cells

Bz

(T)

Pz

(GeV

/c)

Bet

a (m

)

m

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=200 MeV/c, abs=42 cme=2.0cm rad

e=3.0cm rad

Long channel

Harder edge as expected

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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MICE STEP VI ~90m of MICE Channel

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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CAVEAT:

The RF is designed to work with a beam of ~200 MeV/c

When working with 240/170 MeV/c the RF config should be changed properly

I did it “by hand” changing the phase and the peak voltage

Discovered recently (last analysis PC)

COOLING USING AMPLITUDE

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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N.B. RF @ 200 MeV/c: 8.74 MV/m – 90 deg P

(G

eV/c

)

Z (m)

Still not perfect …

9.1 MV/m – ph.shift=30 deg

Pz=170 MeV/cemi=1 mm rad

Z (m)

P (

GeV

/c)

8.74 MV/m – ph.shift=130 deg

Pz=240 MeV/cemi=1 mm rad8.74 MV/m

ph.shift=90

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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beam maximum radius + cooling

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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0.1 cm rad0.3 cm rad0.6 cm rad1.0 cm rad2.0 cm rad3.0 cm rad

PZ=200 MeV/c, abs=42 cm

MICE profilein ICOOL sim

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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=0.1cm rad

=0.3cm rad

downstream PZ=200 MeV/c, abs=42 cm

rati

o

rati

o

40K

heating

cooling

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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=1.0 cm rad

=0.6cm rad

PZ=200 MeV/c, abs=42 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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=2.0 cm rad

=3.0 cm rad

PZ=200 MeV/c, abs=42 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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0.1 cm rad0.3 cm rad0.6 cm rad1.0 cm rad2.0 cm rad3.0 cm rad

PZ=240 MeV/c, abs=42 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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=0.1cm rad

downstream

=0.3cm rad

PZ=240 MeV/c, abs=42 cm

40K

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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e=0.6cm rad

e=1.0cm rad

PZ=240 MeV/c, abs=42 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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e=3.0cm rad

e=2.0cm rad

PZ=240 MeV/c, abs=42 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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0.1 cm rad0.3 cm rad0.6 cm rad1.0 cm rad2.0 cm rad3.0 cm rad

PZ=170 MeV/c, abs=15 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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=0.1cm rad

downstream

=0.3cm rad

PZ=170 MeV/c, abs=15 cm

40K

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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=0.6cm rad

downstream

=1.0cm rad

PZ=170 MeV/c, abs=15 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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=2.0 cm rad

downstream

=3.0 cm rad

PZ=170 MeV/c, abs=15 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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transmittance

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=200 MeV/c, abs=42 cm=0.1cm rad

=0.3cm rad

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=200 MeV/c, abs=42 cme=0.6cm rad

e=1.0cm rad

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=200 MeV/c, abs=42 cme=2.0cm rad

e=3.0cm rad

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=170 MeV/c, abs=15 cm

!!!! 4K !!!!

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=170 MeV/c, abs=15 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=170 MeV/c, abs=15 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=240 MeV/c, abs=42 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=240 MeV/c, abs=42 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=240 MeV/c, abs=42 cm

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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the case of a LONG channel (a la NF),~90 m of MICE repeated cells

Bz

(T)

Pz

(GeV

/c)

Bet

a (m

)

m

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=200 MeV/c, abs=42 cm=0.1cm rad

=0.3cm rad

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=200 MeV/c, abs=42 cme=0.6cm rad

e=1.0cm rad

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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PZ=200 MeV/c, abs=42 cme=2.0cm rad

e=3.0cm rad

marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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marco apollonio/J.Cobb MICE coll. meeting 16- RAL - (10/10/2006)

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