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Transcript of Marco apollonio/J.CobbMICE coll. meeting 16- RAL - (10/10/2006) 1 Transmittance, scraping and...
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Transmittance, scraping and maximum radii for MICE STEPVI
M. Apollonio – University of Oxford
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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’
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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
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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
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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)
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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)
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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
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RF ABS Tracker
TRANSMISSION
Amplitude
ICOOL
NO material or RF
Soft edge
Compare with long channel
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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
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PZ=200 MeV/c, abs=42 cme=2.0cm rad
e=3.0cm rad
Long channel
Harder edge as expected
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MICE STEP VI ~90m of MICE Channel
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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
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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
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beam maximum radius + cooling
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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
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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
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=1.0 cm rad
=0.6cm rad
PZ=200 MeV/c, abs=42 cm
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=2.0 cm rad
=3.0 cm rad
PZ=200 MeV/c, abs=42 cm
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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
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=0.1cm rad
downstream
=0.3cm rad
PZ=240 MeV/c, abs=42 cm
40K
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e=0.6cm rad
e=1.0cm rad
PZ=240 MeV/c, abs=42 cm
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e=3.0cm rad
e=2.0cm rad
PZ=240 MeV/c, abs=42 cm
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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
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=0.1cm rad
downstream
=0.3cm rad
PZ=170 MeV/c, abs=15 cm
40K
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=0.6cm rad
downstream
=1.0cm rad
PZ=170 MeV/c, abs=15 cm
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=2.0 cm rad
downstream
=3.0 cm rad
PZ=170 MeV/c, abs=15 cm
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transmittance
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PZ=200 MeV/c, abs=42 cm=0.1cm rad
=0.3cm rad
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PZ=200 MeV/c, abs=42 cme=0.6cm rad
e=1.0cm rad
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PZ=200 MeV/c, abs=42 cme=2.0cm rad
e=3.0cm rad
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PZ=170 MeV/c, abs=15 cm
!!!! 4K !!!!
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PZ=170 MeV/c, abs=15 cm
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PZ=170 MeV/c, abs=15 cm
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PZ=240 MeV/c, abs=42 cm
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PZ=240 MeV/c, abs=42 cm
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PZ=240 MeV/c, abs=42 cm
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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
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PZ=200 MeV/c, abs=42 cm=0.1cm rad
=0.3cm rad
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PZ=200 MeV/c, abs=42 cme=0.6cm rad
e=1.0cm rad
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PZ=200 MeV/c, abs=42 cme=2.0cm rad
e=3.0cm rad
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