Transcript Muon Cooling and the Muon Collider A. Caldwell MPI f. Physik/Columbia University

Muon Cooling and the Muon Collider
A. Caldwell
MPI f. Physik/Columbia University
• Motivation
• Difficulties
• Focus on Cooling (frictional cooling)
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Why a Muon Collider ?
No synchrotron radiation
problem (cf electron)
P α (E/m)4
Can build a high energy circular
accelerator.
P
P
Collide point
particles rather than
complex objects
2
Dimensions of Some Colliders discussed
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Physics at a Muon Collider
Muon Collider Complex:
• Proton Driver 2-16GeV; 1-4MW leading to
10 22 p /year
•  production target & Strong Field Capture
• COOLING resultant  beam
•  acceleration
•Storage & collisions
• Stopped  physics
From target, stored 
•  physics
= 40000 ee
• Higgs Factory
• Higher Energy Frontier
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HIGH ENERGY MUON COLLIDER PARAMETERS
Baseline parameters for high energy muon colli ders. From “Status of Muon Colli der
Research and Development and Future Plans,” Muon Colli der Collaboration, C. M.
Ankenbrandt et al., Phys. Rev. ST Accel. Beams 2, 081001 (1999).
COM energy (TeV)
p energy ( GeV)
p’s/bunch
Bunches/fill
Rep. rate (Hz )
p power (MW)
/ bunch
 power (MW)
Wall power (MW)
Colli der circum. (m)
Ave bending field (T)
rms p/p (%)
6D  (m)3
rms n ( mm mrad)
* (cm)
z (cm)
r spot (m)
 IP (mrad)
Tune shift
nturns (effective)
Luminosity (cm2 s1)
0.4
16
2.5  1013
4
15
4
2  1012
4
120
1000
4.7
0.14
1.7  1010
50
2.6
2.6
2.6
1.0
0.044
700
1033
3.0
16
2.5  1013
4
15
4
2  1012
28
204
6000
5.2
0.16
1.7  1010
50
0.3
0.3
3.2
1.1
0.044
785
7  1034
5
’s in red
’s in green
Drift region for  decay  30 m
P beam (few MW)
Solenoidal Magnets: few T … 20 T
Target
Simplified emittance estimate:
At end of drift, rms x,y,z approx 0.05,0.05,10 m
Px,Py,Pz approx 50,50,100 MeV/c
Normalized 6D emittance is product divided by (mμc)3
drift6D,N 1.7 10-4 (m)3
Emittance needed for Muon Collider
collider6D,N  1.7 10-10(m)3
This reduction of 6 orders of magnitude must be done with reasonable efficiency !
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Some Difficulties
• Muons decay, so are not readily available – need multi MW
source. Large starting cost.
• Muons decay, so time available for cooling, bunching, acceleration
is very limited. Need to develop new techniques, technologies.
• Large experimental backgrounds from muon decays (for a
collider). Not the usual clean electron collider environment.
• High energy colliders with high muon flux will face critical
limitation from neutrino induced radiation.
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Muon Cooling
Muon Cooling is the signature challenge of a Muon Collider
Cooler beams would allow fewer muons for a given luminosity,
thereby
• Reducing the experimental background
• Reducing the radiation from muon decays
• Allowing for smaller apertures in machine elements, and so
driving the cost down
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Cooling Ideas
RF
 beam
B
B
Gas cell
Ionization cooling (Skrinsky, Neuffer,
Palmer, …): muons are maintained at ca.
200 MeV. Transverse cooling of order
x20 seems feasible (see -factory
feasibility studies 1-2). Longitudinal
cooling not solved.
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Longitudinal Cooling via Emittance
Exchange
Transform longitudinal phase space into
transverse (know how to cool transverse)
Wedge shaped absorber
Bent solenoid produces dispersion
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‘Balbekov Ring’
There are significant
developments in
achieving 6D phase
space via ionization
cooling (R. Palmer,
MUTAC03), but still
far from 106 cooling
factor.
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KEK – focus on FFAG for cooling
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Frictional Cooling
Studies at Columbia University/Nevis Labs
Allen Caldwell, Raphael Galea
+
Stefan Schlenstedt (DESY/Zeuthen)
Halina Abramowitz (Tel Aviv University)
Summer Students:
Emily Alden
Christos Georgiou
Daniel Greenwald
Laura Newburgh
Yujin Ning
Inna Shpiro
Will Serber
Frictional Cooling
Nuclear scattering, excitation, charge
exchange, ionization
• Bring muons to a
kinetic energy (T)
where dE/dx increases
with T
• Constant E-field
applied to muons
resulting in equilibrium
energy
• Big issue – how to
maintain efficiency
• First studied by
Kottmann et al., PSI
Ionization
stops, muon
too slow
1/2 from
ionization
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Problems/comments:
• large dE/dx @ low kinetic energy
 low average density (gas)
• Apply E  B to get below the dE/dx
peak
F = q(E + vxB) – dT/dx
• + has the problem of Muonium
formation

(M) dominates over e-stripping in
all gases except He
•  has the problem of Atomic capture
 small below electron binding energy,
but not known
• Slow muons don’t go far before decaying
d = 10 cm sqrt(T ) T in eV
so extract sideways (E  B )
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Frictional Cooling: particle trajectory
** Using continuous energy loss
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Frictional Cooling: stop the 
• High energy ’s travel a long distance to stop
• High energy ’s take a long time to stop
Optimize for low initial muon momentum,
+ phase rotation
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Phase rotation sections
Cooling cells
Not to scale !!
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Detailed Simulation
Full MARS target simulation, optimized for low energy muon
yield: 2 GeV protons on Cu with proton beam transverse to
solenoids (capture low energy pion cloud).
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Target System
• cool + & - at the
same time
• calculated new
symmetric magnet
with gap for target
GeV
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Target & Drift
Optimize yield
• Maximize drift length for
 yield
• Some ’s lost in Magnet
aperture
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0.4m
28m
’s in red
’s in green
GEANT simulation
View into beam
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Phase Rotation
• First attempt simple form
• Vary t1,t2 & Emax for
maximum low energy yield
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Cooling cell simulation
He gas is used for +, H2 for -.
• Individual nuclear scatters are
simulated – crucial in
determining final phase space,
survival probability.
•Incorporate scattering cross
sections into the cooling
program
•Classical Scattering
T<2KeV
•Born Approx. for T>2KeV
•Include - capture cross
section using calculations of
Cohen (Phys. Rev. A. Vol 62 022512-1)
Electronic energy loss treated as
continuous
•
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Scattering Cross Sections
•Scan impact parameter
and calculate (b), d/d
from which one can get
lmean free path
•Use screened Coulomb
Potential (Everhart et. al. Phys. Rev. 99
(1955) 1287)
•Simulate all scatters
>0.05 rad
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Barkas Effect
•Difference in + & energy loss rates at dE/dx
peak
•Due to extra processes
charge exchange
•Barkas Effect
parameterized data from
Agnello et. al. (Phys. Rev. Lett. 74
(1995) 371)
•Only used for the
electronic part of dE/dx
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Trajectories in detailed simulation
Longitudinal motion
Transverse motion
Motion
controlled
by B field
Lorentz angle drift, with nuclear scattering
Final stages of muon trajectory in gas cell
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E dominates
F = q(E+vB)-dT/dx
vxB dominates
Dangerous because of capture possibility
Oscillations about equilibrium
define emittance.
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Motion in Transverse Plane
+
B
E
Lorentz angle
-
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Yields & Emittance
Look at muons coming out of 11m cooling cell region after initial
reacceleration.
Yield: approx 0.002  per 2GeV proton after cooling cell.
Need to improve yield by factor 3 or more.
Emittance: rms
x = 0.015 m
y = 0.036 m
z = 30 m ( actually ct)
Px = 0.18 MeV
Py = 0.18 MeV
Pz = 4.0 MeV
6D,N = 5.7 10-11 (m)3
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Problems/Things to investigate…
• Extraction of s through window in gas cell
•Must be very thin to pass low energy s
•Must be reasonably gas tight
• Can we apply high electric fields in gas cell without
breakdown (large number of free electrons, ions) ?
Plasma generation  screening of field.
• Reacceleration & bunch compression for injection into
storage ring
• The  capture cross section depends very sensitively on
kinetic energy & falls off sharply for kinetic energies greater
than e- binding energy. NO DATA – simulations use
theoretical calculation
• +…
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First try to demonstrate frictional cooling with protons.
RARAF Facility – Nevis Lab/Columbia University
 4 MeV p
VandeGraaf
accelerator for
biomedical
research
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Accelerating grid
Contains 20nm window
Si detector
To MCP
Proton beam
Gas cell
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Vacuum chamber
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Initial conclusions: no obvious cooling peak, but very low acceptance due to
lack of magnetic field. Use data to tune simulations. Redo experiment with a
solenoidal magnetic field.
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Future Plans
• Frictional cooling tests at MPI with 5T Solenoid, alpha source
• Study gas breakdown in high E,B fields
• R&D on thin windows
• Beam tests with muons to measure  capture cross section
-+H  H+ e+’s
muon initially captured in n=15 orbit, then cascades down to n=1.
Transition n=2n=1 releases 2.2 KeV x-ray.
Si drift detector
Developed my MPI
HLL
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Lab situated at MPI-WHI in
Munich
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Conclusions
• Muon Collider complex would be a boon
for physics
• We need to solve the muon cooling problem
• Different schemes should be investigated
• We are doing some simulation and
experimental studies of frictional cooling.
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