Frictional Cooling for a Muon Collider
A. Caldwell
MPI f. Physik/Columbia University
• Motivation
• Simulation Studies
• Experimental Studies/Plans
1
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
2
’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 !
3
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
• Reducing the radiation from neutrino interactions
• Allowing for smaller apertures in machine elements, and so
driving the cost down
4
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
• Similar idea first studied
by Kottmann et al., PSI
Ionization
stops, muon
too slow
1/2 from
ionization
5
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 Atomic capture
 small above electron binding energy,
but not known. Keep T as high as
possible
Slow muons don’t go far before
decaying
d = 10 cm sqrt(T ) T in eV
so extract sideways (E  B )
+ has the problem of Muonium
formation
(M) dominates over e-stripping in
all gases except He
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Neutralization
From Y. Nakai, T. Shirai, T. Tabata and R. Ito, At.
Data Nucl. Data Tables 37, 69 (1987)
Stripping
For , energy lower by
M/MP
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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
Plots for
1. 10-4 g/cm3 He
Optimize for low initial muon momentum,
+ phase rotation
9
Schematic Layout for  Collider Scheme Studied
Phase rotation sections
Cooling cells
Not to scale !!
10
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).
11
Target System
• cool + & - at the
same time
• calculated new
symmetric magnet
with gap for target
GeV
12
Target & Drift
Optimize yield
• Optimize drift length for 
yield
• Some ’s lost in Magnet
aperture
13
0.4m
28m
’s in red
’s in green
GEANT simulation
View into beam
14
Phase Rotation
• First attempt simple form
• Vary t1,t2 & Emax for
maximum low energy yield
15
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
•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
•Simulation accurately
reproduces ICRU tables for
protons
17
Barkas Effect
•Difference in + & energy loss rates at dE/dx
peak
•Due to charge exchange
for +
•parameterized data from
Agnello et. al. (Phys. Rev. Lett. 74
(1995) 371)
•Only used for the
electronic part of dE/dx
18
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
19
E dominates
F = q(E+vB)-dT/dx
vxB dominates
Dangerous because of capture possibility
Oscillations about equilibrium
define emittance.
20
Initial reacceleration region
E
gas
Reacc section
After gas cell, E(z,t)
T = 4 ns at Z=444m
P = 200 MeV/c
Eff = 40%
21
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 5 or more to match
# /proton/GeV in specifications.
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

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= 5.7 10-11 (m)3
Problems/Things to investigate…
• Extraction of s through windows 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
• +…
23
First try to demonstrate frictional cooling with protons.
RARAF Facility – Nevis Lab/Columbia University
 4 MeV p
VandeGraaf
accelerator for
biomedical
research
24
H2 +
beam
Accelerating grid
Contains 20nm window
Si detector
To MCP
Proton beam
Gas cell
26
Vacuum chamber
27
28
The proton energy spectrum from the Si calculated using SRIM (J. F. Ziegler,
J. P. Biersack and U. Littmark, Pergamon Press, 1985). The transport through the gas
performed with our detailed simulation. Need first to fix the window
thickness and gas pressure.
Min Kin Energy
fixed by reacc
potential
29
Calibration Data:
3 distances, no cell, no grid
Time resolution of system=17ns
Protons have 100-200 KeV after
Si window. Good agreement
with SRIM.
30
Add cell, no gas, no E field.
Extract effective window
thickness by comparison with
simulation. Much thicker than
expected !
Add gas, still no field. Gas
pressure extracted from
comparison with simulation.
Compatible with expectations.
31
Summary of calibration using the time spectrum
32
After background subtraction, see no hint of cooled protons. Also
predicted by simulation. Problem – windows too thick, acceptance,
particularly for slow protons, too small. Need to repeat the experiment
with solenoid, no windows.
33
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
-+He  He+ e+’s
muon initially captured in large n orbit, then cascades down to n=1.
Transition n=2n=1 releases few KeV x-ray.
Si drift detector
Developed my MPI
HLL
34
Lab situated at MPI-WHI in
Munich
35
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.
So far, so good, but a long way to go !
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