Transcript Frictional Cooling - Nevis Laboratories

Frictional Cooling
MC Collaboration Meeting
June 11-12/2003
Raphael Galea
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
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 + v  B ) -
dT
rˆ
dx
•

•
•
m+ has the problem of Muonium formation
s(Mm) dominates over e-stripping in all gases
except He
m- has the problem of Atomic capture
s 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 )
Trajectories in detailed simulation
Transverse motion
Motion
controlled
by B field
Lorentz angle drift, with nuclear scattering
Fluctuations in energy
results in emittance
Final stages of muon trajectory in gas cell
F  q( E + v  B ) -
dT
dx
rˆ
Phase rotation sections
Results of
simulations to
this point
Cooling cells
Full MARS target simulation,
optimized for low energy
muon yield: 2 GeV protons on
Cu/W with proton beam
transverse to solenoids
(capture low energy pion
cloud).
Not to scale !!
 He gas is used for m+, H2 for m-.
There is a nearly uniform 5T Bz
field everywhere, and Ex =5 MeV/m
in gas cell region
 Electronic energy loss treated as
continuous, individual nuclear
scattering taken into account since
these yield large angles.
Summary of Simulations
•Incorporate scattering cross sections into the cooling program
•Born Approx. for T>2KeV
•Classical Scattering T<2KeV
•Include m- capture cross section using calculations of Cohen (Phys. Rev. A. Vol 62 022512-1)
•Difference in m+ & m- 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
•Energy loss in thin windows
•For RARAF setup proton transmitted energy spectrum is input from SRIM,
simulating protons through Si detector
(J.F. Ziegler http://www.srim.org)
Cooling factors of 105-107!!!
Assumed initial conditions
•20nm C windows
•700KeV protons
•0.04atm He
TOF=T0-(Tsi-TMCP)
speed
1. Punch
through
protons
2. Cooled
protons
Kinetic energy
Add windows
300nm
721KeV p
Add gas
No gas/grid/windows
Extract time offsets
Pm 

Pt * G ( t, s ) dt
0.06atm
Cool protons???
MC exp
Flat constant Background
750 ns
# Events 
N
i
 58  82 (55 )
i
 - 5  45 ( 49 )
i
 55  194 ( 77 )
i
 - 42  124 ( 77 )
i 300 ns
400 ns
# Events 
N
i 300 ns

750 ns
# Events 
N
i 200 ns
400 ns
# Events 
N
i 200 ns
Background exponential with m>0

Problems/Things to investigate…
• Extraction of ms through window in gas cell
•Must be very thin to pass low energy ms R&D with industry?
•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 m- capture cross section depends very sensitively on kinetic
energy & falls off sharply for kinetic energies greater than ebinding energy. NO DATA – simulations use theoretical
calculation
• +…
1 student + 1 Postdoc…group is growing…
Lab situated at MPI-WHI in
Munich
Sharper peak in Energy than
peak from measuring time.
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 m capture cross section
m-+H  Hm+ 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
Conclusions
No clear sign of cooling but this is expected from lack
of Magnetic field & geometric MCP acceptance alone
The Monte Carlo simulation can provide a consistent
picture under various experimental conditions
Can use the detailed simulations to evaluate Muon
Collider based on frictional cooling performance with
more confidence….still want to demonstrate the cooling
Work at MPI on further cooling demonstration
experiment using an existing 5T Solenoid and develop
the m- capture measurement
A lot of interesting work and results to come.