Transcript Document

Frictional Cooling
Studies at Columbia University/Nevis Labs
Raphael Galea, Allen Caldwell
+
Stefan Schlenstedt (DESY/Zeuthen)
Halina Abramowitz (Tel Aviv University)
How to reduce beam
Emmittance by 106?
6D,N = 1.7 10-10 (m)3
Summer Students: Emily Alden
Christos Georgiou
Daniel Greenwald
Laura Newburgh
Yujin Ning
Will Serber
Inna Shpiro
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 )
•
Frictional Cooling: particle trajectory
Some obvious statements?
 In 1tm dm=10cm*sqrt{T(eV)}
 keep d small at low T
 reaccelerate quickly
F  q(E + v  B) -
dT
rˆ
dx

** Using continuous energy loss
Phase rotation sections
Cooling cells
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).
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.
•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+ & menergy 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
Yields & Emittance
Look at muons coming out of 11m cooling cell region after
initial reacceleration.
Yield: approx 0.002 m 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
6D,N = 1.7 10-10 (m )3
Problems/Things to investigate…
• Extraction of ms through window in gas cell
•Must be very thin to pass low energy ms
•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 e- binding energy. NO DATA – simulations use
theoretical calculation
• +…
Perform TOF measurements with
protons
2 detectors START/STOP
Thin entrance/exit windows
for a gas cell
Some density of He gas
Electric field to establish
equilibrium energy
NO B field so low acceptance
RAdiological
Research
Accelerator
Facility
Look for a bunching in time
Can we cool protons?
 4 MeV p
Accelerating grid
Contains 20nm window
Si detector
To MCP
Proton beam
Gas cell
Vacuum chamber
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.
Lab situated at MPI-WHI in
Munich
Future Plans
• Frictional cooling tests at MPI with 5T Solenoid, a 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 high n 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
Summary of Frictional Cooling
•Works below
the Ionization
Peak
•Possibility to
capture both
signs
•Cooling factors
O(106) or more?
•Still
unanswered
questions being
worked on but
work is
encouraging.
Nevis Labs work on m- scapture
MPI lab for additional questions
Frictional Cooling: stop the m
 High energy m’s travel a long distance to stop
 High energy m’s take a long time to stop
Start with low initial muon momenta
Motion in Transverse Plane
dT
F  q(E + v  B) rˆ
dx

•Assuming
Ex=constant
B


E
Lorentz angle
Simulations Improvements
•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)
Scattering Cross Sections
•Scan impact parameter
q(b) to get ds/dq from
which one can get lmean free
path
•Use screened Coulomb
Potential (Everhart et. al. Phys. Rev. 99
(1955) 1287)
•Simulate all scatters
q>0.05 rad
Barkas Effect
•Difference in m+ & menergy 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
Target Study
Cu & W, Ep=2GeV, target 0.5cm thick
Target System
 cool m+ & m- at the
same time
 calculated new
symmetric magnet
with gap for target
Target & Drift
Optimize yield
 Maximize drift length for
m yield
 Some ’s lost in
Magnet aperture
Phase Rotation
 First attempt simple form
 Vary t1,t2 & Emax for
maximum low energy yield