frictional cooling mc collaboration meeting june 11 12 2003 l.
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Frictional Cooling MC Collaboration Meeting June 11-12/2003 Raphael Galea Ionization stops, muon too slow Frictional Cooling Nuclear scattering, excitation, charge exchange, ionization Bring muons to a kinetic energy (T) where dE/dx increases with T

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frictional cooling

Ionization stops, muon too slow

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

1/2from ionization

problems comments
  • large dE/dx @ low kinetic energy

 low average density (gas)

  • Apply E  B to get below the dE/dx peak
  • m+has the problem of Muonium formation

s(Mm) dominates over e-strippingin 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
Trajectories in detailed simulation

Transverse motion

Motion controlled by B field

Fluctuations in energy results in emittance

Lorentz angle drift, with nuclear scattering

Final stages of muon trajectory in gas cell


Results of simulations to this point

Phase rotation sections

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).
  • 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.

Not to scale !!

summary of simulations
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 Effectparameterized 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

Cooling factors of 105-107!!!


Assumed initial conditions

  • 20nm C windows
  • 700KeV protons
  • 0.04atm He

Punch through protons

Cooled protons



Kinetic energy


Add windows


721KeV p

Add gas

No gas/grid/windows

Extract time offsets



Cool protons???

MC exp

Flat constant Background

Background exponential with m>0

problems things to investigate
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
  • +…

R&D with industry?

1 student + 1 Postdoc…group is growing…


Lab situated at MPI-WHI in


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 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




  • 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.