Frictional CoolingMC Collaboration Meeting

June 11-12/2003

Raphael Galea

Frictional CoolingFrictional Cooling

• 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

Nuclear scattering, excitation, charge exchange, ionization

1/2 from ionization

Problems/comments:Problems/comments:• large dE/dx @ low kinetic energy

low average density (gas)• Apply E B to get below the dE/dx peak

• has the problem of Muonium formationdominates over e-strippingin 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 )

€

rF = q(

r E +

r v ×

r B ) −

dT

dxˆ r

Trajectories in detailed simulation

Final stages of muon trajectory in gas cell

Lorentz angle drift, with nuclear scattering

Transverse motion

Motion controlled by B field

Fluctuations in energy results in emittance

€

rF = q(

r E +

r v ×

r B ) −

dT

dxˆ r

Cooling cells

Phase rotation sections

Not to scale !!

He gas is used for +, H2 for -. 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.

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).

Results of simulations to this point

Summary of Simulations

•Incorporate scattering cross sections into the cooling program•Born Approx. for T>2KeV•Classical Scattering T<2KeV

•Include - capture cross section using calculations of Cohen (Phys. Rev. A. Vol 62 022512-1)

•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

•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 Kinetic energy

1. Punch through protons

2. Cooled protons

No gas/grid/windows Extract time offsets

Add windows

Add gas

€

Pm = Pt *G(t,σ )dt∫

721KeV p

300nm

0.06atm

Cool protons???

€

# Events = N i

i= 300ns

750ns

∑ = 58 ± 82(55)

# Events = N i

i= 300ns

400ns

∑ = −5 ± 45(49)

€

# Events = N i

i= 200ns

750ns

∑ = 55 ±194(77)

# Events = N i

i= 200ns

400ns

∑ = −42 ±124(77)

Background exponential with m>0

Flat constant Background

MC exp

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• +…

R&D with industry?

1 student + 1 Postdoc…group is growing…

Lab situated at MPI-WHI inMunich

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=2n=1 releases 2.2 KeV x-ray.

Si drift detectorDeveloped my MPIHLL

No clear sign of cooling but this is expected from lack of Magnetic field & geometric MCP acceptance aloneThe 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 coolingWork at MPI on further cooling demonstration experiment using an existing 5T Solenoid and develop the - capture measurement

Conclusions

A lot of interesting work and results to come.