Frictional CoolingFrictional Cooling

Studies at Columbia University/Nevis LabsStudies at Columbia University/Nevis Labs

Raphael Galea, Allen CaldwellRaphael Galea, Allen Caldwell

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Stefan Schlenstedt (DESY/Zeuthen)Stefan Schlenstedt (DESY/Zeuthen)

Halina Abramowitz (Tel Aviv University)Halina Abramowitz (Tel Aviv University)

Summer Students: Emily AldenSummer Students: Emily Alden Christos Georgiou Christos Georgiou

Daniel GreenwaldDaniel Greenwald Laura NewburghLaura Newburgh

Yujin NingYujin Ning Will SerberWill Serber

Inna ShpiroInna Shpiro

How to reduce beam Emmittance by 106?

6D,N = 1.7 10-10 (m)3

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

1/2 from ionization

Ionization stops, muon too slow

Nuclear scattering, excitation, charge exchange, 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 formation

dominates 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

Frictional Cooling: particle trajectorySome obvious statements?

** Using continuous energy loss

€

rF = q(

r E +

r v ×

r B ) −

dT

dxˆ r

In 1 d=10cm*sqrt{T(eV)} keep d small at low T reaccelerate quickly

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 with proton beam transverse to solenoids (capture low energy pion cloud).

•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

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 3 or more.

Emittance: rms x = 0.015 m y = 0.036 m z = 30 m ( actually ct)

Px = 0.18 MeVPy = 0.18 MeVPz = 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 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• +…

RAdiological Research Accelerator FacilityPerform TOF measurements with

protons2 detectors START/STOPThin entrance/exit windows for a gas cellSome density of He gasElectric field to establish equilibrium energyNO B field so low acceptance

Look for a bunching in time Can we cool protons?

4 MeV p

Contains 20nm window

Proton beam

Gas cell

Accelerating grid

Vacuum chamber

To MCP

Si detector

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 inMunich

Future Plans

• Frictional cooling tests at MPI with 5T Solenoid, 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+’smuon initially captured in high n orbit, then cascades down to n=1. Transition n=2n=1 releases 2.2 KeV x-ray.

Si drift detectorDeveloped my MPIHLL

Summary of Frictional Cooling

Nevis Labs work on - capture

MPI lab for additional questions

•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.

Frictional Cooling: stop the

Start with low initial muon momenta

High energy ’s travel a long distance to stop High energy ’s take a long time to stop

Motion in Transverse Plane

€

rE

€

rB

Lorentz angle

€

rF = q(

r E +

r v ×

r B ) −

dT

dxˆ r

•Assuming Ex=constant

Simulations Improvements

•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)

Scattering Cross Sections

•Scan impact parameter (b) to get d/d from which one can get mean free

path

•Use screened Coulomb Potential (Everhart et. al. Phys. Rev. 99 (1955) 1287)

•Simulate all scatters >0.05 rad

Barkas Effect

•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

Target Study

Cu & W, Ep=2GeV, target 0.5cm thick

Target System

cool + & - at the same time calculated new symmetric magnet with gap for target

Target & Drift Optimize yield

Maximize drift length for yield Some ’s lost in Magnet aperture

Phase Rotation

First attempt simple form Vary t1,t2 & Emax for maximum low energy yield