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 10 6 ?

 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 Ionization stops, muon too slow • 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

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 dx

m + has the problem of Muonium formation  m Slow s(Mm) dominates over e-stripping in all gases except He has the problem of Atomic capture s small below electron binding energy, but not known 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 1 t m  d m =10cm*sqrt{T(eV)} keep d small at low T  reaccelerate quickly

F



q

(

E

+

v



B

) -

dT 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 + , H 2 for There is a nearly uniform 5T B z m . field everywhere, and E x =5 MeV/m in gas cell region  Electronic energy loss treated as continuous, individual nuclear scattering taken into account since these yield large angles.

•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 •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)

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) P x P y P z = 0.18 MeV = 0.18 MeV = 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 m s through window in gas cell •Must be very thin to pass low energy m 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 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 • +…

RA

diological

R

esearch

A

ccelerator

F

acility

 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  Look for a bunching in time  Can we cool protons ?



4 MeV p

To MCP Accelerating grid Contains 20nm window Si detector 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 m +H  H m + e+  ’s capture cross section 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(10 6 ) •Still or more? unanswered questions being worked on but work is encouraging.

Nevis Labs work on m s capture 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

F



q

(

E

+

v



B

) -

dT dx

•Assuming E x =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 d s /d q from which one can get l mean 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 + & 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

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 t 1 ,t 2 & E max for maximum low energy yield