Frictional CoolingFrictional Cooling

Studies at Columbia University &Nevis LabsStudies at Columbia University &Nevis Labs

Raphael GaleaRaphael Galea

Allen CaldwellAllen Caldwell

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

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

Summer Students: Summer Students: Christos Georgiou Christos Georgiou Daniel GreenwaldDaniel GreenwaldYujin NingYujin NingInna ShpiroInna ShpiroWill SerberWill Serber

Outline

•Introduction & Motivation •Frictional Cooling•Simulation and Optimization

•Taget and capture•Phase Rotation•Cooling cell

•Nevis experimental work•Results and Conclusions

Physics at a Muon Collider

• Stopped physics• physics• Higgs Factory• Higher Energy Frontier

Muon Collider Complex:• Proton Driver 2-16GeV; 1-4MW leading to 1022p/year• production target & Strong Field Capture• COOLING resultant beam• acceleration•Storage & collisions

Cooling Motivation• s not occur naturally so produce them from p on target – beam – decay to

• & beam occupy diffuse phase space

)()()()()()(6 zyxD PzPyPx

•Unlike e & p beams only have limited time (=2.2s) to cool and form beams

•Neutrino Factory/Muon Collider Collaboration are pursuing a scheme whereby they cool s by directing particles through a low Z absorber material in a strong focusing magnetic channel and restoring the longitudinal momentum

•IONIZATION COOLING COOL ENERGIES O(200MeV)•Cooling factors of 106 are considered to be required for a Muon Collider and so far factors of 10-100 have been theoretically achieved through IONIZATION COOLING CHANNELS

Frictional CoolingFrictional Cooling

• Bring muons to a kinetic energy (T) range where dE/dx increases with T

• Constant E-field applied to muons resulting in equilibrium energy

Problems/Comments:Problems/Comments:

• large dE/dx @ low kinetic energy • low average density

• Apply to get below the dE/dx peak• has the problem of Muonium formation

• dominates over e-stripping in all gases except He

• has the problem of Atomic capture• calculated up to 80 eV not measured below ~1KeV

• Cool ’s extracted from gas cell T=1s so a scheme for reacceleration must be developed

BE

Frictional Cooling: particle trajectory

** Using continuous energy loss

rdx

dTBvEqF ˆ)(

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

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

Coolin

g s

ch

em

e

•Ph

ase

rota

tion

is

E(t

) field

to b

rin

g a

s m

an

y

’s t

o 0

Kin

eti

c en

erg

y a

s p

oss

ible

• P

ut

Ph

ase

rota

tion

in

to t

he r

ing

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

28m

0.4m

’s in red ’s in green

View into beam

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

Phase Rotation

WCu

Frictional Cooling Channel

Time sequence of events…

Cell Magnetic Field

Correction solenoid

Main Ring Solenoid

Extract & accelerate

• Realistic Solenoid fields in cooling ring

Fringe fields produce Uniform Bz=5T

Br=2% Uniform Bz total field

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 Coloumb 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

Frictional Cooling: Particle Trajectory

•50cm long solenoid•10cm long cooling cells• gas for + 0.7atm & - 0.3atm•Ex=5MV/m•Bz=5T realistic field configuration

- use Hydrogen•Smaller Z help in capture

•Lower r fewer scatters

•BUT at higher equilibrium energy

Motion in Transverse Plane

E

B

Lorentz angle

rdx

dTBvEqF ˆ)(

•Assuming Ex=constant

ct vs z for +He on Cu

ct vs z for -H on W

Plong vs Ptrans for +He on CU

Plong vs Ptrans for -H on W

R vs z for +He on CU

R vs z for -H on W

Emittance Calulation

translongD

yxtrans

zlong

PyPx

Pz

6

)()()()(

)()(

'''6

0'

'

)()()()(

)()(

etranslongD

zetrans

long

PzP

Pct

After cooling cylindrical coordinates are more natural

cellsN

Ncmz

cm

100

*12/10)(

200

After drift cartesian coordinatesMore natural

Beamlet uniform z distribution:

yx yPxP

P

2

xy yPxPP

zP

Beamlet coordinates:

z,,

X 100 beamlets

Problems/Things to investigate…

•Extraction of s through window in gas cell •Must be very thin to pass low energy s•Must be gas tight and sustain pressures O(0.1-1)atm

• Can we applied high electric fields in small gas cell without breakdown?•Reacceleration & recombine beamlets for injection into storage ring•The capture cross section depends very sensitively on kinetic energy & fall off sharply for kinetic energies greater than e- binding energy. NO DATA – simulations use calculation

Critical path item intend to make measurement

Conclusions

Cooling factors

6D/’6D

Yield (/p)

trans long D

(1x106)

+He on Cu 0.005 11239 2012 22

-He on Cu 0.002 403 156 0.06

-H on Cu 0.003 1970 406 0.8

+He on W 0.006 9533 1940 18

-He on W 0.003 401 149 .06

-H on W 0.004 1718 347 0.6

Conclusions

• Frictional cooling shows promise with potential cooling factors of O(105-106)– Simulations contain realistic magnet field

configurations and detailed particle tracking

– Built up a lab at Nevis to test technical difficulties

• There is room for improvement– Phase rotation and extraction field concepts very simple

– Need to evaluate a reacceleration scheme