Frictional Cooling NUFACT02

Frictional CoolingFrictional CoolingNUFACT02NUFACT02

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 2001 Students: Summer 2001 Students: Christos Georgiou Christos Georgiou Daniel GreenwaldDaniel GreenwaldYujin NingYujin NingInna ShpiroInna ShpiroWill SerberWill Serber

Raphael Galea, Columbia UniversityNUFACT02 : Imperial College London

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


Cooling scheme

•Phase rotation is E(t) field to bring as many ’s to 0 Kinetic energy as possible• Put Phase rotation into the ring


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


Frictional Cooling Channel


Cell Magnetic Field

Correction solenoid

Main Ring Solenoid

Extract & accelerate

• Realistic Solenoid fields in cooling ring


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


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

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

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

For cooled


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


MCP front MCP side Accelerating Grid

Multi-Wire Proportional Chamber

Work at NEVIS labs

•Want to measure the energy loss, - capture, test cooling principle•Developing Microchannel Plate & MWPC detectors


A simpler approach

•Avoid difficulties of kickers & multiple windows•Without optimization initial attempts have 60% survival & cooling factor 105

•Still need to bunch the beam in time


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

Summary of Frictional Cooling

Nevis Labs work on - capture

•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.

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Frictional Cooling NUFACT02