Frictional Cooling TRIUMF Seminar July 22, 2002

Frictional CoolingFrictional CoolingTRIUMF SeminarTRIUMF Seminar

July 22, 2002July 22, 2002

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

R.Galea, Columbia UniversityTriumf Seminar22/07/02

Outline

•Introduction & Motivation •Frictional Cooling•Simulation and Optimization

•Target and capture•Phase Rotation•Cooling cell

•Nevis experimental work•Results and Conclusions


Why a Muon Collider ?• No synchrotron radiation problem (cf electron)• Muons are point particles (cf proton)

We therefore dream of building a high energy collider. Parameter sets available up to 100 TeV+100 TeV.

• At lower energies, Higgs factory (40000 higher production cross section than electron collider). Very fine energy scans possible since limited radiation from muons.• Neutrinos from target, muon decay allow wide range of physics• Low energy muons allow many important condensed matter, atomic physics experiments


Dimensions of Some Colliders under Discussion


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


Muon Collider as Higgs Factory

Small beam energy spread allows a precision measurement of the Higgs mass (few hundred KeV)

The width can also be measured to about 1 MeV


NATO ASI 2002, June 13 -24 Gail G. Hanson, Lecture #3 20

HIGGS FACTORY PARAMETERSB ase line para m eter s for Hi gg s fa cto ry muo n c o lli der. H ig gs /yea r a ss um es ac ross s e ction o f 5 ×10 4 ,fb H ig gs wi dth of 2.7 M e , V 1 year = 1 0 7 s . F ro m “S tatus of M uon Co llide r R esearc h an d Developm ent a nd Futur e P lans ,” Mu on C ollide r

C ollabo rati ,on C . . M Ankenbrandt et al., P hys . R ev. S T A ccel. Beam s 2 , 08 1001(1 999) .

C OM ener gy (T eV ) 0.1p energ (y Ge V ) 16p ’s /bu nch 5 × 10 1 3

Bunche /s fill 2R . ep r ate (Hz ) 15p powe (r MW ) 4 / bunch 4 × 10 1 2

powe (r MW ) 1W a ll powe r (MW ) 81C ollider circu .m (m ) 35 0Av e bendi ng fiel d (T ) 3r ms δ /p p (% ) 0.1 2 0.0 1 0.0 0 36 D ε 6 ,Ν (m)3 1.7 × 10 −1 0 1.7 × 10 −10 1.7 × 10 −10

r ms εn ( m m mr )ad 85 19 5 29 0β * (cm ) 4.1 9.4 14. 1σ z (cm ) 4.1 9.4 14. 1σ r spot (m) 86 19 6 29 4σ θ I P (mrad ) 2.1 2.1 2.1T u ne shift 0.0 5 1 0.0 2 2 0.0 1 5n turns (effective) 45 0 45 0 45 0Lu minosit y (cm−2 s−1 ) 1.2 × 10 3 2 2.2 × 10 3 1 10 3 1

Higgs /yr 1.9 × 10 3 4 × 10 3 3.9 × 10 3


HIGH ENERGY MUON COLLIDER PARAMETERS

Baseline parameters for high energy muon colliders. From “Status of Muon ColliderResearch and Development and Future Plans,” Muon Collider Collaboration, C. M.Ankenbrandt et al., Phys. Rev. ST Accel. Beams 2, 081001 (1999).

COM energy (TeV) 0.4 3.0p energy (GeV) 16 16p’s/bunch 2.5 × 1013 2.5 × 1013

Bunche /s fill 4 4R . ep r ate(Hz) 15 15p powe (r MW) 4 4/ bunch 2 × 1012 2 × 1012

powe r (MW) 4 28Wa ll powe r (MW) 120 204Collider circ .um (m) 1000 6000Av e bendi ng fiel d (T) 4.7 5.2r msδ /p p (%) 0.1 4 0.1 66 D ε6,Ν (m)3 1.7 × 10−10 1.7 × 10−10

r msεn ( m mmr )ad 50 50β* (cm) 2.6 0.3σz (cm) 2.6 0.3σr spot (m) 2.6 3.2σθ I P (mr )ad 1.0 1.1Tu neshift 0.0 44 0.0 44nturns (effective) 700 785Luminosit y (cm−2 s−1) 10 33 7 × 1034


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

• & beam occupy diffuse phase space

)()()()()()(6 zyxD PzPyPx σσσσσσε =

•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


Phase Space Reduction

Simplified emittance estimate:At end of drift, rms x,y,z approx 0.05,0.05,10 m Px,Py,Pz approx 50,50,100 MeV/c

Normalized 6D emittance is product divided by (mc)3

drift6D,N 1.7 10-4 (m)3

Emittance needed for Muon Collider collider

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

This reduction of 6 orders of magnitude must be done with reasonable efficiency (luminosity calculation assumes typically few 1012 muons per bunch, 1-4 bunches).


Some Difficulties

• Muons decay, so are not readily available – need multi MW source. Large starting cost.• Muons decay, so time available for cooling, bunching, acceleration is very limited. Need to develop new techniques, technologies.• Large experimental backgrounds from muon decays (for a collider). Not the usual clean electron collider environment.• High energy colliders with high muon flux will face critical limitation from neutrino radiation.


Muon Cooling

Muon Cooling is the signature challenge of a Muon Collider

Cooler beams would allow fewer muons for a given luminosity,Thereby• Reducing the experimental background• Reducing the radiation from muon decays• Allowing for smaller apertures in machine elements, and so driving the cost down


Cooling Ideas

The standard approach (Skrinsky, Neuffer, Palmer, …) considered to date is ionization cooling, where muons are maintained at ca. 200 MeV while passed successively through an energy loss medium followed by an acceleration stage. Transverse cooling of order x20 seems feasible (see feasibility studies 1-2). Longitudinal cooling is more difficult, and remains an unsolved problem.

There are significant developments in achieving 6D phase space via ionization cooling


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

• σ dominates over e-stripping σ in all gases except He

• has the problem of Atomic capture• σ 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

BErr

⊥


Frictional Cooling: particle trajectory

** Using continuous energy loss

rdx

dTBvEqF ˆ)( −×+=rrrr

• 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 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


Detailed Simulation

• 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).• Optimized drift length (28m).• Simple phase rotation parameters, optimized to bring muons to Pz<50 MeV/c. Phase rotation is combined with cooling channel.• 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.


Detailed Simulation - continued

• Barkas effect (reduced energy loss for - relative to +) included• - capture cross section included• Windows for gas cells NOT included so far• Time window for accepting muons into cooling channel consistent with rotation time

Muons(pions) are tracked from the target through

to the edge of the gas cell.


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 θ(b) to get dσ/dθ from which one can get mean free path

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

•Simulate all scatters θ>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 σcapture

•Lower r fewer scatters

•BUT at higher equilibrium energy


Motion in Transverse Plane

Er

Br

Lorentz angle

rdx

dTBvEqF ˆ)( −×+=rrrr

•Assuming Ex=constant





























βct vs z for +He on Cu

βct 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 Calculation

translongD

yxtrans

zlong

PyPx

Pz

εεε

σσσσε

σσε

=

=

=

6

)()()()(

)()(

'''6

0'

'

)()()()(

)()(

etranslongD

zetrans

long

PzP

Pct

εεε

σσσφσε

σβσε

φ

=

=

=

After cooling cylindrical coordinates are more natural

cellsN

Ncmz

cm

100

*12/10)(

200

==

=

σ

After drift cartesian coordinatesMore natural

Beamlet uniform z distribution:


yx yPxP

P+

=2φ

xy yPxPP

−= zP

Beamlet coordinates:

z,,φ

X 100 beamlets

Conclusions

Cooling factors

ε6D/ε’6D

Yield (/p)

εtrans εlong ε6D

(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, - σcapture, 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.

Documents

Frictional Cooling TRIUMF Seminar July 22, 2002