Frictional Cooling TRIUMF Seminar July 22, 2002

Studies at Columbia University &Nevis Labs Raphael Galea Allen Caldwell Stefan Schlenstedt (DESY/Zeuthen) Halina Abramowitz (Tel Aviv University)

Summer Students: Christos Georgiou Daniel Greenwald Yujin Ning Inna Shpiro Will Serber

Outline

•Introduction & Motivation •Frictional Cooling •Simulation and Optimization •Target and •Cooling cell

p

capture •Phase Rotation •Nevis experimental work •Results and Conclusions

R.Galea, Columbia University Triumf Seminar22/07/02

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 Neutrinos from muons.

from target, muon decay allow wide range of physics Low energy muons allow many important condensed matter, atomic physics experiments R.Galea, Columbia University Triumf Seminar22/07/02

Dimensions of Some Colliders under Discussion

R.Galea, Columbia University Triumf Seminar22/07/02

Physics at a Muon Collider

Muon Collider Complex:

• Proton Driver 2-16GeV; 1-4MW leading to • • 10 22 p/year p production target & Strong Field Capture COOLING resultant m beam • m acceleration •Storage & collisions • • Stopped m n physics physics • Higgs Factory • Higher Energy Frontier R.Galea, Columbia University Triumf Seminar22/07/02

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 R.Galea, Columbia University Triumf Seminar22/07/02

HIGGS FACTORY PARAMETERS

B a s e line p ara m eter s for Hi gg s fa c to ry muo n c o llider. H igg s /y ea r a ss um es a c ross s e c tion o f 5  10 4 fb, H ig gs wi dth of 2.7 M e V, 1 y ear = 1 0 7 s . F ro m “S tatu s of M uon Co llid e r R e s e a rc h a n d D e v e lop m ent a nd F u tur e P la ns ,” M uon C o llide r C o llabo rat ion, C . M. A n k en b ran d t

et a l

.,

P h ys . R e v . S T A cc e l. B eam s

2

, 0 8 1001 (1 999) .

C OM e ner gy (T e V )

p

en e rg y ( Ge V )

p

’s/bu nc h B un c he s/fill R ep. rate (Hz )

p

po we r ( MW ) m / bu nc h m po we r ( MW ) W a ll po w e r (M W ) C o llider c irc u m. (m ) Av e be n d ing f ie ld (T ) rms 

p/p

( % ) 6 D rms    ( p m ) 3  n ( p m m m rad)  * ( cm )  z ( cm )  r s pot ( m m )   I P (m rad ) T u ne s h ift

n

t u rn s ( e ffe c tive ) Lu mi no sity (cm  2 s  1 ) Hi gg s /yr 0.1 2 1.7  10  1 0 85 4.1

4.1

86 2.1

0.0 5 1 45 0 1.2  10 1.9  10 3 2 3 0.1

16 5  10 1 3 2 15 4 4  10 1 2 1 81 35 0 3 0.0 1 1.7  10  1 0 19 5 9.4

9.4

19 6 2.1

0.0 2 2 45 0 2.2  10 4  10 3 3 1 0.0 0 3 1.7  10  1 0 29 0 14. 1 14. 1 29 4 2.1

0.0 1 5 45 0 10 3 1 3.9  10 3 Gail G. Hanson, Lecture #3 NATO ASI 2002, June 13-24 R.Galea, Columbia University Triumf Seminar22/07/02 20

HIGH ENERGY MUON COLLIDER PARAMETERS

Baseline parameters for high energy muon colli ders. From “Status of Muon Colli der Research and Development and Future Plans ,” Muon Colli der Collaboration, C. M.

Ankenbrandt

et al

.,

Phys. Rev. ST Accel. Beams

2

, 081001 (1999).

COM energy (TeV)

p

energy ( GeV)

p

’s/bunch Bunches/fill Rep. rate (Hz )

p

power (MW) m / bunch m power (MW) Wall power (MW) Colli der circum. (m) Ave bending field (T) rms 

p/p

(%) 6D   ( p m) 3 rms  n ( p mm mrad)  * (cm)  z (cm)  r spot ( m m)   IP (mrad) Tune shift

n

t urns (effective) Luminosity (cm  2 s  1 ) R.Galea, Columbia University Triumf Seminar22/07/02 0.4

16 2.5  10 13 4 15 4 2  10 12 4 120 1000 4.7

0.14

1.7  10  10 50 2.6

2.6

2.6

1.0

0.044

700 10 33 3.0

16 2.5  10 13 4 15 4 2  10 12 28 204 6000 5.2

0.16

1.7  10  10 50 0.3

0.3

3.2

1.1

0.044

785 7  10 34

Cooling Motivation

•

m s not occur naturally so produce them from p on target – – decay to m • p & m beam occupy diffuse phase space  6

D

  (

x

)  (

P x

)  (

y

)  (

P y

)  (

z

)  (

P z

) p beam •Unlike e & p beams only have limited time ( t m =2.2

m s) to cool and form beams •Neutrino Factory/Muon Collider Collaboration are pursuing a scheme whereby they cool m 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 10 6 are considered to be required for a Muon Collider and so far factors of 10-100 have been theoretically achieved through IONIZATION COOLING CHANNELS R.Galea, Columbia University Triumf Seminar22/07/02

Phase Space Reduction

Simplified emittance estimate: At end of drift, rms x,y,z approx 0.05,0.05,10 m P x ,P y ,P z approx 50,50,100 MeV/c Normalized 6D emittance is product divided by (m m c) 3  drift 6D,N 1.7 10 -4 ( p m) 3 Emittance needed for Muon Collider  collider 6D,N 1.7 10 -10 ( p m) 3 This reduction of 6 orders of magnitude must be done with reasonable efficiency (luminosity calculation assumes typically few 10 12 muons per bunch , 1-4 bunches).

R.Galea, Columbia University Triumf Seminar22/07/02

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 .

R.Galea, Columbia University Triumf Seminar22/07/02

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 R.Galea, Columbia University Triumf Seminar22/07/02

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 R.Galea, Columbia University Triumf Seminar22/07/02

Frictional 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 R.Galea, Columbia University Triumf Seminar22/07/02

Problems/Comments:

• large dE/dx @ low kinetic energy • m + • low average density    has the problem of Muonium formation • (Mm) dominates over e-stripping  in all gases except He • m  has the problem of Atomic capture •  calculated up to 80 eV not measured below ~1KeV • Cool m ’s extracted from gas cell T=1 m s so a scheme for reacceleration must be developed R.Galea, Columbia University Triumf Seminar22/07/02

Frictional Cooling: particle trajectory

• 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 r

ˆ

** Using continuous energy loss

R.Galea, Columbia University Triumf Seminar22/07/02

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

R.Galea, Columbia University Triumf Seminar22/07/02

Cooling scheme

•Phase rotation is E(t) field to bring as many m ’s to 0 Kinetic energy as possible • Put Phase rotation into the ring R.Galea, Columbia University Triumf Seminar22/07/02

Target Study

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

R.Galea, Columbia University Triumf Seminar22/07/02

Target System

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

0.4m

28m p ’s in red m ’s in green R.Galea, Columbia University Triumf Seminar22/07/02

View into beam

Target & Drift Optimize yield

• Maximize drift length for m yield • Some p ’s lost in Magnet aperture R.Galea, Columbia University Triumf Seminar22/07/02

Phase Rotation

• First attempt simple form • Vary t 1 ,t 2 & E max for maximum low energy yield R.Galea, Columbia University Triumf Seminar22/07/02

Phase Rotation

Cu

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W

Frictional Cooling Channel

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Time sequence of events…

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Cell Magnetic Field

Correction solenoid Main Ring Solenoid Extract & accelerate • Realistic Solenoid fields in cooling ring R.Galea, Columbia University Triumf Seminar22/07/02

Fringe fields produce Uniform B

z

=5T

D

B

r

=2%

R.Galea, Columbia University Triumf Seminar22/07/02 Uniform B z 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 P z <50 MeV/c. Phase rotation is combined with cooling channel.

• He gas is used for m + , H 2 for m . There is a nearly uniform 5T B z 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.

R.Galea, Columbia University Triumf Seminar22/07/02

Detailed Simulation - continued

• Barkas effect (reduced energy loss for m relative to m + ) • included m 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 .

R.Galea, Columbia University Triumf Seminar22/07/02

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) R.Galea, Columbia University Triumf Seminar22/07/02

Scattering Cross Sections

•Scan impact parameter  (b) to get d  /d  from which one can get l mean free path •Use screened Coulomb Potential (Everhart et. al. Phys. Rev. 99 (1955) 1287) •Simulate all scatters  >0.05 rad R.Galea, Columbia University Triumf Seminar22/07/02

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 R.Galea, Columbia University Triumf Seminar22/07/02

• •50cm long solenoid •10cm long cooling cells r gas for m + 0.7atm & m 0.3atm

•E x =5MV/m •B z =5T realistic field configuration R.Galea, Columbia University Triumf Seminar22/07/02

Frictional Cooling: Particle Trajectory

m - use Hydrogen •Smaller Z help in  capture •Lower r fewer scatters •BUT at higher equilibrium energy

•Assuming E x =constant

Motion in Transverse Plane



F



q

( 

E

+

v

  

B

) 

dT dx r

ˆ 

B



E

Lorentz angle R.Galea, Columbia University Triumf Seminar22/07/02

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

ct vs z for

m

+

He on Cu



ct vs z for

m

-

H on W

P

long

vs P

trans

for

m

+

He on CU

P

long

vs P

trans

for

m

-

H on W

R

f

vs z for

m

+

He on CU

R

f

vs z for

m

-

H on W

Emittance Calculation

After drift cartesian coordinates More natural After cooling cylindrical coordinates are more natural 

long



trans

  (

z

)  (

P z

)   (

x

)  (

P x

)  (

y

)  (

P y

)  6

D

 

long



trans

 '

long

  (  r

ct

)  (

P

r )  '

etrans

 r 0  ( f )  (

P

f )  (

z

)  (

P z

)  ' 6

D

  '

long

 '

etrans

Beamlet uniform z distribution

:

r 0  20

cm

 (

z

)  10

cm

/

N

 100

cells

12 *

N

R.Galea, Columbia University Triumf Seminar22/07/02

X 100 beamlets Beamlet coordinates:

r , f ,

z P

r 

xP x

+ r

yP y P

f 

xP y

 r 2

yP x P z

R.Galea, Columbia University Triumf Seminar22/07/02

Cooling factors  6D /  ’ 6D For cooled m m + He on Cu m He on Cu m H on Cu m + He on W m He on W m H on W

Conclusions

Yield ( m /p) 0.005

0.002

0.003

0.006

0.003

0.004

 trans  long 11239 403 1970 9533 401 1718 2012 156 406 1940 149 347   D (1x10 6 ) 22 0.06

0.8

18 .06

0.6

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 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 m  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 R.Galea, Columbia University Triumf Seminar22/07/02

MCP front MCP side

Work at NEVIS labs

•Want to measure the energy loss, m  capture , test cooling principle •Developing Microchannel Plate & MWPC detectors R.Galea, Columbia University Triumf Seminar22/07/02 Accelerating Grid Multi-Wire Proportional Chamber

A simpler approach

•Avoid difficulties of kickers & multiple windows •Without optimization initial attempts have 60% survival & cooling factor 10 5 •Still need to bunch the beam in time R.Galea, Columbia University Triumf Seminar22/07/02

Conclusions

• Frictional cooling shows promise with potential cooling factors of O(10 5 -10 6 ) – 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 R.Galea, Columbia University Triumf Seminar22/07/02

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  capture