1

Muon Cooling and the Muon ColliderA. Caldwell

MPI f. Physik

• Motivation• Difficulties• Focus on Cooling (frictional cooling)

2

Why a Muon Collider ?

No synchrotron radiation problem (cf electron)

P α (E/m)4

Can build a high energy circular accelerator.

PCollide point particles rather than complex objects

P

3

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 induced radiation.

4

Dimensions of Some Colliders discussed

5

Physics at a Muon Collider

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

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

σµµ→Η= 40000 σee→Η

From target, stored µ

6

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

Bunches/fill 4 4Rep. rate (Hz) 15 15p power (MW) 4 4µ/ bunch 2 × 1012 2 × 1012

µ power (MW) 4 28Wall power (MW) 120 204Collider circum. (m) 1000 6000Ave bending field (T) 4.7 5.2rms δp/p (%) 0.14 0.166D ε6,Ν (πm)3 1.7 × 10−10 1.7 × 10−10

rms εn (π mm mrad) 50 50β* (cm) 2.6 0.3σz (cm) 2.6 0.3σr spot (µm) 2.6 3.2σθ IP (mrad) 1.0 1.1Tune shift 0.044 0.044nturns (effective) 700 785Luminosity (cm−2 s−1) 1033 7 × 1034

7

π’s in redµ’s in green

Solenoidal Magnets: few T … 20 T

Drift region for π decay ≈ 30 m

P beam (few MW)

Target

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 (mµc)3

εdrift6D,N ≈1.7 10-4 (πm)3

Emittance needed for Muon Collider εcollider

6D,N ≈ 1.7 10-10(πm)3

This reduction of 6 orders of magnitude must be done with reasonable efficiency !

8

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• Reducing the radiation from neutrino interactions• Allowing for smaller apertures in machine elements, and so driving the cost down

9

Cooling Ideas

Ionization cooling (Skrinsky, Neuffer, Palmer, …): muons are maintained at ca. 200 MeV. Transverse cooling of order x20 seems feasible (see ν-factory feasibility studies 1-2). Longitudinal cooling not solved.

Gas cell

RF

B B

µ beam

10

Longitudinal Cooling via Emittance Exchange

Transform longitudinal phase space into transverse (know how to cool transverse)

Wedge shaped absorber

Bent solenoid produces dispersion

11

‘Balbekov Ring’

There are significant developments in achieving 6D phase space via ionization cooling (R. Palmer, MUTAC03), but still far from 106 cooling factor.

12

13

KEK – focus on FFAG acceleration

Frictional CoolingFrictional Cooling

Studies at Columbia University/MPIStudies at Columbia University/MPIAllen Caldwell, Raphael Allen Caldwell, Raphael GaleaGalea

++Stefan Stefan Schlenstedt Schlenstedt (DESY/(DESY/ZeuthenZeuthen))

Halina AbramowiczHalina Abramowicz (Tel Aviv University)(Tel Aviv University)

Summer Students: Summer Students: Emily AldenEmily AldenChristos Georgiou Christos Georgiou Daniel GreenwaldDaniel GreenwaldLaura NewburghLaura NewburghYujin NingYujin NingInna Inna ShpiroShpiroWill Will SerberSerber

15

Frictional CoolingFrictional Cooling

• Bring muons to a kinetic energy (T) where dE/dxincreases with T

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

• Big issue – how to maintain efficiency

• Similar idea first studied by Kottmann et al., PSI

Helium

1

10

10 2

10 3

10-4

10-3

10-2

10-1

1 10 102

103

1/β2 from ionization

Ionization stops, muon too slow

Nuclear scattering, excitation, charge exchange, ionization

16

Problems/comments:Problems/comments:• large dE/dx @ low kinetic energy

⇒ low average density (gas)• Apply E ⊥ B to get below the dE/dx

peakF = q(E + vxB) – dT/dx

• µ− has the problem of Atomic captureσ small above electron binding energy,

but not known. Keep T as high as possible

• Slow muons don’t go far before decaying

d = 10 cm sqrt(T ) T in eV so extract sideways (E ⊥ B )

µ+ has the problem of Muoniumformation

σ(Μµ) dominates over e-stripping in all gases except He

Helium

1

10

10 2

10 3

10-4

10-3

10-2

10-1

1 10 102

103

17

Neutralization Stripping

For µ, energy lower by Mµ/MP

From Y. Nakai, T. Shirai, T. Tabata and R. Ito, At. Data Nucl. Data Tables 37, 69 (1987)

18

Frictional Cooling: particle trajectory

B=5 T, E=5 MV/m, ρHe=1 10-4 g/cm3

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

B=5 T, E=5 MV/m, ρHe=1 10-4 g/cm3

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

** Using continuous energy loss

19

Frictional Cooling: stop the µPlots for1. 10-4 g/cm3 He

• High energy µ’s travel a long distance to stop• High energy µ’s take a long time to stop

10-2

10-1

1

10

10 2

10 102 10

-9

10-8

10-7

10-6

10-5

10 102

Optimize for low initial muon momentum, + phase rotation

20

Cooling cells

Phase rotation sections

Not to scale !!

Schematic Layout for µ Collider Scheme Studied

21

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).

22GeV

Target System

beam

π

π

Transverse(symme−tric)scheme

_

+

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

23

Target & Drift Optimize yield

• Optimize drift length for µ yield• Some π’s lost in Magnet aperture

24

28m

0.4m

beam

π

π

Transverse(symme−tric)scheme

_

+

π’s in redµ’s in green

View into beamGEANT simulation

25

Phase RotationPhase Rotation

0

500

1000

1500

2000

2500

3000

3500

4000

0 200 400 600 800 1000

Pz(MeV/c)

µs

cool µs

µ After Drift

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250 300

• First attempt simple form• Vary t1,t2 & Emax for maximum low energy yield

26

Cooling cell simulationHe gas is used for µ+, H2 for µ-.

• Individual nuclear scatters are simulated – crucial in determining final phase space, survival probability.•Incorporate scattering cross sections into the cooling program•Include µ- capture cross section using calculations of Cohen (Phys. Rev. A. Vol 62 022512-1)

• Electronic energy loss treated as continuous

Cross Section Comparisons

10-18

10-17

10-16

10-15

1 10 102

27

Scattering Cross Sections

•Scan impact parameter and calculate θ(b), dσ/dθfrom which one can get λmean free path•Use screened Coulomb Potential (Everhart et. al. Phys. Rev. 99 (1955) 1287)

•Simulate all scatters θ>0.05 rad•Simulation accurately reproduces ICRU tables

28

Barkas Effect

1

10

10 2

10 3

10-3

10-2

10-1

1 10 102

103

104

•Difference in µ+ & µ-

energy loss rates at dE/dx peak•Due to charge exchange for µ+

•parameterized data from Agnello et. al. (Phys. Rev. Lett. 74 (1995) 371)

•Only used for the electronic part of dE/dx

29

Trajectories in detailed simulation

Transverse motion Longitudinal motion

Motion controlled by B field

Lorentz angle drift, with nuclear scattering

Final stages of muon trajectory in gas cell

30

Helium

1

10

10 2

10 3

10-4

10-3

10-2

10-1

1 10 102

103

Oscillations about equilibrium define emittance.

Dangerous because of µ-

capture possibility

vxB dominates

E dominates

F = q(E+v×B)-dT/dx

31

E

Initial reacceleration region

σT = 4 ns at Z=444mP = 200 MeV/cEff = 40%gas Reacc section

After gas cell, E(z,t)

32

Yields & Emittance

Look at muons coming out of 11m cooling cell region after initial reacceleration.

Yield: approx 0.002 µ per 2GeV proton after cooling cell.Need to improve yield by factor 3 or more.

Emittance: rms x = 0.015 my = 0.036 mz = 30 m ( actually βct)Px = 0.18 MeVPy = 0.18 MeVPz = 4.0 MeV

ε6D,N = 5.7 10-11 (πm)3

33

Problems/Things to investigate…

• Extraction of µs through window in gas cell •Must be very thin to pass low energy µs•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 µ− 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• +…

34

First try to demonstrate frictional cooling with protons.

RARAF Facility – Nevis Lab/Columbia University

≤ 4 MeV p

VandeGraafaccelerator for biomedical research

beamH2

+

36

Contains 20nm window

Proton beam

Gas cell

Accelerating grid

Vacuum chamber

To MCP

Si detector

37

38

39

The proton energy spectrum from the Si calculated using SRIM (J. F.

Ziegler, J. P. Biersack and U. Littmark, Pergamon Press, 1985). The transport through the gas performed with our detailed simulation. Need first to fix the window thickness and gas pressure.

Min Kin Energy fixed by reacc potential

40

Calibration Data:3 distances, no cell, no grid

Time resolution of system=17ns

Protons have 100-200 KeV after Si window. Good agreement with SRIM.

41

Add gas, still no field. Gas pressure extracted from comparison with simulation. Compatible with expectations.

Add cell, no gas, no E field. Extract effective window thickness by comparison with simulation. Much thicker than expected !

42

Summary of calibration using the time spectrum

43

After background subtraction, see no hint of cooled protons. Also predicted by simulation. Problem – windows too thick, acceptance, particularly for slow protons, too small. Need to repeat the experiment with solenoid, no windows.

44

Future Plans

• Frictional cooling tests at MPI with 5T Solenoid, alpha source• Study gas breakdown in high E,B fields• R&D on thin windows• Beam tests with muons to measure µ capture cross section

µ-+He → Heµ+ e+γ’s

muon initially captured in large n orbit, then cascades down to n=1. Transition n=2→n=1 releases few KeV x-ray.

Si drift detectorDeveloped my MPIHLL

45

Lab situated at MPI-WHI inMunich

46

Conclusions

• Muon Collider complex would be a boon for physics

• We need to solve the muon cooling problem

• Different schemes should be investigated• We are doing some simulation and

experimental studies of frictional cooling. So far, so good, but a long way to go !