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Muon Collider/Higgs FactoryA. Caldwell

Columbia University

• Motivation

• Difficulties

• Focus on Cooling (frictional cooling)

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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. Parametersets available up to 100 TeV+100 TeV.

• At lower energies, Higgs factory (40000 higher production crosssection 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

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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

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Dimensions of Some Colliders under Discussion

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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

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

HIGGS FACTORY PARAMETERSBaseline parameters for Higgs factory muon collider. Higgs/year assumes across section of 5 104 fb, Higgs width of 2.7 MeV, 1 year = 107 s. From “Statusof Muon Collider Research and Development and Future Plans,” Muon ColliderCollaboration, C. M. Ankenbrandt et al., Phys. Rev. ST Accel. Beams 2, 081001(1999).

COM energy (TeV) 0.1p energy (GeV) 16p’s/bunch 5 1013

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

power (MW) 1Wall power (MW) 81Collider circum. (m) 350Ave bending field (T) 3rms p/p (%) 0.12 0.01 0.003

6D (m)3 1.7 1010 1.7 1010 1.7 1010

rms n ( mm mrad) 85 195 290

* (cm) 4.1 9.4 14.1

z (cm) 4.1 9.4 14.1

r spot (m) 86 196 294 IP (mrad) 2.1 2.1 2.1Tune shift 0.051 0.022 0.015nturns (effective) 450 450 450

Luminosity (cm2 s1) 1.2 1032 2.2 1031 1031

Higgs/yr 1.9 103 4 103 3.9 103

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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 4/ bunch 2 1012 2 1012

power (MW) 4 28Wall power (MW) 120 204Collider circum. (m) 1000 6000Ave bending field (T) 4.7 5.2rms p/p (%) 0.14 0.16

6D (m)3 1.7 10 10 1.7 10 10

rms n ( mm mrad) 50 50

* (cm) 2.6 0.3

z (cm) 2.6 0.3

r spot (m) 2.6 3.2 IP (mrad) 1.0 1.1Tune shift 0.044 0.044nturns (effective) 700 785

Luminosity (cm 2 s 1) 1033 7 1034

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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).

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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.

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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

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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 (see R. Palmer talk).

Here, I focus on an alternative called ‘frictional cooling’. First studied by Kottmann et al., PSI. See talk by R. Galea.

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Frictional CoolingFrictional Cooling

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

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

• Big issue – how to maintain efficiency

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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• small below electron binding energy, but not known

• Slow muons don’t go far before decaying

BE

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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

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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

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Cooling scheme

Phase rotation is E(t) field to bring as many ’s to 0 Kinetic energy as possible (performed in cooling ring.

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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.

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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.

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

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28m

0.4m

’s in red ’s in green

View into beam

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Target & Drift Optimize yield

• Maximize drift length for yield• Some ’s lost in Magnet aperture

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Cooling Cell & Phase Rotationsimplified version

Drift region

Cooling cell

Phase Rotation

Transverse view of cooling cell region. Cooling cell is 20 cm radius cylinder embedded in 11m solenoid with Bz=5T. Ex=5 MV/v in |y|<0.7 m, and Ez=100 kV/m for 0.3<|y|<0.5 m.

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Phase Rotation

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

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Scattering Cross Section

• Individual nuclear scatters are simulated – crucial in determining final phase space, survival probability.•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)

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Scattering Cross Sections

•Scan impact parameter and calculate (b), d/d from which one can get mean free path

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

•Simulate all scatters >0.05 rad

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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

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Energy Fluctuations around Equilibrium

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Motion in Transverse Plane

E

B

Lorentz angle

rdx

dTBvEqF ˆ)(

•Assuming Ex=constant

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Longitudinal profile for +

At cooling cell boundary• Flat in Z• rms ct 1m

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Plong vs Ptrans for +

• rms 50-60KeV

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R vs z for +

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Yields & Emittance

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

Yield: approx 0.002 per 2GeV proton after cooling cell.

Need to improve yield by factor 3 or more.

Emittance: rms x = 0.015 m y = 0.036 m z = 30 m ( actually ct)

Px = 0.18 MeVPy = 0.18 MeVPz = 4.0 MeV

6D,N = 5.7 10-11 (m)3

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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 & bunch compression for injection into storage ring•The 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

Critical path items - intend to make measurement on all these.

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Conclusions

• Muon Collider complex would be a boon for physics

• We need to solve the muon cooling problem

• Different schemes should be investigated