Muon Collider/Higgs Factory A. Caldwell Columbia University

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Muon Collider/Higgs FactoryA. CaldwellColumbia
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. Parameter
• sets available up to 100 TeV100 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

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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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HIGH ENERGY MUON COLLIDER PARAMETERS
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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 (m?c)3
?drift6D,N ?1.7 10-4 (?m)3 Emittance needed for
Muon Collider ?collider6D,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 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

• large dE/dx _at_ low kinetic energy
• low average density
• Apply to get below the dE/dx peak
• m has the problem of Muonium formation
• s(Mm) dominates over e-stripping s in all gases
  except He
• m- has the problem of Atomic capture
• s small below electron binding energy, but not
  known
• Slow muons dont go far before decaying

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Frictional Cooling particle trajectory

• In 1tm dm10cmsqrtT(eV)
• keep d small at low T
• reaccelerate quickly

Using continuous energy loss
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Frictional Cooling stop the m

• High energy ms travel a long distance to stop
• High energy ms take a long time to stop

Start with low initial muon momenta
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Cooling scheme
Phase rotation is E(t) field to bring as many ms
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 Pzlt50 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 m m- at the same time
• calculated new symmetric magnet with gap for
  target

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0.4m
28m
ps in red ms in green
View into beam
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Target Drift Optimize yield

• Maximize drift length for m yield
• Some ps lost in Magnet aperture

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Cooling Cell Phase Rotationsimplified version
Phase Rotation
Drift region
Cooling cell
Transverse view of cooling cell region. Cooling
cell is 20 cm radius cylinder embedded in 11m
solenoid with Bz5T. Ex5 MV/v in ylt0.7 m, and
Ez100 kV/m for 0.3ltylt0.5 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 Tgt2KeV
• Classical Scattering Tlt2KeV
• Include m- 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 q(b), ds/dq
  from which one can get lmean free path
• Use screened Coulomb Potential (Everhart et. al.
  Phys. Rev. 99 (1955) 1287)
• Simulate all scatters qgt0.05 rad

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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

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Energy Fluctuations around Equilibrium
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Motion in Transverse Plane

• Assuming Exconstant

Lorentz angle
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Longitudinal profile for m

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

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Plong vs Ptrans for m

• rms 50-60
• KeV

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Rf vs z for m
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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 MeV Py 0.18
MeV Pz 4.0 MeV ?6D,N 5.7 10-11 (?m)3
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Problems/Things to investigate

• Extraction of ms through window in gas cell
• Must be very thin to pass low energy ms
• 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 m- 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