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Frictional Cooling. Columbia University & the Max-Planck-Institute. R. Galea, A. Caldwell, S.Schlenstedt, H. Abramowicz. What is Frictional Cooling (FC)? Simulation of the frontend of a Muon Collider based on FC Targetry & Capture Magnet Drift Region Phase Rotation Cooling section

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frictional cooling

Frictional Cooling

Columbia University & the Max-Planck-Institute

R. Galea, A. Caldwell, S.Schlenstedt, H. Abramowicz

  • What is Frictional Cooling (FC)?
  • Simulation of the frontend of a Muon Collider based on FC
    • Targetry & Capture Magnet
    • Drift Region
    • Phase Rotation
    • Cooling section
    • Reacceleration
  • Physics covered by simulations
    • Energy loss mechanisms, Nuclear & electronic
    • Muonium Formation
    • m- capture
  • Experimental results & plans
  • Future studies

2004 Workshop on Muon Collider Simulation

What is Frictional Cooling?

Nuclear scattering, atomic excitation, charge exchange…

muon too slow to ionize

1/2 from ionization

At high energy end change is only logarithmic whereas it is roughly proportional to speed at low energies

Bring muons into a kinetic energy range where the dT/ds increases with kinetic energy (T)

A constant accelerating force (an Electric field (E)) can be applied to the muons resulting in an equilibrium kinetic energy

Same as freefall and reaching terminal velocity

Gravity opposing friction

A strong solenoidal field (B) is needed to guide the muons until they are cooled, so apply EB to get below the dT/ds peak
yield is a critical issue
Yield is a critical issue:
  • In this regime dT/ds extremely large
  • Slow ms don’t go far before decaying d = 10 cm sqrt(T) T in eV
  • m+ forms Muonium
  • m- is captued by Atom
  • Low average density (gas)
  • Make Gas cell long as you want but transverse dimension (extraction) small.

s(Mm) dominates over e-strippingin all gases except He

s small above electron binding energy, but not known. Keep T as high as possible

detailed simulation
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).

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


target drift optimize yield
Target & Drift Optimize yield
  • Optimize drift length for m yield
  • Some p’s lost in Magnet aperture
  • Only Muons at the end of 28m were tracked through the rest of the system


p’s in red

m’s in green

GEANT3.21 simulation

View into beam

Phase Rotation:
  • Attempt simple form
  • Vary t1,t2 & Emax for maximum low energy yield


t1=100ns t2=439ns

Simulation of the cooling cell:
  • Length=11m, Radius=0.2m
  • He density 1.25x10-4g/cm3
  • Assume uniform Bz=5T
  • Muons hitting the cell walls before reaching equil. T are considered lost
  • Field extends outside cooling cell but is damped exponentially
  • Smoothly alternate field in order to compensate ExB drift
Simulation of the cooling cell:
  • Initial longitudinal reacceleration to get beamlets out of cooling section


scattering cross sections
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 q>0.05 rad
  • Simulation accurately reproduces ICRU tables
Difference in m+ & m- energy loss rates at dE/dx peak
  • Partly Due to charge exchange for m+
  • parameterized data from Agnello et. al. (Phys. Rev. Lett. 74 (1995) 371)
  • Only used for the electronic part of dE/dx
Muonium Formation

Simulate the effect of muonium formation in the tracking, an effective charge as given by sI/(sF+sI) was used

For m- the capture cross sections were parameterized and included in the simulation

Although earlier studies showed promising results for m- this scheme has not been fully investigated for this flavor.

using calculations of Cohen (Phys. Rev. A. Vol 62 022512-1)

Muon Acceleration:
  • Standalone study take the beam as described and accelerate to a final beam momentum of 147 MeV/c at 30% survival probability

RMS 1ms to 3ns

RMS 1.2MeV/c to 5MeV/c

  • Simulation of previous scheme yielded final beam emittances of
  • 2-6x10-11 (pm)3
  • At yields of 0.001-0.003 m+/GeV proton.
  • Yield could be better yet emittance is better than ”required”
  • Cooler beams
    • smaller beam elements
    • less background
    • lower potential radiation hazard from neutrinos

1.7x10-10 (pm)3

Nevis Experiment already reported at NuFact03

R.Galea, A.Caldwell, L.Newburgh, Nucl.Instrum.Meth.A524, 27-38 (2004)

arXiv: physics/0311059

RAdiological Research Accelerator Facility

  • Perform TOF measurements with protons
    • 2 detectors START/STOP
    • Thin entrance/exit windows for a gas cell
    • Some density of He gas
    • Electric field to establish equilibrium energy
    • NO B field so low acceptance
  • Look for a bunching in time
    • Can we cool protons?
Results of RARAF experiment
  • Various energies/gas pressures/electric field strengths indicated no cooled protons
  • Lines are fits to MC & main peaks correspond to protons above the ionization peak

Experiment showed that MC could reproduce data under various conditions. Simulations of Frictional Cooling is promising.

Exp. Confirmation still desired.

Low acceptance but thicker windows was the culprit

Frictional Cooling Demonstration at MPI Munich
  • Repeat demonstration experiment with protons with IMPROVEMENTS:
  • No windows
  • 5T Superconducting Solenoid for high acceptance
  • Silicon detector to measure energy directly

Cryostat housing 5T solenoid.

Status of Experiment
  • Cryostat & Magnet commissioned
  • Grid constructed & tested. Maintained 98KV in vacuum
  • Source & support structures constructed
  • Electronics & detectors available


  • Silicon Drift Detector gives excellent resolution
  • Thus far Fe55 X-rays
  • Frictional Cooling is being persued as a potential cooling method intended for Muon Colliders
  • Simulations of mostly ideal circumstances show that the 6D emittance benchmark of 1.7x10-10 (pm)3 can be achieved & surpassed
  • physics/0410017
  • Simulations have been supported by data from Nevis Experiment & will be tested further at the Frictional Cooling Demonstration to take place at MPI Munich
  • Future investigations are also on the program:
    • R&D into thin window or potential windowless systems
    • Studies of gasbreakdown in high E,B fields
    • Capture cross section measurements at m beams

Frictional Cooling is an exciting potential alternative for the phase space reduction of muon beams intended for a Muon Collider