M  on Cooling RINGBERG July, 2003 Studies at Columbia University/Nevis Labs & MPI Raphael Galea, Allen Caldwell How to reduce beam Emmittance by 10 6 ?  6D,N = (  m) 3 Why Muons, why Muon Collider? Muon Cooling, Ionization or Frictional Cooling Frictional Cooling with protons Conclusions and future work

R. GaleaRingberg Workshop July, 2003 Why a Muon Collider ? No synchrotron radiation problem (cf electron) P  (E/m) 4 Can build a high energy circular accelerator. Collide point particles rather than complex objects P P

R. GaleaRingberg Workshop July, 2003 Dimensions of Some Colliders discussed

R. GaleaRingberg Workshop July, 2003 Why Cooling? All Colliding beams have some cooling to reduce the large phase space of initial beam STOCHASTIC sample particles passing cooling system correct to mean position ELECTRON principle of heat exchanger RADIATIVE lose the hot particles

R. GaleaRingberg Workshop July, 2003   =  ee  From target, stored 

R. GaleaRingberg Workshop July, 2003 HIGH ENERGY MUON COLLIDER PARAMETERS

R. GaleaRingberg Workshop July, 2003  ’s in red  ’s in green P beam (few MW) Target Solenoidal Magnets: few T … 20 T Drift region for  decay  30 m 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  c) 3  drift 6D,N  (  m) 3 Emittance needed for Muon Collider  collider 6D,N  (  m) 3 This reduction of 6 orders of magnitude must be done with reasonable efficiency !

R. GaleaRingberg Workshop July, 2003 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.

R. GaleaRingberg Workshop July, 2003 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. GaleaRingberg Workshop July, 2003 Cooling Ideas : Ionization Cooling Ionization cooling (Skrinsky, Neuffer, Palmer, …): muons are maintained at ca. 200 MeV. Transverse cooling of order x20 seems feasible (see - factory feasibility studies 1-2). Longitudinal cooling not solved. Gas cell RF  beam B

R. GaleaRingberg Workshop July, 2003 Longitudinal Cooling via Emittance Exchange Transform longitudinal phase space into transverse (know how to cool transverse) Bent solenoid produces dispersion Wedge shaped absorber

R. GaleaRingberg Workshop July, 2003 There are significant developments in achieving 6D phase space via ionization cooling (R. Palmer, MUTAC03), but still far from 10 6 cooling factor. ‘Balbekov Ring’

R. GaleaRingberg Workshop July, 2003 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 First studied by Kottmann et al., PSI Ionization stops, muon too slow Nuclear scattering, excitation, charge exchange, ionization 1/  2 from ionization

R. GaleaRingberg Workshop July, 2003 Problems/comments: large low kinetic energy  low average density (gas) Apply E  B 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 d = 10 cm sqrt(T) T in eV so extract sideways (E  B )

R. GaleaRingberg Workshop July, 2003 Trajectories in detailed simulation Final stages of muon trajectory in gas cell Lorentz angle drift, with nuclear scattering Transverse motion Motion controlled by B field Fluctuations in energy results in emittance

R. GaleaRingberg Workshop July, 2003 Cooling cells Phase rotation sections Not to scale !!  He gas is used for  +, H 2 for  -. 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.  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). Results of simulations to this point

R. GaleaRingberg Workshop July, 2003 Yields & Emittance Look at muons coming out of 11m cooling cell region after initial reacceleration. Yield: approx  per 2GeV proton after cooling cell. Need to improve yield by factor 3 or more. Emittance: rms x = m y = m z = 30 m ( actually  ct) P x = 0.18 MeV P y = 0.18 MeV P z = 4.0 MeV  6D,N = (  m) 3  6D,N = (  m ) 3 Results as of NUFACT02

R. GaleaRingberg Workshop July, 2003 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 ?

R. GaleaRingberg Workshop July, 2003  4 MeV p

R. GaleaRingberg Workshop July, 2003 Contains O(10-100nm) window Proton beam Gas cell Accelerating grid Vacuum chamber To MCP Si detector

Assumed initial conditions 20nm C windows 700KeV protons 0.04atm He TOF=T0-(T si -T MCP ) speedKinetic energy

R. GaleaRingberg Workshop July, 2003 Summary of Simulations 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 ) 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 Energy loss in thin windows For RARAF setup proton transmitted energy spectrum is input from SRIM, simulating protons through Si detector (J.F. Ziegler

R. GaleaRingberg Workshop July, 2003 Cool protons??? Background exponential with m>0 Flat constant Background MC exp

R. GaleaRingberg Workshop July, 2003  No clear sign of cooling but this is expected from lack of Magnetic field & geometric MCP acceptance alone  The Monte Carlo simulation can provide a consistent picture under various experimental conditions  Can use the detailed simulations to evaluate Muon Collider based on frictional cooling performance with more confidence….still want to demonstrate the cooling  Work at MPI on further cooling demonstration experiment using an existing 5T Solenoid and develop the  - capture measurement Conclusions A lot of interesting work and results to come.

R. GaleaRingberg Workshop July, 2003 Lab situated at MPI-WHI in Munich

R. GaleaRingberg Workshop July, 2003 Problems/Things to investigate… Extraction of  s through window in gas cell Must be very thin to pass low energy  s 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  - 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 +…

R. GaleaRingberg Workshop July, 2003 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  capture cross section  - +H  H  + e+  ’s muon initially captured in n=15 orbit, then cascades down to n=1. Transition n=2  n=1 releases 2.2 KeV x-ray. Si drift detector Developed by MPI HLL

Summary of Frictional Cooling Works below the Ionization Peak Detailed simulations Cooling factors O(10 6 ) or more? Still unanswered questions being worked on but early results are encouraging. Kinetic Energy(KeV) Time(ns) Y(cm) X(cm) Proton cooling test