Frictional Cooling NUFACT02 Studies at Columbia University & Nevis Labs Raphael Galea Allen Caldwell Stefan Schlenstedt (DESY/Zeuthen) Halina Abramowitz (Tel Aviv University) Summer 2001 Students: Christos Georgiou Daniel Greenwald Yujin Ning Inna Shpiro Will Serber

Cooling Motivation ms not occur naturally so produce them from p on target – p beam – decay to m p & m beam occupy diffuse phase space Unlike e & p beams only have limited time (tm=2.2ms) to cool and form beams Neutrino Factory/Muon Collider Collaboration are pursuing a scheme whereby they cool ms by directing particles through a low Z absorber material in a strong focusing magnetic channel and restoring the longitudinal momentum IONIZATION COOLING COOL ENERGIES O(200MeV) Cooling factors of 106 are considered to be required for a Muon Collider and so far factors of 10-100 have been theoretically achieved through IONIZATION COOLING CHANNELS Raphael Galea, Columbia University NUFACT02 : Imperial College London

Frictional Cooling Bring muons to a kinetic energy (T) range where dE/dx increases with T Constant E-field applied to muons resulting in equilibrium energy Raphael Galea, Columbia University NUFACT02 : Imperial College London

Problems/Comments: large dE/dx @ 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 calculated up to 80 eV not measured below ~1KeV Cool m’s extracted from gas cell T=1ms so a scheme for reacceleration must be developed Raphael Galea, Columbia University NUFACT02 : Imperial College London

Frictional Cooling: particle trajectory In 1tm dm=10cm*sqrt{T(eV)} keep d small at low T reaccelerate quickly ** Using continuous energy loss Raphael Galea, Columbia University NUFACT02 : Imperial College London

Frictional Cooling: stop the m High energy m’s travel a long distance to stop High energy m’s take a long time to stop Start with low initial muon momenta Raphael Galea, Columbia University NUFACT02 : Imperial College London

Cooling scheme Phase rotation is E(t) field to bring as many m’s to 0 Kinetic energy as possible Put Phase rotation into the ring Raphael Galea, Columbia University NUFACT02 : Imperial College London

Target System cool m+ & m- at the same time calculated new symmetric magnet with gap for target Raphael Galea, Columbia University NUFACT02 : Imperial College London

View into beam p’s in red m’s in green 0.4m 28m Raphael Galea, Columbia University NUFACT02 : Imperial College London

Target & Drift Optimize yield Maximize drift length for m yield Some p’s lost in Magnet aperture Raphael Galea, Columbia University NUFACT02 : Imperial College London

Phase Rotation First attempt simple form Vary t1,t2 & Emax for maximum low energy yield Raphael Galea, Columbia University NUFACT02 : Imperial College London

Frictional Cooling Channel Raphael Galea, Columbia University NUFACT02 : Imperial College London

Cell Magnetic Field Realistic Solenoid fields in cooling ring Correction solenoid Main Ring Solenoid Extract & accelerate Realistic Solenoid fields in cooling ring Raphael Galea, Columbia University NUFACT02 : Imperial College London

Simulations Improvements Incorporate scattering cross sections into the cooling program Born Approx. for T>2KeV Classical Scattering T<2KeV Include m- capture cross section using calculations of Cohen (Phys. Rev. A. Vol 62 022512-1) Raphael Galea, Columbia University NUFACT02 : Imperial College London

Scattering Cross Sections Scan impact parameter q(b) to get ds/dq from which one can get lmean free path Use screened Coloumb Potential (Everhart et. al. Phys. Rev. 99 (1955) 1287) Simulate all scatters q>0.05 rad Raphael Galea, Columbia University NUFACT02 : Imperial College London

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 Raphael Galea, Columbia University NUFACT02 : Imperial College London

Frictional Cooling: Particle Trajectory m- use Hydrogen Smaller Z help in scapture Lower r fewer scatters BUT at higher equilibrium energy 50cm long solenoid 10cm long cooling cells rgas for m+ 0.7atm & m- 0.3atm Ex=5MV/m Bz=5T realistic field configuration Raphael Galea, Columbia University NUFACT02 : Imperial College London

Motion in Transverse Plane Assuming Ex=constant Lorentz angle Raphael Galea, Columbia University NUFACT02 : Imperial College London

Emittance Calulation Beamlet uniform z distribution: After drift cartesian coordinates More natural After cooling cylindrical coordinates are more natural Beamlet uniform z distribution: Raphael Galea, Columbia University NUFACT02 : Imperial College London

X 100 beamlets Beamlet coordinates: Raphael Galea, Columbia University NUFACT02 : Imperial College London

bct vs z for m+He on Cu

bct vs z for m-H on W

Plong vs Ptrans for m+He on CU

Plong vs Ptrans for m-H on W

Rf vs z for m+He on CU

Rf vs z for m-H on W

Conclusions Cooling factors e6D/e’6D Yield (m/p) etrans elong e6D (1x106) m+He on Cu 0.005 11239 2012 22 m-He on Cu 0.002 403 156 0.06 m-H on Cu 0.003 1970 406 0.8 m+He on W 0.006 9533 1940 18 m-He on W 401 149 .06 m-H on W 0.004 1718 347 0.6 For cooled m

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 & recombine beamlets for injection into storage ring The m- capture cross section depends very sensitively on kinetic energy & fall off sharply for kinetic energies greater than e- binding energy. NO DATA – simulations use calculation Critical path item intend to make measurement Raphael Galea, Columbia University NUFACT02 : Imperial College London

Work at NEVIS labs MCP front MCP side Accelerating Grid Want to measure the energy loss, m- scapture, test cooling principle Developing Microchannel Plate & MWPC detectors Raphael Galea, Columbia University NUFACT02 : Imperial College London Multi-Wire Proportional Chamber

A simpler approach Avoid difficulties of kickers & multiple windows Without optimization initial attempts have 60% survival & cooling factor 105 Still need to bunch the beam in time Raphael Galea, Columbia University NUFACT02 : Imperial College London

Conclusions Frictional cooling shows promise with potential cooling factors of O(105-106) Simulations contain realistic magnet field configurations and detailed particle tracking Built up a lab at Nevis to test technical difficulties There is room for improvement Phase rotation and extraction field concepts very simple Need to evaluate a reacceleration scheme Raphael Galea, Columbia University NUFACT02 : Imperial College London

Summary of Frictional Cooling Works below the Ionization Peak Possibility to capture both signs Cooling factors O(106) or more? Still unanswered questions being worked on but work is encouraging. Nevis Labs work on m- scapture