1. Quantitative Optimisation Studies of the Muon Front-End for a Neutrino Factory S. J. Brooks, RAL, Chilton, Oxfordshire, U.K. Tracking Code Non-linearised 3-dimensional simulation –PARMILA was being used before Uses realistic initial  + distribution –Monté-Carlo simulation by Paul Drumm Particle decays with momentum kicks Solenoid end-fields included OPERA-3d field maps used for FFAG-like magnets in chicane (by Mike Harold) Numerical Details Typically use 20k-50k particles Tracking is done by 4 th order classical Runge- Kutta on the 6D phase space –Currently timestep is fixed at 0.01ns Solenoids fields and end-fields are a 3 rd order power expansion Field maps trilinearly interpolated Particle decays are stochastic, sampled Tracking Code Non-linearised 3-dimensional simulation –PARMILA was being used before Uses realistic initial  + distribution –Monté-Carlo simulation by Paul Drumm Particle decays with momentum kicks Solenoid end-fields included OPERA-3d field maps used for FFAG-like magnets in chicane (by Mike Harold) Numerical Details Typically use 20k-50k particles Tracking is done by 4 th order classical Runge- Kutta on the 6D phase space –Currently timestep is fixed at 0.01ns Solenoids fields and end-fields are a 3 rd order power expansion Field maps trilinearly interpolated Particle decays are stochastic, sampled Optimisation Optimiser Architecture How do you optimise in a very high-dimensional space? –Hard to calculate derivatives due to stochastic noise and sheer number of dimensions –Can use a genetic algorithm Begins with random designs Improves with mutation, interpolation, crossover… –Has been highly successful so far in problems with up to 137 parameters Phase Rotation Plan Optimisation Optimiser Architecture How do you optimise in a very high-dimensional space? –Hard to calculate derivatives due to stochastic noise and sheer number of dimensions –Can use a genetic algorithm Begins with random designs Improves with mutation, interpolation, crossover… –Has been highly successful so far in problems with up to 137 parameters Phase Rotation Plan Distributed Computing Results Improved Transmission Decay channel: –Original design: 3.1%  + out per  + from rod –12-parameter optimisation  6.5%  + /  + 1.88% through chicane –137 parameters  9.7%  + /  + 2.24% through chicane Re-optimised for chicane transmission: –Original design got 1.13% –12 parameters  1.93% –137 parameters  2.41% Signs of solenoids Original design had alternating (FODO) solenoids Optimiser independently chose a FOFO lattice Has to do with the stability of off-energy particles Results Improved Transmission Decay channel: –Original design: 3.1%  + out per  + from rod –12-parameter optimisation  6.5%  + /  + 1.88% through chicane –137 parameters  9.7%  + /  + 2.24% through chicane Re-optimised for chicane transmission: –Original design got 1.13% –12 parameters  1.93% –137 parameters  2.41% Signs of solenoids Original design had alternating (FODO) solenoids Optimiser independently chose a FOFO lattice Has to do with the stability of off-energy particles Future Work Future Optimisations Chicane and RF phase rotation designs are starting to be run now –Initial results promising –Baseline design for chicane and linac transmitted 1.36% –Baseline design for RF phase rotation transmitted 1.70% Cooling ring optimisation coming later, including shapes of liquid hydrogen absorbers as variables Check http://stephenbrooks.org/muon1 for project statushttp://stephenbrooks.org/muon1 Future Work Future Optimisations Chicane and RF phase rotation designs are starting to be run now –Initial results promising –Baseline design for chicane and linac transmitted 1.36% –Baseline design for RF phase rotation transmitted 1.70% Cooling ring optimisation coming later, including shapes of liquid hydrogen absorbers as variables Check http://stephenbrooks.org/muon1 for project statushttp://stephenbrooks.org/muon1 Beamline Pion to Muon Decay Channel Challenge: high emittance of target pions –Currently come from a 20cm tantalum rod –Initial emittance ~13000  mm mrad Solution: superconducting solenoids –Superconductivity enables a high focussing field –Larger aperture than quadrupoles Basic lattice uses regular ~4T focussing –Initial smaller 20T solenoid around target –30m length = 2.5 pion decay times at 200MeV RF Phase-Rotation 31.4MHz RF at 1.6MV/m (2003 design) –Reduces the energy spread –180±75MeV to ±23MeV –Cavities within solenoidal focussing structure –Feeds into cooling ring Beamline Pion to Muon Decay Channel Challenge: high emittance of target pions –Currently come from a 20cm tantalum rod –Initial emittance ~13000  mm mrad Solution: superconducting solenoids –Superconductivity enables a high focussing field –Larger aperture than quadrupoles Basic lattice uses regular ~4T focussing –Initial smaller 20T solenoid around target –30m length = 2.5 pion decay times at 200MeV RF Phase-Rotation 31.4MHz RF at 1.6MV/m (2003 design) –Reduces the energy spread –180±75MeV to ±23MeV –Cavities within solenoidal focussing structure –Feeds into cooling ring Chicane Phase-Rotation Chicane is a fixed field map, not varied Solenoid channels varied as before –Both sides of chicane –Length up to 0.9m now RF voltages 0-4MV/m Any RF phases ~580 parameters RF phase rotation: Similar solenoids, phases (no field map) RF voltages up to 1.6MV/m ~270 parameters Internet-based / FTP –Individuals download the program which regularly uploads its results ~450GHz of processing power ~130 users active, 75`000 results sent in last week Periodically exchange sample results file Can test millions of designs Accelerator design-range specification language –Includes “C” interpreter The pion beam in the early decay channel Muon cooling ring design Particles of various energies (120-270 MeV) tracked through the bending chicane Decay Channel Parameters 0.5 [0.5,1] D2+ 0.5718 [0.5,1] D1 Length (m) Drifts 0.5 [0.5,1] D2+ 0.5718 [0.5,1] D1 Length (m) Drifts 12 parameters –Solenoids alternated in field strength and narrowed according to a pattern 137 parameters –Varied everything individually 0.1 [0,0.5]Angle (radians) 0.01[fixed] Radius (m) 0.2[fixed] Length (m) 0.2033 (S1 centred) [0,0.45] Z displacement (m) from S1 start Tantalum Rod 0.1 [0,0.5]Angle (radians) 0.01[fixed] Radius (m) 0.2[fixed] Length (m) 0.2033 (S1 centred) [0,0.45] Z displacement (m) from S1 start Tantalum Rod Original parameters / Optimisation ranges 4 million designs plotted by muon transfer against calculation time Website where current optimisations and user accounts can be monitored FODO lattice FOFO lattice Beam shape optimised for mid-energiesGeometry of the bending chicane Over 80% caught in linac bucket RF phase rotation reduces the energy spread Longitudinal phase-space out of decay channel Chicane phase rotation decreases the bunch length Nontrivial optimum found Preferred length? Narrowing can only be due to nonlinear end-fields Design Optimised for Chicane Transverse orbits for particles of various energies in periodic linear solenoidal focussing channels Optimal design for solenoid channel has same-sign fields Optimum for solenoid channel is different when optimised jointly with the chicane Graphs of progress in the two optimisations Then optimised the same ranges with the chicane filtering the transmitted particles