1. Stephen Brooks / RAL / May 2004  Optimisation of the RAL Muon Front End Design

2. Stephen Brooks / RAL / May 2004 Contents Designs considered –Decay channel with chicane –Decay channel with phase rotation, cooling Tracking code Optimisation approach Results Future work –…and issues still to be solved

3. Stephen Brooks / RAL / May 2004 Design Components Pion to muon decay channel –Accepts pions from the target –Uses a series of wide-bore solenoids “Phase rotation” systems –FFAG-style dipole bending chicane (2001) For short bunch length  400MeV muon linac –31.4 MHz RF phase rotation (2003) For low energy spread  ionisation cooling ring

4. Stephen Brooks / RAL / May 2004 Pion to Muon Decay Channel Challenge: high emittance of target pions –Currently come from a 20cm tantalum rod

5. Stephen Brooks / RAL / May 2004 Pion to Muon Decay Channel Challenge: high emittance of target pions –Currently come from a 20cm tantalum rod Evolution of pions from 2.2GeV proton beam on tantalum rod target

6. Stephen Brooks / RAL / May 2004 Pion to Muon Decay Channel Challenge: high emittance of target pions –Currently come from a 20cm tantalum rod Solution: superconducting solenoids –S/C 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

7. Stephen Brooks / RAL / May 2004 Chicane Phase-Rotation (or rods) RAL design 2001-02 by Grahame Rees (…or liquid mercury jet, rotating levitating band, granular water-cooled target, etc…) 4MV/m

8. Stephen Brooks / RAL / May 2004 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

9. Stephen Brooks / RAL / May 2004 Muon1 Particle 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 (Mike Harold)

10. Stephen Brooks / RAL / May 2004 Muon1 Tracking Code 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

11. Stephen Brooks / RAL / May 2004 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

12. Stephen Brooks / RAL / May 2004 Decay Channel Parameters Drifts Length (m) D10.5718 [0.5,1] D2+0.5 [0.5,1] Solenoids Field (T)Radius (m)Length (m) S1 20 [0,20] 0.1 [fixed] 0.4066 [0.2,0.45] S2-4 −3.3, 4, −3.3 [-5,5] 0.3 [0.1,0.4] 0.4 [0.2,0.6] S5-S24 ±3.3 (alternating) [-4,4] S25+ 0.15 [0.1,0.4] Final (S34)0.15 [fixed] 12 parameters –Solenoids alternated in field strength and narrowed according to a pattern 137 parameters –Varied everything individually Tantalum Rod Length (m)0.2 [fixed] Radius (m)0.01 [fixed] Angle (radians)0.1 [0,0.5] Z displacement (m) from S1 start 0.2033 (S1 centred) [0,0.45] Original parameters / Optimisation ranges

13. Stephen Brooks / RAL / May 2004 Phase Rotation Plan 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

14. Stephen Brooks / RAL / May 2004 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% 3`900`000 runs so far 1`900`000 runs 330`000 runs

15. Stephen Brooks / RAL / May 2004 NuFact Intensity Goals “Success” is 10 21   /yr in the storage ring Proton Energy/GeVIntensity/MWTarget eff (pi/p)MuEnd eff (mu/pi)Operationalmu/year in storage ringCurrent/uA 8420%1.0%30% 5.90497E+19500 "Not great" scenario 8160%2.0%35% 1.03337E+20125 ISIS MW only to reach 10^20 8560%3.5%40% 1.03337E+21625 "Quite good" 5MW scenario (gets 10^21) 851.758.5%55% 1.00646E+22625 Required to reach 10^22 1.75 = PtO2 target inclined at 200mrad, see Mokhov FNAL PiTargets paper20% = 2.2GeV dataset from Paul Drumm

16. Stephen Brooks / RAL / May 2004 Distributed Computing System How do you run 3`900`000 simulations? Distributed computing –Internet-based / FTP –~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 –Examples: SolenoidsTo15cm, ChicaneLinacASolenoidsTo15cmChicaneLinacA

17. Stephen Brooks / RAL / May 2004

18. Optimised Design for the Decay Channel (137 parameters) Maximum Length Minimum Drift Maximum Aperture Maximum Field (not before S6) (mostly) (except near ends) (except S4, S6)

19. Stephen Brooks / RAL / May 2004 Why did it make all the solenoid fields have the same sign? Original design had alternating (FODO) solenoids Optimiser independently chose a FOFO lattice Has to do with the stability of off-energy particles FODO lattice FOFO lattice

20. Stephen Brooks / RAL / May 2004 Design Optimised for Transmission Through Chicane Nontrivial optimum found Preferred length? Narrowing can only be due to nonlinear end-fields

21. Stephen Brooks / RAL / May 2004 Future Optimisations Chicane and RF phase rotation designs are starting to be run now –Initial results promising Cooling ring later this year

22. Stephen Brooks / RAL / May 2004 RAL Design for Cooling Ring 10-20 turns Uses H 2 (l) or graphite absorbers Cooling in all 3 planes 16% emittance loss per turn (probably)

23. Stephen Brooks / RAL / May 2004 Unresolved Issues (to-do) Solenoid field clipping distance Need ‘solid’ solenoids for best accuracy –ICOOL has recently added these New target dataset needed for 8GeV –Trying to get MARS –Possibility of target energy optimisation Code could do with variable timesteps and/or error control

24. Target Area Losses Muon1 modified to count lost particle energies For a 4MW p + beam: –35kW deposited in S1 (r=10cm) –Large >1kW amounts deposited up to S5 Added “collimators” to the simulation –Decreases losses to 10’s of watts in all but S1 and S2 –S1 needs enlarging to accommodate an entire Larmor rotation Consistent target-area layout is needed