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 4th order classical Runge-Kutta on the 6D phase space

–Currently timestep is fixed at 0.01ns

•Solenoids fields and end-fields are a 3rd 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 4th order classical Runge-Kutta on the 6D phase space

–Currently timestep is fixed at 0.01ns

•Solenoids fields and end-fields are a 3rd 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 ComputingDistributed Computing

ResultsImproved 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

ResultsImproved 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 WorkFuture 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 status

Future WorkFuture 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 status

BeamlinePion 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

BeamlinePion 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

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0.2

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Solenoid Field Solenoid Radius Solenoid Length Drift Length

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0.1

0.2

0.3

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Length

Radius

0.463 m

0.402−0.003n m

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

0.15 [0.1,0.4]

S25+

0.15 [fixed]Final (S34)

±3.3 (alternating)

[-4,4]

S5-S24 0.4

[0.2,0.6]

0.3

[0.1,0.4]

- 3.3, 4, - 3.3

[-5,5]S2-4

0.4066 [0.2,0.45]

0.1 [fixed]20

[0,20]S1

Length (m)Radius (m)Field (T)Solenoids

0.15 [0.1,0.4]

S25+

0.15 [fixed]Final (S34)

±3.3 (alternating)

[-4,4]

S5-S24 0.4

[0.2,0.6]

0.3

[0.1,0.4]

- 3.3, 4, - 3.3

[-5,5]S2-4

0.4066 [0.2,0.45]

0.1 [fixed]20

[0,20]S1

Length (m)Radius (m)Field (T)Solenoids

• 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-energies Geometry 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 thetransmitted particles