Optimisation of the RAL Muon Front End Design

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

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 à 400MeV muon linac

31.4 MHz RF phase rotation (2003)

For low energy spread à ionisation cooling ring

Pion to Muon Decay Channel

Challenge: high emittance of target pions

Currently come from a 20cm tantalum rod

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

Chicane Phase-Rotation

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

Muon1 Particle Tracking Code

Non-linearised 3-dimensional simulation

PARMILA was being used before

Uses realistic initial p⁺ 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)

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

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

Decay Channel Parameters

12 parameters

Solenoids alternated in field strength and narrowed according to a pattern

137 parameters

Varied everything individually

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

Results- Improved Transmission

Decay channel:

Original design: 3.1% m⁺ out per p⁺ from rod

12-parameter optimisation à 6.5% m⁺/p⁺

1.88% through chicane

137 parameters à 9.7% m⁺/p⁺

2.24% through chicane

Re-optimised for chicane transmission:

Original design got 1.13%

12 parameters à 1.93%

137 parameters à 2.41%

NuFact Intensity Goals

“Success” is 10²¹ m⁺/yr in the storage ring

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, ChicaneLinacA

Slide 17

Optimised Design for the Decay Channel (137 parameters)

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

Design Optimised for Transmission Through Chicane

Nontrivial optimum found

Preferred length?

Narrowing can only be due to nonlinear end-fields

Future Optimisations

Chicane and RF phase rotation designs are starting to be run now

Initial results promising

Cooling ring later this year

RAL Design for Cooling Ring

10-20 turns

Uses H₂(l) or graphite absorbers

Cooling in all 3 planes

16% emittance loss per turn (probably)

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

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


	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


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 à 400MeV muon linac
	31.4 MHz RF phase rotation (2003)
		For low energy spread à ionisation cooling ring


	Challenge: high emittance of target pions
		Currently come from a 20cm tantalum rod


	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


	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


	Non-linearised 3-dimensional simulation
		PARMILA was being used before
	Uses realistic initial p⁺ 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)


	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


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 parameters
		Solenoids alternated in field strength and narrowed according to a pattern
	137 parameters
		Varied everything individually


	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


Decay channel:
	Original design: 3.1% m⁺ out per p⁺ from rod
	12-parameter optimisation à 6.5% m⁺/p⁺
		1.88% through chicane
	137 parameters à 9.7% m⁺/p⁺
		2.24% through chicane
Re-optimised for chicane transmission:
	Original design got 1.13%
	12 parameters à 1.93%
	137 parameters à 2.41%


	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, ChicaneLinacA


	Original design had alternating (FODO) solenoids
	Optimiser independently chose a FOFO lattice
	Has to do with the stability of off-energy particles


	Nontrivial optimum found
	Preferred length?
	Narrowing can only be due to nonlinear end-fields


	Chicane and RF phase rotation designs are starting to be run now
		Initial results promising




	Cooling ring later this year


	10-20 turns
	Uses H₂(l) or graphite absorbers
	Cooling in all 3 planes
	16% emittance loss per turn (probably)


	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


	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