stephen brooks / ral / may 2004 optimisation of the ral muon front end design

Stephen Brooks / RAL / May 2004

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 400MeV muon linac

– 31.4 MHz RF phase rotation (2003)• For low energy spread ionisation cooling ring


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




• 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

(or rods)

RAL design 2001-02 by Grahame Rees

(…or liquid mercury jet, rotating levitating band, granular water-cooled target, etc…)

4MV/m


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 + 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 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


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

Drifts Length (m)

D1 0.5718 [0.5,1]

D2+ 0.5 [0.5,1]

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

S120

[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


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% + 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


NuFact Intensity Goals

• “Success” is 1021 /yr in the storage ring

Proton Energy/GeV Intensity/MW Target eff (pi/p) MuEnd eff (mu/pi) Operational mu/year in storage ring Current/uA

8 4 20% 1.0% 30% 5.90497E+19 500 "Not great" scenario

8 1 60% 2.0% 35% 1.03337E+20 125 ISIS MW only to reach 10^20

8 5 60% 3.5% 40% 1.03337E+21 625 "Quite good" 5MW scenario (gets 10^21)

8 5 1.75 8.5% 55% 1.00646E+22 625 Required to reach 10^22

1.75 = PtO2 target inclined at 200mrad, see Mokhov FNAL PiTargets paper 20% = 2.2GeV dataset from Paul Drumm


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


Optimised Design for the Decay Channel (137 parameters)

0

5

10

15

20

25

Fie

ld (

Te

sla

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Siz

e (

me

tre

s)

Solenoid Field Solenoid Radius Solenoid Length Drift Length

•Maximum Length

•Minimum Drift

•Maximum Aperture

•Maximum Field

(not before S6)

(mostly)

(except near ends)

(except S4, S6)


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


Design Optimised for Transmission Through Chicane

• Nontrivial optimum found

• Preferred length?

• Narrowing can only be due to nonlinear end-fields

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Length

Radius

0.463 m

0.402−0.003n m


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

Microsoft Excel Worksheet

stephen brooks / ral / may 2004 optimisation of the ral muon front end design

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