1

FFAG Role as Muon Accelerators

Shinji Machida

ASTeC/STFC/RAL

15 November, 2007

http://www.astec.ac.uk/intbeams/users

/machida/doc/othertalks/machida_20071115.pdf & ppt

2

Contents

• Neutrino factory and FFAG (5 slides)

• Tracking studies (6 slides)– “Longitudinal emittance blowup in FFAG muon accelerators”, b

y S. Machida, Phys. Rev. ST AB 9, 104002 (2006).– “Orbit and optics distortion in FFAG muon accelerators” b

y S. Machida and D. J. Kelliher, accepted to Phys. Rev. ST AB.

• EMMA overview (3 slides)

• Summary

3

Neutrino factory and FFAG

4

Neutrino factory and FFAG (1)Schematic view

• Neutrino Factory requires 20 to 50 GeV muon beam.– Muon accelerators are the most costly part of the machine complex.– FFAG is considered as the most cost effective option.

neutrino factory complex

• International Scoping Study has been completed last year.

• International Design Study has started.

5

Neutrino factory and FFAG (2) FFAG in one word

• FFAG is a Fixed Field Alternating Gradient accelerator.– It separates the guiding field from the accel

eration process. No synchronization.– Quick acceleration is possible. The rate onl

y depends on voltage.

• Nonscaling FFAG looks like a “storage ring”.– Lattice with ordinary dipoles and quadrupol

es.– Dispersion function is small enough to give

large momentum acceptance. – Orbit shift from injection to extraction is sma

ll.

lattice functions of 10 to 20 MeV electron model

6

Neutrino factory and FFAG (3) nonscaling and scaling

• Constant gradient magnets give a focusing force inversely proportional to particle momentum.

• With acceleration, the machine

‘tune’ decreases.

– > Nonscaling FFAG

• Field nonlinearities can make

the tune constant.

– > Scaling FFAG

€

1

f=dBdx ⋅L

pe

Nonlinear field profile cancel chromaticity.

Scaling FFAG

7

Neutrino factory and FFAG (4) why nonscaling for muons?

• Magnets of a nonscaling FFAG are expected to be– smaller because of smaller orbit shift,– simpler because no nonlinearities.

• However, the machine tune changes a lot during acceleration.– Revolution frequency depends on the t

ransverse amplitude.– Crossing of ‘resonance’ becomes a co

ncern.

40

30

20

10

0

403020100Qx

10 GeV/c

20 GeV/c

Tune excursion from 10 to 20 GeV/c muon ring.

8

Neutrino factory and FFAG (5) ongoing projects

• Understand beam dynamics with particle tracking simulation.– A new code development.– Identify accelerator physics issues.

• Demonstrate a nonscaling FFAG– EMMA project at Daresbury laboratory.

9

Tracking studies

10

Tracking studies (1)new acceleration scheme and issues

• There is a path outside of a bucket.

• A beam is accelerated in the path.

Phase (1/2 pi)

dp/p

(no

rmal

ized

) Phase space with high frequency rf

• Large amplitude particles take more time to finish one revolution.– Those particles do not come

back to the same phase.– They may be decelerated.

20

18

16

14

12

10

1.00.80.60.40.20.0RF phase/2Pi

36 mm25

0Amplitude effects

11

Tracking studies (2)longitudinal emittance growth and its cure

• Deterioration is observed.• Chromaticity correction mitigates the emittance growth in l

ongitudinal phase space.

20

18

16

14

12

101.00.80.60.40.20.0

rf phase/2

20

18

16

14

12

101.00.80.60.40.20.0

rf phase/2

Linear lattice Lattice with sextupole

12

Tracking studies (3)amplitude depending revolution time

• Orbit shift becomes twice as much.– Need a bigger aperture

magnet.

-80

-40

0

40

201816141210momentum [GeV/c]

no correction with sext.

• Exchange of transverse emittance.– Can be cured by tune choice?

2.0

1.5

1.0

0.5

0.012008004000

number of cells

H no correction

V no correction

H with sext.

V with sext.

16.280

16.275

16.270

16.265

16.260201816141210

momentum [GeV/c]

no correction with sext.

• Time of flight range increases 50%.– Need a higher voltage.

13

Tracking studies (4)single particle behavior

• Orbit distortion is not necessarily excited when a particle crosses integer tune with large harmonic strength.

-10

0

10

35 30 25 20 15horizontal tune

-10

0

10

25 20 15 10 5vertical tune

1.0

0.8

0.6

0.4

0.2

0.035 30 25 20 15

horizontal tune

1.0

0.8

0.6

0.4

0.2

0.025 20 15 10 5

vertical tune

14

Tracking studies (5) rms orbit distortion

• rms orbit distortion due to alignment errors agrees with random walk model.

• Distortion for different acceleration rates.– Circles are simulation results.– Lines are random walk

model.

120

80

40

012008004000

number of steps

600

500

400

300

200

100

0806040200

total turn number

horizontal vertical ?

model

tracking

17 turns

15

Tracking studies (6) a limitation of the model

• When the acceleration becomes slower, ‘resonance’ behavior starts appearing.

600

500

400

300

200

100

06000400020000

number of steps

horizontal vertical

16

EMMA overview

17

EMMA overview (1) aims

• EMMA will be a Proof of Principle nonscaling FFAG.– Electron Model of Muon Acceleration

or Electron Model of Many Applications

• Demonstrate that a nonscaling FFAG works as expected.– Examine quick acceleration and large acceptance.– Study acceleration outside bucket in detail.– Study “resonance” crossing in detail.

PoP scaling FFAG (2000): The world’s first proton FFAG with MA rf cavity.

EMMA is a nonscaling counterpart.

18

EMMA overview (2) difficulties in demonstrating a nonscaling FFAG

• Nonscaling FFAG is for a high energy muon accelerator.– A beam is supposed to be already relativistic at injection.– Electron beam of 10 MeV (=20) is needed.

• Beam dynamics rely on a high periodicity lattice.– Muon ring has 84 periods.– Electron model should have the same order of periodicity.

• Beams stay in the ring for only 10 to 20 turns.– Diagnostics for single path measurements.– Inject a beam with full momentum range to scan.

19

EMMA overview (3) injector

• Energy Recovery Linac Prototype at Daresbury Laboratory provides:– Variable injection momentum from 10 to 20 MeV.– Small emittance to scan FFAG phase space.– Sufficient intensity in a bunch for single path diagnostics.

10 m

ERLP

EMMA

20

Summary

21

• We have identified beam dynamics issues in a nonscaling FFAG for muon acceleration in a neutrino factory.

• Large transverse amplitude particles suffer phase slip.– This can be mitigated by chromaticity correction.

• Random walk is the correct way to understand orbit and optics distortion in a muon ring.– However, resonance behavior starts appearing when the acceleratio

n rate is 5 times slower.

• EMMA will be the world first nonscaling FFAG.

22

Backup slides

23

Beam dynamics study

24

Beam dynamics study (1) “resonance” crossing

• Integers and half-integers total tune are crossed.– If not much errors, they should not

be any problem.

• Cell tune is between 0 and 0.5.

• Cell tune of 1/3 and 1/4 are crossed.– If nonlinearities are not significant,

they should not be any problem.

cell tune

40

30

20

10

0

403020100Qx

10 GeV/c

20 GeV/c

total tune = 84 x cell tune

25

Beam dynamics study (2) “resonance” crossing

• Single particle trajectory does not show any “resonance” behavior.

• Rms orbit deviation over many different lattices shows almost square root growth.– Implies random kicks cause orbit d

istortion, not by resonances.

H.

orbi

t di

stor

tion

12x10-3

8

4

040003000200010000

number of steps

26

Beam dynamics study (3) outside bucket acceleration

• Time of flight is a function of transverse amplitude as well as momentum.

• Large amplitude particles have too much phase slip to be accelerated to the maximum energy.

20

18

16

14

12

10

1.00.80.60.40.20.0RF phase/2Pi

0 pi mm-rad

10 pi mm-rad

20 pi mm-rad

30 pi mm-rad

phase (1/2 pi)

dp/p

(no

rmal

ized

) 1.3674

1.3672

1.3670

1.3668

1.3666

1.3664

201816141210kinetic energy [GeV]

0 pi mm-rad 10 pi mm-rad 20 pi mm-rad

kinetic energy

Tim

e of

flig

ht

mom

entu

m [

GeV

/c]

phase (1/2 pi)

(This is only for zero amplitude.)

0

emittance of 20

20

0

27

Beam dynamics study (4) outside bucket acceleration

• As a whole beam, longitudinal emittance blows up and momentum spread increases when the transverse amplitude is included.

• Chromaticity correction cures the problem (S. Berg, Nucl. Inst

rum. Methods, 2006), but it reduces aperture.

20

18

16

14

12

10

1.00.80.60.40.20.0RF phase/2Pi

20

18

16

14

12

10

1.00.80.60.40.20.0RF phase/2Pi

zero transverse emittance 30 mm transverse emittance

phase (1/2 pi)phase (1/2 pi)

mom

entu

m [

GeV

/c]

mom

entu

m [

GeV

/c]

28

Hardware status

29

Hardware status (1) ERLP (injector)

• ERLP has been built.• It is currently being commissioned.

30

Random walk model (7) a limitation of the model

• When the acceleration becomes slower, random walk model breaks down more quickly for optics distortion.

40x10-3

30

20

10

040003000200010000

number of steps

model

tracking

31

Conclusions

32

• Amplification factor is 100~150. Growth factor is 250.– Practically important to determine magnet aperture.

• Orbit and optics distortion can be rather explained by random kick (walk) model, not by ‘resonance’ crossing.– One of EMMA goals: “See effects of resonance crossing” -> “See

effects of machine errors”

• If we make the acceleration speed slower, 5 times or 85 turns for example, resonance behavior appears in addition to random kicks. That is the mixed regime of resonance and random kicks.