High Intensity Beam Dynamics Simulation for theDAEδALUS Cyclotrons

J.J. Yang1, A. Adelmann, L. Calabretta

May 11, 2012

European Cyclotron Progress Meeting 2012, PSI Switzerland

1MIT & PSI post-doc.1 / 22

Outline

Introduction

DIC cyclotron study

DSRC cyclotron study

2 / 22

Outline

Introduction

DIC cyclotron study

DSRC cyclotron study

3 / 22

DAEδALUS Cyclotrons For CP violation

Generalized perveance:

K =qI

2πε0mγ3β3

1. DIC: K of 5 mA, 35 keV/n H+2 equal to 2 mA, 30 keV proton

2. DSRC: K of 5 mA, 800 MeV/n H+2 equal to 2.5 mA, 800 MeV proton

3. “Easier” extraction by stripping than proton, higher bonding energy than H−

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OPAL Introduction

OPAL is a tool for charged-particle optics in large accelerator structuresand beam lines including 3D space charge. Two of the flavors are:

I OPAL-t : RF gun, XFEL, beam line

I OPAL-cycl : cyclotron, FFAGI tracks particles with 3D space charge including neighboring turnsI Use 4th-order RK and Leap Frog integratorI Also can do single particle tracking and betatron tune calculation

Recent development on OPAL-cycl

I 4 new elements: stripper, probe(r/phase), collimator(r/z), septum

I Multiple 3D RF field maps handling

I A faster integrator MTS (by M. Toggweiler)

I Bunch compress/decompress effects of RF cavity

I Easer interface between OPAL-t and OPAL-cycl

I Machine global aperture (r/z)

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Outline

Introduction

DIC cyclotron study

DSRC cyclotron study

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Basic Facts of the DIC

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120

Tur

n se

para

tion

(mm

)

Turn #

-10 0

10 20 30 40

20 40 60 80 100

RF

phas

e (d

eg.)

turn number

I Compact cyclotron with axialinjection @ 70keV/n H+

2

I Reach 61.7 MeV/n in 107 turnswith 4 double-gap cavities

I Maximal average radius 2.1 m(3.7 m for PSI Injector 2)

I Single turn extraction withelectrostatic deflector

I ∆R rises to 20 mm at extraction

I Integrated phase slipping less than< 20◦ during accelaration

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Stationary Matched Beam FormationTracking initial mismatched coasting beam (1.5MeV, 5mA) in 100 turns

1

2

3

4

5

6

7

0 20 40 60 80 100

rms

size

(m

m)

Turn #

horizentallongitudinal

vertical

0

1

2

3

4

5

0 π 2π 3π 4πrm

s si

ze (

mm

)

azimuth (rad)

horizontallongitudinal

vertical

snapshot after per turn last 2 turns final distribution at 0◦

I r-θ vortex motion causing longitudinal focusing effects

I The compact stationary matched distribution develops formed at lowenergy

I Flat-top cavity is NOT needed, like PSI Injector 2

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Space Charge Effects in AccelerationPhase space after 100 turns

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Acceleration Simulation of 5 mA BeamAcceleration and collimation

OPAL simulation settings

I Start at the exit of central region

I εn(2σ)=0.6 πmm-mrad in thetransverse directions

I Assume phase acceptance of 10◦

I Initial energy spread of 0.4% (2σ)

I Different collimation schemes arestudied, preferred solution is 4collimators at 1.9 MeV/n, cutting10% particles

I Gaussian distribution with 106

macroparticles

I 643 grid for space charge calculation

0

2

4

horizontal

with collimationwithout collimation

0

2

4

rms

size

(m

m)

longitudinal

0

2

4

0 20 40 60 80 100

Turn #

vertical

1. Radial size increased slowly

2. Longitudinal size increase slowly→phase width compressed

3. Phase shift destroys longitudinalspace charge focusing at last turns

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Acceleration Simulation of 5 mA beamBeam Extraction

Last 4 turns’ radial profile r-z projection of last 2 turns with collim.

rms parameter r z εr,n εz,n θ ∆E/Emm mm πmm-mr πmm-mr deg %

Inj. 0.84 1.85 0.15 0.15 1.67 0.2Ext. (collim.) 2.55 1.22 0.37 0.35 1.34 0.16

Ext. (no collim.) 2.75 1.46 0.43 0.49 1.50 0.17

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Sensitivity of Beam Loss at Septum

100

101

102

103

104

105

106

1840 1850 1860 1870 1880 1890 1900 1910

Inte

nsity

(ar

b. u

nits

)

R (mm)

1 mA, 10 deg5 mA, 10 deg

10 mA, 10 deg100

101

102

103

104

105

106

1840 1850 1860 1870 1880 1890 1900 1910

Inte

nsity

(ar

b. u

nits

)

R (mm)

1 mA, 20 deg5 mA, 20 deg

10 mA, 20 deg

Initial phase width 1 mA 5 mA 10 mA10◦ 30 W 120 W 1200 W20◦ 70 W 110 W 1580 W

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Conclusions on DIC Cyclotron

1. DIC is a space charge dominated cyclotron:I helps to form a stationary compact beamI enlarges the radial beam size, which increase beam loss on septum

2. Phase slipping at extraction enlarges bunch length, but does notaffect radial size

3. Magnet design is well improved based on the space charge study

4. Up to 5mA maximal current, the beam loss at extraction is onlyabout 120W, i.e., the extraction efficiency of 99.98%, which isacceptable

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Outline

Introduction

DIC cyclotron study

DSRC cyclotron study

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Acceleration Simulation for Different Current

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400

vert

ical

max

siz

e (

mm

)

Turn #

0 mA5 mA

10 mA

1. Energy reaches 800MeV/n in 400turns

2. Vertical beam extent < 30 mm (hillgap is 80 mm)

3. Stationary compact shape is notdeveloped, full length ≈ 20 cm !

4. SC force splits beam into 3 subbunches longitudinally

0 mA 5 mA 10 mA

Top view of the final turn at extraction15 / 22

Radially Neighboring Bunch (NB) Effects

Computation Model and Tool (PhysRevSTAB.13.064201)

1. Use the ”Start-to-Stop” numerical model, which is uniquelyimplemented in OPAL

2. Start with single bunch and automatically transfer to multi-bunchtracking where NB effects become important

3. A small scale simulation: 512× 64× 16 grid, 103 particle/bunchtakes 2 weeks on 64 processors

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Bunches During Acceleration for 10◦ initial Phase

0 mA 5mAI SC and NB introduce vertical beam halo, but the influence is small

I Beam halos extends vertically to ±20 mm, still far away from themagnet sector and vacuum chamber (hill gap is 80 mm)

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Particle Distribution on Stripper

0

500

1000

1500

2000

2500

3000

4755 4756 4757 4758 4759 4760 4761

Inte

nsity

(ar

bitr

ary)

Radius (mm)

5 mA

0

500

1000

1500

2000

-25-20-15-10 -5 0 5 10 15 20 25

Inte

nsity

(ar

bitr

ary)

Vertical (mm)

5 mA

0

200

400

600

800

1000

1200

-0.8 -0.4 0 0.4 0.8

Inte

nsity

(ar

bitr

ary)

∆ E/E (%)

5 mA

0

500

1000

1500

2000

2500

3000

-8 -6 -4 -2 0 2 4 6 8

Inte

nsity

(ar

bitr

ary)

Phase (deg)

5 mA

parameter rms 90%r (mm) 0.9 3.2z (mm) 3.3 12.0

∆E/E(%) 0.2 0.8∆φ(◦) 1.6 2.0εr,n 1.1

(mm-mr)εz,n 1.4

(mm-mr)

Note: extracted beam iscontributed by 15 turns

I This is taken as the initial distribution for extraction simulation innext slides, and input of the temperature calculation by H. Okuno

I 100% extraction efficiency assumed, physics is not included yet

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10 mA Proton Beam Extraction

-4

-2

0

2

4

-4 -2 0 2 4

y [m

]

x [m]

-1

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

Bz

(T)

s (m)

B field along path

I Protons experiences complicated bending fields including nonlinearfringe fields

I Protons are accelerated and decelerated for 3 times

I Extra dipole field with 1.6 kG/cm is applied at the inner free spaceto strengthen vertical focusing

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10 mA Proton Beam Extraction

0

10

20

30

40

50

60

0 2 4 6 8 10 12 14

rms

size

(m

m)

s (m)

horizontalvertical

longitudinal

Phase space at the last point:

I Vertically well focused withthe help of extra dipole field

I Momenta dispersion increasehorizontal and longitudinalbeam size

I Exotic phase space caused bymulti-turn stripping scheme

horizontal vertical longitudinal

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Conclusions on DSRC

1. Magnet design is optimized based on the space charge study

2. The important beam properties on the stripper are dominated by theinitial conditions

3. SC and NB introduce the vertical beam halo, but the influence issmall

4. In order to reduce the beam size and energy spread, a smaller initialphase is preferred

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Acknowledgment

I A. Calanna and D. Campo for providing field maps

I M. Toggweiler, C. Kraus and Y. Ineichen for computer-sciencerelated discussions

I H. Zhang, R. Dolling and C. Baumgarten for helpful discussions

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