heavy-ion beam dynamics in the ria accelerators and ...€¦ · p.n. ostroumov, “heavy-ion beam...

P.N. Ostroumov, “Heavy-Ion Beam Dynamics in the RIA Accelerators” , October 25, 2002 1

Heavy-Ion Beam Dynamics in the RIA Acceleratorsand Development of RT Accelerating Structures for the RIA

• Layout of the RIA accelerators.• Acceleration of multiple-charge state heavy-ion beams.• Driver Linac:

- Injector system: ECR-LEBT-RFQ;- Design of 57.5 MHz cw RFQ;- Parametric resonance of transverse motion;- Beam steering compensation and electric field

symmetry in SRF cavities;- Beam Dynamics optimization and simulation;- Isopath transport of multi-q beams;- BD in high-E section: Triple-Spoke vs Elliptical cavities.

• Design of the Post-Accelerator:- RT accelerating structures and beam dynamics.

• Summary and outlook.


Rare Isotope Accelerator Facility

4007373He

100 (400)400238U

400451136Xe

400900p

Beam power (kW)

Beam energy (MeV/u)

Species


Beam

Beam

f, MHz 57.5 57.5 57.5 115 172.5 345

f, MHz 805 805 805


ANL spoke cavity

JLABellipticalcavity


Acceleration of synchronous particle

sc0us TLeEA

qW M' cos,

Aq

constEconstE

A

q00 /

,

0n

qsnsn0n

EA

qconst

constEA

qn ,cos,cos MM

0s0

snn

A

q

A

q,coscos MM

Fixed velocity profile(RFQ, RT DTL)

Multi-q heavy-ionaccelerator

Variable velocity profile(SC Linac)

E0=const,Tune phases of individual cavities


-60

-50

-40

-30

-20

-10

0

65 70 75 80 85 90

Charge state

Pha

se (

deg)

Synchronous phase as a function of uranium ion charge state. The designed synchronous phase is

–30q for q0=75.


E0

q=75

Ms

Eg(z)

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

Distance, m

Zt

q=77

q=73

Earlier arrival Later arrival

Single accelerating gap


' p /p , % 2 q = 7 7 q = 7 5 1 q = 7 3 0 -1 -2 -8 0 -4 0 0 4 0

P hase , d e g

-0.8

-0.4

0

0.4

0.8

-15 -10 -5 0 5 10 15

Phase (deg)

'p

/p (

%)

q=77 q=75 q=73

Separatrix and small longitudinal oscillations


xxxx

xxxxx

xxxxx

xxxx

M

HEDJ

PDPPJ

PEPDP

c�c�

»¼

º«¬

ª��

�

22 2

sincossin

sinsincos

Lf

SRF cavitiesSolenoid

Transverse beam dynamics


54

56

58

60

62

64

72 73 74 75 76 77 78

Charge state

Pha

se a

dvan

ce

Px

(deg

)

0

100

200

300

400

500

Pha

se a

dvan

ce

)x

(deg

)

Px

)x

Phase advance over the period Px and total phase advance )x (modulo 360 q) in the medium-beta

section (12 MeV/u – 85 MeV/u)


0

10

20

30

40

1 2 3 4 5 6 7 8 9 10

Emittance growth factor

N/N

0, %

Transverse emittance growth in the focussing channel with alignment errors (±300 Pm)

Corrective one-element steering

No steering


Stripping foil

ECR ion source

Booster Injector

ATLAS section

Diagnostic area

40q Bend Reg ion

Slits, Faraday Cup

Multi-q beam experiment on ATLAS (ANL)

W=1.2 MeV/uq=35,36,37,38,39,40,41,42,43,44

W=2.9 MeV/u

q_average=51


-3

-2

-1

0

1

2

3

-30 -20 -10 0 10 20 30

Phase, deg

'W

/W, %

35+

36+

37+

38+

39+

40+

41+

42+

43+

Beam Dynamics Simulations

0

0.25

0.5

0.75

1

1.25

0 400 800 1200 1600

Distance, cmB

ea

m s

ize

, cm

35+ 36+37+ 38+39+ 40+41+ 42+43+


35 36 37 38 39 40 41680

690

700

710

Measurement

Simulation

Bea

m E

nerg

y (M

eV)

Charge State

Multi-q beam energy at the exit of the Booster

Equivalent to the RIA design req.


0.00

0.05

0.10

0.15

0.20

0.25

35 36 37 38 39 40 41 42 43 44

Charge state

Nor

mal

ized

cur

rent

(re

l. va

lue)

94% Transmission of Multi-Q Accelerated Beam Through the Booster


Accelerating and Focusing Lattice of the Driver Linac

Focusing:• In the DTL: superconducting solenoids.• In the high-E linac: warm SNS-type quadrupole

doublets (baseline design) or SC solenoids.• Length of focusing period is determined by the

stability conditions and required small beam size for high-intensity ion linacs:

- DTL: Raperture/R rms_beam= 11-12- High-E linac: Raperture/R rms_beam= 20-25

Acceleration:

• Superconducting resonators except in the Front End.


Layout of the Driver Linac

Front End

RFQ LEBTMEBT

Low-E

High-E

Medium-E


Low-energy achromatic 120° bend

Phase space plots

-10 -8 -6 -4 -2 0 2 4 6 8 10

-30

-20

-10

0

10

20

30

Ex=E

y =100p mm*mrad

y plane

x (bending) planex|,y| mrad

x,y mm

B

-6 -4 -2 0 2 4 6

-40

-30

-20

-10

0

10

20

30

Q=29

Q=28

Ex=124pmm*mrad x

| ,mrad

X ,mm

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

-15

-10

-5

0

5

10

15

Q=29

Q=28

Ey=132 pmm*mrad

y| ,mrad

y ,mm


Longitudinal phase space plots of two-charge state uranium beam along the LEBT

21

20

q1

q1

1

cAm

eV22

L�

O


�CW regime;

� Wide dynamic range of rf power level from P0/70 to P0for acceleration of various ion species from protons to uranium;

� Simultaneous acceleration of two charge-state heavy-ion beams;

� Maintaining an extremely small longitudinal emittance formed by the external multi-harmonic buncher;

� Exit of the RFQ: beam waist in both H- and V-planes for easer matching to the following MEBT.

Basic features of the 57.5 MHz RFQ


• Adiabatic bunching;• Internal ‘klystron’ bunching;• External multi-harmonic buncher: Extremely low long.

emittance (ISAC-1 RFQ, TRIUMF). Simultaneous acceleration of 2 charge states for heavy ions.

RFQ design options

a) High-efficiency SRF cavities for the following acceleration;

b) Moderate peak surface fields in the RFQ to provide reliable operation in CW mode;

c) High quality two-charge-state beam parameters;d) Large transverse acceptance.e) Possibility to increase inter-vane voltage to accept lower

charge states (higher intensities!).

Frequency is 57.5 MHz:


Accelerating by an RFQ

2

1

2

2

0

EO

EO

S

�

cL

m

aR

k

ma

a - Aperture

- Maximum distance from axis to electrodes


RFQ resonant structure

~4000

I 510


Vane Tip

¸¹

·¨©

§��

�

¸¹

·¨©

§��

�

kzsin1m

1m1Ry

kzsin1m

1m1Rx

0

0

eR2

Longitudinal modulationTransverse cross-section


-2 -1 0 1 20

1

2

3

4

5

6

Ele

ctric

fie

ld (

MV

/m)

Distance from RFQ center (m)

-2 -1 0 1 2-8

-6

-4

-2

0

2

4

6

8

Ele

ctric

fie

ld (

MV

/m)

Distance from RFQ center (m)

Electric field distribution along the RFQ

f=57.5 MHz

Absolute

Ex Ey

Operating mode f=57.5 MHz

Upper mode 1 f=68.4 MHz

f=93.5 MHz


Cross Section of the Octagonal ResonatorS

= 5

13

S = 513

Internal dimension


� ��

��> @

��

��> @

��

��> @

��

��> @

57.5 MHz RadioFrequency QuadrupoleAccelerator


RF Induced Heat Flux

Heat FluxW/cm2

Heat flux distribution determined with ANSYS RF analysis, heat loads scaled to 8.0 kW per segment

0.0 1.84 2.76 3.68 4.60 5.52 6.44 7.36 8.28.92


Radial displacements of Vanes at symmetry plane

Radial Displacementinches

-1.94e-3 inches

-2.58e-4

-1.91e-3

-2.59e-4

-1.94e-3 -1.73e-3 -1.51e-3 -1.30e-3 -1.08e-3 -8.62e-4 -6.46e-4 -4.29e-4 -2.14e-4 2.30e-6

Path 1this vane at tipstart this sidesee next slide

Path 2this vane at tipstart this sidesee next slide


Characteristics of the RFQ resonator

• Modular structure. The brazing technique which is well established for 4-vane RFQs can be applied. Brazing provides the best electrical properties of rf structures;

• Small transverse dimensions for low frequencies;• Large frequency separation of non-operating modes;• Uniform field distribution along the z-axis;• High shunt impedance (45 kW for 4 meter structure);• Symmetric design guarantees low field perturbations

due to possible thermal distortion, no dipole component of the fields in the aperture;

• Provides good mechanical stability of the construction together with precise alignment ability.


¦

¦

¦

¦ ¦

f

��

f

��

f

�

�

f

f

�

��

��

��¸̧¹

·¨̈©

§

»¼

º«¬

ª��

042,1212

0)12(212,22

0

)12(2

012,00

1 112202

4cos])12[(),(

)12(2cos)2(),(

)12(2cos),(

)12cos(),(2cos),(),(),,(

mmmnn

mmmnn

m

m

m

n nnn

U

mkrnIArF

mnkrIArF

mR

rArF

kznrFnkzrFrFzrU l

-T

TT

TT

T-T-

104

AT �

S

- Accelerating efficiency

01

2

02

0

2

4A

Rcm

UeK l

¸¸¹

·¨¨©

§�

O- Focusing efficiency

Electric potential in RFQ aperture


Coupling of Longitudinal and Transverse Motions

Separatrix of longitudinal oscillationscalculated at the beginning of the RFQ(k=2.38)

� �� )sin(Icos2

),H( 00

02

ss zkkrzkAW

TZeUcz MM

S

EE �'�'�

' ''

-8 -4 0 4

-0.2

-0.1

0.0

0.1

'E 1

03

'z (mm)

R=0.4 mm

R=0.25 mm

R=0

Initial particle distribution

sEEE � ' Difference between particle velocity and synchronous value

czzz � ' The corresponding difference between longitudinal coordinates

EO

S2 k


Longitudinal emittances at the exit of RFQ

Phase (deg) Phase (deg)

Phase (deg) Phase (deg)

'W

/W (

%)

'W

/W (

%)

'W

/W (

%)

'W

/W (

%)

1 2

3 4

0.5 1.0 1.5

1.4

1.6

1.8

2.0

2.2

2.4

2.6

Norm. transverse emittance (S mm mrad)

Out

put l

ong.

em

ittan

ce

( S k

eV/u

nse

c)1

2

3

4

Longitudinal emittance99.9 % of particles

50000 particles are simulated


Transverse Emittances at the RFQ Exit

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

-0.01

0.00

0.01

0.02

dX/d

z (m

rad)

X (cm)-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

-0.01

0.00

0.01

0.02

dY/d

Z (

mra

d)Y (cm)

X plane Y plane

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

-0.01

0.00

0.01

0.02

dX/d

z (m

rad)

X (cm)-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

-0.01

0.00

0.01

0.02

dY/d

Z (

mra

d)Y (cm)

X plane Y plane


BEAM RESONATOR TYPE 2-GAP QWR, EG=0.062, f=57.5 MHz 2-GAP QWR, EG =0.15, f=115 MHz

BEAM

BEAM

RESONATOR TYPE

2-GAP HW, EG=0.19,f=172.5 MHz

4-GAP SPOKE, EG =0.5,f=345 MHz

BEAM

BEAM

3.98 m

BEAM

5.80 m

4-GAP SPOKE, EG =0.5, 0.62f=345 MHz

RIA Driver Linac


Driver Linac

400-580177-250113-177Length of the focusing period, cm

46 (38)2010Number of cryostats

805 (345)172.5-34557.5-115Frequency, MHz

105

52

129

20

10.1-85.0

Medium E

28.520Surface field SRF cavities, MV/m

260 (197)55Length, m

46 (38)42Number of focusing periods

166 (140)85Number of resonators

81.0-403.00.2-10.2Uranium beam energy, MeV/u

High ELow E


Some design solutions � Multi-q beam acceleration.� Low longitudinal emittance of two charge-state uranium beam.� Inter-cryostat space will contain only vacuum valves and a small beam

diagnostics box. � Beam steering coils will be combined with the SC focusing solenoids

and will not require an additional space along the beamline.� Standard accelerating SRF cavities can be switched to the mode of a

beam phase monitor in order to set up phases and amplitudes of the accelerating fields in the upstream cavities.

� Transverse matching between the cryostats is facilitated by the absence of the first SRF cavity in the very first focusing period of the cryostats.

� Long. matching between the cryostats is provided by the setting of phases in the SRF cavities.

� Beam energy at stripper locations is determined from the condition of lowest possible long. emittance of multi-q uranium beam.

� Triple spoke cavities vs elliptical.


Simulation codes • TRACE, TRANSPORT, COSY, GIOS;

• CST Microwave Studio; SIMION;

• DESRFQ, DYNAMION;

• RAYTRACE, TRACK.

TRACK:

• multiparticle simulation of multi-q ion beams in 6D phase space;

• 3D electromagnetic fields from MWS in rectangular mesh;• Fringing fields of magnets and multipoles as in RAYTRACE code;

• Realistic fields in solenoids;

• Integration of equations of motion by 4th order Runge-Kutta method;

• Misalignments and random errors are included.

Detailed BD simulations are necessary for cost-effective design of the accelerators


Beam envelopes along the driver linac


The condition for a n-th orderparametric resonances of transverse motion in a smooth approximation lt 2

nPP

Resonance width sn2tsn ba 'P' ��

� � 2u

sm2f

3ss

scm

sineES1

A

q

2

M

OJE

S' Defocusing factor

sl 2 'P

n=1 and Ms=30q: a1| 0, b1|1.79n=2 a2| 3.93, b2|4.31.

Longitudinal phase advance

Parametric resonance


0 100 200 300 400

20

40

60

80

100

n=2

n=1

Pha

se a

dva

nce

(de

g)

Beam Energy (MeV/u)

EG=0.49

EG=0.62

EG=0.81

0 100 200 300 400

20

40

60

80

100

n=2

n=1

Pha

se a

dva

nce

(de

g)

Beam Energy (MeV/u)

EG=0.49

EG=0.62

EG=0.81


0

1

2

3

4

0 10 20 30 40 50 60 70

Distance (m)E

mitt

ance

gro

wth

fact

or

Hz

Hx

Hy

RMS emittance, Pt=30q

Emittance containing99.9% of the particles

DTL section, 172. 5 MHz

0

1

2

3

4

0 10 20 30 40 50 60 70

Distance (m)

Em

ittan

ce g

row

th fa

ctor

Pt =30°

Pt =50°Pt =40°

Win=10 MeV/u


Emittance evolution along the ECL linac for 4-cavity and 3-cavity lattices

1

1.1

1.2

1.3

0 10 20 30 40 50 60 70 80 90

Distance (m)

Em

ittan

ce g

row

th fa

ctor

3-cavity

4-cavity

$90 tP

Emittance evolution along the ECL linac for 4-cavity and 3-cavity lattices

1

1.1

1.2

1.3

0 10 20 30 40 50 60 70 80 90

Distance (m)

Em

ittan

ce g

row

th fa

ctor

3-cavity

4-cavity

$90 tP

BEAMBEAMProposed latticefor the first sectionof the ECL (EG=0.49)


0 5 10 15 20 25 30 35 40-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

Hx

Ez

10*Ey

Distance (cm)

10*E

y, Ez (

MV

/m)

-8

-6

-4

-2

0

2

4

6

8

Hx (

kA/m

)

Beam steering in QWR*

*A. Facco&V. Zviagintsev PAC91, N. Kakutani et al in EPAC98

Beam


D727 D(G�D(I�D+

dz)kzsin()z(E-C2/L

2/Lyd0Ed ³ �

�

MD

dz)kzsin(z

)z(E

2

Cy 2/L

2/L

z00Ef ³ �

w

w

�

MD

dz)kzcos()z(HCc2/L

2/Lx00H ³ �

�

MPED

Beam center deflection angles in QWR


0 5 10 15 20 25 30 35 40-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

Hx

Ey

Ez

D istance (cm )

Ey,

Ez (

MV

/m)

-8

-6

-4

-2

0

2

4

6

8H

x (kA

/m)

Compensation of the beam-steering effect(1) By cavity displacement in vertical plane: useful for heavy ions,

accepted as a baseline design for the ISAC-II(2) By reshaping of the drift tubes: universal far all regimes.


-1.2

-0.8

-0.4

0

0.4

0.05 0.15 0.25 0.35

E

Def

lect

ion

angl

e (m

rad)

Without compensation

With compensation

Beam steering in QWR


Defocusing asymmetry in 106 MHz QW SRF resonator, EEG=0.085, q/A=1

-0.5

0

0.5

1

1.5

2

2.5

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

beta

Def

ocus

ing

angl

e (m

rad)

x=1mm

(-y-0+y2_)/2

Defocusing field asymmetry in DT SRF cavities*

*Details will be presented in EPAC2002 by B. Laxdal, P.N. Ostroumov and M. Pasini.

Beam


Defocusing angles in 57.5 MHz QW SRF resonator, EEG=0.062, q/A=1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

beta

Def

ocus

ing

angl

e (m

rad)

x=1mm

(y1_75mm-y-0_25mm)/2

Defocusing field symmetry in DT SRF cavities


QUADRUPOLE COMPONENT OF TRANSVERSERF ELECTRIC FIELD

0 5 10 15 20 25

-50000

0

50000

EI

quad

Er

quad

Er

axial

Er,E

I , V/cm r=2/3R

a

z ,cm

Harmonic analysis of the electric field along the axis of HWR in cylindrical coordinates

)2sin(21

)2cos(22

)2cos(

22

2020

222

220

I

I

I

I rAr

V

rE

rArAr

VE

rArAV

r

� w

w�

� w

w�

��


Longitudinal phase space, W=199 keV/u

Input beam, 2 charge states:100% of particles2.4 S keV/u-nsec0.5 S mm-mrad


0

0.25

0.5

0.75

1

1.25

1.5

0 10 20 30 40 50 60Distance (m)

Bea

m s

ize

(cm

)

Yrms

Ymax

Yerror

Cavity aperture

Beam envelopes along the prestripper section


0

5

10

15

20

1 1.2 1.4 1.6 1.8 2 2.2 2.4

Emittance growth factor

N/N

0 (%

)

RMS emittance growth of two-charge state uranium beam in themisaligned focusing channel of low-E linac with the steering correction.


Compact 9 Tesla SC Magnet Assembly

-2

0

2

4

6

8

10

-30 -20 -10 0 10 20 30

Distance (cm)

Mag

netic

Fie

ld (

T)

Higher current in the bucking coils

Lower current in the bucking coils

Focusing by SC solenoids:- proven technology with SC resonators; - multi-q beam is less sensitive to mismatched conditions;- the fringing fields can be suppressed by bucking coils;- alignment of the solenoids should be easier;- beam is less sensitive to solenoid misalignments.


1

2

3

4

5

0 10 20 30 40 50 60

Distance (m)

Long

itudi

nal r

ms

emitt

ance

(4S

keV

/u-n

sec)

q=28.5

q=28 and 29

Longitudinal emittance along the prestripper linac


-2.00E-04

0.00E+00

2.00E-04

-1.20E-01 0.00E+00 1.20E-01

phase (rad)

' 'W

/W (

%)

q=69 q=73

Particle trajectories in the longitudinal phase space

Synchronous phase


Longitudinal phase space, W=9.4 MeV/u

10 S keV/u-nsec


29 S keV/u-nsec

Phase space plots of 5 charge state uranium beam at the location of second stripper linac

85 MeV/u


-20 -10 0 10 20-0.50

-0.25

0.00

0.25

0.50

Ene

rgy

Spr

ead

(%)

Phase (deg of 805 MHz)

Phase space plots of four charge state uranium beam at the exit of the driver linac. Includes all rf field errors and multiplicity

of charge states throughout whole SC Linac


-1 0 1 2 3 4 5 6 7 8-1

0

1

2

3

4

5

6

7

8

Dis

tanc

e (m

)

Distance (m)

Q1,2

SRF

B8

B7

B6

B5B

4B3

B2

B1

Q8Q

3

Q9,10

Q6,7

Q4,5

0 2 4 6 8 10 12 14 16 18

-40

-30

-20

-10

0

10

20

30

40

q=90q=88-92

B7,8

B5,6SRFB

3,4B

1,2

Q9,10

Q8

Q6,7

Q4,5

Q3

Q1,2

y (mm)

x (mm)

s (m)

System for selecting multiple q state beams through a 180° bend at 80 MeV/u.


-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-6-5-4-3-2-10123456 q=91

q=90 q=89

l (mm)

GK (x10-3)

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3 q=91 q=90 q=89

y (mm)

b (mrad)

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3 q=91 q=90 q=89

x (mm)

a (mrad)

-15 -10 -5 0 5 10 150

2

4

88899091Z=92

x ,mm


Main sources of longitudinal emittance growth:- Multiplicity of charge state (different synchronous

phase, frequency jumps);- Random errors of rf field;- Passage through the stripper;- Coupling of r-z motion in the RFQ.

Main sources of transverse emittance growth:

- Coherent oscillations of multi-q beams due to the misalignment of focusing elements;

- Mismatch of multi-q beam;- Passage through the stripper;- Higher-order distortions in the post-stripper transport

systems.


RMS emittance growth of multi-q uranium beamin the driver Linac

1.831.05High-E

12.34.4TOTAL

1.041.12Stripper 2

5.241.95Medium-E

1.11.06Stripper 1

1.121.80Low-E

LongitudinalTransverse


Triple Spoke vs Elliptical

MS=-30o MS=-25o

BEAM

3.98 m

BEAM

5.80 m


Triple Spoke vs Elliptical

ECL TSCL Number of cavity types 3 2 Peak surface field (MV/m) 27.5 28. Frequency (MHz) 805 345 Total number of cavities 188 140 Number of cryostats (focusing periods) 47 38 Length in the tunnel (m) 260 200 Operating temperature (qK) 2.1 4.5 Synchronous phase (deg) -30 -25 Longitudinal acceptance (keV/u-nsec) 60 280 Aperture diameter (mm) 80 40 Transverse normalized acceptance (S mm-mrad) 70 35


0

0.4

0.8

1.2

1.6

2

0 50 100 150 200

Distance (m)

Bea

m s

ize

(cm

)

rms size

Maximum size

Cavity aperture

0

5

10

15

20

25

0 50 100 150 200

Distance (m)

Pha

se (

deg)

rms width

(full width)/2

Synchronous phase


12

11

10

5 9

1 2 3 4 6 7 8

6.9 –20 MeV/u

0.68 –2.0 MeV/u

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Particletrajectories in the Hybrid RFQ


Summary

• The technique of multi-q beam acceleration and transport is understood well;

• A detailed design has been developed for the focusing-accelerating lattice of the RIA accelerators;

• Substantial progress has been made in beam dynamics studies in the SRF DTL;

• Detailed BD studies in the driver linac taking into account errors and misalignments have been carried out;

• Several design concepts related to the driver linac have been successfully tested on the existing SC linac ATLAS.

heavy-ion beam dynamics in the ria accelerators and ...€¦ · p.n. ostroumov, “heavy-ion beam...

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