Lattice design for PLS-II

Lattice design for PLS-II

9

^th

April 2009

Eun-San Kim

Introduction

 have designed the lattices of 5 to 7 nm emittances

 have calculated dynamic apertures with machine errors

 have performed lattice corrections with machine errors

 have investigated parameters for injection scheme

 Optimizations toward an engineering lattice have been performed.

One cell lattice

_{low b}

y

Major ring parameters

Energy 3.0 GeV

Emittance 6.4 nm (7.5nm with 20 IDs) Beam current 400 mA

Circumference 281.82 m Cell /structure 12 / DBA

Straight section 12x6.8m+12x3.1m Harmonic number 470

Bunch length 6.5 mm (6.1mm with 20 IDs) Energy spread 1.1E-3 (1.0E-3 with 20 IDs) RF voltage 3.6 MV

RF bucket height 2.53 % ( 2.23% with 20 IDs) Betatron tune 14.15/9.35

Major ring parameters

Dipole field (T) 1.45 (combined) Dipole length (m) 1.8

Critical energy dipole (keV) 8.7 Number of B/Q/S 24/120/120 Synchrotron tune 0.01

SR loss/turn, dipole (MeV) 1.0 (1.42 with 20 IDs) Momentum compac. factor 1.48E-3

Second order compac. factor 3.33E-3

Natural chromaticity -27.2/-25.7 RF frequency 500 MHz

Damping time (ms) 3.8/5.4/3.4 (3.0/3.9/2.32 with 20IDs) Damping partition number 1.4/1/1.6 (1.3/1/1.7 with 20IDs)

Magnet parameters

 Dipole (2 per cell)

B L=1.8 m k1= -4.45 T/m

 Quadrupole (10 per cell)

Q1 L=0.24 m B^/= -11.39 T/m Q2 L=0.35 m B^/=14.89 T/m Q3 L=0.24 m B^/= 12.02 T/m Q4 L=0.53 m B^/= 17.79 T/m Q5 L=0.35 m B^/= -10.86 T/m

 Sextupole (10 per cell)

S1 L=0.2 m B^//= -141.6 T/m² S2 L=0.2 m B^//= 280 T/m² S3 L=0.2 m B^//= 240.4 T/m² S4 L=0.2 m B^//= 402.3 T/m² S5 L=0.2 m B^//= -432.1 T/m²

Dynamic aperture

(with multipole errors)

Dipole

Systematic : B2/Bo=3.0E-3 B4/Bo = 1.88E-4 Random : B2/Bo = 1E-4

B3/Bo = 8E-5 B4/Bo = 1.88E-4 Quadrupole

Systematic : B5/B1=5.1E-5

Random B2/B1=3E-4 (skew) B2/B1=1.5E-4

B3/B1=3.6E-4 B5/B1=1.01E-4 Sextupole

Random Bo/B2=1.1E-4 B4/B2=4.5E-4

dp/p = -2%, 0%, 2% Synchrotron oscillation is included.

-30 -20 -10 0 10 20 30

0 5 10 15

Y (mm)

X (mm) Multipole errors

No error

Effects of 20 IDs

( Species of ID are not still determined) X-ray undulator (6EA)

Period : 2 cm Length : 2 m Field : 1.2 T Brilliance : 4E19 @ 2 keV

EPU6 (6 EA)

Period : 6cm Length : 4 m Field : 0.69 T Brilliance : 1E19 @ 0.8 keV

U7 (4EA)

Period : 7cm Length : 4m Field : 0.99T MPW (4EA)

Period : 14 cm Length : 2 m Field : 2 T

EPU6 EPU6 EPU6

EPU6

U7 U7

U7 U7

EPU6 EPU6

RF Injection

X-ray Und. X-ray Und.

X-ray Und. X-ray Und.

X-ray Und.

X-ray Und.

MPW MPW

MPW MPW

Insertion devices

6 EPU6, 4 U7, 6 X-ray und., 4 MPW

Dynamic aperture (with 20 IDs)

dp/p = -2%, 0%, 2% Synchrotron oscillation is included.

-30 -20 -10 0 10 20 30

0 3 6 9 12 15

Y(mm)

X(mm) 20 IDs

No error

-30 -20 -10 0 10 20 30 0

3 6 9 12 15

Y(mm)

X(mm)

machine errors+COD correction No error

Dynamic aperture

(with machine errors and COD correction)

Machine errors

Magnetic field error(rms) DK 5E-4 Qaud*

DK 5E-4 Bend*

DK 5E-4 Sext*

Rotation error (rms) DTHETA 0.2E-3 Quad*

DTHETA 0.2E-3 Sext*

DTHETA 0.2E-3 Bend*

Misalignment error(rms) DX 80 mm Quad*

DX 100 mm Sext*

DY 80 mm Quad*

DY 100 mm Sext*

DX 120 mm Bend*

DY 120 mm Bend*

Dynamic aperture

(with 20 IDs+machine errors and COD correction)

dp/p = -2%, 0%, 2% Synchrotron oscillation is included.

-30 -20 -10 0 10 20 30

0 3 6 9 12 15

Y(mm)

X(mm)

20IDs+machine errors+COD correction No error

Bare lattice

(without machine errors and 20 IDs)

Lattice distortions

(with machine errors and 20 IDs)

After COD correction

( with machine errors and 20 IDs )

CODx,y ~ 100 um rms

8BPM /8HC/8VC each cell

Sextupoles

are with HC and VC.

include matchings in beta-function, alpha function, dispersion function in LS and SS, and COD correction.

After lattice corrections

(with machine errors and 20 IDs)

Optics is well recovered to bare lattice.

0 20 40 60 80 100 120 140 -0.4

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Q5 Q3 Q2

Q1 Q4

K1=B'L/B

Number of quad.

K1 values of quad. in corrected lattice

possibility of the use of shunt coils

0 20 40 60 80 100 -0.6

-0.4 -0.2 0.0 0.2 0.4 0.6

Kick angle [mrad]

Number of horizontal corrector

0 20 40 60 80 100

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Kick angle [mrad]

Number of vertical corrector

Strength of correctors in corrected lattice

possibility of the re-use of present correctors

Beam trackings

in transverse phase space

x/sqrt(b_x) y/sqrt(b_y)

(ax+b xx')/sqrt(b x) (ax+b xy')/sqrt(b y)

Intervals of initial coordinates of particles are 10s_x and 10s_y.

120s_x ⁷⁰s_y

z/sqrt(b_z) (az+b zd)/sqrt(b z)

Beam trackings

in longitudinal phase space

Interval of initial coordinated of particles is dp/p=0.5%

dp/p=2%

Amplitude-dependent tune shift

0 20 40 60 80 100

0.0 0.1 0.2 0.3 0.4 0.5

Tune x,y

Beam size /s_x,y

horizontal vertical

Chromaticity correction

-0.04 -0.02 0.00 0.02 0.04 14.0

14.1 14.2 14.3 14.4 14.5

_x

_y

dp/p

 x

9.0 9.1 9.2 9.3 9.4 9.5

 y

x

x =0.02,

x

y= 0.01 after chromaticity correction

-0.04 -0.02 0.00 0.02 0.04

2 4 6 8 10

dp/p

bm b

x

bx

RF phase diagram

Main rf bucket second row rf-buckets Momentum compaction factor : 1.38E-3

Second order compaction factor : 3.69E-3

RF phase diagram

a₂=0 a₂=2x3.69E-3 a₂=3x3.69E-3

Dependence of rf bucket on 2^nd momentum compaction factor

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0

15 30 45 60 75 90

Lifetime (h)

Momentum acceptance

Touchek lifetime

1% coupling constant

Aperture acceptance required for injection

A_inj = (A²_x,max b(s)/b_x,max + (h_x(s)d)²)^1/2 ,(d=4%)

Required aperture at the location of maximum horizontal beta function is 28.5 mm.

Aperture required at injection point is 20.5 mm.

Horizontal required aperture acceptance of the ring

Momentum deviation : d=4%

Vertical required aperture acceptance of the ring

Momentum deviation : d=4%

Injection scheme for PLS-II

Horizontal phase space in injection point

15mm Bump height septum

PA= 22 mm

Stored beam Bumped stored beam

injected beam

X'

X

A=10mm

h =15 mm bump height

Layout of injection section

1.9m 0.6m 1.55m

K1 K2 K3 K4

Is 1.9m available for space of septum?

q=h/l=BL/B=9.67mrad B_kicker=0.16T

Injection beam tracking

Injection beam tracking

15 mm bump height

Initial particles : 1000, Machine errors + COD correction

Vertical half aperture : 4 mm

Linac emittance 50 nm rms energy spread 0.25 % rms

bunch length 100 ps rms

Time (~5ms)

Injection scheme

15 mm 12.4 mm

5.7 mm

Bumped stored beam Bump height

4-turn injection

1^st

2^nd

3^rd

4^th

Which one between 1-turn and 4-turn injection prefers to orbit stability during injection ?

Summary

 Designed lattice shows dynamic aperture

enough for beam injection and beam storage under the machine errors.

 Designed lattice shows flexible and well- tuning in optics matching.

 Discussions for engineering design will be continuously performed.

 Issues on impedance and nonlinear effects

due to narrow ID gaps may be a next subject.