Activities on the Orbit Feedback Systemfor the Super-SOR Light Source

SRL-ISSP, University of TokyoNorio Nakamura

3rd International Workshop on Beam Orbit Stabilization - IWBS2004, Hotel Kirchbühl, Grindelwald, Switzerland, December 6-10, 2004

Super-SOR Project

• The Super-SOR project aims to construct a 3rd-generation VUV and soft X-ray synchrotron radiation source in Japan.• Proposed site is in the new campus of the University of Tokyo (Kashiwa campus).

Plan View of Super SOR Light Source

ICCR&Four Centers

New Graduate School

Super SOR(planned)

ISSP

Super-SOR Accelerators

• Designed to meet top-up injection• Pre-Injector Linac: E=200MeV, Single- and Multi-bunch modes• Booster synchrotron : E=0.2-1.8GeV, x=50-100 nm rad Variable momentum compaction (=0.003-0.01) • Storage ring : E=1.8GeV, x=7-8 nm rad, I=400mA

1.8GeV Storage Ring

200MeV LinacÅ@

93.7m

81.1m

35m22m

1.8GeV Synchrotron

circumference: 280.55m

Å@

Super-SOR Storage Ring

• 14 DBA cells with 2 x 17m and 12 x 6.2m long straight sections• Flexible optics with high- and low-beta straight sections• Vertical beam size at insertion devices : y = 10 - 30 m

(a) High-beta mode

(b) Hybrid mode

Optics of half ring

Design Goal of Orbit Feedback System

• Fast and High-resolution Beam Position Measurement　 Resolution < 1 m @ sampling rate > 2 kHz

• Wide Frequency Range 　　 BW > 100Hz ( Noise attenuation: < -20dB @ 10Hz )

• High Position Stability at Insertion Devices　 New orbit correction scheme

　 Submicron Stability

Outline of Orbit Feedback System

140 BPM(10 BPM/cell)

70 FS(5 FS/cell)

Centralcontroller

Ring Control System

Localcontroller

Localcontroller

Localcontroller

Localcontroller

Localcontroller

Localcontroller

Localcontroller

Localcontroller

Localcontroller

Localcontroller

Localcontroller

Localcontroller

Localcontroller

Localcontroller

BPM

FS

FSFS

FS

FS

FSFS

FS

FS

FS

FS

FS

FS

FS

BPM

BPM

BPM

BPM

BPM

BPM

BPMBPM

BPM

BPM

BPM

BPM

BPM

Ethernet

Fast Data Transfer System(by Shared memory etc.)

FS:Fast Steering MagnetBPM:Beam Position Monitor

New Orbit Correction Scheme

Vector of residual COD:

(1)y : beam position before correction (M): kick angle of steering magnet (N)R : Response matrix (M x N)

Constraint conditions:

(2)

Minimize the norm of under the constraint conditions by introducing the following function of S (Lagrange’s method of indeterminate multipliers).

(3)

Set derivatives of the function S with respect to and to zero.

(4)(5)

Solution of the above equations:

(6)

where

(7) (8)

(9)

Definition of the matrix A-1 :

　　 (NV N), (10)

vi : i-th eigenvector of the matrix Ai: i-th eigenvalue of the matrix A

For i~0, 1/i in the matrix A-1 is replaced with zero to avoid very large kick angles. The condition of NV NC is required for the existence of the inverse matrix P-1.

If z is taken as the electron (or photon) beam positions measured at arbitrarily selected BPMs (or photon BPM) and C as the corresponding response matrix, the beam positions at the selected BPMs are fixed at zero by this correction. For the electron beam and BPMs, Eq. (6) can be rewritten in a simplified form.

(11)

€

CiT ⋅θ + zi = 0 ( i = 1,LL , NC )

€

S =1

2( Rθ + y )2 + μ i (Ci

T

i

Nc∑ θ + zi )

€

R T Rr

θ + R T r y + C

r μ = 0

€

C Tr

θ +r z = 0

€

r= B

r y − D

r z

€

B= (− A−1 + A−1CP −1C T A−1 )R T

€

D = A−1CP −1

€

A= R T R

€

P = C T A−1C

€

A−1 =r v i

r v i

T

λ ii=1

Nv∑

€

r= B* y

Principle of eigenvector method with constraints (call “EVC” or “SVDC” here)

€

r≡ R

r θ +

r y

See Proceedings of EPAC98 and PAC99

Orbit Correction Simulation

Simulations confirm that the global and local corrections are compatible in the new method.

(1) COD sources are all the quadrupole magnets with vertical position errors of =50 m.(2) Constraint conditions are that positions at 28 BPMs on both sides of 14 long straight sections are zero.(3) 140 BPMs and 70 fast steering magnets are used for correction simulations.

-6

-4

-2

0

2

4

6

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 50 100 150 200 250

Number of eigenvectors = 50

Before CorrectionAfter Correction

Length [m]

0.6

0.8

1

1.2

1.4

30 40 50 60 70

Max AngleRMS angle

Number of eigenvectors

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 10 20 30 40 50 60 70

All BPMs

without constraintswith constraints

Number of eigenvectors

Orbit Correction Study at PF ring (1)

Experimental study of the new orbit correction method at PF ring

Outline of correction study1. Vertical COD is artificially generate

d by each vertical dipole and then several times corrected by 28 fast steering magnets using eigenvector methods with and without constraints. The number of the used eigenvectors is 14.

2. Constraint conditions are that beam positions at 4 BPMs on both sides of the two long straight sections are zero.

3. Measured response function is used.4. RMS CODs for the constrained 4 BP

Ms and for all the BPMs are obtained for the two kinds of correction methods.

VD12FS09 FS24

VD33BPM16BPM17

BPM50BPM49

PF ring (2.5GeV) 65 BPMs 4 constrained BPMs (BPM01,41,42,65) 28 Fast Steering Magnets(FSs) 42 Vertical Dipoles(VDs)

Orbit Correction Study at PF ring (2)Example of vertical COD before and after correction

-40

-20

0

20

40

-400

-200

0

200

400

0 10 20 30 40 50 60

with constraints (VD25)

after correctionbefore correction

.BPM No

-40

-20

0

20

40

-400

-200

0

200

400

0 10 20 30 40 50 60

without constraints (VD25)

after correctionbefore correction

.BPM No

Orbit Correction Study at PF ring (3)

1 m

Local correction performance of the new method is a sub-micron level !

Global correction performances of the two methods are almost the same.(The global correction performance for VD 40 - VD05 can easily be compensated by adding 1 or 2 steering magnets in the section.)

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40

Constrained 4 BPMs with constraintswithout constraints

. No of VD used for COD generation

0.01

0.1

1

10

100

0 5 10 15 20 25 30 35 40

Constrained 4 BPMs with constraintswithout constraints

. No of VD used for COD generation

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40

All BPM with constraintswithout constraints

. No of VD used for COD generation

0.01

0.1

1

10

100

0 5 10 15 20 25 30 35 40

All BPM

with constraintswithout constraints

. No of VD used for COD generation

1 m

Linear plot Log plot

Linear plot Log plot

Orbit Correction Study at PF-AR Ring (1)

Experimental study of the new orbit correction method at PF-AR ring

Outline of correction study1. Vertical COD is artificially genera

ted by each vertical dipole (VD) and several times corrected by the other 78 VDs using eigenvector methods with and without constraints. The number of the used eigenvectors are 40.

2. Constraint conditions are that positions at 6 BPMs on both sides of the three long straight sections are zero.

3. Measured response matrix is used.4. RMS CODs for the 6 BPMs and al

l the BPMs are obtained for the two kinds of correction methods.

VD20

VD19

VD61

VD62

VD60

VD59

VD21

VD22

BPM19

BPM20

BPM21

BPM22

BPM23 BPM61

BPM62

BPM63

BPM64

BPM65

PF-AR ring (6.5GeV) 83 BPMs (total) 6 constrained BPMs (BPM25,26,36,37,41,42) 79 Vertical Dipoles(VDs)

Orbit Correction Study at PF-AR Ring (2)

BPMResolution(~8m)

BPMResolution(~8m)

Local correction performance of the new method is better than BPM resolution.

Global correction performances of the two methods are almost the same.

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80

Constrained 6 BPMs correction with constraintscorrection without constraints

. No of VD used for COD generation

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80

All BPMs correction with constraintscorrection without constraints

. No of VD used for COD generation

BPM System (1)

Example of BPM location

Prototype of BPM support

BPMBellows

Absorber flange

SR

Cooling water

• BPM block (SUS) with SMA feedthroughs • Fixed on the girder by BPM support• Reduction of vacuum chamber stress by bellows • Protection from SR irradiation by absorber

Prototype of BPM block

BPM System (2)

Design of BPM Electronics using Multiplexing & Heterodyne method

ATT

ATT

ATT

ATT

SW BPF1

RFAMP1

BPF2

RFAMP2

ATT BPF3

IFAMP2DividerMIX1 MIX2

LPF

AMP

-3dB -3.5dB

-15dB +19.5dBNF=3dB

+19.5dBNF=3dB

0dB ~ -30dB +19dB

NF=6dB

BPMLO

-8dB

+40dB100kHz

-8dBLimit AMP

Bypass-0.5dB Bypass

-0.5dBBypass-0.5dB

fc=500MHz

• S/N is more than 90dB at 200mA ( < 0.3m in resolution).

• Single-bunch operation is also considered.

• BPM signals can be switched to another system for turn-by-turn measurement.

PROBLEMS

• Position error by coherent synchrotron oscillations

• Cost effectiveness

Another type of BPM electronics is also under consideration.

Fast Steering Magnet System (1)

Prototype of Fast Steering MagnetPower Supply Models for Fast Steering Magnets Upper : Switching type Lower : Linear amp. type

• Fast steering magnet is made of 0.5-mm silicon steel laminations.• Two types of power supply (linear amp. and switching types) are tested.• Linear amp. type is superior to switching type in ripple noise.

Fast Steering Magnet System (2)

Steering magnet + Bellows ductMeasured frequency response

• All the fast steering magnets are installed on the RF-shielded bellows ducts.• Bellows duct is made of stainless steel and RF shields of 0.4mm-thick BeCu. • Effects of bellows on frequency response are negligibly small.

-5

-4

-3

-2

-1

0

1

2

-100

-80

-60

-40

-20

0

20

40

1 10 100 1000

Gain(without bellows)Gain(with bellows)

Phase(without bellows)Phase(with bellows)

Frequency[Hz]

Feedback Control System (1)

Local controller x 2 (prototype model) Block diagram of local controller

• Target feedback period Ts < 0.5ms (sampling rate > 2 kHz)• 140 BPM data are shared with all the controllers by a shared memory network.• CPU board computes beam positions at 10 BPMs and coil currents of 5 FSs.

Feedback Control System (2)

Measurement result of consumed time for each feedback process

Feedback period of less than 0.2 ms can be achieved.

Tim

e[s

ec]

Feedback process

BP

Mread

ing P

I con

trol

Position

calcu

lation M

atrixcalcu

lation D

ata tran

sfer T

otalS

teeringsettin

g

Noise Attenuation

-60

-50

-40

-30

-20

-10

0

10

1 10 100 1000

Gain(Ts=0.5ms)Gain(Ts=0.2ms)

Frequency(Hz)

Closed loop gain

Frequency Bandwidth > 100Hz

Summary

• An orbit feedback system is planned for the Super-SOR project to suppress the brilliance reduction due to orbit drifts and vibrations. Final goal is sub-micron stability at the source points and at the experimental stations.

• A new orbit correction method, the eigenvector method with constraints (“EVC” or “SVDC”), can unite global and local orbit feedbacks and enhance the beam stability at insertion devices up to a sub-micron level. We will try to stabilize photon beams using this correction method and photon BPMs.

• Design and R&D of the BPM, fast steering and feedback control systems are in progress. The feedback system can achieve position resolution of less than 1m and the frequency bandwidth of more than 100 Hz.