Method of beam extraction from a synchrotron by the instrumentality of

multilayer Cu-Fe shield

Bondarenko Alexey

Classic method of beam extraction from a synchrotron

Beam trajectory after increase of magnetic field in pulsed magnets and activation of the kicker

Beam trajectory after increase of magnetic field in pulsed magnets

Unperturbed beam orbit

Septum-magnet

Dipole&

B B

B B

Type of septum-magnets• Lambertson septum. Magnetic field is perpendicular to septum sheet

which consists of ferromagnetic material (typically iron).

• Pulse septum. Magnetic field is parallel to septum sheet which consists of high-conductivity material (typically copper).

beam before the kicker activation

copper

beam position after the kicker activation

electric steel

B

beam before the kicker activation

electric steel

beam position after the kicker activationB

coil

Method of beam extraction by the instrumentality of magnetic shield

Beam trajectory after increase of magnetic field in the chicane and activation of the kicker

Beam trajectory after increase of magnetic field in the chicane

Unperturbed beam orbit

Dipole&

Magnetic shield

B B

B B

Main idea: Perturbation of pulse external magnetic field by multilayer Cu-Fe shield can

be significantly reduced

Fe Cu Cu-Fe

Field perturbation vs. external magnetic field

Slow rise ofexternalmagneticfield B0(t)

There is B0(t) forwhich field

perturbation isminimal

Fast rise ofB0(t)

Necessary condition of minimal field perturbation

2R

In optimal case:

(t) is a flux through a shield wall per unit of length

RtBt 2)()(2 00

Shielding equation

t

ArotArot

0

1)( μ

.2,

11

,

,

Fe

Fei

i

i

ii

i

Fe

i

ii

i

CuCu

i

ii

hh

h

h

h

h

h

h

h

h

h

h

σhσ

A – vector potential– average conductivity– tensor of average relative permeability –permeability of free space

║ and ┴ are parallel and perpendicular to layers.

hCu – thickness of copper layershFe – thickness of iron layers

Estimation of 0(t)

t

AA

rr

Ar

rrzzz

02

2

2

11

20

20

22

2

2

4.0811

R

AA

R

A

rz

200 4.0

R

A

rR

A

In the neighborhood of

t

A

r

A

rzz

01

rR

rR

A

r

BHr

rrr

Ar

rrz

0

0 )(11

r – penetration depth of magnetic field

r

Az=A0

Az=0B

Magnetic field penetration into planar wall in case of linear rise of external field

E0

y

j0

y

H0

y

Bs – saturation field

Bs

y

c

scBE 0

00

tH

H0 – external field

scBEj 00

tcBctjH s2

00

sBc

0

sctBt )(0

tR

Bt s

20

0 σ)(B

RtBt 2)()(2 00

RtctBs 22

20 σ

αR

Bs

Estimation of B0(t)

Numerical simulation of magnetic field penetration into shield wall

The flux flowing through the multilayer copper–iron shield wall per unit oflength depending on time and rise rate of external magnetic field.

0 0.5 1 1.5 2 2.5t, m s

0

0.001

0.002

0.003

0.004

0.005

0.006

L

, T

·m

0.5 T per 1 .25 m s0.5 T per 1 .5 m s0.5 T per 1 .75 m s0.5 T per 2 m s0.5 T per 2 .25 m s0.5 T per 2 .5 m s

Numerical simulation of field perturbation vs. rise rate of external magnetic field

0.01 0.1 1 100.02 0.05 0.2 0.5 2 5

dB/dt, T /m s

0

20

40

60

80

100

120

140

160

180

200B

ma

x, m

T

elliptical Cu-Fe shield: outer half-axes 11 and 17 mm, external magnetic field increase linearly from 0 to 0.5 T

Measurement of magnetic field perturbation by Cu-Fe shield

Magnetic shield consists of 12 iron and 12 copper layers. Thickness of iron layer is 0.08 mm, thickness of copper layer is 0.1 mm.

5.5

Ø12

Ø19

40

40

Cu-Feshield

- core

- coil

A

A

A-A

100

200

search coil

— search coil— Cu-Fe shield

— dipole

Measurement of optimal rise rate of external magnetic field

2.5

B0

0.45 мс

B

t

B

B0

0.45 мс

B

t

B0

0.45 мс

B

t

Maximum of magnetic field perturbation vs. rise rate of external magnetic field

0 0.02 0.04 0.06 0.08 0.1 0.12B 0 , T

0

1

2

3

4

5

6

Bm

ax, m

T

B0 – field at 0.45 ms since the dipole is activated .

Optimal rise rate of external magnetic field is 0.108 T per 0.45 ms

Measurement of (B) in case of B<1.1 Т

channel 1 – voltage on coil, channel 3 – voltage on shunt (Rsh=0.4 Ω )

Parameters of toroidal coil:Average radius of core is 37,5 mmEffective area is 193 mm2

Coil is 113 turns

Ugen U1

U3

Rsh

Measurement of (B) in case of 2.3 T<B<2.9 T

channel 1 – signal from current sensor ACS754SCB-200channel 2 – signal from capacitance integrator(R=102.8 kΩ , С=0.195 µF )

Parameters of toroidal coil:Average radius of core is 20,5 mmEffective area is 33 mm2

Test coil is 40 turnsCurrent coil is 188 turns

L

Currentsensor

R

C

U1

U2

Ugen+

Ugen-

Magnetic permeability vs. magnetic induction was measurement

0

100

200

300

400

500

600

0 0,5 1 1,5 2 2,5 3B, T

μ

The distribution of the field perturbation near the magnetic shield in the dipole centre

x is the distance to the shield centre and t is the time since the dipole is activated

1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0x , m m

- 2

- 1

0

1

2

3

B, m

T

measurements numerical simulations

1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0x , m m

- 2

- 1

0

1

2

3

B, m

T

t= 5 0 µ st= 1 5 0 µ st= 2 5 0 µ st= 3 5 0 µ st= 4 5 0 µ s

The distribution of the field perturbation near the magnetic shield (40 mm from the dipole centre)

x is the distance to the shield centre and t is the time since the dipole is activated

1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0x , m m

- 5

- 4

- 3

- 2

- 1

0

1

2

B, m

T

1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0x , m m

- 5

- 4

- 3

- 2

- 1

0

1

2

B, m

T

t= 5 0 µ st= 1 5 0 µ st= 2 5 0 µ st= 3 5 0 µ st= 4 5 0 µ s

measurements numerical simulations

The distribution of the field perturbation near the magnetic shield (55 mm from the dipole centre)

x is the distance to the shield centre and t is the time since the dipole is activated

1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0x , m m

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

012

B, m

T

1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0x , m m

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

012

B, m

T

t= 5 0 µ st= 1 5 0 µ st= 2 5 0 µ st= 3 5 0 µ st= 4 5 0 µ s

measurements numerical simulations

Project of 2.2 GeV booster

Lattes functions of a booster half-ring

Parameters of extraction kicker:Voltage 50 kVDistance between plates 27 mmAngle 1.7 mrad

Project of extraction chicane

• vertical rms beam size is about 0.4 mm• horizontal rms beam size is 2.6 mm• βx=10 m• βy=20 m• Trajectory shift by kicker 20 mm

2.1°80

74

480

33

0

370

laminated electrical steel

Beam trajectory after increase of magnetic field in the chicaneUnperturbed beam orbit

Beam trajectory after increase of magnetic field in the chicane and activation of the kicker

480

Field perturbation by Cu-Fe shield

electrical steelcopper

12 20

24

32

ms

tTB

5.145.0

y - the distance to the shield centre B – field perturbation

1 0 1 5 2 0 2 5 3 0 3 5 4 0y , m m

0

5

10

15

20

B, m

T t= 0 .3 m st= 0 .6 m st= 0 .9 m st= 1 .2 m st= 1 .5 m s

K0

0 0.3 0.6 0.9 1.2 1.5t, m s

-0 .1

0

0.1

0.2

0.3

K0,

mra

d

213.072

20103.02

y22

30

1 mm

marctg

Karctg

K0 leads to orbit shift

K1

0 0.3 0.6 0.9 1.2 1.5t, m s

0

0.002

0.004

0.006

0.008

0.01K1,

m-1

015.04

2001.0

4

008.04

1001.0

41

1

11

mmKQ

mmKQ

yy

xxBetatron frequencies shift

K2

0 0.3 0.6 0.9 1.2 1.5t , m s

- 5

- 4

- 3

- 2

- 1

0K2,

m-2

202.022

2054.02

222

22

31

ммммK yy

1) sextupole resonances

3y=22x+y =22) additional chromatism,

maximum dispersion in chicane D≈5cm

4.04

20505.0

4

K 22

mmmD

Field perturbation by vacuum chambers

Time of field rise is 1.5 ms. In case of cylindrical vacuum chamber field perturbation is minimal because:

• Walls of cylindrical vacuum chamber can be made thinner.

• Field perturbation in cylindrical vacuum chamber by homogenous magnetic field is homogenous. Higher multipoles are results of image the vacuum chamber in magnet gap.

Comparison with other extraction system from booster

HIGS Booster in Duke University, 1.2 GeV, vertical extraction, Lambertson septum

K0 K1 K2

0 0.02 m-1 4 m-2

Booster of SPEAR Storage Ring in Stanford Synchrotron Radiation

Laboratory, 3.5 GeV, horizontal extraction, pulse Lambertson septum.

K0 K1 K2

0.2 mrad 0.005 m-1 ?

Project of extraction system 2.2 GeV.

K0 K1 K2

0.3 mrad 0.01 m-1 5 m-2

Numerical simulation of beam extraction

Beam loss in % depends on betatron phase incursion per one turn

μy/2π

μx/2π

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.0

0.1

0.2

0.3

0.4

0.00

0.05

0.10

0.20

0.30

0.40

0.50

Conclusion

• It was shown that in case of external magnetic field linear rise the rate of magnetic flux penetration into multilayer copper-iron shield wall is constant. This effect can be used for minimization of magnetic field perturbation by multilayer copper-iron shield.

• The prototype of multilayer copper-iron shield was made. Measurement and numerical simulation of magnetic field perturbation by shield were performed. The measurement confirms correctness of method and model which are used for simulation of field perturbation.

• The numerical simulation and analytical estimation of beam dynamics under the influence of field perturbation by multi-layer Cu-Fe shield prove possibility of using the magnetic shield for extraction from synchrotron.

Particle coordinates transformation per one turn

),,(cossin

),,(cossin

,sincos

,sincos

111

111

1

1

nnynyynn

nnxnxxnn

yynynn

xxnxnn

yxyyyy

yxxxxx

yyy

xxx

Calculation of field perturbation by vacuum

chambers using image method.

electrical steel

coil

190

115

y

Field perturbation in vacuum chambers

y – the distance to the centre of vacuum chamber

diameter is 110 mm, thickness is 1mm, located at in first and second dipole

diameter is 75 mm, thickness is 1,5 mm, located at in third and fourth dipole

-0 .06 -0.04 -0.02 0 0.02 0.04 0.06y , m

-0 .029

-0.028

-0.027

-0.026

-0.025

-0.024

B, Ò

-0 .04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04y , m

-0 .025

-0.024

-0.023

-0.022

B,T

K0 by vacuum chambers

0 0.3 0.6 0.9 1.2 1.5t, m s

0

0.01

0.02

0.03

0.04

K0,

mra

d

K1 by vacuum chambers

0 0.3 0.6 0.9 1.2 1.5t, m s

-0 .0025

-0.002

-0.0015

-0.001

-0.0005

0

K1,

m-1