scaling laws and field quality · e levichev -- scaling laws and field quality wiggler field...

E Levichev -- Scaling Laws and Field Quality

SCALING LAWS AND FIELD QUALITYSCALING LAWS AND FIELD QUALITY

E.LevichevE.Levichev


Content

- Task definition

- CLIC damping wiggler parameters

- Field parameters vs. magnet parameters

- Nonlinear feature of the wiggler magnetic field


Task definition

(1) Scaling laws depend on the wiggler type (permanent magnet, superconducting, electromagnet, etc.), design, etc.

(2) We restricted our self with the permanent magnet damping wiggler for the CLIC damping ring and study the following parameters of the device:

♦ Field amplitude♦ Transverse field distribution♦ Longitudinal field distribution

as a function of wiggler’s

♦ Gap♦ Period length♦ Pole (magnet) width


CLIC damping wiggler parameters

Period: 10 cm 12 cm 14 cmGap: 12 mm 14 mm 16 mmPole width: 50 mm 60 mm 60 mmLength: 2 m Field amplitude: 1.7 T 1.8 T 1.69 TField quality @ ±1 cm: 10-3

Total length: 160 m Total radiation power: 1.7 MV at 1 A current


CLIC damping wiggler configuration

Permendure pole.

Permanent magnet.

Iron yoke.

Wiggler gap.

Nonmagnetic spacer.

Beam direction

Length (cm)

Zero magnetic potential.


CLIC damping wiggler field distribution

Longitudinal field distribution (kG, cm).

Transverse field distribution (kG, cm).

Bmax = 17.1 kG

∆B/B < 5x10-3 at 1 cm.


Peak field amplitude vs. pole gap

Bmax as a function of gap

10

12

14

16

18

20

22

10 12 14 16 18 20

gap (mm)

Bm

ax (

kG)

per=14 cm

per=12 cm

per=10 cm

⋅−∝

w

gB

λπ

expmax

- for barely permanent magnet devices (M.N.Smolyakov, PRST Vol.4, 040701 (2001))

Peak field is linear for reasonably small change of pole gap.


Peak field amplitude vs. period length

Peak field tends to be saturated with increasing of the period length.

Bm vs. period length

y = -0.2047x2 + 5.9793x - 22.213

10

12

14

16

18

20

22

24

8 9 10 11 12 13 14 15

Bm (kG)

Per

iod

len

gth

(cm

)


Peak field amplitude vs. pole width

CLIC wig gap=12 mm per=10 cm

16.5

17

17.5

18

18.5

19

4 4.5 5 5.5 6 6.5 7

Pole width (cm)

Bm

ax (

kG)

Peak field has to be compromised with acceptable transverse field quality.

CLIC wig gap=12mm per=10 cm

-3

-2.5

-2

-1.5

-1

-0.5

04 4.5 5 5.5 6 6.5 7

Pole width (cm)

2B"(

kG/c

m2)


Field quality vs. pole width


-10

-8

-6

-4

-2

0

2

0 0.5 1 1.5 2

X (cm)

1000

*dB

/B

4 cm5 cm6 cm7 cm

By choosing of the proper pole size and shimming rather good transverse field quality can be achieved.

-0.5-0.057

-3.5-0.096

-32-0.455

--6.534

@ 2 cm@ 1 cm

1000×∆B/BPoleWidth(cm)


Longitudinal distribution of magnetic field


-25

-20

-15

-10

-5

0

5

10

15

20

25

0 2 4 6 8 10 12

L (cm)

By

(kG

)

gap=12 mm l=12 cmgap=13 mm l=12 cmgap=14 mm l=12 cm

∑∝k

kBi 22

Damping integral is proportional to the quadratic sum of longitudinal field harmonics

0.4%A9

2%A7

5%A5

7%A3

100%A1

Relative harmonics content


Wiggler field quality

Pole width and shims can provide rather good quality of the transverse magnetic field in the permanent magnet systems (~5x10-4).

In real life the field quality is defined by

? Magnetic material characteristics.

? Pole material characteristics and pole saturation.

? Quality of manufacture and assembling (especially gap manufacture tolerance).


Wiggler nonlinearity

3)(241 ysnH =∆ ( )

2

28

ww

w

BB

lnρλ

πρλ

=⋅′′′

=⋅

The main effect is due to the wiggler magnets edge field producing strong vertical cubic nonlinearity.

( ) yww

ywyy J

LJ ⋅

⋅=∆ 22

2

ρλ

βπν

?

and relevant amplitude-dependent tune shift is given by


Example of wiggler reduction of dynamic aperture

Wiggler DA simulation: 3 GeV light source, single 2.4-m 3.5 T wiggler with period length 6.4 cm.

Wiggler model with vertical 1D octupole.

Wiggler model with vertical 1D octupole and sextupoles.


Conclusions

♦ Scaling laws are useful to select wigglers parameters. In real life the wiggler field behaviour depends on wiggler type, material features, saturation, etc. so it seems for every particular case scaling laws can be found by simulation only.

♦ In principle rather high quality of the wiggler transverse field can be achieved. However to take into account influence of production tolerance, material characteristics, etc. small (2-3 periods) prototype development and measurement is desirable.

♦ The main nonlinear component of the wiggler field is the vertical 1D octupole but its effect might be minimized by regular octupole magnets placed at azimuth with high beta-y and low beta-x value.

scaling laws and field quality · e levichev -- scaling laws and field quality wiggler field...

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