Impedance simulations of the LHC beam screen including the weld

Preliminary analysis

C. Zannini, E. Metral, G. Rumolo, B. Salvant

Model studiedLHC design as it is built and installed

weld

In this step we are only interested to understand the effect of the weld .

Model studied

a

ba=46.4 mmb=36.8 mmw=2 mmL=1m

w

L

Comparing dipolar terms

-20 -15 -10 -5 0 5 10 15 20-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

W[V

/fC]

x[mm]

noweld weld weld2

-10 -5 0 5 10-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

W[V

/fC]

x[mm]

noweld weld weld2

xdip weld 2*xdip_noweldxdip 2weld 2*xdip_weld

xbayxbayxbay

weld

weld

noweld

332

22

11

)mm*fC/(V.bfC/Va

)mm*fC/(V.bfC/V.a)mm*fC/(V.bfC/Va

027000150090

00700

33

22

11

Impedance simulations• With CST Particle Studio we obtain the dipolar wake potential at different

beam positions• Via CST FFT for each wake potential we obtain the real and imaginary

dipolar impedance and then the real and the imaginary dipolar impedance versus beam position

• The dipolar components of the impedance is the slope of these curves in the linear region

• We are interested specially at the impedance at 40MHz and 8KHz

• β=1 40MHz 7.5m 25ns

• β=1 8KHz 32.5Km 0.125ms

• To have impedance simulations at these frequency we need to reach these frequency (simulating a sufficiently long wake) and to have vanish wake (to make a good FFT).

The scaling technique• If we use the real dimension of the beam-screen it is

impossible to go down in frequency until 8KHz. • To keep the same electromagnetic configuration we can

scale by the same factor all the geometrical parameters and the skin depth.

ExampleParameters: Scaled parameters:S=1 mm k=1000 S=1000 mmσ=1e9 S/m σ=1e3 S/m

The scaling technique work very well: Comparing 20Km (k=1000) 100Km (k=10000)1000Km (k=100000)

Comparing with and without weld dipolar impedance in the range 1KHz-50MHz calculating for a displacement of 5mm

Comparing with and without weld dipolar component of the impedance in the range 1KHz-50MHz calculating from the slope in the range 0-5mm

Obtaining dipolar components at 40MHz

xbaZxbaZxbaZ

weldIm

weldRe

noweldImRe

33

22

11

mm/Ohm.bOhm.a

mm/Ohm.bOhm.amm/Ohm.,.bOhma

00378002300003560022300018700017800

33

22

11

Real dipolar impedance with weld 2*Real dipolar impedance without weldImaginary dipolar impedance with weld 2* Imaginary dipolar impedance without weld

-2.5 0.0 2.5 5.0 7.5

0.00

0.02

0.04

0.06

f=40MHz

Z [O

hm]

x [mm]

Rew Imw Renw Imnw

Obtaining dipolar components at 8KHz

Real dipolar impedance with weld 1.2*Real dipolar impedance without weldImaginary dipolar impedance with weld 1.5* Imaginary dipolar impedance without weld

xbaZxbaZxbaZ

weldIm

weldRe

noweldImRe

33

22

11

mm/Ohm.bOhm.a

mm/Ohm.bOhm.amm/Ohm.bOhm.a

191082501450261012500000

33

22

11

-2.5 0.0 2.5 5.0 7.5-1

0

1

2

3

f=8kHz

Z [O

hm]

x [mm]

Rew Imw Renw Imnw

Conclusions

• At the frequency of 8KHz a weld of 2mm introduces a factor 1.2 on the dipolar real impedance and a factor 1.5 on the dipolar imaginary impedance.

• At 40MHz a weld of 2mm introduces a factor 2 in the dipolar real and imaginary impedance

Future step

• To calculate the quadrupolar component of the impedance.