Resistive Effects in Ceramic Kicker Chamber.Roughness Effects in Undulator Chamber.

Andranik Tsakanian,

Uni Hamburg

DESY, 16 April 2007

Topics

• Impedance Structure Investigation for Ceramic Kicker Vacuum

Chamber with metallic coats.

• Resistive and Geometrical Wakes.

• Influence of Surface Roughness in Undulator Chamber on

the Beam.

DESY, 16 April 2007

DESY, 16 April 2007

Impedance Structure Investigation of Ceramic Kicker Vacuum

Chamber with Metallic Coats.

M. Ivanyan, V. Tsakanov, Phys. Rev. ST-AB, 2004

kU

jZkZ

0

342334233443

342334233443

03

3222 2

aRaRaSaR

aRaRaSaRaaU

- combination of Bessel functions.SSRR ,,,

Single layer cylindrical tube

aKbIaIbK

aKbIaIbKaaU

0000

1010

0

2 2

Longitudinal Impedance. Monopole term.

ii j0 ii j 0

1a/ ii

4433

4433

30

32 12

dthdth

dthdthaaU

2/1

43

1

dctha

aU

0

2 2

Metallic type layers

Good approximation - the smallness of each layer skin depth with respect to the layer inner radius

Single layer tube

132 a

DESY, 16 April 2007

)()(

)()(12

433

433

30

32

dnkthjdth

dnkthdthjaaU

Ceramic type layers with metallic coats

Good approximation:

Actually for all the practical applications, the formula (*) is valid and well approximates the exact solution.

204 n 12

4 njk143 a

132 a

ldnkdtha

aU

ldnkdctha

aU

2)(2

)(2

43330

32

43330

32

ckj 03 kjc 03 Metallic layer

Ceramic layer

4

3

3

4

12 nn

Nl

*

DESY, 16 April 2007

Numerical Examples

Ceramic Kicker Vacuum chamber: Ceramic with Titanium-Stabilized High Gradient Steel (TSHGS) coats

m 0.9 -Lenght

m 0.01 - Radius

1-m 12-10 R/L - Resistance

m 0.7 - Thickness

-1-16 mΩ100.18946)(2.0841σ

TSHGS Parameters

Vacuum Chamber Parameters

DESY, 16 April 2007Parameters from T. Wohlenberg

DESY, 16 April 2007

Longitudinal Impedance Per Unit Length. Monopole term.

0 2 4 6 8 100

10

20

30

40

50Ceramic+TSHGSTSHGS finiteTSHGS infinitecopper

Longitudinal monopole impedance as function of dimensionless wave number for several cases of vacuum chamber material: 1. Ceramic with TSHGS coats. 2. TSHGS single layer tube with finite and infinite thickness. 3. Copper single layer tube.

0sk

s0 characteristic distance: mcas 4.63/231

02

0

2.5 2.5000000530.754

30.756

30.758

Ceramic+TSHGSTSHGS

1 1.5 2 2.530

35

40

45

50finiteinfinite

0ks

.

5 105

0 5 105

200

100

0

100

200

Ceramic+TSHGSTSHGS FiniteTSHGS infiniteCopperGauss

1 104

2 104

3 104

4 104

5 104

6 104

50

0

50

100

150

Ceramic+TSHGSTSHGS FiniteTSHGS infiniteCopper

Resistive Wall Wakes

Resistive wall longitudinal wake potentials of Gaussian bunch with for several cases of vacuum chamber material: 1. Ceramic with TSHGS coats. 2. TSHGS single layer tube with finite and infinite thickness. 3. Copper single layer tube.

mb 20

Ceramic+TSHGS TSHGS Copper

Loss Factor[kV / nC]

-108.43 -108.4 -26.29

Energy Spread [%] 0.288 0.288 0.12

GeVE 5.17

DESY, 16 April 2007

.

Geometrical Wakes

Geometrical longitudinal wake potentials of Gaussian bunch mb 20

Entrance Exit Total

Loss Factor[kV / nC]

0.36 -462.39 -462.1

Energy Spread [%] 1.12*10^(-3) 1.057 1.058

GeVE 5.17

DESY, 16 April 2007

mma 102 mma 251

mL 9.0

5 105

0 5 105

600

400

200

0

200

TotalGaussEntranceExit

.

Surface Roughness in Undulator Section

DESY, 16 April 2007

mm

R.m.s. distortion m568.0

0 200 400 600 8006

4

2

0

2

4CorugatedIdeal

0 200 400 6001

0.5

0

0.5

1CorugatedIdeal

Measurement data from T. Wohlenberg

.

DESY, 16 April 2007

1

0

( ) ( )( ) 1

2 2s sZ ZR

Z iR c Z

( ) ( ) ( )Ls s sZ Z Z

( )( )s

iZ

( )LsZ i L

G.V.Stupakov, SLAC-PUB-8208, 1999M.Dohlus, M.I. Ivanyan, V.M. Tsakanov, TESLA-FEL 2000-26,2000M.Dohlus. TESLA 2001-26, 2001

mmR 4.4

mΩ1085σ -1-16

where

Surface Impedance

Inductance define as

22

20 ),(

~

2zx

zzxzx

kk

kkkRdkdk

ac

ZL

Where is spectral density defined as Fourier Transformation

of Autocorrelation function: ),(

~zx kkR

),(

ˆˆ)]ˆ,ˆ()ˆ,ˆ([),(

1),(

zxA

zdxdzzxxrzxrzxA

zxR

2m

.

Ideal Corugated

Loss Factor [kV / nC] -50.698 -52.703

Energy Spread [%] 0.286 0.33

DESY, 16 April 2007

Wake Potential of Corrugated pipe

5 105

0 5 105

150

100

50

0

50

100IdealCorugatedGauss

DESY, 16 April 2007

AL_AU AL_CU AL_ELP AL_UNB AL_GEB

Meas. 1 0.568 0.371 0.395 0.567 2.835

Meas. 2 0.547 0.745 0.360 0.520 ------------

Meas. 3 0.514 0.418 0.346 0.457 ------------

R.m.s. value of the roughness in m

AU Gold

CU Copper

ELP Electro polish

UNB Untreated (Unbehandelt)

GEB Etched (Gebeizt)

Abbreviations

AL_AU AL_CU AL_ELP AL_UNB AL_GEB

Meas. 1 0.425 0.288 0.312 0.463 2.202

Meas. 2 0.430 0.362 0.285 0.418 ------------

Meas. 3 0.410 0.333 0.274 0.356 ------------

Arithmetical Mean Roughness ][Ra m

Acknowledgements:

Thanks to Martin Dohlus, I. Zagorodnov,T. Wohlenberg, M. Ivanyan and

V. Tsakanov for stimulating discussions.

Summary

• Impedance Structure for Ceramic Kicker Vacuum Chamber was

Investigated. For Kicker was shown that Wake Potential for two

layer tube can be estimated by single layer tube formula.

• Was analyzed the transition Wakes influence on the beam.

• Influence of surface corrugation in Undulator vacuum chamber on the beam was

calculated.