transverse short range wake in TESLA modules and 3rd harmonic cavities

estimated contribution to emittance growth (3rd harm.)

long range: HOM damping - 3rd harmonic cavities

- TESLA cavities

(some bands)

!

Wakes in Cavities

possible working point

1.3 GHz system: 130 MV @ 0 deg --> 130 MeV 447.5 MV @ 0.74 deg --> 577.5 MeV3.9 GHz system: 97.3 MV @ -142.2 deg --> 500 MeVBC2 r56 = -103.5 mm --> compression factor = 201.3 GHz system: 1500 MV @ 0 deg --> 2000 MeVBC3 r56 = -20.7 mm --> compression factor = 5

sensitivity (10% change of compression)

1.3 GHz system before BC2: |V| < 0.19 MV, || < 0.023 deg3.9 GHz system: |V| < 0.071 MV, || < 0.060 deg

I. Zagorodnov: TESLA Report 2003-19 (TESLA module) TESLA Report 2004-01 (LOLA & 3rd harm. cavity)

-wake / cavity scales with fundamental mode frequency ** 2

12 / 24 3rd harm. cavities ~ 13 / 27 TESLA modules !

12 - 3rd harm. cavities

13.5 TESLA modules

mms

CmV

sW

/

-wake

transverse short range wake in TESLA modules and 3rd harmonic cavities

μm 1LMeV 500|| eV

N =12

N = 24

~

0

mm 1

r

s

1.23

1.74

1.02

1.04

mm 1

mm 0

r

s

mm 5.0

mm 0

r

s

1.005

1.011

mm 5.0

mm 1.0

r

s

1.008

1.021

222

2

||

2 rmsrsx NN

V

Wq

3rd harmonic cavity emittance growth due to discrete slice centriod kick:

21~

x

nC 1qmm 4.2

m/z

m/y

100MHz/f

xD~

m 40x cavities of numberNerror systematics

error randomr

systematic and random offsetof cavity axis

f / GHz

e2Q

c = 600 m 60 m

eQ

deg

iffi Q

R

quality

phase advancein periodic structure

of middle cells

(HFSS calc.with ee or mm

boundary cond.)

(ee/mm boundary)2 M/m2

3rd harmonic cavity long range / multi bunch

phase advancein periodic structure

of middle cells

f / GHz

e2Q

c = 600 m 60 m

eQ

deg

iffi Q

R

quality

(mm boundary)

fc

*

*

TESLA 2002-05

0.45 M/m2

TESLA cavity long range / multi bunch

from:

1st & 2nd dipole band

scatter of Q values ~ factor ten

??? field distribution coupler tuning

TESLA cavity