computation by W. Ackermann: field maps (ASTRA format) different resolution, different coupling (pen = 0 ..10mm) decay-mode

preparation for ASTRA: center of cavity to origin conversion to fill-mode and sw-mode easy to use --> http://www.desy.de/fel-beam/s2e/codes.html

discrete coupler kicks:

extensive simulations: of XFEL-ACC1, all working-points (20pC .. 1nC)

High-Precision Field-Maps of TESLA Cavitysome conclusions

data reduction: discrete coupler kicks

czjzyxczyxdzyx z exp,,,,,~

BeEV

normalized complex coupler kick

0,0

~,

~,

zV

yxyx

VV

yVxVyxV

yVxVVyxV

yVxVVyxV

yzxzz

yyxyyy

yxxxxx

,,

,,

,,

1 ,

,

,

(normalized) coupler kick coefficients

xyyx

yyxx

y

x

VV

VV

V

V

,,

,,

horizontal kickvertical kickdipole kick (from Maxwell Eq.)skew kick (symplecticity)

kicks per coupler

centerdown

center

up

exp,~

exp,~

czjyx

czjyx

V

V

naive upstream/downstream splitting does not work

yxyxyx ,~

,~

,~

downup VVV

with sensitive to position of center(if off axis)

solution: extract monopole part

d

d

zmzm

zmzm

rQBQrB

rQEQrE

2

12

1 rBrBB

rErEE

m

m

centerdown

center

up

exp,~

exp,~

czjyx

czjyx

BEV

BEV

with

0,0~zVnormalization to !!!

insensitive !

cavity operation

a) penetration depth of power coupler (downstream)

b) fill mode

pen/mm Qe/1E6 0 12.6 2 8.3 4 5.57 6 3.81 8 2.67 10 1.90

decay mode (no forward power), simulated by W.A.“perfect” fill mode (no reflected power)standing wave mode

close to standard operation conditions

approximation: decay

decay

Im

Re

BB

EESW

SW

j

decaydecayfill

decaydecayfill

ImRe

ImRe

BBB

EEE

j

j

independent of cavity operation

dependent on cavity operation

upstream coupler kick

downstream: vertical and skew kick

422.0456.3mm10

785.0009.1mm10

58.008.4110

76.1080.5610

6,

6,

6

6

jV

jV

jV

jV

yx

xx

y

x

009.088.2mm10

95.755.36106

,

6

jV

jV

yx

y

compensation ofvertical kickis not bad !

horizontal, downstram – no wonder!

Re, Im hor. kick, no comp.time dependent !

dipole kick

beam dynamics simulation with full field mapASTRA, XFEL-ACC1, 1nC casepenetration depth 8mm

average horizontal and vertical offset

vs. beamline coordinate

length of ACC1 with 8 cavities is ~ 10m

mm

x

mm

y

mz

ASTRA, XFEL-ACC1, 1nC casepenetration depth 8mm

after ACC1: normalized slice emittance

vs. bunch coordinate

mm

x

mm

y

horizontalverticalh-projectedv-projected

rz sw fill decay

beam dynamics simulation with full field map

comparison(a) complete 3D fields(b) rz-field + coupler kicks(c) rz-field + offset-independent coupler kicks

(a) (b) (c)offset:

emittance:

computation by W. Ackermann: field maps (ASTRA format) different resolution, different coupling (pen = 0 ..10mm) decay-mode

preparation for ASTRA: center of cavity to origin conversion to fill-mode and sw-mode easy to use --> http://www.desy.de/xfel-beam/s2e/index.html

discrete coupler kicks: upstream/downstream – horizontal/vertical/dipole/skew-kicks mode and coupling dependent: downstream: horizontal & dipole

extensive simulations: of XFEL-ACC1, all working-points (20pC .. 1nC) 0th order: xav, x’av, yav and y’av depend on mode, coupling and working point 1st order: growth of proj. emittance (time- & offset-dependence) growth of vert. slice emittance (offset-dependence)

High-Precision Field-Maps of TESLA Cavitysome conclusions