A Transverse Deflecting RF Structure for

Sub-Micrometer Bunches at 5 to 50 MeV

LOLA (Greg Loew, Rudy Larsen and Otto Altenmueller)

REGAE (Relativistic Eelectron Gun for Atomic Exploration)

a first idea about numbers

REGAE

bunch

TDS (Transverse Deflecting Structure) measurement

two examples

rf structures

Remarks / other ideas

literature

LOLA in the FLASH facility

transverse deflecting structures are standard diagnostic devices in FELS

(there is no FEL without them)

1 TDS in FLASH

1 in PITZ

x in LCLS, SACLA, Swiss FEL, FERMI, …

3 in European XFEL

from Christopher Behrens, Groemitz 2010, Betriebsseminar

LOLA setup: horizontal plane

TDS: vertical plane

from Christopher Behrens, Groemitz 2010, Betriebsseminar

OTR-2 → longitudinal phase space

compressed bunch uncompressed bunch

REGAE

gun

buncher

waveguide (3 GHz) longitudinal focus

bunch length

(Relativistic Eelectron Gun for Atomic Exploration)

Astra calculation

bunch length

energy

longitudinal phase space

nm 253sim =σ nm 190sim =σ nm 256sim =σ nm 568sim =σ

(a first discussion with Klaus Flöttmann)

not the last!

first idea about numbers

Q ≈ 100 fC

TDS measurement without spectrometer magnet

TDS drift + screen

1s

3y

length L, strength K’ length D

drift + screen

223 yDyy ′+=

( ) ( ) 1113 2 sKLDLyDLyy ′++′++=→

1 2 3

′

1

1

1

1

δs

y

y

′→

2

2

2

2

δs

y

y

′

′

′≈

′

δδs

y

y

K

K

s

y

y

dZ

d

0

1

′′′

′′

=

16/2/

0100

010

02/1

322

2

LKLKLK

LK

LKz

T

1→2: (period averaged) equation of motion in TDS

E

yEeK

λπ2=′with

′=

′→

1

1

1

1

2

2

2

2

δδs

y

y

Ts

y

y

with

( ) sKpsEev

sFvdZ

dpzy

zy

z

y ′≈

≈≈λπ2

sin11

z

y

p

py

dZ

dy =′=

notation: uppercase Z for beam line coordinate

lowercase s for bunch coordinate

transport matrix

δδ

σσσ CCCCCC

e

syys

e

yyyyyye LL44 344 21

LL4444 34444 21

LLL

2vert-long,

2vert,

2 +++++= ′′′′

( ) ( ) 1113 2 sKLDLyDLyy ′++′++=more general

′=

1

1

1

1

3

δs

y

y

wy

measured

( )22

,1

,1

,1

,1

,1

,1

,1

,1

2,3

23 me

t

t

fw

C

s

y

y

s

y

y

wy σσ

δδ

σ

ν

ν

ν

ν

ν

ν

ν

ν

ν +×=

′

′==

44 344 21

with 2,12

νσ sm = ( )( )22 KLDLf ′+=

systematic error

and

vertical optics (~ spot size without deflection)

vertical - longitudinal correlation

correlation matrix

what we want to know

ν is particle index

correlations with energy

( )4321 wwwww =with coefficients

error from vertical phase space

( ) ( )( )( ) KLDL

DLDL yyyyve ′+

+++−=

2

2 22

,

γαβεσ

vertical emittance and Twiss parameters

velocity effects: additional error from uncorrelated energy spread

δδ σγσ

2/

3/

2 2, LD

LDL

re +

+≈ uncorrelated (relative) energy spread δδδσ C=2

period averaged equation of motion in TDS

with velocity effects (γ−2 terms)

′

′

′≈

′−

δγ

δs

y

y

K

K

s

y

y

dZ

d

r2

1

( )442746353

4232

2534232

3635242

2

322

2

24/5040/720/120/

24/6/2/

2/120/24/6/

6/720/120/24/

1

16/2/

0100

010

02/1

−+

′′′′′′′

′′′′′′′′

+

′′′

′′

= rr

O

LKLKLKLK

LLKLKLK

LKLKLKLK

LKLKLKLK

LKLKLK

LK

LKL

T γγ

two examples

bunch

aperture rfλ∝A

Ayx

Example 1:(not optimized)

w = ���� � �� ����

beam width

z/m

y/m

� 0

relative focus

s = 0

aperture

aperture:

� ����

A = 0.6 mm

L = 5 mmz/m

� �

� � �/2mm 3≈λ

w = ���� � �� ����

beam width

z/m

y/m

� 0 s = 0

aperture

relative focus

� �

� � �/2

DL +

L

Example 2:(not optimized)

aperture:

� ����

rf structures

Massimo Dal Forno, et. Al.

rf breakdown tests of mm-wave metallic accelerating structures

Phys. Rev. Accel. Beams 19, 011301 – Published 6 January 2016

f = 115 .. 140 GHz

Eacc < 0.3 GV/m

Esurface < 1.5 GV/m

pulse length 2.4 nsec

accelerating structure from

P. Arcioni, M. Bressan, F. Broggi, G. Conciauro, L. Perregrini, P. Pierini:

The Groove Guide as an Interaction Structure for Microwave FEL

Nuclear Instruments and Methods in Physics Research, Section A 358, pp. 108-111, 1995

H-type groove waveguide from

might overcome the aperture limitation (for x direction)

but: linear range is still small!

remarks

time resolution limited by: maximal field

length/γ2 and aperture

open: working point, frequency, SW or TW regime

structure technology

rf source

couplers

even the method

increase energy (ACC+TDS?) or reduce resolution

TDS focus changes with K’

other ideas ???

external field self-field + geometry

observe beam effect

observe field resonator → radiationundulator → radiation

TDS + screen wake + instability

+screen ~ Q2

observe

stimulate

sa σγ >

resonator → radiationundulator → radiation

22

2

ph 2

21~2

γλλ

γλπσ uus

K ≈+=

required undulator period su σπγλ22~

µm 60nm 100102 2 ≈⋅⋅π1002 6mm 1mm/100yes!

no!

short magnet + spectrometer

take one magnet from the undulator → coherent short magnet radiation

multichannel infrared spectrometer

ph~2nm 200 λπσ s<

optical spectrometer

literature

Klaus Floettmann and Valentin V. Paramonov

Beam dynamics in transverse deflecting rf structures

Phys. Rev. ST Accel. Beams 17, 024001 – Published 5 February 2014

Benno Zeitler, Klaus Floettmann, and Florian Grüner

Linearization of the longitudinal phase space without higher harmonic field

Phys. Rev. ST Accel. Beams 18, 120102 – Published 30 December 2015

ragae:

tds:R. Akre, L. Bentson, P. Emma, P. Krejcik

Bunch length measurements using a transverse rf deflecting structure in the SLAC linac

SLAC-PUB-9241, PAC2002

structures:

P. Arcioni, M. Bressan, F. Broggi, G. Conciauro, L. Perregrini, P. Pierini:

The Groove Guide as an Interaction Structure for Microwave FEL

Massimo Dal Forno, et. Al.

rf breakdown tests of mm-wave metallic accelerating structures

funny beam dynamics:

−=

′ 0001.0001.0

1

1

y

y

=

0

0

1

1

δs

=

′ 0001.0

1

1

y

y

−=

′ 0002.0001.0

1

1

y

y

′

′

′≈

′

δδs

y

y

K

K

s

y

y

dZ

d

0

1

( )Zy

Z

=

0

0

1

1

δs

=

0

0

1

1

δs

′

′

′≈

′−

δγ

δs

y

y

K

K

s

y

y

dZ

d

r2

1

parameters as for example 2

( )22

1 −∞ ++= r

r

OTTT γγ γ

( ) ( ) 1XZTZX =