Impact of the Cathode Roughness on the Emittance of an Electron Beam M.Krasilnikov, DESY Zeuthen WSHQE, Milano 4-6.10.2006

Impact of the Cathode Roughness on the Emittance of an Electron Beam

M.Krasilnikov, DESY Zeuthen

WSHQE, Milano4-6.10.2006

2

Outline

• Motivation• Cathode roughness models• Cathode roughness effects:

– Geometric• Normal emission, 2D vs. 3D• 2D model with emission distribution

– Electric field• Schottky effect, electron affinity• Single bump model

• Conclusion

3

Motivation. XFEL Photo Injector

0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14 16 18z, m

mm

mra

d

Xemit (Ek=0.55eV), mm mrad



Xemit (Ek=1eV), mm mrad

Xrms, mm

L-Band (1.3GHz) 1.5-cell RF gun with

Cs2Te photo cathodeEcath=60MV/m

Ek = thermal kinetic energy of electrons at photo cathode

Normalized transverse emittance after XFEL injector

as function of the initial kinetic energy of the photo

emitted electrons

0.8

0.85

0.9

0.95

1

1.05

1.1

0.4 0.6 0.8 1 1.2Ek, eV

emitt

ance

, mm

mra

dSlice emittance @z=18m

0

0.5

1

1.5

2

2.5

3

-5 -4 -3 -2 -1 0 1 2 3 4 5z-<z>, mm

sl.e

mit.

, mm

mra

d

0

0.2

0.4

0.6

0.8

1

1.2

1.4

sl.emittance (Ek=0.55eV), mm mradsl.emittance (Ek=0.75eV), mm mrad

sl.emittance (Ek=1eV), mm mradcharge density, a.u.

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

5 7 9 11 13 15 17

RMS normalized emittance in XFEL injector

4

Motivation. Cathode roughnessRoughness measurements by INFN/LASA

Profile

Paolo Michelato, INFN Milano – LASA“High QE Photocathodes lifetime and dark current investigation”,PITZ collaboration meeting 4-5.02.006

5

Motivation. Cathode roughnessRoughness measurements (imaging) by INFN/LASA

Paolo Michelato, INFN Milano – LASA“High QE Photocathodes lifetime and dark current investigation”,PITZ collaboration meeting 4-5.02.006

6

Motivation. Thermal emittance

Measurements at PITZ

cathode #61, QE ~ 1.5%

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

5.0 10.0 15.0 20.0 25.0Efield , MV/m

emitt

ance

, mm

mra

d

emitt Xemitt Y

Ecath=42MV/mEemis=24MV/m

Ecath=60MV/mEemis=42MV/m

7

Cathode Roughness Models

-1

0

1

-4 -2 0 2 4 k*x

z/h

n

v

8

Periodic Roughness. 2D vs. 3D

n

v

-1

0

1

-4 -2 0 2 4 k*x

z/h n

v k/2

period roughness

hkh 2

parameter roughness

)(sin1

)sin(220

kx

kxvvx

)cos(kxhz )cos()cos( kykxhz

22022

1

112

hmceEp xxx

Dx

)(sin)(cos)(cos)(sin1

)cos()sin(222220

kykxkykx

kykxvvx

,)(2 2023 Ih

mceE

p xxxD

x

.

sincoscossin1cossin

4)(

where

22222

22

2

2

dYYXYX

YXdXI

emission normal ,0 Case

Transverse component of the velocity at the cathode surface

Transverse emittance induced by the cathode roughness0.7

0.71

0.72

0.73

0.74

0.75

0.76

0 1 2 3 4 5 6 7 8 9 10=2*h/

3D/ 2D

9

2D Periodic Model with Emission Distribution

-1

0

1

-4 -2 0 2 4 k*x

z/h

n

v

dxpdd

mcEp

x

kx

m2

2

00

2

sin

sincoscoscossin2

surface cathoderough at the momentum Transverse

Without roughness

)cos1(6cos3cos22 3

2,

m

mmkx

flatthx mc

E

eVEeVETeCs kA 75.0;2.0:cathode photo For 2

affinityelectron where,arccos AkAm EEE

];0[ Case m

2D (x,z) cathode roughness

10

2D Periodic Model with Emission Distribution

-1

0

1

-4 -2 0 2 4 k*x

z/h n

v

m

m

mmmmmkx

roughthx mc

E

tan where

,)cos1(6

)cos1)(cos1(2cos)cos3cos2(2

cathoderough thefrom emittance Thermal33

2,

)cos1(cos3cos2

cos12cos 3

3

,

,

mmm

mmflatth

x

roughthx

Thermal emittance growth due to the cathode roughness Vs. roughness parameter Vs. roughness period (h=10nm)

0

20

40

60

80

0 2 4 6 8 10 12 14 16 18 20=2*h/

ther

mal

em

ittan

ce

grow

th, %

0

10

20

30

40

50

60

0 100 200 300 400 500 600 700 800 900 1000, roughness period, nm

ther

mal

em

ittan

cegr

owth

, %

h=10nmh=70nmh=100nm

11

Dependence on Electric FieldThermal emittance growth due to the cathode roughness as

function of electron affinity and roughness period (h=10nm)

1 1 1 12 2 2

2

4 4

4

4

6

6

6

6

8

8

8

8

10

10

10

10

15

15

15

15

20

20

20

20

25

25

25

30

30

30

35

35

35

40

40

45

45

50

50

55

55

60

60

65

65

7075

80859095

, nm

EA, e

V

20 40 60 80 100 120 1400

0.05

0.1

0.15

0.2

0.25

emission theofmoment at the cathode at the field electric

factor t enhancemen fieldstatus surface

cathode theof change the todue increased

affinity initial

,4

:affinityelectron effect,Schottky Including

0

0,

00

3

0,

E

E

EeEE

ph

A

phAA

12

Dependence on Electric Field

00.20.40.60.8

11.2

-10 -8 -6 -4 -2 0 2 4 6 8 10x/b

z/z(0)a/b=0.01a/b=10a/b=100

11 22

2

xb

abz

Single Bump Model

Electric field of the bumped surface

ow EE

-8 -6 -4 -2 0 2 4 6 80

5

10

15

x. a.u.

z, a

.u.

22 abzix

bzixiEiEE ozx

Conformal transformation

plane capacitorincluded!effect charge space no

1

1)(

;)()(

)(

EquationsMain

22

2

z

x

zx

z

x

z

x

pp

ppzx

ctdd

EE

mce

mcpmcp

ctdd

.0)0(;0)0(;)0(;)0(

:(emission) conditions Initial

00

tptpztzxtx

znxn

nnnn

Emission points for simulations

u

v

x

z

.

24

...1;;

22222222

0

0

aubauubabz

NnNunubz

bux

nnnn

Nnn

nn

bbazzN 2201.0)0(01.0

w

ibaibizxiwu 22

0 2 4 6 8 100

1

2

3

4

5

6

7

8

9

10

u,a.u.

v,a.

u.w

,a.u

.

u,a.u.0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

4

5

6

7

8

9

10

x,a.u.

z,a.

u.z,

a.u.

x,a.u.

Conformal transformation

13

Dependence on Electric FieldSimulated divergence (h=10nm)

00.20.40.60.8

11.21.41.61.8

2

0 0.2 0.4 0.6 0.8 1u/u0

px,m

rad

20MV/m 24MV/m36MV/m 42MV/m46MV/m

00.20.40.60.8

11.21.41.61.8

2

0 0.2 0.4 0.6 0.8 1u/uN

px,m

rad


00.10.20.30.40.50.60.70.80.9

1

0 0.2 0.4 0.6 0.8 1u/uN

px, m

rad


nm

10nm

100nm

nm

Ecath, MV/m E0=Ecath*sin(emission), MV/m

42 24

60 42

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.2 0.4 0.6 0.8 1u/uN

px,m

rad

20MV/m24MV/m36MV/m42MV/m46MV/mbump profile

p

14

Dependence on Electric Field

Maximum divergence vs. Emission Field E0 for various roughness width (roughness depth h=10nm)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

20 25 30 35 40 45 50E0, MV/m

max

(px)

, mra

d

=1nm

=10nm =100nm

Ecath, MV/m E0=Ecath*sin(emission), MV/m

42 24

60 42

px,max,px,max,px,max,

mMVEp

mMVEppmMVE

mMVE

emx

emxx

emthx

emthx

thx

/24/24

/24/24

-20%

-10%

0%

10%

20%

30%

40%

50%

20 25 30 35 40 45 50E0, MV/m

(E

0)/

(24M

V/m

)-1

Emit.growth, lym=1nm



15

Conclusion

Thermal emittance growth due to the cathode roughness

)21(110 FFthth

“Geometric” roughness factor ~10-50% Induced by the electric field increase ~30%

-20%

-10%

0%

10%

20%

30%

40%

50%

20 25 30 35 40 45 50E0, MV/m

(E

0)/

(24M

V/m

)-1




Emittance growth ~10÷65%

0

10

20

30

40

50

60

0 100 200 300 400 500 600 700 800 900 1000, roughness period, nm

ther

mal

em

ittan

cegr

owth

, %

h=10nmh=70nmh=100nm

Documents

Impact of the Cathode Roughness on the Emittance of an Electron Beam M.Krasilnikov, DESY Zeuthen WSHQE, Milano 4-6.10.2006