Transcript 28th International Free Electron Laser Conference FEL 2006

Ninth Annual Directed Energy Symposium 2006
Albuquerque, NM 30 October - 2 November 2006
THE CALCULATED EMITTANCE
OF A PHOTOCATHODE
K. L. Jensen,
J. Yater, J. Shaw,
N. A. Moody, D. W. Feldman,
P. G. O’Shea
Code 6841, ESTD, Naval Research Laboratory
Washington, DC 20375-5347 USA
IREAP, University of Maryland
College Park, Maryland, D 20742-3511 USA
Funding provided by
Joint Technology Office and Office of Naval Research
Acknowledgements (alph): S. Beidron, C. Bohn, C. Brau, M. Cahay, D. Dimitrov,
D. Dowell, Y.Y. Lau, J. Lewellen, E. Nelson, J. Petillo, J. Smedley, M. Virgo
SLIDE 1
INTRODUCTION
High brightness beams for high rep rate MW-class FELs require robust,
long-lived, high duty factor photocathode with needs at odds w/ drive laser.
Cs-based controlled porosity dispenser cathode is basis of UMD/NRL exp.
& theoretical effort to make rugged, self-rejuvenating cathode with high QE
Characterization & prediction of QE from Cs-covered surfaces lead to a
material- and laser-parameter dependent model from which the emission
distribution can be used to calculate Emittance and Brightness.
 Accuracy is confirmed by comparison to exp. measurements of QE
from cesiated W and Ag, and bare metals
From this model, we derive an asymptotic limit for expressions for
Emittance and Brightness and compare it to numerical calculations using
the full transport model, with specific accommodations for:
 Scattering
 Surface Work function
 Quantum Effects
SLIDE 2
BACKGROUND
Photoemitter Capable of in situ Rejuvenation With a High Quantum
Efficiency (QE) Needed for High Power FELs & Linear Accelerators.
 Coatings Such As Cesium Reduce Work Function = Affects QE
GOALS:


Custom Engineered Controlled
Porosity Photocathodes
Photoemission Models Validated By
Experiment and Adapted to Needs
of Beam Simulation Codes
Bare
Metals
Coated,
Solid Metals
Coated Porous
Metals
Surface
Diffusion
Dispenser
Cathode
STATUS




Development of Advanced Photo-Electron Emission Microscope System for
the characterization of metals, semiconductors, cesiated surfaces
Prototype Dispenser Cell; QE vs. Coverage Diagnostic Tool (UMD)
From Integrated Simulation Model, We have Developed Photoemission
Modules Appropriate for Beam Simulation Code
Parallel development of theoretical models with experimental effort
SLIDE 3
EMISSION “MOMENTS” CALCULATIONS
“Moments” of the Emission Distribution:
 Electron E augmented by photon, but direction of propagation distributed over sphere
 Photon absorbed by an electron at depth x: Probability of escape depends upon
 occupation of initial state, probability electron final state is empty
 electron path to surface & probability of collision,
 energy component directed at barrier & probability of escape
 
M n  2

3
 2m 
 h2 
3/ 2


0
E dE 
1/ 2
 /2
0

 2m  sin ( ) 
sin  d  2 E  2 
cos ( ) 
h
2

n/ 2


T (E  h )cos 2  f  (cos , E  h ) f FD (E) 1  f FD (E  h )
1 4 44 2 4 4 43 1 4 4 2 4 4 3 1 4 4 4 4 2 4 4 4 4 3
transmission probability
scattering factor
Longitudinal (n = 1) - CURRENT DENSITY
Transverse (n = 0 & 2) - EMITTANCE
Energy distribution & occupation
2mE / h cos
 2mE / h sin 
n  1
kz 
n  0,2 
k2
2
2
2
SLIDE 4
EMITTANCE DOMINATED BEAMS
Emittance and Beam Brightness  Quality of Electron Source Used to
Generate Bunches; Beams with higher current and smaller emittance…
 Enable Shorter Wavelength / More Powerful Fels
electron beam must be focused inside laser beam for interaction
 Emittance Related to Gain of FEL
its magnitude is a critical and oft-used measure
of beam quality, as is brightness.
for an axisymmetric, flat, circular,
uniformly emitting surface:
Emittance
h
 n,rms (z) 
mc
 Intrinsic emittance – what originates at
photocathode – important:
x2
kx2
Brightness
Bn  2I e /  n 
cannot be compensated for by subsequent beam optics
2
Expectation Value
r r r r
r r
drdkO r, k f r, k

O 
r r r r
 drdkf r, k
2
kx2 
k
2
  
 
exp   h k / 2mk dk


2  exp   h k / 2mk dk

0
2
T

0
2
T
2

2

3


kx


x
SLIDE 5
MODEL CALCULATION: THERMAL EMITTANCE
Apply “Moments” of the Emission Distribution to Thermionic emitters
h  0
 No photon
 Uniform Emission: distribution
function independent of x:
x
2

1
2
  
2
 
1
2
2
c

 T(E): Richardson Approximation
T E   E      4QF
 No Scattering factor
(e- at barrier)
f  1
 Incident Distribution is
Maxwell-Boltzmann
f FD E  exp  T E   ;
 No “final state” occupation issue
1  f FD E  1
h  c2 
 n,rms (z) 
mc  2 
1/2

 


F is q x Field
T is temperature
 is Fermi level
 is Work function
T  1 / k BT





1/2
  k 3 exp   h2 k 2 / 2m dk 
T

 
 0 
 

2 2
 2 0 k exp  T h k / 2m dk 


hc  M 2 

2mc  2M 0 
1/2

c
4 T mc
2
Common representation
of the emittance of a
thermionic cathode
 n,rms 
c  kBT 
1/2


2  mc 2 
SLIDE 6
QUANTUM (FIELD) EFFECTS
10
The General Equation of Electron Emission (M1)
hkx
T (kx ) fFD
3 
m
2  0
e


Transmission Probability based on WKB form

Widely used D(E) = exp(-2(E)) not good near barrier max
T kx   1 / 1  exp F (Eo  Ex 
WKB Factors Determined From “Area Under Curve”
 F   E E  Em ; Eo  Em   Em  /  F 
 E       2 
x
x
Voltage
r
E(k ) d 3k
2m
V (x)  E dx
h2
Current [a.u.]
J(F,T ) 

Emission from a Tungsten Needle heated to 1570 K
7
10
6
10
5
10
4
10
3
10
2
10
1
 F-like
T-like 
J. W. Gadzuk, E. W. Plummer,
Phys. Rev. B3, 2125 (1971)
Figure 2: Experimental Data
-3
Q1/ 4 F 3/ 4     E 
Fowler Nordheim Form (for Near Fermi Level )


4v(y)
3t(y)
 E  
2m 3 1 
E   
3hF
 2v(y)

-1
0
F = field in eV/nm
 = Fermi level in eV
2
3
4
5
F
Num.
FN-like
Quad


15
10
5.0
0.0
 = 4.8 eV
 = 8 eV
T = 1570 K
F = 4 eV/nm
-5.0
-10
J is the current density
T = 1/kBT in 1/eV
1
20
Area Under Curve
1  2m 

2
h2 
 E    

-2
E-E
Quadratic Form (for Near Barrier Max)
1/2
400
500
600
800
1000
1200
1600
7
8
9
10
Energy
11
12
SLIDE 7
1st & 2nd GEN. MODELS FOR BEAM CODES
QE Algorithm used in distributed code:
U h    / kBT 
q

m

QE 
F 
1  R( )
h  hk(E) (E) 
U  / kBT 
F 

 /2
0

 x
x

d  exp   
dx
0
  cos( )v(E) (E,T ) 


0

d  exp x /  dx
0
100
 Scattering factor is proportion of e- to get from
excitation site to surface
delta(W)
%R(W)
delta(Cu)
%R(Cu)
delta(Au)
%R(Au)
R[%] and 
Revised Fowler Dubridge Model Parts:
Scattering (F,where E  h   )
10
Reflectivity (R) & Penetration depth ()
 Calculated from exp. dielectric n & k data
0.1
1
Wavelength [micron]
Emission Probability (U(x))
Emission Models For Beam Codes developed with
increasing complexity and inclusion of materialdependent factors
Next Gen Code: “Moments” based analysis
12
1 2 2
U x   x 
2
6
U(x)
U(x)
 Probability that photo-excited e- will surmount or
tunnel through surface barrier
 Ratio of incident to transmitted J for allowed e Depends on Temp, Photon E, Barrier Height 
10
8
4
-4
-2
0
Argument
2
4
SLIDE 8
COVERAGE DEPENDENT WORK FUNCTION


Gyftopolous-Levine Theory for
Coverage-Dependent Work function:
Determination of depends on
 ro 
r 
 C

 Factors f and w = “Atoms Per Cell”
Values Depend on Crystal Face:
 x  x / 2rx 
2
 
2
 R
3/ 2


f
Dipole modification factor
5
Work Function [eV]
 n factor: alkali (n = 1); alkaline-earth (n = 1.65)
C
 
2

2  rW  
1    
w  R  

G  
3

 rC   
9n
f
1  n   1 
8

 R   
 Work function of bulk f and monolayer m
W

Modified Gyftopolous-Levine Theory
 Covalent Radii rx and their sums R
 General Surface = “Bumpy [B]”
 f : w = 1:4 (Cs on W, Mo, Ta)
= 1:2 (Ba on Sr, Th, W, etc)
 
    f   f  m  2 3  2 1 G 
Ba Dispenser (Theory)
Longo
Haas
Cs on W (Theory)
Wang
Taylor
4
3
2
1
0
0.2
0.4
0.6
0.8
1
Coverage (fraction of monolayer)
Hard Sphere Model of Surface Dipole
C-S Wang, JAP44, 1477 (1977)
J. B. Taylor, I. Langmuir, PR44, 423 (1933).
R. T. Longo, E. A. Adler, L. R. Falce, Tech. Dig. of IEDM 1984, 12.2 (1984).
G. A. Haas, A. Shih, C. R. K. Marrian, ASS16, 139 (1983)
SLIDE 9
Scattering in metals due to acoustic phonons and e-e
(electron). If mechanisms independent, then:
Mathiessen’s Rule
Values of  & Ks from Monte Carlo & Thermal Conductivity data
Phonons:
• TD = Debye Temp
  = Deformation potential
• vs = Sound velocity
 ac 
h v TD / T 
5
3 2
s
mk BTk F 
2

s5ds
 TD /T
 0
es  1 1 es




1






Electron-Electron: (Lugovskoy & Bray [1])
 E = Electron energy above Fermi level
• qo = Thomas Fermi Screening wave number
• Ks = Dielectric constant
1

E     2k F  
 ee  2
1




  mc 2 (k BT )2   k BT   qo  

tan 1 x 2  x 2 
x 3  1
x

 (x) 
tan x 

2

4 
1 x
2  x2


4hK s2

[1] A. V. Lugovskoy, I. Bray, JPD:AP31, L78 (1998)

14
Cu
12
10
8
6
ln(Tau [fs])
ln(Tac)
ln(Tee)
ln(TOTL)
Liq. Nitrogen
Room Temp
4
2
0
-2
0
1
2
Empirical thermal
conductivity data
3
4
5
6
7
ln(Temperature [Kelvin])
100
Relaxation Time [fs]
1
 1   ee1   ac1   imp
ln(Relaxation Time [fs])
THEORETICAL EVALUATION OF SCATTERING
Cu
Tau
Lugovskoy Ks =1
Lugovskoy Ks=5.2
tau-ee [fs]
tau-ac [fs]
80
60
Monte Carlo
simulation of e-e
scattering
40
20
0
0
0.5
1
1.5
2
2.5
3
3.5
4
E-E [eV]
F
SLIDE 10
COMPARISON TO EXPERIMENT: Metals
2.0
Charge [nC]
Bulk Metal Comparisons for Low Laser
Intensity & Field - Methodology:
 Thermal Photoemission Moments Approach
(Next Gen Model) using ee(E=+h) for each
incident laser intensity or wavelength
• Pulses were Gaussian in time: Total E and Q
evaluated via integration over pulse (Laser) and
Emitted charge profile (electron)
9.28.06
Field = 39 MV/m
Beta = 1
t = 16 ps
A = š(0.39 mm)^2
 = 266 nm
1.5
1.0
Charge [nC] 2% Any
Charge 70Þ p
Charge 70Þ s
Time Dep. Theory
0.5
• Parameters = standard values obtained from
Literature or Source (no adjustable parameters)
Rosenzweig, et al., NIMA341,379 (1994)
0.0
0
20
40
60
80
100
Laser [µJ]
-3
Quantum Efficiency
Exp (SLAC)
4.31 eV
5.1 eV
60:40 Mix
Lead (Pb)
 = 3.0
F = 1.0 MV/m
10
o
T = 300 K
Data: J. Smedley
-4
SLAC:
Two grain model
of Cu Surface
10
-5
10
Copper (Cu)
 = 1.0
F = 0.01 MV/m
60% 4.31 eV
(Dowell)
 = 4.31 eV
T = 300 K
Data: D. Dowell
40% 5.1 eV
[100] face
o
Exp (BNL)
Theory ( = 4.0 eV)
-6
10
200
220
240
260
Wavelength (nm)
280
300
200
220
240
260
Wavelength (nm)
280
300
SLIDE 11
COMPARISON TO EXPERIMENT: Cs on Metals
EFFICIENCY [%]
QUANTUM
Quantum
Efficiency
log scale
Cesium on Argon-Cleaned Tungsten Surface
0.1
Cesium on Silver
0.12
808 nm
655 nm
532 nm
405 nm
375 nm
Theo
Theo x 0.85
ExpA
ExpB
0.08
Cs on Ag
 = 405 nm
F = 0.0174 MV/m
 = 1.6 eV
0.01
0.04
min
808
655
532
405
375
0.1
0.08
0.06
nm
nm
nm
nm
nm
 = 5.3 Angstroms
0.00
0
0.04
0.02
0
0
20
40
60
Theta [%]
80
100
20
40
60
 [%]
80
100
Notes
1. Standard Library Parameters for
W,Ag,Cs: No Adj. Parameters
2. Cs-Ag Data taken by A. Balter:
Low  : Difficulty removing Cs
from prior runs
SLIDE 12
ASYMPTOTIC EMITTANCE FORMULA
Take the weak-field, low temperature limit: Transmission probability and
Fermi-Dirac distributions replaced by Step Functions
M n  2 
3
 2m

h





 h2

m
p E  
;
hk(E) (E)
(n 3)/2
G a,b, y  
Length
Ratio
Mn 
1
2 2
 n,rms 


R

c
2

1




x

1


0  h   


x 1 x
b
 dx;
2 y
xa
(n  3)/2


E

f cos , E  
Energy
Ratio



1/2 h  

 3h   
4     p h     1 
M2
 6  h   
 c
2M 0
3hc h   
laser penetration depth
relaxation time
reflectivity
Fermi Level
1
n

G  p (   )(x  1),
,  dx
x  1 2 

h  
=
 
Angular
integral
 2m

 h2 h   
(n1)/2
1
barrier height
Laser freq.
Electron energy
angle wrt normal to surface

1


0
 z

z
exp   
dz
  l E cos 

 z
0 exp     dz
cos
cos  p E 
scattering
factor
n  2 
n  0 
Generic Causes of Theory-Exp. Differences:
• Non-linear Field Components in Cavity;
• Wakefields;
• Non-uniformity of the Laser Illumination Source;
• Thermal Effects;
• Quantum Efficiency Non-uniformity Due to
Contamination or Cathode Structure;
• Space-charge Effects for Sufficiently High Bunch
Charge
SLIDE 13
EMITTANCE & BRIGHTNESS (analytic)
 n,rms 
Ratio of Brightness to Absorbed Laser Power
2
n
2 3
6  h   
3hc
 
c
B
1  R  I  A
3qmc h   h   
2  h 1  p   h 
1.0
D. H. Dowell, F. K. King, R. E. Kirby,
J. F. Schmerge, J. M. Smedley,
PRST-AB 9, 063502 (2006).
Copper Cathode
 Work function
4.31 eV
(surface cleaned with hydrogen)
 Illumination area
4 mm2
 Field
110 MV/m
 Exp. Value (Dowell, et al.):
rms(233 nm)
0.60 mm-mrad
0.42 mm-mrad
Emittance [mm-mrad]
Consider conditions from:
 Theory Value
rms(233 nm)

BN 
0.8
2I e
4 rms 2
150
0.6
0.4
200
100
For BN, an optimal
wavelength exists
50
0.2
Copper @ 110 MV/m
Brightness:
 Relaxation time approximation for
Copper Parameters (based on fit)
(time in fs, energy in eV)
0.0
0.05
Norm. Brightness [C/J]
Emittance
0
0.1
0.15
0.2
0.25
0.3
Wavelength [µm]
 ee (E)  42.9 E   
1.90
SLIDE 14
NUMERICAL STUDY: Cu (LHS) & Cs on Cu (RHS)
M(0)
cos()
cos()
M(0)
Fermi
Level
M(2)
F = 110 MV/m
= 7.0 eV
T = 300.0 K
 = 4.5 eV
 = 266 nm
c = 0.113 mm
cos()
cos()
M(2)
Energy [eV]
F = 110 MV/m
= 7.0 eV
T = 300.0 K
 = 1.6 eV
 = 266 nm
c = 0.113 mm
Energy [eV]
SLIDE 15
NUMERICAL VS ANALYTIC: Cu
0.6
180 nm
180 nm
210 nm
210 nm
240 nm
240 nm
270 nm
270 nm
0.4
0.3

n,rms
[mm-mrad]
0.5
0.2
300K
0.1
0
10
1
2
10
10
FIELD [MV/m]
1600K
3
10 100
1
2
10
10
FIELD [MV/m]
10
3
PERFORMANCE
 Analytic model works best
when F & T not large, and
photon energy significantly
higher than barrier

Error @ 1 MV/m, 300K: -5% to 10%
NUMERICAL EVALUATION
ASYMPTOTIC FORMULA (photo)
Bare copper metal
 Work function
4.5 eV
ASYMPTOTIC FORMULA (thermal)  Illumination radius 1.13 mm
SLIDE 16
NUMERICAL VS ANALYTIC: Cs on Cu
0.7
180 nm
180 nm
210 nm
210 nm
240 nm
240 nm

n,rms
[mm-mrad]
0.8
0.6
300K
270 nm
10
0
1
PERFORMANCE
 Analytic model works best when
F & T not large, and photon
energy significantly higher than
barrier

2
10
10
FIELD [MV/m]
Error @ 1 MV/m, 300K: -6% to -13%
1600K
270 nm
3
10 10
0
1
2
10
10
FIELD [MV/m]
NUMERICAL EVALUATION
ASYMPTOTIC FORMULA (photo)
10
3
Copper W/ Cs coating
 Work function
1.6 eV
ASYMPTOTIC FORMULA (thermal)  Illumination radius 1.13 mm
(not visible)
SLIDE 17
DISPENSER PHOTOCATHODES
IDENTIFY factors that affect QE (e.g., laser, environment, photocathode material)
DEVELOP a custom-engineered controlled porosity photo-dispenser cathode
7
Interpore ≈ 6 µm; Grain Size≈
4.5 µm; Pore Diam. ≈ 3 µm
Conventional Dispenser
Top
View
6
NUMBER
Metal
bin size = 8 pixels
Log-Normal Parameters
 = 35.3 pixels
 = 0.786
Mean pore-to-pore:
35.3 x (10 m / 143 pixel) = 2.47 m
5
4
LogNorm(x)
3
2
1
Cs
O
Side
View
0
Controlled Porosity
Diameter (microns)
Dispenser Cathode Surface showing pores & grains
8
16 32 48 64 80 96 112 128 144 160
SEPARATION (pixel)
Grain Size
Ave Diam = 4.8 m
6
4
2
0
Cs Dispenser Cathode
0
1
2
3
4
5
Grain Index
6
7
8
SLIDE 18
WORK FUNCTION MODEL FOR BEAM CODE
 Analysis of dispenser cathode surface shows grains
 Different faces have different f factors in GL Theory
 Work function variation may impact beam: perform
modeling of emission using MICHELLE
Grain A
4000
421 Pixels
COUNT
Grain C
y
Cutoffs
Value
3000
Scale:
421 Pixels
= 67 µm
Grain B
2000
A1
1417
B1
52.062
A
3198.8
B
62.608
A
3
3440.7
B3
82.955
2
2
1000
2


 n  B j 

y(n)   A j 

1


j1


 8 

1
3
0
0
20
40
60
80
100
120
GRAY SCALE (RGB index)
SLIDE 19
GENERATION OF MICHELLE MODEL FOR GRAIN
Use actual image and its behavior under processing to motivate method
for creating “artificial” grain surface
 Method: Generate random matrix of RGB Pixels
 Smooth (iterate 3 - 5 times)
 Rescale & Truncate
at Cut-off values
Exp
Pi,nj 

1
1
1
Ro  1Pi,nj1   k  1  l  1 Pi n1k, j l
Ro  8

Model
SLIDE 20
CONCLUSION
NEED FOR PHOTOCATHODE
 Rugged & Long-lived Photocathodes Critical for MW-class FELs
Demands Placed on Photocathode Reflect Needs of Drive Laser & Visa Versa.
EXPERIMENTAL - THEORETICAL PROGRAM
 QE of Bare Metals & with (sub)-monolayer coatings of Cs:
GOOD AGREEMENT
 Development of Custom Controlled Porosity Photocathodes
 Validated Photoemission Models for Beam Simulation Codes
HIGHLIGHTS
 Next Generation (Moments based) Models for PIC & Beam Simulation
 Analytical Models for Emittance, Brightness
Analytical Scattering Operator based on Model of Lugovsky & Bray
Reflectivity model of surface based on experimental grain distribution
 Surface non-uniformity distribution and analysis
SLIDE 21