slide 1 the calculated emittance of a photocathode ninth annual directed energy symposium 2006...

THE CALCULATED EMITTANCE OF A PHOTOCATHODE

THE CALCULATED EMITTANCE OF A PHOTOCATHODE

Ninth Annual Directed Energy Symposium 2006Albuquerque, NM 30 October - 2 November 2006

K. L. Jensen, N. A. Moody, D. W. Feldman, J. Yater, J. Shaw, P. G. O’Shea

Code 6841, ESTD, Naval Research Laboratory

Washington, DC 20375-5347 USA

IREAP, University of MarylandCollege 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

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

BACKGROUNDPhotoemitter 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

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

Bare Metals

Coated, Solid Metals

Coated Porous Metals

Surface Diffusion

Dispenser Cathode

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

Mn= 2π( )

−3 2mh2

⎛

⎝⎜⎞

⎠⎟

3/ 2

E1/ 2dE sinθdθ2mh2

Esin2(θ)cos2(θ)

⎧⎨⎩⎪

⎫⎬⎭⎪

⎛

⎝⎜

⎞

⎠⎟

n/ 2

×0

π / 2

∫0

∞

∫T (E +hω)cos2θ{ }

transmission probability1 24 4 4 34 4 4

fλ (cosθ,E +hω)scattering factor

1 24 4 34 4fFD(E) 1− fFD(E +hω){ }

Energy distribution & occupation1 24 4 4 4 34 4 4 4

Longitudinal (n = 1) - CURRENT DENSITY

Transverse (n = 0 & 2) - EMITTANCE

n =1⇒ kz = 2mE / h2( )cosθ

n=0,2 ⇒ kρ2 = 2mE / h2( )sin2θ

Emittance and Beam Brightness Quality of Electron Source Used to Generate Bunches; Beams with higher current and smaller emittance…

Enable Shorter Wavelength / More Powerful Felselectron beam must be focused inside laser beam for interaction

Emittance Related to Gain of FELits magnitude is a critical and oft-used measure of beam quality, as is brightness.

Intrinsic emittance – what originates at photocathode – important: cannot be compensated for by subsequent beam optics

EMITTANCE DOMINATED BEAMS

O ≡drrd

rkO

rr,

rk( ) f

rr,

rk( )∫

drrd

rkf

rr,

rk( )∫

kx2 =

kρ2

2≈

exp −βTh2kρ2 / 2m{ }

0

∞

∫ kρ3dkρ

2 exp −βTh2kρ2 / 2m{ }

0

∞

∫ kρdkρ

Expectation Value

x

kx

εn,rms(z) =

hmc

x2 kx2

εn,rms(z) =

hmc

x2 kx2

Emittance

Bn =2Ie / πεn( )2

Bn =2Ie / πεn( )2

Brightness

for an axisymmetric, flat, circular, uniformly emitting surface:

MODEL CALCULATION: THERMAL EMITTANCE

Apply “Moments” of the Emission Distribution to Thermionic emitters

No photon

Uniform Emission: distribution function independent of x:

T(E): Richardson Approximation

No Scattering factor (e- at barrier)

Incident Distribution is Maxwell-Boltzmann

No “final state” occupation issue

x2 = 1

2ρ2 = 1

2ρc

2

x2 = 1

2ρ2 = 1

2ρc

2

hω =0 hω =0

T E⊥( ) =Θ E⊥ −μ −Φ+ 4QF( ) T E⊥( ) =Θ E⊥ −μ −Φ+ 4QF( )

fλ =1 fλ =1

f

FDE( ) ∝ exp −βT E −μ( ){ } ; βT =1/ kBT

fFD

E( ) ∝ exp −βT E −μ( ){ } ; βT =1/ kBT

1− fFD E( ) =1 1− fFD E( ) =1

F is q x FieldT is temperatureμ is Fermi level

Φ is Work function

F is q x FieldT is temperatureμ is Fermi level

Φ is Work function

εn,rms (z) =h

mc

ρ c2

2

⎛

⎝⎜⎞

⎠⎟

1/2 k⊥3

0

∞

∫ exp −βT h2k⊥2 / 2m{ }dk⊥

2 k⊥0

∞

∫ exp −βT h2k⊥2 / 2m{ }dk⊥

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪

1/2

=hρ c

2mc

M 2

2M 0

⎛

⎝⎜⎞

⎠⎟

1/2

=ρ c

4βT mc2

εn,rms (z) =h

mc

ρ c2

2

⎛

⎝⎜⎞

⎠⎟

1/2 k⊥3

0

∞

∫ exp −βT h2k⊥2 / 2m{ }dk⊥

2 k⊥0

∞

∫ exp −βT h2k⊥2 / 2m{ }dk⊥

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪

1/2

=hρ c

2mc

M 2

2M 0

⎛

⎝⎜⎞

⎠⎟

1/2

=ρ c

4βT mc2

Common representation of the emittance of a thermionic cathode

εn,rms =ρ c

2

kBT

mc2

⎛⎝⎜

⎞⎠⎟

1/2

101

102

103

104

105

106

107

-3 -2 -1 0 1 2 3 4 5

Emission from a Tungsten Needle heated to 1570 K

400500600800100012001600

E-EF

Voltage

J. W. Gadzuk, E. W. Plummer,

Phys. Rev. B3, 2125 (1971)Figure 2: Experimental Data

QUANTUM (FIELD) EFFECTSThe General Equation of Electron Emission (M1)

Transmission Probability based on WKB form Widely used D(E) = exp(-2θ(E)) not good near barrier max

WKB Factors Determined From “Area Under Curve”

Quadratic Form (for Near Barrier Max)

Fowler Nordheim Form (for Near Fermi Level μ)

T kx( ) ≈1 / 1+ exp βF (Eo −Ex( )⎡⎣ ⎤⎦T kx( ) ≈1 / 1+ exp βF (Eo −Ex( )⎡⎣ ⎤⎦

J(F,T ) =

e2π( )3

hkx

mT(kx)

0

∞

∫ fFD E(rk)( )d3k

J is the current density F = field in eV/nm

βT = 1/kBT in 1/eV μ = Fermi level in eV

θ E( ) =

1

2π

2m

h2

⎛⎝⎜

⎞⎠⎟

1/2

Q1/4F−3/4 μ + φ − E( ) θ E( ) =

1

2π

2m

h2

⎛⎝⎜

⎞⎠⎟

1/2

Q1/4F−3/4 μ + φ − E( )

βF = −∂Eθ E = Em( ); Eo = Em + θ Em( ) / βF( )

θ E < μ + φ( ) = 22m

h2V (x) − E( )dx

x−

x+

∫

θ E( ) =

4v(y)

3hF2mΦ3 1+

3t(y)

2Φv(y)E − μ( )

⎧⎨⎩

⎫⎬⎭

F-likeT-like

-10

-5.0

0.0

5.0

10

15

20

7 8 9 10 11 12

Num.FN-likeQuadμμ+φ

Energy

Φ = 4.8 eV μ = 8 eV

= 1570 T K = 4 /F eV nm

1st & 2nd GEN. MODELS FOR BEAM CODES

QE Algorithm used in distributed code:

Revised Fowler Dubridge Model Parts:

Scattering (Fλ,where ) Scattering factor is proportion of e- to get from

excitation site to surface

Reflectivity (R) & Penetration depth () Calculated from exp. dielectric n & k data

Emission Probability (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

Emission Models For Beam Codes developed with increasing complexity and inclusion of material-dependent factors

Next Gen Code: “Moments” based analysis

Fλ ≈dθ

0

π /2

∫ exp −x−

xcos(θ)v(E)τ (E,T )

⎛⎝⎜

⎞⎠⎟0

∞

∫ dx

dθ0

π

∫ exp −x / ( )0

∞

∫ dx

10

100

0.1 1 10

delta(W)%R(W)delta(Cu)%R(Cu)delta(Au)%R(Au)

[ ]Wavelength micron

10

100

0.1 1 10

delta(W)%R(W)delta(Cu)%R(Cu)delta(Au)%R(Au)

[ ]Wavelength micron

QE =

qhω

Fλm

hk(E)τ (E)⎛⎝⎜

⎞⎠⎟1−R(ω)( )

U hω −φ( ) / kBT⎡⎣ ⎤⎦U μ / kBT[ ]

QE =q

hωFλ

mhk(E)τ (E)

⎛⎝⎜

⎞⎠⎟1−R(ω)( )

U hω −φ( ) / kBT⎡⎣ ⎤⎦U μ / kBT[ ]

E =hω + μ

4

8

12

-4 -2 0 2 4

U(x)

Argument

4

8

12

-4 -2 0 2 4

U(x)

Argument

U x( )≈12

x2 +π 2

6

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Ba Dispenser (Theory)LongoHaasCs on W (Theory)WangTaylor

Coverage (fraction of monolayer)

Gyftopolous-Levine Theory for Coverage-Dependent Work function: Determination of Φθ depends on

Covalent Radii rx and their sums R

Work function of bulk f and monolayer m

Factors f and w = “Atoms Per Cell” Values Depend on Crystal Face: General Surface = “Bumpy [B]” f : w = 1:4 (Cs on W, Mo, Ta)

= 1:2 (Ba on Sr, Th, W, etc)

n factor: alkali (n = 1); alkaline-earth (n = 1.65)

COVERAGE DEPENDENT WORK FUNCTION

x =x / 2rx( )

2

β R

Hard Sphere Model of Surface Dipole

W

C

Modified Gyftopolous-Levine Theory Φ θ( ) =φf − φf −φm( )θ 2 3−2θ( ) 1−G θ( ){ }

G θ( ) =

rorC

⎛

⎝⎜⎞

⎠⎟

2

1−2w

rWR

⎛

⎝⎜⎞

⎠⎟

2⎛

⎝⎜⎜

⎞

⎠⎟⎟

1+ nrCR

⎛

⎝⎜⎞

⎠⎟

3⎛

⎝⎜⎜

⎞

⎠⎟⎟

1+9n8

fθ( )3/ 2⎛

⎝⎜⎞

⎠⎟

fθ

Dipole modification factor

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)

THEORETICAL EVALUATION OF SCATTERINGScattering in metals due to acoustic phonons and e-e (electron). If mechanisms independent, then:

Values of & Ks from Monte Carlo & Thermal Conductivity data

[1] A. V. Lugovskoy, I. Bray, JPD:AP31, L78 (1998)

Mathiessen’s Rule τ −1 =τee

−1 +τ ac−1 +τ imp

−1

-2

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7

ln(Tau [fs])ln(Tac)ln(Tee)ln(TOTL)Liq. NitrogenRoom Temp

ln(Temperature [Kelvin])

Cu

0

20

40

60

80

100

0 0.5 1 1.5 2 2.5 3 3.5 4

TauLugovskoy Ks =1Lugovskoy Ks=5.2tau-ee [fs]tau-ac [fs]

E-EF [eV]

Cu

τ ac =πρh3vs

2 TD / T( )5

mkBTkF2

s5ds

es −1( ) 1−e−s( )0

TD /T

∫⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

−1

Phonons:• TD = Debye Temp = Deformation potential• vs = Sound velocity

Electron-Electron: (Lugovskoy & Bray [1]) E = Electron energy above Fermi level• qo = Thomas Fermi Screening wave

number• Ks = Dielectric constant

τee =4hKs

2

α 2πmc2(kBT)2

1+E −μπkBT

⎛

⎝⎜⎞

⎠⎟

2kF

qo

⎛

⎝⎜⎞

⎠⎟⎡

⎣⎢⎢

⎤

⎦⎥⎥

−1

(x) =x3

4tan−1 x+

x1+ x2

−tan−1 x 2 + x2

( )

2 + x2

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

Empirical thermal conductivity data

Monte Carlo simulation of e-e

scattering

COMPARISON TO EXPERIMENT: Metals

Bulk Metal Comparisons for Low Laser Intensity & Field - Methodology:

Thermal Photoemission Moments Approach (Next Gen Model) using τee(E=μ+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)

• Parameters = standard values obtained from Literature or Source (no adjustable parameters)

10-6

10-5

10-4

10-3

200 220 240 260 280 300

Exp (BNL)Theory (Φ = 4.0 )eV

( )Wavelength nm

Lead (Pb)β = 3.0F

o = 1.0 MV/m

T = 300 KData: J. Smedley

200 220 240 260 280 300

Exp (SLAC)4.31 eV5.1 eV60:40 Mix

Wavelength (nm)

Copper (Cu)β = 1.0F

o = 0.01 /MV m

Φ = 4.31 eV = 300 T K

: . Data D Dowell

SLAC:Two grain model

of Cu Surface

60% 4.31 eV(Dowell)

40% 5.1 eV[100] face

0.0

0.5

1.0

1.5

2.0

0 20 40 60 80 100

Charge [nC] 2% AnyCharge 70˚ pCharge 70˚ sTime Dep. Theory

Laser [µJ]

Field = 39 MV/mBeta = 1t = 16 psA = π(0.39 mm)^2λ = 266 nm

, ., 341,379 (1994)Rosenzweig et al NIMA

9.28.06

COMPARISON TO EXPERIMENT: Cs on Metals

Notes1. Standard Library Parameters for

W,Ag,Cs: No Adj. Parameters2. Cs-Ag Data taken by A. Balter:

Low θ : Difficulty removing Cs from prior runs

0

0.02

0.04

0.06

0.08

0.1

0 20 40 60 80 100Theta [%]

808 nm655 nm532 nm405 nm375 nm

0.01

0.1808 nm655 nm532 nm405 nm375 nm

Cesium on Argon-Cleaned Tungsten Surface

0.00

0.04

0.08

0.12

0 20 40 60 80 100

Theo

Theo x 0.85

ExpA

ExpB

θ [%]

Cs on Agλ = 405 nm = 0.0174 /F MV m

Φmin

= 1.6 eV

α = 5.3 Angstroms

Cesium on Silver

QU

AN

TU

M E

FF

ICIE

NC

Y [

%]

ASYMPTOTIC EMITTANCE FORMULA

Take the weak-field, low temperature limit: Transmission probability and Fermi-Dirac distributions replaced by Step Functions

M n = 2π( )−3

2mh2 hω −φ( )⎡

⎣⎢⎤⎦⎥

(n+3)/2 μhω −φ( )

+ x−1⎡

⎣⎢

⎤

⎦⎥0

1

∫(n+1)/2

G p (μ +φ)(x+1)( ),1

x+1,n2

⎡⎣⎢

⎤⎦⎥dx

fλ cosθ,E( ) =exp −

z−

zl E( )cosθ

⎛

⎝⎜⎞

⎠⎟dz

0

∞

∫

exp −z

⎛⎝⎜

⎞⎠⎟dz

0

∞

∫

=cosθ

cosθ + p E( )scattering

factor

εn,rms =

ρ c

2

M 2

2M 0

⇒ρ c

3hc

6μ hω − φ( )

hω + μ( ) εn,rms =

ρ c

2

M 2

2M 0

⇒ρ c

3hc

6μ hω − φ( )

hω + μ( )

M n ≈1

2π( )22mh2 hω −φ( )⎡

⎣⎢⎤⎦⎥

(n+3)/2 μ1/2 hω −φ4 μ +φ( ) p hω + μ( ) +1⎡⎣ ⎤⎦

μ3 hω + μ( )

n=2( )

1 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

μ barrier heightω Laser freq.E Electron energyθ angle wrt normal to surface

laser penetration depthτ relaxation timeR reflectivityμ Fermi Level

p E( ) =

mhk(E)τ (E)

; G a,b,y( ) =x 1−x2( )

y

x+ ab

1

∫ dx; =hω −φμ +φ

LengthRatio

Angularintegral

EnergyRatio

0.0

0.2

0.4

0.6

0.8

1.0

0

50

100

150

200

0.05 0.1 0.15 0.2 0.25 0.3Wavelength [µm]

Copper @ 110 MV/m

EMITTANCE & BRIGHTNESS (analytic)

Consider conditions from:

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.):εrms(233 nm) 0.60 mm-mrad

Theory Value εrms(233 nm) 0.42 mm-mrad

Brightness:

Relaxation time approximation for Copper Parameters (based on fit)(time in fs, energy in eV)

τ ee(E) = 42.9 E − μ( )−1.90

BN =2Ie

4πεrms( )2

For BN, an optimal wavelength exists

εn,rms =

ρ c

3hc

6μ hω − φ( )

μ + φ εn,rms =

ρ c

3hc

6μ hω − φ( )

μ + φ

Emittance

Bn

1−R ω( )( ) I λA≈

3qmc2

2π 2μ 3hωhω + μ( ) hω −φ( )1+ p μ +hω( )( )

Bn

1−R ω( )( ) I λA≈

3qmc2

2π 2μ 3hωhω + μ( ) hω −φ( )1+ p μ +hω( )( )

Ratio of Brightness to Absorbed Laser Power

Energy [eV]

co

s(θ

)c

os

(θ)

Energy [eV]

co

s(θ

)c

os

(θ)

NUMERICAL STUDY: Cu (LHS) & Cs on Cu (RHS)

F = 110 MV/mμ = 7.0 eVT = 300.0 KΦ = 4.5 eVλ = 266 nmρc = 0.113 mm

M(2)

M(0)

F = 110 MV/mμ = 7.0 eVT = 300.0 KΦ= 1.6 eVλ= 266 nmρc = 0.113 mm

FermiLevel

M(2)

M(0)

100 101 102 103

FIELD [MV/m]

270 nm

240 nm

210 nm

180 nm

1600K0.1

0.2

0.3

0.4

0.5

0.6

100 101 102 103

[ / ]FIELD MV m

270 nm

240 nm

210 nm

180 nm

300K

NUMERICAL VS ANALYTIC: Cu

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)

ASYMPTOTIC FORMULA (thermal)

Bare copper metal

Work function 4.5 eV

Illumination radius 1.13 mm

100 101 102 103

FIELD [MV/m]

270 nm

240 nm

210 nm

180 nm

1600K

0.6

0.7

0.8

100 101 102 103

[ / ]FIELD MV m

270 nm

240 nm

210 nm

180 nm

300K

NUMERICAL VS ANALYTIC: Cs on Cu

PERFORMANCE

Analytic model works best when F & T not large, and photon energy significantly higher than barrier

Error @ 1 MV/m, 300K: -6% to -13%

NUMERICAL EVALUATION

ASYMPTOTIC FORMULA (photo)

ASYMPTOTIC FORMULA (thermal) (not visible)

Copper W/ Cs coating

Work function 1.6 eV

Illumination radius 1.13 mm

IDENTIFY factors that affect QE (e.g., laser, environment, photocathode material)DEVELOP a custom-engineered controlled porosity photo-dispenser cathode

DISPENSER PHOTOCATHODES

Metal

TopView

CsO

SideView

Interpore ≈ 6 µm; Grain Size≈ 4.5 µm; Pore Diam. ≈ 3 µm

Conventional Dispenser

Controlled Porosity

0

2

4

6

8

1 2 3 4 5 6 7 8

Grain Index

Grain SizeAve Diam = 4.8 μm

0

1

2

3

4

5

6

7

0 16 32 48 64 80 96 112 128 144 160

SEPARATION (pixel)

LogNorm(x)

bin size = 8 pixelsLog-Normal Parametersμ = 35.3 pixelsσ = 0.786

- - :Mean pore to pore35.3 (10 x μ / 143 ) = 2.47 m pixel μm

Cs Dispenser Cathode

Dispenser Cathode Surface showing pores & grains

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

421 Pixels

Scale: 421 Pixels = 67 µm

0

1000

2000

3000

4000

0 20 40 60 80 100 120

yCutoffs

GRAY SCALE (RGB index)

Value

1417A1

52.062B1

3198.8A2

62.608B2

3440.7A3

82.955B3

y(n) = Aj

n−Bj

8⎛⎝⎜

⎞⎠⎟

2

+1⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

−1

j=1

3

∑

Grain A Grain B Grain C

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

Pi, jn =

1Ro + 8

Ro −1( )Pi, jn−1 + Pi+k, j+l

n−1l=−1

1∑k=−1

1∑( )

ModelExp

CONCLUSION

NEED FOR PHOTOCATHODE

Rugged & Long-lived Photocathodes Critical for MW-class FELsDemands 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 1 the calculated emittance of a photocathode ninth annual directed energy symposium 2006...

Documents