ANL 1

SURVEY OF THE EMISSION PROCESSSURVEY OF THE EMISSION PROCESSSURVEY OF THE EMISSION PROCESS

Kevin L. JensenCode 6841, ESTDNaval Research LabWashington, DC 20375

Kevin L. JensenCode 6841, ESTDNaval Research LabWashington, DC 20375

ANL THEORY INSTITUTE ON PRODUCTION OF BRIGHT ELECTRON BEAMSSeptember 22-26, 2003, Argonne National Laboratory, Argonne, IL

Donald W. Feldman, Patrick G. O’Shea Inst. Res. El. & Appl. Phys.University of MarylandCollege Park, MD 20742

ACKNOWLEDGEMENTS FUNDING & SUPPORT

ANL 2

ISSUES AND QUESTIONS

QUESTIONS AND COMMENTS BY C. SINCLAIR [1]

Fundamental R&D / theory question(s):

What combination of achievable, external fields results in the maximum charge density in 6-D phase space (from a zero thermal emittance source)? For a CW source, it is not obvious whether DC or RF fields are best (particularly for room temperature RF, where the fields are limited by thermal considerations). For low duty factor applications, the consensus appears to be RF, but that must depend on the bunch charge.

How should emittance be measured, and what is required to have a high quality measurement?

Regarding the relation between thermal emittance and bunch duration at the cathode: space charge fields are reduced by making larger bunches and emitting from a smaller area (which increases longitudinal and transverse emittance) - therefore, for a given bunch charge, what is the optimal emitting area and bunch duration to achieve bets final charge density in 6-D phase space (the answer will depend on whether fields are static or dynamic).

Application and requirements dictate photocathode: needs of low repetition rate, high charge bunches differ from CW pulse trains of lower bunch charges

A goal for progress in photoemission guns: develop reliable methods for generating uniformly populated (transversely and longitudinally) optical pulses to generate uniform charge distributions from the cathode and result in minimum emittance.

[1] Emails to K. Jensen, and Kwang-Je, et al., September 2003

ANL 3

AN INTRODUCTION TO

ELECTRON EMISSION THEORY AND PROCESSES Nature Of The Emission Barrier

Tunneling, Density, and Current Integral: FN and RLD Equations Complications: Semiconductors, Emission Near Maximum A Thermal - Field Emission Formula Photoemission Considerations Quantum Efficiency A Thermal - Photoemission Formula

Laser Heating of the Electron Gas Laser Heating of the Electron Gas Time-dependent Model of Laser-induced Thermal Photoemission Dispenser Cathode Experiment

Complicating Circumstances Field Enhancement Emission at the Barrier Maximum

OUTLINE

ANL 4

Exchange Correlation

Potential

Dipole Term

Ionic CoreEMISSION FROM METALS

Large Density of Electrons Exist In Conduction Band (> 60 Billion / µm3);

Very Small Fraction Contribute to Current (A/cm2 ≈ 62 per µs per µm2)

EMISSION BARRIER

ValenceBand

ConductionBand

Band Gap

Vacuum level

EF

€

Vo =−∂∂ρ

ρεxc(ρ)[ ] −Δφ+ ε ion

The Largest Component of the Barrier Is Due to the

Exchange Correlation Potential

ANL 5

Electron Number Density ρElectrons Incident On Surface

Or Interface Barrier Are

Distributed In Energy

According To A 1-D

“Thermalized” Fermi Dirac

Distribution Characterized By

The Chemical Potential and

Called The “Supply Function”

€

ρ(o)=13π 2

2mo

h2

⎛ ⎝ ⎜

⎞ ⎠ ⎟3/ 2

=kF3

3π 2

€

f (k)=2

2π 2

2πk⊥dk⊥

1 +expβ(E||+ E⊥ −)( )0

∞

∫

=m

πβh2 ln 1+eβ (−E(k ))[ ]

€

f (k)=22π 2

2πk⊥dk⊥

1 +expβ(E||+ E⊥ −)( )0

∞

∫

=m

πβh2 ln 1+eβ (−E(k ))[ ]

€

ρ() =2Mc

m2πβh2

⎛ ⎝ ⎜

⎞ ⎠ ⎟

3/22

πy

1 + (expy−β)dy

0

∞

∫

=Nc

2π

F1/ 2(β)

€

(T) =o 1−112

πβo

⎛ ⎝ ⎜

⎞ ⎠ ⎟

2

−180

πβo

⎛ ⎝ ⎜

⎞ ⎠ ⎟

4

+K ⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

€

(T) =o 1−112

πβo

⎛ ⎝ ⎜

⎞ ⎠ ⎟

2

−180

πβo

⎛ ⎝ ⎜

⎞ ⎠ ⎟

4

+K ⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

Density Does Not Change With Temperature, So µ Must:

DISTRIBUTION OF ELECTRONS IN METAL

Zero Temp. ((0 ˚K) = o = EF)

ANL 6

Metals

0

5

10

15

1 10 100r

EXCHANGE-CORRELATION POTENTIAL

The Density ρ of an Electron Gas Is

€

Vxc(x)=−∂∂ρ

ρ εex +εcorr( )[ ]

€

ρ=2

2π( )3 fFD E(k)( )d3k=

kF3

3π 20

∞∫

€

εke =2

2π( )3

hk( )2

2mfFD E(k)( )d3k=

35

0

∞∫ ρ

€

εex =2

2π( )3 fFD E( )vq(kF )d

3k0

∞∫ =−

34

Q3ρπ ⎛ ⎝ ⎜

⎞ ⎠ ⎟1/3

vq(kF ) =2Q

q2θ kF −

r k +

r q( )∫ d3q

€

εcorr =−2Qao

0.876r + 7.811 ⎛ ⎝ ⎜

⎞ ⎠ ⎟

ρ(r)=3

4π rao( )3

Correlation (Potential) Energy Form due to WignerExchange (Potential) Energy

Kinetic Energy

CuAuNa

1019

#/cm3

ANL 8

+

–xi

0

0.3

0.6

0.9

1.2

-15 -10 -5 0

ρe( )x

ρe( ) ( )x approx

(+)Background

kF( –x x

o)

DIPOLE COMPONENT

Origin (xi) Of + Background Differs From That Of Electrons (x = 0) To Preserve Global Charge Neutrality

€

0 = ρe(x)−ρi (x){ }dx−∞

∞∫

€

ρe(x) =12π

f (k)ψ k(x)2dk

0

∞

∫ρi(x) =ρoθ(x−xi )

Electrons

Ion cores

Tanh-Approx.: Match ρ(xi), ∂xρ(xi)

€

ρe(x) ≈ρo2

1−tanhλkF x−xi( )[ ]{ }

λ ≈58; xi ≈xo−

52kF

Magnitude of Dipole (Tanh-model: Qualitative, Overestimates Magnitude)

€

Δφ=q2ρoεo

1

4λ2kF2

⎛

⎝ ⎜

⎞

⎠ ⎟

(ln u)1 +u

du0

1

∫ =−64π225

QkF

ANL 9

SIMPLE MODEL OF TUNNELING

SQUARE BARRIER OF WIDTH “L”

Match ψ(x) and ∂xψ(x) where V(x) Changes

Incident

eikx

Reflected

r(k) eikx

Transmitted

t(k) eikx

€

jk x( )=h2mi

ψ k * ∂xψ k −ψ k∂xψ k *( )

€

T k( )=jtrans(k)j inc(k)

=2κk( )

2

2κk( )2+ κ 2 +k2( )sinh2 κL( )

€

T k( )=jtrans(k)j inc(k)

=2κk( )

2

2κk( )2+ κ 2 +k2( )sinh2 κL( )

€

κ =1h

2mVo−E(k)( )

κL = θ(E)= “Area under Curve”κL fi θ(E)

T(E<Vo) ≈ exp{–2θ(E)}T(E>Vo) fi 1

€

1 1ik −ik

⎛

⎝ ⎜

⎞

⎠ ⎟

1r(k)

⎛

⎝ ⎜

⎞

⎠ ⎟ =

1 1κ −κ ⎛

⎝ ⎜

⎞

⎠ ⎟ab

⎛

⎝ ⎜ ⎞

⎠ ⎟

€

eκL e−κL

κeκL −κe−κL ⎛

⎝ ⎜

⎞

⎠ ⎟ab

⎛

⎝ ⎜ ⎞

⎠ ⎟ =

eikL e−ikL

ikeikL −ike−ikL

⎛

⎝ ⎜

⎞

⎠ ⎟t(k)0

⎛

⎝ ⎜

⎞

⎠ ⎟

Vo

ANL 10

IMAGE CHARGE POTENTIAL

Schrödinger’s Equation:

If We Let: ψk(x) = R(x) exp[i S(x)]

Density Velocity

€

jk(x) =R(x)2hm∂xS(x)

⎧ ⎨ ⎩

⎫ ⎬ ⎭

€

ψ k(x) ∝ κ(x)−1/2expi κ(x)dx∫{ }

Slowly varying density and constant current:

€

−h2

2m∂x2 +V(x)

⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪ψ k(x)=E(k)ψ k(x)

€

jk2

R4 −1R∂2

∂x2R−

i

R2∂∂x

jk =κ2

0 0

E

0

4

8

0 5 10 15 20

No ImageImage

x [Å]

y = (4FQ)1/2/

€

Vi(x) = −q2

4πεo(2 ′ x )2 ⎧ ⎨ ⎩

⎫ ⎬ ⎭d ′ x

x

∞

∫ =−q2

16πεox≡

Qx

Q = 0.36 eV-nmy = 0.038 eV {F[MV/m]}1/2/[eV]

2xForce Between

Electron and Image: Vi is Energy to Remove Image to infinity from x

ANL 12

€

J T,F( )=qm

2π 2βh3 e−θ (E )

0

∞

∫ ln1 +eβ (−E)( )dE

€

J T,F( )=qm

2π 2βh3 e−bfn /F e−cfn (−E)

0

∞

∫ ln 1 +eβ (−E )( )dE

RICHARDSON EQUATION: THERMIONIC EMISSION Dimensionless Parameter n = β /b is small

€

−(1 + cfn) (exp−cfn){ }

Semiconductor

EMISSION EQUATIONS

€

bfn=43h

2m3v(y); cfn =2

hF2mt(y)

FOWLER NORDHEIM: FIELD EMISSION Dimensionless Parameter n = β /b is large

€

=qm

2π2h3cfn2 exp−

bfnF

⎛

⎝ ⎜ ⎞

⎠ ⎟

Field

€

cfnπ / β(sincfnπ / β)

Thermal-Field

€

J (T,F )=qm

2π 2βh3 Θ +φ−E( ) ln1 +eβ (−E)( )0

∞

∫ dE

€

eβ (−E )

+φ

∞

∫ dE=mq

2π 2h3 kB2T2exp−φ / kBT( )

€

φ=− 4QF

ANL 13

RLD & FN SUMMARY part II

Field Emission

Large # of electrons with low transmission probability

Relatively T-independent

High Work Functions For Canonical Metals

“High” Current Densities But Generally Small Emission Sites

Thermal Emission

Small # of electrons with near-unity transmission probability

Exponential T-dependence

Low Work Functions for Coated Materials

“Low” Current Densities but Generally Large Areas

1300

1400

1500

1600

1700

1800

2 4 6 8 10Field [MV/m]

4.4

0.0

2.2

kA/cm2

= 2.0 eV = 2.0 eV

Ba-Coated Tungsten

Tem

per

atur

e [K

elvi

n]

300

640

980

1320

1660

2000

2 4 6 8 10Field [GV/m]

6.6

0.0

3.3

GA/cm2

= 4.6 eV = 4.6 eV

Bare Tungsten

Tem

per

atur

e [K

elvi

n]

ANL 14

Poisson’s Equation (o = bulk):

10-4

10-3

10-2

10-1

100

0.01 0.1 1

Low φs Highφ

sExact

[ / ]Vacuum Field eV Å

Surface φ [ ]eV

BAND BENDING

Ec

Ev

µo Fvac

c

µ

ZECA: f(x) is the same as that which would exist if no current was emitted.

ZECA: f(x) is the same as that which would exist if no current was emitted.

€

F φs( )2=

2Nc

Ks3εo πβ

expβo( ) expβφs( )−βφs−1[ ]

€

F φs( )2=2π 2Nc

3βKs3εo

βπ ⎛ ⎝ ⎜

⎞ ⎠ ⎟1/ 2

85

βπ ⎛ ⎝ ⎜

⎞ ⎠ ⎟2

+1 ⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

Asymptotic Case: β ≤ –2:

Asymptotic Case: β » 1:

€

∂∂φ

F 2 =Nc

K sεo

2π

F1/2 β o +φ( )[ ] −F1/ 2 βo( ){ }

ANL 15

FN ( =4.4 eV)

FN ( =2 eV)

RLD ( =2 eV)

FN: Corrupted When Barrier Max Is Too Close to Fermi Level or Slope of ln(T(E)) Exceeds ln(f(E))

Maximum Field: β > 6

Minimum Field: cfn < 2β

FN AND RLD DOMAINS

DOMAINS

RLD: Corrupted When Tunneling Near Barrier Max Is Non-negligible

€

F <14Q

−6kBT( )2

€

F >4h

2m( )kBT

€

F <2m

10hkBT

⎛

⎝ ⎜

⎞

⎠ ⎟

4/3

Q1/3

10-4

10-3

10-2

10-1

100

400 800 1200 1600

Field [eV/Å]

Temperature [K]

Fie

ld [

eV/Å

]

Fmax(1000K) = 11.1 MV/m

Fmax(2eV,1000K) = 1527 MV/m

Fmin(2eV,300K) = 750 MV/m

Thermionic

Photocathode

Field

Typical Operational Domain of Various Cathodes

Note: Photocathodes Typically Run at or Near 300 K

and Surface Roughness Increases F

ANL 16

0.001

0.01

0.1

1

10

100

2 3 4 5 6 7 8 9 10

300 K3000 KFermi Level

E(k)

Electron Momentum Into Barrier Determines Emission Probability

Finite Temperature (β = 1/kBT)

T(E) (b = slope of -ln[T(E)])E(k)

T(E)4 GV/m

T(E)10 MV/m

ELECTRON DISTRIBUTION

€

f kx( ) = fFD E( )d2k⊥

2π( )2

0

∞

∫

€

fFD E( ) = 1+expβ E−( )[ ]{ }−1

f kx( ) =m

πβh2ln 1+expβ −E(kx)( )[ ]{ }

MaxwellBoltzmann

Regime

0 K-like Regime

€

T E( ) = 1+expb E−Ec( )[ ]{ }−1

€

Ec = +bfnFcfn

Ec = + − 4QF

Field

Thermal 0.0

0.50

1.0

1.5

5.5 6 6.5 7 7.5Energy [eV]

731 MV/m300 K

664 MV/m @ 550 K

217 MV/m900 K

J(F,T) ≈ 1 A/cm2

= 2.0 eVS

up

ply

Fu

nct

ion

f(E

) [#

/nm

2]

Tra

nsm

iss

ion

Co

eff

T(E

)

ANL 20

€

NA =n n+1( )n+1[ ]

n+1e−p

NB =n2

πλ

Ng Erf λ bφ−xp( )[ ] −Erf λxp[ ]{ }

NC = 1−nep−bφ

n+1

⎛

⎝ ⎜

⎞

⎠ ⎟e−bnφ

Nomenclature:T(E) ≈ To / {1+exp[b(Ec–E)]}x = b(Ec – E)p = b(Ec – )n = β/bxp Integrand Approximated λ By Gaussian of FormNg Ng exp[- (x-xp)2]

GENERALIZED J(F,T) EQUATION

Using the Tanh-form Best Fit of T(E):

€

J (F ,T ) =qm

2π2h3To

β 2

⎛

⎝ ⎜

⎞

⎠ ⎟

ln1+en(x−p)[ ]

ex +1

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥dx

−∞b+ p∫ ⎧

⎨ ⎪

⎩ ⎪

⎫

⎬ ⎪

⎭ ⎪

=qm

2π2h3To

β 2

⎛

⎝ ⎜

⎞

⎠ ⎟N −∞,b + p( )

€

J (F ,T ) =qm

2π2h3To

β 2

⎛

⎝ ⎜

⎞

⎠ ⎟

ln1+en(x−p)[ ]

ex +1

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥dx

−∞b+ p∫ ⎧

⎨ ⎪

⎩ ⎪

⎫

⎬ ⎪

⎭ ⎪

=qm

2π2h3To

β 2

⎛

⎝ ⎜

⎞

⎠ ⎟N −∞,b + p( )

Separate N Into 3 Regions:

Field: NA = N(p,b+p)

Intermediate: NB = N(-b+p,p)

Thermal: NC = N(-∞,-b+p)

FN: n = ∞ limit of NA

RLD: n = 0 limit of NC

ANL 21

T(WKB)

T(FN)

T(RLD)0

0.2

0.4

0.6

0.8

1

6.50 7.00 7.50

T(E)T

a(E)

T(E)f(E)

[a.u.]

Energy [eV]

= 5.875 eV

Φ = 2.0 eVF = 0.04 eV/nmT = 600 K

≤20%

≤20%

-16

-14

-12

-10

-8

-6

-4

-2

0

0.01 0.1 1

NA + N

B + N

C

NumericalN(FN)N(RLD)

Field [V/nm]

T = 600 K = 2 eVn

o = 0.75

RESULTS

Current Integrand BehaviorRLD: Cut-off at Apex E Too Extreme

FN: Over-predicts T(E) at Apex

Variation of n-factor with FieldLarge Range of n Obscures Differences:20% Error: RLD: F = 0.22; FN: F = 1.7

ANL 22

€

J λ T,F ,( ) =q1−R( )Iλ (t)hω

⎛ ⎝ ⎜

⎞ ⎠ ⎟U β hω −φ( )[ ]

U β[ ]

⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪

+ARLDT 2exp−βφ[ ]

€

J λ T,F ,( ) =q1−R( )Iλ (t)hω ⎛ ⎝ ⎜

⎞ ⎠ ⎟U β hω −φ( )[ ]

U β[ ]

⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪

+ARLDT 2exp−βφ[ ]

€

U x( ) = ln 1 +ey( )dy−∞

x

∫

=ex 1−beax( ) x≤0( )

12

x2 +π 2

6−e−x 1−be−ax( ) x> 0( )

⎧

⎨ ⎪

⎩ ⎪

“Fowler factor”

10-5

10-4

10-3

10-2

10-1

100

12 14 16 18 20 22Energy [eV]

T(E)

T(E+hν)

( +2T E hν)

( +3T E hν)

( +4T E hν)

( )f E

Field significantly exaggerated to show detail

T(E

); f

(E)

[101

6 #

/cm

2]

THERMAL PHOTO-CURRENT (I)

Product/sum of Several Factors:

Electron Charge (q)

Absorption Factor (1-R)

# of photons (Iλ/hω)

Probability That Photo-Absorbing Electron in Consequence Has Sufficient Energy to Surmount Surface Barrier (Ratio of U’s) [1]

Standard Thermal Emission Due to Laser Heating (JRLD)

[1] “The precise hypothesis which succeeds so well in correlating the observed effect near the threshold is that the photoelectric sensitivity or number of electrons emitted per quantum of light absorbed is to a first approximation proportional to the number of electrons per unit volume of the metal whose kinetic energy normal to the surface augmented by hν is sufficient to overcome the potential step at the surface.

R. H. Fowler, PR38, 45 (1931). (italics in original)

= 1064 nm

ANL 23

QUANTUM EFFICIENCY (1D)

ΔQ / ΔE = Jλ / Iλ: Therefore, QE Governed by U[ (h U( )

€

QE1D ≈

2 1−R( )

β( )2 exp−β φ−hω( )[ ] β hω −φ( )⇒ −∞[ ]

1−R( )hω −φ

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

β hω −φ( ) ⇒ ∞[ ]

⎧

⎨

⎪ ⎪

⎩

⎪ ⎪

€

QE1D ≈

2 1−R( )

β( )2 exp−β φ−hω( )[ ] β hω −φ( )⇒ −∞[ ]

1−R( )hω −φ

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

β hω −φ( ) ⇒ ∞[ ]

⎧

⎨

⎪ ⎪

⎩

⎪ ⎪

STANDARD PHOTOEMISSION (Photo-excited Electrons Below Fermi Level)

€

U x( ) ≈ex x<<−1( )12

x2 x>> +1( )

⎧ ⎨ ⎪

⎩ ⎪

€

J λ T,( ) ⇒q

hω1−R( )Iλ (t)

hω −φ

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

€

β hω −φ( ) ⇒ ∞

€

J λ T,( ) ⇒ 1−R( )2πh( )

2

mω2 Iλ (t)J RLD T,φ−hω( )

€

β φ−hω( ) ⇒ ∞

THERMAL PHOTOEMISSION (PHOTO-EXCITED ELECTRONS IN THERMAL TAIL)

1-D ASYMPTOTIC EXPRESSION FOR

QUANTUM EFFICIENCY

ASYMPTOTIC LIMITS OF FOWLER FUNCTION(Richardson Approximation Implicit in U(x) - must be modified if tunneling becomes significant)

ANL 24

AN INTRODUCTION TO

ELECTRON EMISSION THEORY AND PROCESSES Nature Of The Emission Barrier

Tunneling, Density, and Current Integral: FN and RLD Equations Complications: Semiconductors, Emission Near Maximum A Thermal - Field Emission Formula Photoemission Considerations Quantum Efficiency A Thermal - Photoemission Formula

Laser Heating of the Electron Gas Laser Heating of the Electron Gas Time-dependent Model of Laser-induced Thermal Photoemission Dispenser Cathode Experiment

Complicating Circumstances Field Enhancement Emission at the Barrier Maximum

OUTLINE

ANL 25

ChemicalPotential

electron-electron scattering

electron-lattice scattering

Power transfer by electrons to lattice

285.1 GW / K cm3 for W

Laser EnergyAbsorbed

Electron & LatticeSpecific Heat

€

Ce∂∂t

Te=∂∂z

κ(Te,Ti )∂∂z

Te ⎛ ⎝ ⎜

⎞ ⎠ ⎟−g Te−Ti( ) +G z,t( )

Ci∂∂t

Ti =g Te−Ti( )

LASER HEATING OF ELECTRON GAS

Differential Eqs. Relating Electron (Te) to Lattice Temperature (Ti)

Thermal Conductivity & Relax. Time

1

1.5

2

2.5

2.6 2.8 3 3.2log

10(Temperature [K])

Tungsten

τeeτ

ph

τ300 K128 fs

1000 K25 fs

2000 K8 fs

€

κ Te,Ti( ) =23m

τ Te,Ti( )Ce Te( )

1τ=

1τee Te( )

+1

τ ph Ti( )

€

τee Te( ) =hAo

1kBTe

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

=Aee

Te2

τ ph Ti( ) =h

2πλo

1kBTi

⎛ ⎝ ⎜

⎞ ⎠ ⎟=

Bep

Ti

ANL 26

lattice

electrons

SPECIFIC HEAT APPROXIMATIONS

High Temp (> 300 K) Specific Heat Approximations

Specific Heat Variation in Energy Density With Temperature

€

C T( ) =∂∂T

U

€

Ce Te( ) =∂∂Te

E−( )De E( )

expβe E−( )e[ ] +1dE

0

∞

∫

Ci Ti( ) =∂∂Ti polarizations

∑hωDi ω( )

expβihω i[ ]−1dω

0

ω D

∫

€

Ce Te( ) =γ Te

1+740

πβe ⎛ ⎝ ⎜

⎞ ⎠ ⎟

2 ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

Ce Te( ) =γ Te

1+740

πβe ⎛ ⎝ ⎜

⎞ ⎠ ⎟

2 ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

γ Tungsten( )=136.48 Joule

Kelvin2meter2

Tungsten( )=18.08 eV

€

Ci Ti( ) =3NkB

1+120

TD

Ti

⎛ ⎝ ⎜

⎞ ⎠ ⎟2 ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

Ci Ti( ) =3NkB

1+120

TD

Ti

⎛ ⎝ ⎜

⎞ ⎠ ⎟2 ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

N Tungsten( )= 183.84grammole

⎛ ⎝ ⎜

⎞ ⎠ ⎟−1

19.3gram

cm3

⎛ ⎝ ⎜

⎞ ⎠ ⎟

TD Tungsten( )=400 Kelvin0.0

1.0

2.0

3.0

500 1000 1500 2000 2500

Data 4

10 x Ce(T)

Ci(T)

Temperature [Kelvin]

TUNGSTEN

Room Temp

C(T

) [J

ou

les/

Ke

lvin

cm

3]

€

β ≡1

kBT

ANL 28

ABSORBED LASER POWER

€

U x( ) =ex 1−beax( ) x≤0

12

x2 +16π 2−e−x 1−be−ax

( ) ⎛ ⎝ ⎜

⎞ ⎠ ⎟

x> 0

⎧

⎨ ⎪ ⎪

⎩ ⎪ ⎪

a=12π 2−12 ln 2( )

12−π 2

⎛

⎝ ⎜

⎞

⎠ ⎟; b=1−

π 2

12

0.6

0.7

0.8

0.9

1

2.8 3 3.2 3.4 3.6 3.8 4

Log10( [ ])Temperature K

1064 nm

532 nm

355 nm

266 nm = 0.0 /Field MV m

Abs

orbe

d E

nerg

y F

acto

r

Fowler Function

€

G(z,t) = 1−R( )Iλ (t)e−z/δ

δ ⎛

⎝ ⎜

⎞

⎠ ⎟ 1−

U β hω −φ( )[ ]U β[ ]

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

Iλ (t) =Ioe−(t−to) /Δt[ ]

2

penetration depthemission barrier heightU terms: Energy lost from direct photoemission

Laser Term G(z,t) Is a Product Of:

Reflection Coefficient

Incident Laser Power

Penetration Factor

Absorbed Energy Factor

ANL 29

0

20

40

60

80

100

101

102

103

104

105

106

107

0.01 0.1 1λ [ ]µm

[%]Reflectivity

Absorption Length δ [ ]nm

Classical Free Electron Theory of Simple Metals (Drude):

Motion of Electrons in Metals Is Damped Due to Collisions of

Electrons With Non-ideal Lattice. Bound Electrons Are Ignored.

Valid for Low Frequency.

Classical Free Electron Theory of Simple Metals (Drude):

Motion of Electrons in Metals Is Damped Due to Collisions of

Electrons With Non-ideal Lattice. Bound Electrons Are Ignored.

Valid for Low Frequency.

REFLECTION AND PENETRATION (Theory)

Complex Dielectric Constant fi Optical Properties Of Metals as function of λ Real: index of refraction n

Imag: damping constant k

Related to Reflectivity R and absorption length of light in metal δ.

Plasma Frequencies: • = e- concentration• o = dc conductivity)

€

ωp2 =

q2ρmεo

;ωo =εoω p

2

σ o

In terms of Plasma Frequency: [ = 2 c/

€

2nk=ωoω p

2

ω ω2 +ωo2( ); n2 −k2 =1−

ω p2

ω2 +ωo2( )

€

:Reflectivity R=n−1( )

2+ k2

n+1( )2+k2

:Absorption Lengthδ = c2ωk

= λ4πk

€

:Reflectivity R=n−1( )

2+ k2

n+1( )2+k2

:Absorption Lengthδ = c2ωk

= λ4πk

Drude Equations

ρ = 1.68x1023 #/cm3

σ = 3.6E5 (Ohm-cm)-1

ANL 30

Quantum Mechanical Treatment of Optical Properties

IR Behavior: Free electronsVisible/UV: Bound Oscillators

Extract n and k from Exp. Data & Apply Drude Equations

0

20

40

60

80

100

0

5

10

15

20

25

30

0 0.5 1 1.5 2λ [ ]µm

[%]Reflectivity

Absorption Length δ [ ]nm

Tungsten

REFLECTION AND PENETRATION (Practice)

Complex Dielectric Constant fi Optical Properties Of Metals as function of λ Real: index of refraction n

Imag: damping constant k

Related to Reflectivity R and absorption length of light in metal δ.

Plasma Frequencies: • = e- concentration• o = dc conductivity)

€

ωp2 =

q2ρmεo

;ωo =εoω p

2

σ o

In terms of Plasma Frequency: [ = 2 c/

€

2nk=ωoω p

2

ω ω2 +ωo2( ); n2 −k2 =1−

ω p2

ω2 +ωo2( )

€

:Reflectivity R=n−1( )

2+ k2

n+1( )2+k2

:Absorption Lengthδ = c2ωk

= λ4πk

€

:Reflectivity R=n−1( )

2+ k2

n+1( )2+k2

:Absorption Lengthδ = c2ωk

= λ4πk

Drude Equations

ANL 31

Diff Eqs. Governing T-Evolution

Diffusion Equation

Discretization (j=time, i=space)Standard Crank-Nicholson

Non-linearity

different t-scale

TIME EVOLUTION SIMULATION

€

Ce(Te)∂∂t

Te=∂∂z

κ(Te,Ti )∂∂z

Te ⎛ ⎝ ⎜

⎞ ⎠ ⎟−g Te−Ti( ) +G z,t( )

Ci (Ti )∂∂t

Ti =g Te−Ti( )

€

∂tT =D∂z2T +G( z,t)

€

M • T[ ] j, i =DΔt

2Δx2Tj,i+1−2Tj,i +Tj,i−1( )

I −M[ ] • v Tj+1= I + M[ ] •

v Tj +

v G(s)ds

tj

tj+1∫

€

M • T[ ] j, i =DΔt

2Δx2Tj,i+1−2Tj,i +Tj,i−1( )

I −M[ ] • v Tj+1= I + M[ ] •

v Tj +

v G(s)ds

tj

tj+1∫

TIME SCALES:Engagement Time 10 sLaser Pulse-to-Pulse 4 nsLattice Therm (Ci/g) 8.4 psRelaxation (RT): 128 fs∆t (600K & ∆x = 20 nm): 0.4 fsRatio: 10000000

Straight-forward Numerical Program Not Feasible To Model

Multiple ns-Separated Laser Pulses Incident On Cathode - Require Separate Time Scale

Models For Single / Multi pulses

Straight-forward Numerical Program Not Feasible To Model

Multiple ns-Separated Laser Pulses Incident On Cathode - Require Separate Time Scale

Models For Single / Multi pulses

LENGTH SCALES:Cathode 1.0 cmThermal Distance 200 nmLaser 10 nmRatio: 100000000

ANL 32

€

Te(x,t) =To + ΔT u x,tk+s( )−u−2L−x,tk+s( ){ }k=0

N

∑

MACRO-TIME SCALE PRF HEATING (I)

Bulk T = Sum of Gaussian

Laser Pulses Io exp(-(t/δt)2)

Effect = Sum of N Dirac-delta

T- Pulses at Surface

Magnitude of Temperature

Rise Dictated by Deposited

Laser Energy ΔE

Temp. Depends on Location

of Fixed Boundary L

Bulk T = Sum of Gaussian

Laser Pulses Io exp(-(t/δt)2)

Effect = Sum of N Dirac-delta

T- Pulses at Surface

Magnitude of Temperature

Rise Dictated by Deposited

Laser Energy ΔE

Temp. Depends on Location

of Fixed Boundary L

surface image

Δt

k k+1

δt

€

Te(x,t) =To +ΔT

4πDoΔtSN α−(x),

tΔt

⎛ ⎝ ⎜

⎞ ⎠ ⎟−SN α+(x),

tΔt

⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎧ ⎨ ⎩

⎫ ⎬ ⎭

€

Te(x,t) =To +ΔT

4πDoΔtSN α−(x),

tΔt

⎛ ⎝ ⎜

⎞ ⎠ ⎟−SN α+(x),

tΔt

⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎧ ⎨ ⎩

⎫ ⎬ ⎭

€

SN (α ,s)= k+ s( )−1/2

exp−α

k+ s ⎛ ⎝ ⎜

⎞ ⎠ ⎟;

k=0

N

∑ α± x( ) =L2

4DoΔt1± 1+

xL

⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎡

⎣ ⎢

⎤

⎦ ⎥

s =1/2: Evolution of surface temperature with pulse number Ns > 1/2: Cooling of surface after N pulsestk+s = (k+s)Δt

€

u x,t( ) = 4πDot( )−1/ 2

exp−x2

4Dot ⎛

⎝ ⎜ ⎞

⎠ ⎟

ΔT =Tc

2Tb + Tc

2 +Tb

2 ⎛ ⎝

⎞ ⎠

−1/2

Do ≈κ To,To( ) / Ce(To)

Diffusion functions

€

Tc =2δπDoΔt( )

1/4 ΔEγ ⎛ ⎝ ⎜

⎞ ⎠ ⎟1/2

Tb =1

2γδ2γTo + πgΔt( ) πDoΔt( )

1/2

ΔE= 1−R( ) Io(t)dt−∞

∞∫

Single Pulse Heating

ANL 3365 mg NaCl

MACRO-TIME SCALE PRF HEATING (II)

Characteristic Temperature: Tmax

is temperature at surface when

T(x) profile is linear (asymptote

as N fi ∞ at surface)

Ex: 1 GW/cm2 = A Pulse of

E = 0.71 mJ with t = 40 ps

Incident on 1 mm2 Area

Characteristic Temperature: Tmax

is temperature at surface when

T(x) profile is linear (asymptote

as N fi ∞ at surface)

Ex: 1 GW/cm2 = A Pulse of

E = 0.71 mJ with t = 40 ps

Incident on 1 mm2 Area

€

Tmax=To + ΔTLδCe Te( )Δtκ Te,Ti( )

⎛

⎝ ⎜ ⎞

⎠ ⎟

≈To +6 1−R( )mLI oδt

Δt2gτ

€

=To + 662KelvinL[ ] cm δt[ ] ps Io[GW / cm2 ]

Δt[ ]ns( )2τ[ ]fs

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

600

620

640

660

680

700

720

10-9 10-7 10-5 0.001 0.1 10

COOLING

T(x=0) [K]Bulk

t [sec]

600

620

640

660

680

700

720

10-9 10-7 10-5 0.001 0.1 10

HEATING

T [K]Tmax

t [sec]

€

I o =ΔEπAδt

ANL 34

TIME SIMULATION MATRIX EQUATIONS

Matrix Equation

Matricies

Non-linearity: Finite Difference Multi-point

Algorithm Preserves Stability

Boundary Tbc: RHS: reflect / LHS: absorb Temp BC Given by Macro-scale

Time Simulation and Held Fixed

€

Ce + J −D( )t+Δt

• Te t +Δt( )= Ce−J +D( )t• Te t( ) + 2J • Te(t) +

12

G(t)dt +Tbc∫D+ H( )

t+Δt• Ti t +Δt( )= D + H( )

t• Ti t( ) + H • Te(t + Δt) +Te(t)( )

Electrons

Lattice

Matricies Require Evaluation of Ce(Te) / κ(Te,Ti) at Advanced Time Steps:

USE OF PREDICTION/CORRECTION SCHEME: “Guess” j+1 elements - solve - use results in next guess

€

Ce[ ]i, j=

12Δt

Ce T t + Δt( )[ ] +Ce T t +Δt( )[ ]{ }δij

Ci[ ]i, j =12Δt

Ci T t + Δt( )[ ] +Ci T t +Δt( )[ ]{ }δij

H[ ]i, j=12

gδij ; J[ ]i, j=

g Ci[ ]i, j

2 Ci[ ]i, j +gδij

€

D(t)[ ]i, j =1

4Δx2κ Te,Ti( )[ ] j−1 + κ Te,Ti( )[ ] j ⎧ ⎨ ⎩

⎫ ⎬ ⎭δi, j−1

−1

2Δx2 κ Te,Ti( )[ ] j−1+ 2 κ Te,Ti( )[ ] j

+ κ Te,Ti( )[ ] j+1 ⎧ ⎨ ⎩

⎫ ⎬ ⎭δi, j

+1

4Δx2κ Te,Ti( )[ ] j−1 + κ Te,Ti( )[ ] j ⎧ ⎨ ⎩

⎫ ⎬ ⎭δi, j+1

ANL 36

Go(t)/Go(0)

0

0.2

0.4

0.6

0.8

1

-20 0 20 40 60t - t

o [ps]

65 mg NaCl

MICRO-TIME SCALE: SINGLE PULSE

Scandate Dispenser Cathode Field Enhancement = 3.1 Chemical Potential = 18.08 eV Wavelength = 1.064 microns (W) = 4.7 eV; (Ba) = 1.8 eV Field = 10 MV/m; Theta = 50 % Peak Intensity = 710 Mw/cm2

Reflectivity = 58.5%; = 22.7 nmIncident Gaussian Laser Pulse: “Bulk” Boundary Held Fixed At Temperature Dictated By Macropulse Analysis

Gaussian: y(t) = exp{-[(t-to)/ t]2}Laser t 10.00 ps

to 0.00 ps

Resulting Temp. Distribution (Numerical Sol’n of Time-dependent Heat Equations)fi Long Decay Time Affects Subsequent Photoemission; Long Thermal Tail

Current Distribution Is Wider

Electron t 8.36 ps to 0.93 ps

(T(t)-To)/(Tmax-To)

J(t)/J(0)

Pre-fit8.94 ps1.45 ps

Post-fit8.75 ps0.55 ps

= 1064 nm

ANL 37

0

0.2

0.4

0.6

0.8

1

-20 0 20 40 60t - t

o [ps]

Go(t)/Go(0)

65 mg NaCl

MICRO-TIME SCALE: SINGLE PULSE

Scandate Dispenser Cathode Field Enhancement = 3.1 Chemical Potential = 18.08 eV Wavelength = 0.266 microns (W) = 4.7 eV; (Ba) = 1.8 eV Field = 10 MV/m; Theta = 50 % Peak Intensity = 710 Mw/cm2

Reflectivity = 46.2%; = 8.65 nmIncident Gaussian Laser Pulse: “Bulk” Boundary Held Fixed At Temperature Dictated By Macropulse Analysis

Gaussian: y(t) = exp{-[(t-to)/ t]2}Laser t 10.00 ps

to 0.00 ps

Resulting Temp. Distribution (Numerical Sol’n of Time-dependent Heat Equations)fi Long Decay Time Affects Subsequent Photoemission; Long Thermal Tail

Current Distribution Is Same

Electron t 10.01 ps to 0.00 ps

(T(t)-To)/(Tmax-To)

J(t)/J(0)

= 266 nm

ANL 38

EXPERIMENTAL APPARATUS

• Scandate cathodes fabricated by Spectra-Mat Inc.

• Field between cathode and anode varied from 0-2.5 MV/m

• Laser focused to circular spot on cathode with FWHM area of approximately 0.3 cm2

• Q-switched Nd:YAG laser gave Gaussian pulses FWHM 4.5 ns

Current TransformerIon

Pump

Laser InAnode

Window

Cathode

Harmonic λ[nm] QE[%]2 532 0.00653 355 0.02004 266 0.0800

For n=2,3,4 harmonics: Electron emission exhibited "normal" photoemission, i.e., emission proportional to laser

intensity & independent of field

For n=2,3,4 harmonics: Electron emission exhibited "normal" photoemission, i.e., emission proportional to laser

intensity & independent of field

ANL 39

Profilimetry Data

-0.4

-0.2

0.0

0.2

0.4

0.6

0 20 40 60 80 [Radial ]m

SurfaceImage

DISPENSER CATHODE

Consequence: Field Enhancement At

Local Emission Sites

(e.g., Hemisphere: β = 3)

Nd:Yag1064 nm

Scandate Dispenser Cathode(Fabricated by Spectra-Mat)

Work Function: 1.8 eVPartial Coverage of Surface

[0.1 mm]2

Work Function: 1.8 eVPartial Coverage of Surface

ANL 40

Ion Bombardment

ThermalDesorption

CATHODE SURFACE

Interpore ≈ 6 µm; Grain Size≈ 4.5 µm; Pore Diam. ≈ 3 µm (cf M. Green, Tech. Dig IEDM, (1987), p925

€

Dbulk(T )=Dbulko exp−Ed

bulk / kBT[ ]

Dmono(T )=Dmonoo exp−Ed

mono / kBT[ ]θ5

“…the interaction between the barium adsorbate and the substrate plays a crucial role in determining the nature of te surface dipole, which acts to lower the work function ...”

[1] A. Shih, D. R. Mueller, L. A. HemstreetIEEE-TED36, 194 (1989)

[2] L. A. Hemstreet, S. R. Chubb, W. E. Pickett PRB40, 3592 (1989)

BaO

SideView

W

TopView

Bulk vs Monolayer evaporationOne Monolayer At Most Exists On

Cathode Surface

ANL 41

THERMAL - PHOTOCURRENT (II)

Photocurrent Has Two Components

Thermal Emission From Laser-heated Electron Gas

Direct Photoemission

€

φ=− 4QF

€

ΔQ= πro2( ) θJ λ Te(t),( ) + 1−θ( )J λ Te(t),W( )[ ]dt

−∞

∞

∫

1D Model: Emitted Charge ΔQ Originates From Two Sources

“Bare” Regions With Work Function of W (1θw)

Ba-Covered Low Work Function Region (θ)

€

J λ T,( ) =q1−R( )I λ (t)hω

U β hω −φ( )[ ]U β[ ]

⎛

⎝ ⎜

⎞

⎠ ⎟ + ARLDT

2 exp−βφ[ ]

Effect of Field F: Schottky Barrier Lowering (Q = 0.36 eV-nm)

€

U x( ) = ln 1 +ey( )dy−∞

x

∫

€

β =1

kBTe

ANL 42

EXPERIMENTAL CONSIDERATIONS

COMPLICATIONS TO THE 1-D MODEL

• LASER INTENSITY VARIATION

Simulation Area (for FWHM Area = 0.3 cm2) implies ρo =0.5249 cm.

• MACROSCOPIC FIELD VARIATION

Cathode = 1.27 cm Diameter.Anode: Tube With 1.27 cm ID / 2.54 cm ODAnonde-cathode Separation = 0.4 Cm. POISSON: 1 kV Anode = 0.17 Mv/m @ center

• TEMP VARIATION ACROSS SURFACE

Electron Temperature Greatest Where Laser Strongest (Center of Beam): for 1-D Theory, "Effective" θ < Actual Coverage Factor

FWHM ValuesArea = 0.3 cm2

Pulse = 4.5 ns

€

G(ρ,t) =Goexp−ρρo

⎛ ⎝ ⎜

⎞ ⎠ ⎟

2

−tΔt ⎛ ⎝ ⎜

⎞ ⎠ ⎟2 ⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

0

0.1

0.2

0.3

0.4

10 15 20 25 30 35

I(A)(12kV)12kV fitI(A)(6kV)6 kV fit

Time [ns]

To = 516 K

Δ = 22 E mJ

Δ = 2.52t

Δ = 2.58t

€

tFWHM =2 (ln 2)Δt

Emitted Charge Current Density

€

JAmpcm2

⎡

⎣ ⎢

⎤

⎦ ⎥≈

ΔQ[nC]tFWHM[ns]AFWHM [cm2 ]

ANL 44

“Prediction” of Work Function from Exp. QE

-6.0

-4.0

-2.0

4.3 4.4 4.5 4.6 4.7 4.8 [ ]eV

λ = 266 nm

Tungsten

Goldsimulation

Experimental Data† for QE for Au & W:

QE [%] [eV] Predict

Au 7.54x10-6 4.72 - 4.78 4.69

W 3.49x10-5 4.63 - 5.25* 4.52

* Various W faces have different : values shown are for (100) and (111) faces, respectively.

† N. A. Papadogiannis, S. D. Moustaïzis, J. of Phs. D: Appl. Phys. 34, 499 (2001).

€

QE=hωq

ΔQΔE ⎛ ⎝ ⎜

⎞ ⎠ ⎟=

hωq

J λ Tmax( )Iλ (0)

⎛

⎝ ⎜ ⎞

⎠ ⎟Δte

Δtλ

→ 1−R( )hω −

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

Gaussian Laser Pulses: ratio of order unity

Simulation Assumptions• Low Laser Intensity (Eliminates JRLD)

• No Field (Eliminates Schottky Barrier)• UV Light (Over the Barrier Emission)• Δt ratio taken as unity

Simulation Assumptions• Low Laser Intensity (Eliminates JRLD)

• No Field (Eliminates Schottky Barrier)• UV Light (Over the Barrier Emission)• Δt ratio taken as unity

QUANTUM EFFICIENCY & WORK FUNCTION

asymptotic form

ANL 45

2D AND TEMPORAL VARIATION

EXPERIMENTAL QUANTUM EFFICIENCY

€

QE2D =θ 1−R( )

1q

dt 2πρdρ0

∞

∫−∞

∞

∫ J λ t,ρ,T(t,ρ)( )

1hω

dt 2πρdρ0

∞

∫−∞

∞

∫ Iλ t, ρ( )

€

limβ hω−φ( )→ ∞

QE2D =θ 1−R( )hω −φ

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

€

limβ φ−hω( )→ ∞

QE2D =θ 1−R( )QE1D Tmax( )

w+1( )3/2

w=131−

ToTmax

⎛ ⎝ ⎜

⎞ ⎠ ⎟2 +

φ−hω( )kBTmax

⎛

⎝ ⎜ ⎞

⎠ ⎟

LIMIT: Standard (phonon + > barrier)

LIMIT: Thermal-Photo (phonon + < barrier)

BULK T, INTENSITY, AND FIELD DEPENDENT

1064 nm

10-7

10-6

10-5

10-4

10-3

10-2

0.4 0.6 0.8 1

Experiment

β[ /hc λ - φ] >> 1

β[φ - /hcλ ] >> 1

[Wavelength ]m

= 11.836 , ∆E mJ To = 300 K

= 1.7 /Field MV mθ = 0.3085

Qua

ntum

Eff

icie

ncy

standard

thermal-photo

266 nm355 nm532 nm

Bulk T, Intensity, and Field Independent

ANL 46

“THERMAL-PHOTO” EMISSION

For Electrons Excited

From Thermal Tail,

Current Density in

Asymptotic Limit

Appears As a

“Shifted”

Richardson - Laue -

Dushman Equation

And Should Therefore

Be Linear on a

Richardson Plot As

Function of 1/Tmax

€

J λ T,( ) ∝ Iλ (t)J RLD T,φ−hω( )

€

β φ−hω( ) ⇒ ∞

-11

-10

-9

-8

-7

-6

-5

-4

11 12 13 14

TheoryExp

(1/kBT

max) [1/eV]

Field = 1.7 MV/mBulk T = 300 Kθ = 0.3085

ANL 47

10-9

10-7

10-5

10-3

10-1

101

1 10 100

4, 0.3085, 2.55, 10641, 0.6000, 2.55, 10641, 0.6000, 2.55, 8001, 0.6000, 10.00, 8001, 0.6000, 100.00, 800

Laser Intensity [MW/cm2]

Δt = 2.70 ps

βa θ F λ

PROJECTED QUANTUM EFFICIENCY

Successive Approximations:

Present Cathode

Smooth Surface, Increase Coverage

Lower Wavelength to Ti-Saph (800 nm)

Increase Field to Naval ApplicationsQE(118 MW/cm2 = 2.15%)

Increase Field to Accelerator ApplicationsQE(118 MW/cm2) = 5.52%

Extension Simulation From Exp. Parameters to Operational ParametersIntensity Restricted So That Tmax + 300K < Melting Point of W

ANL 48

AN INTRODUCTION TO

ELECTRON EMISSION THEORY AND PROCESSES Nature Of The Emission Barrier

Tunneling, Density, and Current Integral: FN and RLD Equations Complications: Semiconductors, Emission Near Maximum A Thermal - Field Emission Formula Photoemission Considerations Quantum Efficiency A Thermal - Photoemission Formula

Laser Heating of the Electron Gas Laser Heating of the Electron Gas Time-dependent Model of Laser-induced Thermal Photoemission Dispenser Cathode Experiment

Complicating Circumstances Field Enhancement Emission at the Barrier Maximum

OUTLINE

ANL 52

REGIONS OF CURVATURE ENHANCE FIELD: Model Field Enhancement Effect By:

Line Charge of Length L In External Field Fo

tip radius = as, height = zo; length of line = L = [(zo - as)zo]1/2

FIELD ENHANCEMENT

Apex Field = 6.5 FoApex Field = 6.5 Fo

V(x) for as = zo/5V(x) for as = zo/5

FoFo

5.61 Fo

Fo

LL

LL

€

V ρ, z( ) =−Foz+ FozovL ⎛ ⎝ ⎜

⎞ ⎠ ⎟

Q1 u / L( )Q1 zo / L( )

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

Q1 x( ) =12

xlnx+1x−1 ⎡

⎣ ⎢

⎤

⎦ ⎥−1; u±v= z±L( )

2 + ρ2

€

Ftip =zo−as

as

⎛ ⎝ ⎜

⎞ ⎠ ⎟Q1

zozo−as

⎛

⎝ ⎜ ⎞

⎠ ⎟ ⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

−1

Fo

FIELD ENHANCEMENT

FIELD VARIATION ALONG SURFACE

€

F ρ, z( ) u=zo=

as

ρ2 + as2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟Ftip

Schottky Factor at Apex for Fo = 10 MV/m for as = zo/5

€

4QFtip =0.6 eV

ANL 53

0

5

10

15

20

25

-10 -5 0 5 10

Radial ρ [ ]µm

V(ρ,z)

Field Lines

EmitterEmitter

AnodeAnode

LASER ILLUMINATION OF NEEDLE

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30

266 nm355 nm512 nm

Anode Voltage [kV]

QE(33kV) = 1.3E–2

QE(33kV) = 3.8E–10

QE(33kV) = 8.8E–7

0

0.2

0.4

0.6

0.8

19 10 11 12

[ ]Energy eV

Vmax

– hf

λ = ∞ nmF = 10.0 /V nm

0.30˚

8 9 10

Energy [eV]

Vmax

– hf

λ = 512 nmF = 2.2 /V nm

0.24 ˚

0

0.2

0.4

0.6

0.8

18 9 10

[ ]Energy eV

Vmax

– hf

λ = 355 nmF = 2.2 /V nm

0.70˚

7 8 9 10

Energy [eV]

Vmax

– hf

λ = 266 nmF = 2.2 /V nm

29.7˚

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30

266 nm355 nm512 nmGarcia/Brau

Anode Voltage [kV]

QE(33kV) = 1.3E–2

QE(33kV) = 3.8E–10

QE(33kV) = 8.8E–7

Hernandez-Garcia, Brau, Nucl. Inst. Meth. Phys. A483 (2002) 273

† K. L. Jensen, P. G. O’Shea, D. W. Feldman, 5th Dir. Energy Symp. (Monterey, 11/12/02).

Laser Heating of Electron Gas and Subsequent Thermal-photo-field Emission Model Based on Steady State ad hoc Linear Relation Between Electron Temperature and Illumination†

Affects Emittance of Photo-emission From Protrusions

Laser Heating of Electron Gas and Subsequent Thermal-photo-field Emission Model Based on Steady State ad hoc Linear Relation Between Electron Temperature and Illumination†

Affects Emittance of Photo-emission From Protrusions

ANL 54

ISSUES AND QUESTIONS

QUESTIONS AND COMMENTS BY C. SINCLAIR [1]

Fundamental R&D / theory question(s):

What combination of achievable, external fields results in the maximum charge density in 6-D phase space (from a zero thermal emittance source)? For a CW source, it is not obvious whether DC or RF fields are best (particularly for room temperature RF, where the fields are limited by thermal considerations). For low duty factor applications, the consensus appears to be RF, but that must depend on the bunch charge.

How should emittance be measured, and what is required to have a high quality measurement?

Regarding the relation between thermal emittance and bunch duration at the cathode: space charge fields are reduced by making larger bunches and emitting from a smaller area (which increases longitudinal and transverse emittance) - therefore, for a given bunch charge, what is the optimal emitting area and bunch duration to achieve bets final charge density in 6-D phase space (the answer will depend on whether fields are static or dynamic).

Application and requirements dictate photocathode: needs of low repetition rate, high charge bunches differ from CW pulse trains of lower bunch charges

A goal for progress in photoemission guns: develop reliable methods for generating uniformly populated (transversely and longitudinally) optical pulses to generate uniform charge distributions from the cathode and result in minimum emittance.

[1] Emails to K. Jensen, and Kwang-Je, et al., September 2003