# Presentation: 802062

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

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

## 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

## 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

**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**

## EMISSION 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 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**

- The Largest Component of the Barrier Is Due to the
- Exchange Correlation Potential

## Electron Number Density 

- Electrons 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”*

- Density Does Not Change With Temperature, So μ Must:

**DISTRIBUTION OF ELECTRONS IN METAL**

- Zero Temp. (**(0  ̊K) = ***o* = *E**F*)

## EXCHANGE-CORRELATION  POTENTIAL

**EXCHANGE-CORRELATION  POTENTIAL**

- The Density* **** *of an Electron Gas Is

- Correlation (Potential) Energy* *
- Form due to Wigner

- Exchange (Potential) Energy

- Kinetic Energy

## ELECTRON   DENSITY

**The Electron Density Near the Surface Barrier Is Obtained From the Supply Function and the Wave Function for Each *****k***

**ELECTRON   DENSITY**

- Density and Wave Function
- Square Barrier (*V**o* = **; Width L_x0008_)

- fi 1

- fi –*kx**o*

- In the Limit of Large *V**o* and *L*

## DIPOLE   COMPONENT

**DIPOLE   COMPONENT**

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

- Tanh-Approx.:  Match ***(x**i**), ∂**x****(x**i**)*

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

## SIMPLE MODEL OF TUNNELING

**SIMPLE MODEL OF TUNNELING**

**SQUARE BARRIER OF WIDTH “L”**
- Match ***(x)* and ∂*x****(x)* where *V(x)* Changes

- Incident
*e**ikx*

- Reflected
*r(k) e**ikx*

- Transmitted
*t(k) e**ikx*

***L* = ***(E)= *“Area under Curve”
***L* fi***(E)*
*T*(*E*<*V**o*)  ≈  exp{–2***(E)*}
*T(E*>*V**o*) fi 1

*V**o*

## IMAGE CHARGE POTENTIAL

- Schrödinger’s Equation:

- If We Let:   ***k*(*x*) = *R(x)* exp[*i S(x)*]

- Slowly varying density and constant current:

- Q = 0.36 eV-nm
*y* = 0.038 eV {*F*[MV/m]}1/2/**[eV]

## RLD & FN  SUMMARY part I

**RLD & FN  SUMMARY part I**

- Current Density =  Velocity  X  Transmission Probability  X  Distribution

*Field Emission*

*Thermionic Emission*

## EMISSION  EQUATIONS

- RICHARDSON EQUATION:  THERMIONIC EMISSION
- Dimensionless Parameter *n = *** /*b *is small

**EMISSION  EQUATIONS**

- FOWLER NORDHEIM: FIELD EMISSION
- Dimensionless Parameter *n =* ** /*b *is large

## 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**

## Poisson’s Equation (o = bulk):

**BAND BENDING**

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

- Asymptotic Case:   ** ≤ –2:

- Asymptotic Case:   ** » 1:

## FN AND RLD DOMAINS

- FN:  Corrupted When Barrier Max Is Too Close to Fermi Level or Slope of ln(T(E)) Exceeds ln(f(E))
- Maximum Field:  ** > 6
- Minimum Field:  *c**fn* < 2*** *

**FN AND RLD DOMAINS**

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

- Typical Operational Domain of Various Cathodes
- Note:  Photocathodes Typically Run at or Near 300 K ***and*** Surface Roughness Increases *F*

**Notes:**
Last modification on 3/13/02.  Original in UMD seminar

## Electron Momentum Into Barrier Determines Emission Probability

Finite Temperature ( = 1/kBT)

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

**Electron Momentum Into Barrier Determines Emission Probability**
**Finite Temperature (**** = 1/*k**B**T***)**
**T(E)   **(*b* = slope of -ln[T(E)])

**ELECTRON DISTRIBUTION**

**Maxwell**
**Boltzmann**
**Regime**

**0 K-like Regime**

**Supply Function f(E) [#/nm****2****]**

**Transmission Coeff T(E)**

## TANH-WKB   APPROXIMATION

- Estimate Of *E**m* Is Required

**TANH-WKB   APPROXIMATION**

- Form of Analytic T(E) Suggests a Hyperbolic-tangent Approximation

**Relationships** (prime = differentiation)
- Terms Evaluated at *E**m *(Max of J Integrand)

**WKB, FN, and RLD Are All ****Inadequate**** ****for *****n***** = O(1) Conditions**

- FN:  	Linearization of WKB at *E* = **
- RLD:  	Emission over Barrier
- n	= ***/b *= 1*/bk**B**T*

## T(E) SYNTHESIS

**T(E) SYNTHESIS**

- Combine Airy and WKB Results

## EVALUATION OF C(E)

**EVALUATION OF *****C(E)***

**In Bohm (*****Quantum Potential*****) Form of Schrödinger’s Equation:**
**Where:**
- Steady State (∂*x**j* = 0):  Match ** & ∂*x*** at *x* = *x**–* For Incident Plane Waves to Derive the Transmission Coefficient

## GENERALIZED  J(F,T)  EQUATION

- Nomenclature:
*T(E) ≈ T**o** */ {1+exp[*b*(*E**c*–*E*)]}
*x **	**= b(E**c** – E)*
*p **	**= b(E**c** – ****)*
*n **	**= ****/b*
*x**p* 	Integrand Approximated
*** **	*By Gaussian of Form
*N**g* 	*N**g* exp[-(*x*-*x**p*)2]

**GENERALIZED  *****J(F,T)*****  EQUATION**

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

- Separate *N* Into 3 Regions:
- Field:  *N**A** = N(p,b****+p)*
- Intermediate:  *N**B** = N(-b****+p,p)*
- Thermal:  *N**C** = N(-∞,-b****+p)*
- FN:  *n* = ∞ limit of *N**A*
- RLD:  *n* = 0 limit of *N**C*

## RESULTS

**RESULTS**

**Current Integrand Behavior**
- RLD:  Cut-off at Apex *E* Too Extreme
- FN:  Over-predicts *T(E)* at Apex

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

## THERMAL PHOTO-CURRENT (I)

**THERMAL PHOTO-CURRENT (I)**

**Product/sum of Several Factors:**
**Electron Charge ***(q)*
**Absorption Factor ***(1-R)*
**# of photons **(*I***/h**)
**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 ***(J**RLD**)*
- [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 h**** is sufficient to overcome the potential step at the surface*.
- R. H. Fowler, PR38, 45 (1931). (*italics in original)*

-  = 1064 nm

## QUANTUM   EFFICIENCY (1D)

******Q / ********E = J******** / I********:  Therefore, QE Governed by **U[(hU()

**STANDARD PHOTOEMISSION **
**(Photo-excited Electrons Below Fermi Level)**

**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)

## 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

**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**

## LASER HEATING OF ELECTRON GAS

**LASER HEATING OF ELECTRON GAS**

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

- Thermal Conductivity & Relax. Time

## SPECIFIC HEAT APPROXIMATIONS

**SPECIFIC HEAT APPROXIMATIONS**

- High Temp (> 300 K) Specific Heat Approximations

**Specific Heat         Variation in Energy Density With Temperature**

## TEMPERATURE VS. LASER POWER

**TEMPERATURE VS. LASER POWER**

**Steady State Formulation Valid When...**** **
**Scattering Times = O(0.01-0.1 ****ps****)**
**Experimental Laser Pulses = O(****ns****)**

**Assumption:  *****T******e******(z)***** Profile Is Exponentially Decaying**

***T******max***

**STEADY STATE ESTIMATE OF T( z = 0 )**

## ABSORBED LASER POWER

**ABSORBED LASER POWER**

- Fowler Function

**Laser Term G(z,t) Is a Product Of:**
**Reflection Coefficient**
**Incident Laser Power**
**Penetration Factor**
**Absorbed Energy Factor**

## REFLECTION AND PENETRATION (Theory)

**REFLECTION AND PENETRATION (Theory)**

- Complex Dielectric Constant fi Optical Properties Of Metals as function of **
- Real:	index of refraction ***n***
- Imag:	damping constant ***k***
- Related to Reflectivity ***R*** and absorption length of light in metal ******.

**Plasma Frequencies:**
- 	 = e- concentration
- 	o = dc conductivity)

-  = 1.68x1023 #/cm3
-  = 3.6E5 (Ohm-cm)-1

## REFLECTION AND PENETRATION (Practice)

**REFLECTION AND PENETRATION (Practice)**

- Complex Dielectric Constant fi Optical Properties Of Metals as function of **
- Real:	index of refraction ***n***
- Imag:	damping constant ***k***
- Related to Reflectivity ***R*** and absorption length of light in metal ******.

**Plasma Frequencies:**
- 	 = e- concentration
- 	o = dc conductivity)

## Diff Eqs. Governing T-Evolution

Diffusion Equation

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

**Diff Eqs. Governing T-Evolution**
**Diffusion Equation**
**Discretization (*****j*****=time, *****i*****=space)**
**Standard Crank-Nicholson**

**TIME EVOLUTION SIMULATION**

_**TIME SCALES:**_
**Engagement Time****	****10 s**
**Laser Pulse-to-Pulse****	****4 ns**
**Lattice Therm (C****i****/g)****	****8.4 ps**
**Relaxation (RT):****	****128 fs**
**∆****t (600K & ∆x = 20 nm):****	****0.4 fs**
**Ratio:****	****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

_**LENGTH SCALES:**_
**Cathode****	****1.0 cm**
**Thermal Distance****	****200 nm**
**Laser****	****10 nm**
**Ratio:****	****100000000**

**Notes:**
Notes on this page:

∆t = ∆x^2 / D, and is evaluated at room temperature using D = kappa(RT,RT)/Ce(RT)

Thermal distance is sound velocity for tungsten times laser time scale

## MACRO-TIME SCALE  PRF HEATING (I)

**MACRO-TIME SCALE  PRF HEATING (I)**

**Bulk T = Sum of Gaussian Laser Pulses ****I****o**** exp(-(*****t/************t*****)****2****)**** **
**Effect = Sum of N Dirac-delta T- Pulses at Surface**
**Magnitude of Temperature Rise Dictated by Deposited Laser Energy ********E**
**Temp. Depends on Location of Fixed Boundary *****L***

- surface

- image

- s =1/2:	Evolution of surface temperature with pulse number N
- s > 1/2:	Cooling of surface after N pulses
*t**k+s**	**= (k+s)****t*

## MACRO-TIME SCALE  PRF HEATING (II)

**MACRO-TIME SCALE  PRF HEATING (II)**

- Characteristic Temperature:  *T**max* 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

## TIME SIMULATION MATRIX EQUATIONS

**Matrix Equation**
**Matricies**
**Non-linearity:  **
**Finite Difference Multi-point Algorithm Preserves Stability**
**Boundary T****bc****:**
**RHS: reflect / LHS: absorb**
**Temp BC Given by Macro-scale Time Simulation and Held Fixed**

- Matricies Require Evaluation of *C**e*(*T**e*) / **(*T**e**,T**i*) at Advanced Time Steps:  **USE OF PREDICTION/CORRECTION SCHEME:  “Guess” j+1 elements - solve - use results in next guess**

## Numerical Evolution of Dirac-delta Pulse With Reflecting RHS Boundary Compared to Analytical Solution
BC: 	RHS = reflecting	LHS = absorbing
PARAMETERS
x = 1 nm
t = 0.0368 fs
Pulse Height = 5 Kelvin
Room Temperature background
Discrete Coefficient = 1000(non-iterative max = 40)

**Numerical Evolution of Dirac-delta Pulse With Reflecting RHS Boundary Compared to Analytical Solution**
**BC: ****	****RHS = reflecting****	****LHS = absorbing**
**PARAMETERS**
******x = 1 nm**
******t = 0.0368 fs**
**Pulse Height = 5 Kelvin**
**Room Temperature background**
**Discrete Coefficient = 1000****(non-iterative max = 40)**

**Temperature [Kelvin]**

- CONCLUSION:
- Numerical Model Functions Well Compared to Analytical (Exact) Solution

**VALIDATION OF TIME DEP. MODEL**

## MICRO-TIME SCALE:  SINGLE PULSE

- 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 nm
**Incident 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

-  = 1064 nm

## MICRO-TIME SCALE:  SINGLE PULSE

- 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 nm
**Incident 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

## 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

- For n=2,3,4 harmonics:  Electron emission exhibited "normal" photoemission, i.e., emission proportional to laser intensity & independent of field

## DISPENSER   CATHODE

**Surface**
**Image**

**DISPENSER   CATHODE**

**Consequence:  ****Field Enhancement At Local ****Emission Sites**
**(e.g., Hemisphere:  ******** = 3)**

**[0.1 mm]****2**

**Work Function: 1.8 eV**
**Partial Coverage of Surface**

## CATHODE SURFACE

**CATHODE SURFACE**

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

**“...****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. Hemstreet	IEEE-TED36, 194 (1989)
- [2]	L. A. Hemstreet, S. R. Chubb, W. E. Pickett 	PRB40, 3592 (1989)

**Bulk vs Monolayer evaporation**
**One Monolayer At Most Exists On Cathode Surface**

**Notes:**
APS 1999 Slide

## THERMAL - PHOTOCURRENT  (II)

**THERMAL - PHOTOCURRENT  (II)**

**Photocurrent Has Two Components**
**Thermal Emission From Laser-heated Electron Gas**
**Direct Photoemission**

**1D Model:  Emitted Charge ********Q Originates From Two Sources**
**“****Bare” Regions With Work Function of W (********w****)**
**Ba-Covered Low Work Function Region (********)**

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

## EXPERIMENTAL   CONSIDERATIONS

**EXPERIMENTAL   CONSIDERATIONS**

**COMPLICATIONS TO THE 1-D  MODEL**** **
**LASER INTENSITY VARIATION**** **
**	****Simulation Area (for FWHM Area = 0.3 cm****2****) implies ********o**** =0.5249 cm.  **
**MACROSCOPIC FIELD VARIATION**
**	****Cathode = 1.27 cm Diameter.****Anode: Tube With 1.27 cm ID / 2.54 cm OD****Anonde-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" ******** < Actual Coverage Factor**

**FWHM Values**
**Area = 0.3 cm****2**
**Pulse = 4.5 ns**

## COMPARISON:  THEORY & EXPERIMENT

**EXPERIMENTAL**
**Anode Potential *****V******a***
**Bulk Temperature *****T******o ***
**Laser Intensity x pulse length ********E**
**SIMULATION ADJUSTABLABLES**
**Field Enhancement Factor ***********a***
**Thermal Decay Length Parameter *****n***
**Surface Coverage Factor ********
**MEASUREMENT / OUTPUT**
**EMITTED CHARGE ********Q**
**Conversion Factors**
**Potential/Field:****	****1 kV = 0.17 MV/m**
**Energy/Intensity:****	****1 mJ = 0.2414 MW/cm****2**
**Current/Charge:****	****1 nC = 0.741 A/cm****2**

**VARIATION PARAMETERS**
**Anode Potential V****a**** [kV]****	****	****0 -15**
**Bulk Temperature T****o**** [K]****	****	****297-1040**
**Deposited Energy [mJ]****	****	****4.87 - 22**
**DIMENSIONLESS**
**Field enhancement ********a****	****4.0**
**Decay Length Parameter n****	****26.8086**
**Surface Coverage ********	****0.12 - 0.31**
**Scattering Coeff. A****o**** (e-e)****	****32.0514**
**Scattering Coeff. ********o**** (e-ph)****	****0.0243**
**Thermal e mass ratio (W)****	****1.2038**
**DIMENSIONAL**
**Chemical Potential (W) [eV] ****	****18.08**
**Work Function [eV]****	****1.80**
**Penetration depth (W) [nm]****	****10.10**
**Reflection [%]****	****50.00**
**Laser Wavelength [nm]****	****1064.00**
**Illumination Radius [mm]****	****5.25**

## “Prediction” of Work Function from Exp. QE

- simulation

**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).

- Simulation Assumptions
- Low Laser Intensity (Eliminates JRLD)
- No Field (Eliminates Schottky Barrier)
- UV Light (Over the Barrier Emission)
-  ******t ratio** taken as unity

**QUANTUM EFFICIENCY & WORK FUNCTION**

- asymptotic form

## 2D AND TEMPORAL VARIATION

**EXPERIMENTAL   QUANTUM EFFICIENCY**

**LIMIT:  Standard (phonon + ******** > barrier)**

**LIMIT:  Thermal-Photo (phonon + ******** < barrier)**

## “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/T****max**

## PROJECTED QUANTUM EFFICIENCY

**PROJECTED QUANTUM EFFICIENCY**

**Successive Approximations:**
**Present Cathode**
**Smooth Surface, ****Increase Coverage**
**Lower Wavelength to ****Ti-Saph (800 nm)**
**Increase Field to ****Naval Applications****QE(118 MW/cm****2**** = 2.15%)**
**Increase Field to ****Accelerator Applications****QE(118 MW/cm****2****) = 5.52%**

- Extension Simulation From Exp. Parameters to Operational Parameters
**Intensity Restricted So That T****max**** + 300K < Melting Point of W**

## 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

**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**

## SIMPLE MODEL OF 3-D

**SIMPLE MODEL OF 3-D**

- Bump On Surface/ Distant Anode

- Floating Sphere / Close Anode

***a***

*r*

***V(a,************) *****= 0; **
***V(D+a,*****0*****) = V******a***

## Emission Tip + Close Anode (Diode) Crudely Modeled As Line Charge & Its Image About Anode Axis With Parameters Adjusted Such That
V = 0 fi Emitter Surface

- Emission Tip + Close Anode (Diode) Crudely Modeled As **Line Charge** & **Its Image **About Anode Axis With Parameters Adjusted Such That
- V = 0 fi Emitter Surface

- Potential for Line Charge of Length L

- Emitter height = *L + a**o*; Apex Radius = *a*
- ( = charge/length)

- Free Line Charge + Anode Image

- Embedded Line + Anode (*L»a*)

***Ratio(Free/Embed) ≈ (D+L)/L***

**“****LINE” MODEL OF EMISSION TIP**

## Hyperbolic Case (tip specified by o)

Ellipsoidal Case (tip specified by o)

**Hyperbolic Case**** **(tip specified by ***o*)
**Ellipsoidal Case**** **(tip specified by ***o*)

**FIELDS: APEX AND SURFACE**

## 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

**Line Charge of Length L In External Field F****o**** **
**tip radius = a****s****, height = z****o****; length of line = L = [(z****o**** - a****s****)z****o****]****1/2**

**FIELD ENHANCEMENT**

**FIELD ENHANCEMENT**

**FIELD VARIATION ALONG SURFACE**

## LASER ILLUMINATION OF NEEDLE

**LASER ILLUMINATION OF NEEDLE**

**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**

## 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