# Presentation: 626726

## ARGONNE NATIONAL LABORATORY DECEMBER 6, 2005     Argonne, IL

**ARGONNE NATIONAL LABORATORY**** ****DECEMBER 6, 2005     Argonne, IL**

- ANL Beams and Applications SeminarHost:  John Lewellen ASD
- Bldg. 401, Room A1100 Tuesday, 1:30 pm

**Notes:**
SA03-0503
Theory & Simulation of Photocathodes for Free Electron Lasers
NAVSEA
Eugene Nolting
202-781-3175/ noltingee@navsea.navy.mil
Dr. Kevin L. Jensen
202-767-3114/ kevin.jensen@nrl.navy.mil

## OUTLINE

- Electron Sources
- Photocathodes and Photocathode Issues
- The Dispenser Photocathode Concept
- Electron Emission Fundamentals
- 1st Generation Emission Model & Usage
- Next Generation Components & Application
- Bare Metals
- Cesiated Surfaces & Gyftopoulos-Levine Model
- Quantum Distribution Function
- Quantum Effects on Barrier & Scattering
- Conclusion

## ELECTRON  EMISSION

**ELECTRON  EMISSION**

**The Manner in Which Electrons Are Extracted Dictates the Technological Gambits Invoked**

- HeatWave Labs
- http://www.cathode.com/c_cathode.htm

- ANL-BNL-JLAB Gun:  Ilan Ben-Zvi
- www.agsrhichome.bnl.gov/eCool/MAC_Ilan.pdf

- Photo

## PHOTOINJECTORS & PHOTOCATHODES

- Critical Components of Free Electron Lasers, Synchrotron Light & X-ray Sources

**High Power FEL**** Demands **on Photocathode:
- CHARGE PER BUNCH:	0.1 - 1 nC in 10-50 ps pulse
- FIELD:	10 - 100 MV/m in pressure of 10-8 Torr (approx)
- OPERATION:	Robust, Prompt, Operate At Longest 
- LIFETIME:	Longevity & Reliability Paramount

## PHOTOCATHODE RESPONSE TIME

**PHOTOCATHODE RESPONSE TIME**

- Pulse Shaping
- Optimal Shape for emittance:  beer-can (disk-like) profile
- Laser Fluctuations occur (esp. for higher harmonics of drive laser)
- Fast response:  laser hash reproduced
- Slow response: beer-can profile degraded
- Optimal:  1 ps response time
- Mathematical Model (n = 2*n/T*)

- Formulation based on model of J. Lewellen

**Notes:**
Do not include this slide in DEPS presentation

## CATHODE + LASER NONUNIFORMITY

- Laser

- Cathode Emittance Is Important (esp. in Gun)
- Pulse Shape Can Result in Reduction of Emittance
- Prediction of Photocathode / Drive Laser Combos & Beam Crucial to Design of Larger Systems
- Realistic Initial Distributions Needed: Advanced Codes (Michelle, Argus, Magic, Mafia, Vorpal, Etc.) Need Adequate Emission Models, Photoemission Studies Sparse, Emission Distributions Are Unknown

- Laser
- Nonuniformity

- Work Function
- Nonuniformity

**Notes:**
TRANSFER THIS SLIDE TO NATE’S TALK

## PROGRAM OBJECTIVE

- DEVELOP a custom-engineered controlled porosity photo-dispenser cathode

**PROGRAM OBJECTIVE**

- Generic Parameter Range
- Assumptions:
- Charge = 1 nC
- Wavelength = 266 nm
- Pulse FWHM = 10 ps
- Example Cases of Io(QE)
- For Radius of 0.3 cm
- Io(1%) 	= 0.165 MW/cm2
- Io(0.01%)	= 16.5 MW/cm2
- For Radius of 0.1 cm
- Io(1%) 	= 1.48 MW/cm2
- Io(0.01%)	= 148 MW/cm2

## DISPENSER CATHODE POROSITY ANALYSIS

**DISPENSER CATHODE POROSITY ANALYSIS**

- Central Questions:
- Pore-to-Pore separation &Grain Size
- Desorption & migration rates of low work function coating over surface

- SEMS:  Nathan Moody, UMD

- Grain Size:  Effective Diameter

**Notes:**
Move to Nathan’s presentation

## Electron Number Density 

Zero Temperature ( ̊K = o = EF)

N does not change with T so  must:

- Zero Temperature (** ̊K = ***o* = *E**F*)
- N does not change with T so  must:

**STATISTICAL MECHANICS OF ELECTRON GAS**

- Electrons Incident On Barrier Are Distributed In Energy According To A 1-D “Thermalized” Fermi Dirac Distribution Characterized By The Chemical Potential and Called The “Supply Function”
*f(k)* obtained by integrating over the transverse momentum components

- BAND BENDING
- Metal vs. Semiconductor

## CURRENT - A CLASSICAL APPROACH

*f(x,k,t)* is the probability a particle is at position *x* with momentum hk at time t
- Conservation of particle number:

- to order O(dt)

- Boltzmann Transport Equation

- “Moments” give number density  and current density J:  Continuity Equation

- velocity & acceleration

## CURRENT IN SCHRöDINGER REPRESENTATION

- Consider a pure state

- The form most often used in emission theory
- Basis for FN & RLD Equations

- Schrödinger’s Equation

- Time-dependence of Operators governed by commutators with Hamiltonian

## The most widely used forms of:
Field Emission:  Fowler Nordheim (FN)
Thermal Emission: Richardson-Laue-Dushman  (RLD)

- Field Emission:  Fowler Nordheim (FN)
- Thermal Emission: Richardson-Laue-Dushman  (RLD)

**THERMIONIC VS FIELD EMISSION**

- High Temperature
- Low Field

- Low Temperature
- High  Field

- Transmission Probability
- Electron Supply
- Emission Equation

- Constants for Work Function in eV, T in Kelvin, F in eV/nm

## A GENERAL THERMAL-FIELD EQUATION

**A GENERAL THERMAL-FIELD EQUATION**

- Maxwell
- Boltzmann
- Regime

- 0 K-like Regime

- Supply Function
- General Transmission Coefficient
- Define Slope Ratio:
- n « 1:  Richardson-Laue-Dushman Eqn » 1:  Fowler Nordheim Equation

- f(7,300)

- f(0.01,2000)

- T(0.01,2000)

- T(7,300)

- X(F[GV/m],T[K])

- Fermi

## INTEGRATED SCATTERING & EMISSION MODEL

**INTEGRATED SCATTERING & EMISSION MODEL**

- Quantum Distribution Function (QDF) Simulation Simultaneously Relates Scattering (), Barrier Emission (), Thermal () and Density Effects

## EXP. VALIDATED PHOTOEMISSION MODEL

**EXP. VALIDATED PHOTOEMISSION MODEL**

- GOAL
- Predict Quantum Efficiency From Laser & Material Parameters
- Analyze Experimental Results from UMD, NRL, Colleagues in FEL Program
- Emission Model For Beam Code for NRL, SAIC, Tech-X, NIU, Colleagues

- Photocurrent depends on
- Scattering Factor: f
- Absorbed laser power: (1-R) I
- Escape Probability: U-terms

- First Generation Beam Code Model

- Next Generation Beam Code Model

## DETERMINATION OF R[%] & 

- Algorithm:
- Spline-fit experimental optical data (e.g., CRC, AIP Handbook) for index of refraction (n), damping constant (k)
- Designate incident angle = 
- Use Equations to determine Reflectance R[%] and penetration depth of laser for given wavelength

## POST-ABSORPTION SCATTERING FACTOR

- Factor (*f*) governing proportion of electrons emitted after absorbing a photon:
- Photon absorbed by an electron at depth *x*
- Electron Energy augmented by photon, but direction of propagation distributed over sphere
- Probability of escape depends upon electron path length to surface and probability of collision (assume any collision prevents escape)
- path to surface &scattering length
- To leading order, *k* integral can be ignored

- ko:  minimum k  of  e- that can escape after photo-absorption
- :  penetration of laser (wavelength dependent); : relaxation time

- Ex:  Copper:
- 	= 266 nm
- 	= 12.9 nm
- 	= 0.85 fs
-  	= 7.0 eV
- F 	= 4.3 eV

- sec(y)	= 7.7
- f		= 0.038

**Notes:**
Modified Nov 7, 2005

## QM-EXTENSION OF FOWLER-DUBRIDGE EQ.

- QM contributes for photon E near barrier height, large fields,and cold temperatures

- Copper *
-  = 266 nm; F = 5 MV/m;  = 3
- R = 33.6%,  = 4.3 eV, EF = 7.0 eV
- QE [%] (analytic)	1.31E-2
- QE [%] (time-sim)	1.36E-2
**QE [%] (exp)****	****1.40E-2**

**QM-EXTENSION OF FOWLER-DUBRIDGE EQ.**

- RLD-based Fowler Dubridge Model
- U(x): depends on thermal distribution and barrier *** *for emission probability
- Reflectivity R and Scattering Factor *f*****depends on material & relaxation time

- coating = 2.0 eV

- Exp data:  T. Srinivasan-Rao, et al., JAP69, 3291 (1991).

**Notes:**
Modified Nov 7, 2005

## SCATTERING & Electrical / Thermal Conductivity

- If an electric field F (or temperature gradient T) is removed, then distribution “relaxes” back to equilibrium after a “relaxation time” 

- Distribution for Fermi-Dirac is approximately constant except near Fermi Energy 

- Electric Field

- Temperature

## LASER HEATING OF ELECTRON GAS

- Do acts as Length2 / time
- Length ≈ O(laser penetration depth)
- Model captures physics... *as long as there is an estimate for t**o*

**LASER HEATING OF ELECTRON GAS**

- Differential Eqs. Relating Electron to Lattice Temp

## PHOTOEMISSION MODULES IN BEAM CODE

**PHOTOEMISSION MODULES IN BEAM CODE**

- Goal:  modules for 3D RF gun / beam codes for the analysis of beam generation and transport.
- Present model: high-T scattering operator with T evaluated using Delta-diffusion model as function of laser intensity for copper;  probability of emission factor based on Fowler Dubridge but without QM
- Next generation to include all-temperature scattering, QM, metal & coating library

- SIMULATION CODE:  MICHELLE (SAIC)
- Photoemission from laser-illuminated Cu hemisphere Using 1st generation photoemission model
- J. Petillo, *et al.*, 8th DEPS, Lihue, HI (2005)

- Hemisphere unit cell model

- SIMULATION CODE:  VORPAL (TECH-X)
- 3D visualization of photo emitted electron particles (white dots) following the beam emission and its evolution at different times from simulations with steady-state photocathode model.
- Cu photocathode at left boundary. Front of laser pulse has reached the photocathode and emission of the electron beam has started.
- D. Dimitrov, *et al.*, 8th DEPS, Lihue, HI (2005)

## THEORETICAL EVALUATION OF SCATTERING

**THEORETICAL EVALUATION OF SCATTERING**

- Scattering in metals due to collisions with lattice (_ac_oustic phonons & defects) and _e-e_ collisions.  If mechanisms independent, then:

- For T > TD (Debye Temp), then ac goes as T, but at low T, goes as T^5.  Scattering cross section is also related to
- deformation potential  (related to stress on lattice)
- sound velocity vs

- Ag
- Cu
- Au
- W
- Pb

- Phonons:

- Electron-Electron:
- e-e scattering in simple metals is *not* simple.  Model of Lugovskoy & Bray [1] depends on electron energy above Fermi Level (E) and Thomas-Fermi Screening Wave Number qo (depends on electron density) & dielectric Ks

- [1] A. V. Lugovskoy, I. Bray, J Phys D: Appl. Phys. 31, L78 (1998)

- Mathiessens Rule

## EXPERIMENT VS. THEORY (BULK METALS)

**EXPERIMENT VS. THEORY (BULK METALS)**

- Field Enhancement	3.0
- Macroscopic field	1.0 MV/m
- Work Function	3.97 eV
- Temperature	300 K
- Data & ImageCourtesy of **J. SMEDLEY (BNL)**

- BNL

- SLAC

**Field Enhancement****	****1.0**
**Macro field (MV/m)****	****0.01**
**Work Function****	****4.31 eV**
**Temperature****	****300 K**
**Data Courtesy of **D. DOWELL (SLAC)

**Notes:**
Last Modified  11/04/2005

## EXPERIMENT VS. THEORY (PART II)

- Measured (UMD), calculated (NRL), & literature for various **DISPENSER CATHODES**
- (**1st Generation model used**)
- B-TYPE:
- B. Leblond, NIMA317, 365 (1992)
- UMD experimental data
- M-TYPE
- UMD experimental data
- SCANDATE
- UMD experimental data

## COVERAGE DEPENDENT WORK FUNCTION

- Gyftopolous-Levine Theory relates Work Function to coverage factor.  Dependent upon Covalent Radii *r**x*, Factors “*f*” and “*w*” (Act As “Atoms Per Cell”,  Values of which Depend on Crystal Face).
- General Surface = “Bumpy [B]”
- alkali metal (n = 1)
- alkaline-earth metal (n = 1.65)

- Modified Gyftopolous-Levine Theory

## GYFTOPOLOUS-LEVINE MODEL PERFORMANCE

**GYFTOPOLOUS-LEVINE MODEL PERFORMANCE**

- LEAST SQUARES ANALYSIS:Minimize Difference between GL theory & Exp. Data With Regard to scale factor, monolayer work function value, and *f* coverage factor

- C-S Wang, J. Appl. Phys. 44, 1477 (1977)
- J. B. Taylor, I. Langmuir, Phys. Rev. 44, 423 (1933).
- R. T. Longo, E. A. Adler, L. R. Falce,  Tech. Dig. of Int'l. El. Dev. Meeting 1984, 12.2 (1984).
- G. A. Haas, A. Shih, C. R. K. Marrian, Applications of Surface Science 16, 139 (1983)

- Tightly constrained parameter variation
- Unique determination of theory based on experimental values
- Predictive ability from basic experiments

## EXPERIMENTAL MEASUREMENTS @ UMD

**EXPERIMENTAL MEASUREMENTS @ UMD**

- Test and evaluation chamber @ 2E-10 Torr
- Surface preparation using H-ion beam
- Surface deposition of various coatings
- Deposition monitor (+/- 0.01nm thickness)
- Femto-ampere current measurements (for QE)
- Solid state CW lasers on single-axis robot
- QE as function of time, temp, coverage, wavelength, and laser intensity (AUTOMATED)

## QE OF Cs ON W:  EXP. VS. THEORY

**QE OF Cs ON W:  EXP. VS. THEORY**

**CONDITIONS:**
- Coverage Is Uniform
- Field & Laser intensity low:  Schottky barrier lowering & heating negligible
**For ****407 nm**
- Cs deposited rapidly:  Exp measured mass by a “depth” factor.  Therefore: Scale factor = (100%/Atomic diameter)
**For ****532 nm**** and ****655 nm**
- Cesium deposited slowly:  accumulation rate affected by desorption (scale )
- Peak value affected by residual cesium left on W (center xmax)
- Presence of O (hard to remove) affects work function variation
- To account for effects:

- 405 nm:	x 1   (theory x 1.40)

- 532 nm:	x 4   (theory x 1.40)

- 655 nm:	x 35  (theory x 0.84)

**Notes:**
Last modified:  11/04/2005

## QE OF Cs ON W:  EFFECT OF TEMPERATURE

**QE OF Cs ON W:  EFFECT OF TEMPERATURE**

**Consider “typical” conditions of:**
**Laser Intensity****10 MW/cm****2**
**Field at cathode ****10 MV/m**
**Field enhancement ****2 (generic)**
**Pulse length****10 ps**
- Relaxation Time Is Temperature-dependent: **Impact of Operating Photocathode at Lower Temperatures Is to Raise QE **(all other things being equal)

- Under these conditions
- For r = 0.1 cm2:

## QE OF Cs ON Ag:  EXP. VS. THEORY

**QE OF Cs ON Ag:  EXP. VS. THEORY**

**Cs ON Ag Exp:**
- INITIAL COMPARISON METHODS for data taken week of Aug 8 2005
- Experimental conditions same as for Cs-W for 532 and 655 nm exp.
- Used same scale  as Cs on W
- Shift factor aligns peaks for each experiment
- Data taken by ANNE BALTER

**Notes:**
Let nate show this one

Nate will discuss why the discrepancies occur at low coverage due to residual Cs.

## HYPOTHESES OF  EXP-THEORY DIFFERENCES

- Actual surfaces differ from theory models because of
- Surface geometry (altered by cleaning?)
- Reflectivity changes with exposed face (inc. angle)
- Crystal Faces can have different work functions (e.g., Cu(111) = 4.86, Cu(110) = 5.61, etc)
- Contaminants (e.g., Carbon-based  ≈ 5.5 eV) & possibility of only sub-area contributing

**Notes:**
Transfer this to Nate’s presentation

## IMPACT OF COATINGS ON WORK FUNCTION

**IMPACT OF COATINGS ON WORK FUNCTION**

- Conventional View:  charged atoms at surface & image charge = dipole
- QM View:  Electron penetration of barrier determined by height and width
- Exchange-Correlation & Poisson’s Eq:  Changes in density = changes in V(x)

- L. A. Hemstreet, *et al.* PRB40, 3592 (1989)

- W cores

- W cores

**ExCorr**
**+**
**Poisson**

**ENERGY**

**POSITION (x/a****o****)**

## EXCHANGE CORRELATION ENERGY OF e-

**EXCHANGE CORRELATION ENERGY OF e****-**

- Aspects of system of
- interacting e- in ground state
- determined by density
- Exch.-Corr. Potential: change in  gives rise to change in V
-  = Fermi Level
- = electron density
- ao = Bohr radius

- Kinetic
- Energy

- e-e
- interaction

- e-lattice
- interaction

- self-interaction of
- background

**Typical **
**Metals**

## OTHER CONTRIBUTIONS TO SURF. BARRIER

- Simple Theory:  Wave function penetration creates dipole & gives Friedel Oscillations

- Why bother looking at Friedel Oscillations? For two good reasons:
- Friedel Density profile has analytic V(x) sol’n
- Metal + Ba Density profile can be decomposed into Friedel component + Gaussian add-on: enables an analytic solution to Poisson Eq... or at least a very easily solved solution
- How?
- Approximations exist for location of background positive charge
- Poisson’s Eq. easily solved with Friedel Density where  = 2*k**F*(xi – xo)

## QUANTUM DISTRIBUTION FUNCTION

- Contours mimic classical trajectories; when potentials are smooth and slowly varying, they _*are*_ classical trajectories

**QUANTUM DISTRIBUTION FUNCTION**

- Heisenberg
- Representation

- Wigner Distribution function (WDF)

## ANALYTICAL WDF MODEL:  GAUSSIAN V(x)

**ANALYTICAL WDF MODEL:  GAUSSIAN V(x)**

- How does V(x,k) behave?  Consider a solvable case where V(x) is a Gaussian:

- Sharp
- x2 = 5.0

- Broad
- x2 = 0.1

- small x samples f(x,k') far from k

- large x samples f(x,k') near k

## ANALYTICAL WDF MODEL (II):  GAUSSIAN V(x)

- The behavior of V(x,k) signals the transition from classical to quantum behavior:
- Sharp:  classical distribution
- Broad:  quantum effects
- Can V(x,k) give a feel for when thermionic or field emission dominates?
- Consider most energetic electron appreciably present(corresponds to E =  or k = kF)
- If sin(kFx) does not “wiggle” muchover range x, QM important
- Thermionic Emission:x is very large - expectclassical description to be good
- Field EmissionkFx = O(2) implies

- Image Charge Potential

## ELECTRON DENSITY TO EMISSION BARRIER

- Numerically solve QDF to Obtain Electron Density
- Render Density in Terms of Friedel Components
- Evaluate Potential From Exchange-Correlation Relation & Poisson’s Equation from the Friedel Representation
- Change in Barrier seen to be due to shift in F and xo terms

## EMISSION BARRIER TO TRANSMISSION PROB.

- Modified Airy Function Approach:
- V(x) = Vo + F(x-xn):
- V(x) V(xn):  N Linear Segments at xn
- , ∂x Matched at xn, xn+1, etc.

- Zi = Linear combinations of Airy Functions Ai(z), Bi(z)

## CONCLUSION

- Components of the Photocathode Program
- Analysis of Coated & Bare Metals (extend to semiconductors)
- Development Custom Engineered Controlled Porosity Photocathodes
- Creation of Photoemission Models Validated By Exp. for Beam Codes
- Theory Components included in photoemission code
- Work function dependence on coverage & components; local variation
- Spatial & Time Dependence of Temperature for laser & material parameters
- Fundamental models of scattering, photoemission, QE & Barrier
- Validation by bare and coated metal QE (macro) measurements
- Status of Modeling Effort
- Integrated Simulation Model Framework Without Recourse (Insofar As Possible) to “Fit” Parameters for “Library” Metals Using Quantum Distribution Function, Emission Theory, Coatings Theory
- Photoemission Modules Appropriate for Beam Simulation Code (1st Generation Model distributed) From Integrated Simulation Model

**Notes:**
3.2 Specific Content.

3.2.1 Summary of First Years Work.  Highlight the technical issues encountered, milestones achieved, resources applied, and progress made to date.

3.2.2 Technical Approach for Proposed Second Years Work.  Discuss the technical challenges, resource management, feasibility, conceptual design, and design trade space.  Include areas such as military utility, technical innovation, potential payoffs, and uniqueness of effort toward technological breakthroughs in high energy laser development in light of the work conducted during the first year. 

3.2.3 Schedule and Budget.  Provide a schedule and budget information within the presentation.  Identify major risks, their impact, and proposed means of mitigating them. Budget should be broken down by major tasks.  In addition, address other funding sources leveraged to accomplish this work if any. 

3.2.4 Conclusion.  Summarize the main points of the presentation and state why the JTO should select the proposed second year work for award.