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UNIVERSITY OF CALIFORNIA

Los Angeles

Observation of High Gain and Intensity Fluctuations in Self-Amplified

Spontan eous Emission Free-Electron Lasers

A d issertation submitted in p artial satisfaction of the requ irements for the d egree

Doctor of Philosophy in Ph ysics

by

Mark Jeffrey Hogan

1998

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Copyright by

Mark Jeffrey Hogan

1998

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The dissertation of Mark Jeffrey Hogan is app roved.

David Cline

Harold Fetterman

James Rosenzw eig

Claudio Pellegrini, Committee Chair

University of California, Los Angeles

1998

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This work is ded icated to my m other and father.

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Table of Contents

Chapter 1

Introd uction an d Motivation ......................................................................1

1.1 Motivat ion For Th ese Experimen ts ..................................................................2

1.2 Organ ization .........................................................................................................5

Chapter 2

SASE-FEL Theory......................................................................................... 8

2.1 Overview................................................................................................................9

2.2 Sp on taneous Emission ......................................................................................132.3 Bunchin g ..............................................................................................................15

2.4 Th e FEL In stab il ity ............................................................................................17

2.5 1D Mod el ...........................................................................................................18

2.6 Slip page ...............................................................................................................20

2.7 Flu ctu ations .........................................................................................................20

2.8 3D Models..........................................................................................................22

2.9 Ginger...................................................................................................................24

2.10 Conclusion .........................................................................................................25

Chapter 3

UCLA SASE Experiment........................................................................... 263.1 Experimentalists View of an FEL...................................................................27

3.2 Th e PBPL Facility ...............................................................................................28

3.2.1 The PBPL Linac.....................................................................................30

3.2.1.1 The PBPL Drive Laser System .....................................................30

3.2.1.2 The Gun ........................................................................................33

3.2.1.3 The PWT.......................................................................................33

3.2.1.4 Electron Beam Diagnostics...........................................................33

3.2.1.5 Magnetic Opt ics ...........................................................................34

3.3 The Electron Beam .............................................................................................34

3.3.1 Spot Size ................................................................................................343.3.2 Emittance...............................................................................................38

3.3.3 Energy and Energy Spread .................................................................40

3.3.4 Pu lse Length and Peak Cur ren t .........................................................43

3.4 Th e UCLAKIAE Unulator ..............................................................................45

3.5 IR Diagn ostic Beamline ....................................................................................48

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3.5.1 IR Tran sport Line .................................................................................49

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3.5.2 Wavelength Determina tion ................................................................50

3.5.3 Determining the Coherent Fraction...................................................53

3.5.4 X-ray Background and Detector Noise.............................................53

3.5.5 Detector Calibration .............................................................................54

3.6 Gain Measu remen ts...........................................................................................56

3.6.1 Intensity as a Function of Charge ......................................................573.6.2 Subtracted IR In ten sity ........................................................................60

3.6.3 Comp arison w ith Theory an d Simu lations ......................................61

3.7 Flu ctu ation Measuremen ts ...............................................................................64

3.8 Ch ap ter Su mmary ..............................................................................................66

Chapter 4The UCLA/ LANL SASE Experiment .....................................................67

4.1 The AFEL Facility...............................................................................................68

4.1.1 The AFEL Linac....................................................................................68

4.2 The Electron Beam .............................................................................................70

4.2.1 Spot Size ................................................................................................70

4.2.2 Electron Beam Peak Current...............................................................71

4.2.3 Energy and Energy Spread .................................................................75

4.3 The UCLA-RRC-KIAE Undulator...................................................................77

4.4 IR Diagn ostic Beamline ....................................................................................80

4.4.1 IR Tran sport Line .................................................................................80

4.5 Wavelength Measurements..............................................................................81

4.6 Gain Measu remen ts...........................................................................................82

4.6.1 Average Power Measurements..........................................................834.6.2 Comparison with GINGER.................................................................84

4.7 Flu ctu ation Measuremen ts ...............................................................................86

4.8 Ch ap ter Su mmary ..............................................................................................89

App endix A

SASE FELCAD -UCLA ............................................................................90

App endix B

SASE FELCAD UCLA/ LAN L ............................................................102

App endix C

Pu lsed Wire MathCAD ...........................................................................113

References..................................................................................................121

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List of Figures

Figure 1.1: FELs have operated in a wide var iety of configurations, beam energies

and wavelengths. Figure courtesy of G. Travish..................................2

Figure 2.1: Schematic d iagram of basic FEL componen ts: an und ulator of

magn etic period u and length Lu , an electron beam, and the outp utrad iation field of radiation wavelength . ...........................................9

Figure 3.1: The PBPL linac showing all of the cpmponents necessafor the

prod uction, acceleration, transport, characterisation and d isposal

of the electron beam................................................................................29

Figure 3.2: The PBPL drive laser systemproduces the roughly 200 J of UV

laser light ,in pulses a few ps wide at a rep rate of 5 Hz, necessary

for generating the beam from the copper photocathode in the RF

gun.............................................................................................................32

Figure 3.3: Brookhaven gun cathode surface prior to installation at UCLA

showing the dark peanut shaped laser damage at the center ofthe backplane.. .........................................................................................36

Figure 3.4: PBPL electron beam spot size versus charge at the phosph or screens

before (PS8) and after (PS9) the undulator..........................................37

Figure 3.5: Composite image of dark current and photoelectron beams at

phosphor screens 8 and 9, before and after the un du lator respectively.

At PS 8, the photoelectrons are difficult to distinguish against the

dark current background. At PS 9 (after the undulator) the .dark

current is all but gone and the ph otoelectrons are clearly visible.

The large dark curren t background makes the spot size measurements

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in Figure 3.4 difficult...............................................................................37

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Figure 3.6: The PBPL slit based emittance measurement system. The beam is

broken up into a series of individu al beamlets in w hich the emittance

term of the envelope equation is the d ominant effect. The image of

the beamlets is analysed to d etermine the peak positions and w idths.

Based on the know n geometry of the slits that created the beamlets

and the distance propagated to the phosphor, the phase space areais calculated..............................................................................................39

Figure 3.7: Normalized emittance of the PBPL electron beam versus charge as

measured in the horizontal transverse plane with the emittance slits.

The data are fit corresponding to charge independant term adding

in squares with another term growing linearly with charge. The

horizontal bars are the width of the charge bins used to compute

the mean (data point) and spread (vertical bar).................................40

Figure 3.8: Measured un correlated energy sp read as versu s charge for the PBPL

electron beam. The horizontal bars are the w idth of the charge binsused to compute the mean (data point) and spread (vertical bar).

The data are fit correspond ing to a charge ind epend ant term ad ding

in squares with another term growing linearly with charge............43

Figure 3.19: Peak current as a function of charge, calculated from the m easured

uncorrelated energy spread...................................................................44

Figure 3.10: An internal crosssection of the PBPL undulator. The markers refer

to 1) VanadiumPermandur Cshaped yokes, 2)

NeodyniumIronBoron pole tip magnets, 3) SamariumCobalt

booster magnets, 4) Halldetectors support plate, 5) Translation stagefor support plate......................................................................................46

Figure 3.11: Target of the letters UCLA in 4 point font, imaged from the end

of the beamline through the 4 mm inner diameter vacuum pipe of

the PBPL undulator. The visibility of all four letters indicates the

beam pip e insid e th e u nd ulator is prop erly aligned ..........................48

Figure 3.12: The PBPL IR diagnostic beamline showing all of the components

necessary for transporting the FEL output from the exit of the

beamline to the Cu :Ge detector. An iris used to quantify contributions

from outside th e coherent solid angle is shownalong w ith the filtermaterials used to d etermine the contributions from h igher harm onics

or CSE at a wavelength on the order of the electron beam bunc

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length... .....................................................................................................49

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Figure 3.13: Transmission curve of IR through the KrS5 windows at the exit of

the beamline and at the entrance of the IR detector. KrS5 has a

nearly constant transmission of 70% over the sensative range of the

detector .....................................................................................................50

Figure 3.14: Schematic of the monochromator used in the SASE experimentdiscussed in Chapter 4. Incident light reflects off mirror M1 onto a

focusing mirror C and onto a diffraction grating G. The grating

disperses the light with a wavelength-position correlation. After

propagating out off mirrors F and M2, the position and width of

the exit slit selects the central wavelength and bandwidth

respectively. Diffraction makes monochromators of reasonable size

and resolution lossy in the Infrared .. ...................................................51

Figure 3.15: Transmission curve for the Calcium Fluoride filter used to block the

fundamental (16 m) while allowing higher harmonics to pass to

the IR detector and be quan tified . ........................................................52

Figure 3.16: Transmission curve for the Potassium Chloride filter used to pass

the fund amental (16 m) as w ell as other harmon ics, while blocking

any p ossible contributions from coherent sp ontaneous emission from

wavelengths on the ord er of the electron beam bun ch length (a few

mm). ..........................................................................................................52

Figure 3.17 Schematic layout of calibration system for the UCLA Cu:Ge IR

detector. The FierFly FEL provided ps pulses of IR at a wavelength

of 24.7 m. Based on the measured energy at th e calibrated energy

meter and the known value for the splitter, the response of theUCLA Cu:Ge detector in mV was measured for various input

energies. By dividing the inpu t energy by the energy per photon at

24.7 m and offseting the value by the difference in detector

sensativity a t 16m, yields the calibration plot in Figure 3.19. ........55

Figure 3.18 Absolute calibration of UCLA Cu:Ge IR detector using setup in

Figure 3.18. The absolute calibration allows for comparison with

the calculated spontaneous emission for the electron beam in the

absen ce of SASE......................................................................................56

Figure 3.19: Histogram of raw detector signal including both IR from the FELand all detector backgrounds. The data represent electron bunch

charges ranging from 0.5 0.58 nC. The data for a given charge

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range is assigned a m ean and a standard deviation. .........................58

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Figure 3.20 Histogram of just the detector backgroun ds measured by introd ucing

a paper block in the path of the IR. Analogous to Figure 3.16, the

background is assigned a mean value and a standard deviation.

The mean value is then subtracted linearly from th e vlaue measured

in Figure 3.16 and th e standard deviationis subtracted in squ ares.59

Figure 3.21 Measured mean IR Intensity versus mean electron beam charge.

The data are binned around the mean charge 2.5%. The solid

green line is the calculated value for spontaneous emission using

the detector calibration in Figure 3.20. The plotted data can be

compared to the calculated spontaneous emission............................60

Figure 3.22 Mean IR intensity after subtracting the m easured contribution from

detector noise (Figure 3.17), contributions from harmonics measured

using KCl and CaF2 filters, and contributions from outside the

coherent solid angle. The plotted data can be compared to the

calculated spontaneous emission..........................................................61

Figure 3.23 IR at 16 m within the coherent solid angle fit to an Equation of the

form given by Equation 3.10. The fit gives a value for the exponent

of 3.7 at the highest charge case of 0.56 nC, indicating 3.7 power

gain lengths. The plotted data can be compared to the calculated

spontaneou s emission .............................................................................62

Figure 3.24 Results of the simulation code Ginger norm alized to the 0.2 nC d ata

point and plotted with the measured values to compare the pred icted

growth rate with the experimentally determined value. The plotted

data can be comp ared to the calculated sp ontaneous emission.......63

Figure 3.25 Histogram of total output intensities (including background and

detector moise, for the UCLA SASE-FEL Experiment. The data is

for a mean electron beam charge of 0.56 nC 2.5%. The signnal has

a mean value of 78 mV with a stand ard deviation of 14 mV............65

Figure 4.1: The AFEL accelerator including the UCLA 2 m un du lator and relevant

electron beam diagnostics......................................................................68

Figure 4.2: Measured average RMS electron beam tran sverse size plotted versus

average micropulse charge. The data are fit to a function in whichthe spot size is the superposition of a zero charge value (119 m)

adding quadractically with another term growing linearly with

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charge (38 m/ nC)..................................................................................71

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Figure 4.3: Calibration of the streak camera measurements accomplished by

introdu cing a series of known delays into the streak camera trigger

and plotting the delay time versus the displacement of the image

centroid on the screen.............................................................................72

Figure 4.4: OTR from the titanium foil between the accelerator and the und ulatorwas sent to a streak camera to measure the longitudinal electron

beam microbunch profile. The profiles are Gaussian. ......................73

Figure 4.5: Measured RMS electron beam pulse length plotted versus average

micropulse charges. The data are fit to a function in which the spot

size is the superposition of a zero charge value (3 ps) adding

quad ractically with an other term growing linearly with charge (2.2

ps/ nC).......................................................................................................74

Figure 4.6: Calculated electron beam p eak current based on the m easured values

of electron beam micropulse charge and pu lse length. .....................75

Figure 4.7: Relative energy spread, measured at the dipole spectrometer,

averaged over three macropulses containing 600 individual 2.5 nC

microp ulses. .............................................................................................76

Figure 4.8: The UCLARRCKIAE 2 m undu lator showing the aluminum

support structure with side access OTR port, the wiggle magnets

and the extra magn ets oriented to prod uce the quad rup ole focussing

force in the wiggle plane necessary for equal two plane focussing.79

Figure 4.9: IR diagnostic layout showing the optics fro transpoting the SASE todiagnostics including fast (Cu:Ge) and slow (HgCdTe) detectors, a

monochromator and energy meter.......................................................80

Figure 4.10: Average spectral linewidth of macropulses containing 600 2.5 nC

micropulses measured w ith a monochromator w ith 75 nm resolution.

....................................................................................................................82

Figure 4.11: Average FEL micropulse energy versus charge. Each data point

represents an average of 780 individu al micropulses. The error bars

are smaller than the data points............................................................83

Figure 4.12: Measured average SASE output energy from 780 micropulses plotted

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versu s measu red electron beam micropulse peak current................84

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Figure 4.13: The measured average SASE is compared with the predictions of

the simulation code Ginger. The Ginger outpu ts, which are depend ant

on the initial noise or bunching in the electron micropu lse, have

been norm alized to th e experimental d ata at the 167 A d ata point so

that the growth rates can be comp ared. The Ginger simu lations at

167 A give a power gain length of 12.5 cm, corresponding to a gainof 3 x 105....................................................................................................85

Figure 4.14: A histogram of the shot-to-shot fluctuations of the FEL output for

1520 individual 2 nC micropulses measured at the Cu:Ge detector.

The data have a mean value of 76 mV with a standard deviation of

28 mV corresponding to fluctuations in the output intensity of

37%................... .........................................................................................87

Figure 4.15: A histogram of the shot-to-shot fluctuations of the FEL output for

1520 individual 2 nC micropulses measured at the Cu:Ge detector

with a the predicrted Gamma probability distribution functioncorresponding to an M value of 8.8 for comparison..........................88

Figure C.1: Measured detector voltage (corresponding to a given deflection

angle) as a function of wire displacement from center in th e wiggle

(XZ) plane...............................................................................................115

Figure C.2: Measured detector voltage (corresponding to a given deflection

angle) as a function of wire displacement from center in the YZ

plane........................................................................................................116

Figure C3: The second integral of B gives the trajectory of the un du lator throu ghthe und ulator.. .......................................................................................118

Figue C.4: Wiggle amp litud e of wire as a function of wire d isplacement in the

YZ plane. As the wire approaches the magnetic pole pieces, the

field strength and thus the wiggle amplitud e increase quadratically.

..................................................................................................................119

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List of Tables

Tab le 2.1: A list of notation used in this d ocum ent..............................................11

Tab le 3.1: Characteristics of the PBPL dipole spectrometer used for measuring

the beam energy and energy spread. The energy spread is used to

estimate the electron beam bu nch length............................................42

Tab le 3.2: Measured electron beam param eters for the PBPL Linac.................45

Tab le 3.3: The characteristics of th e UCLAKIAE Un dulator ............................47

Tab le 3.4: Summary of the experimental and simulation results and are

presented . .................................................................................................64

Tab le 3.5: Sum mary of the measured and pred icted fluctuations are presented.

....................................................................................................................66

Tab le 4.1: Measured electron beam micropulse parameters for the AEL

accelerator. The d ata represent the range of param eters over wh ich

data was taken for the FEL experiment . ..............................................77

Tab le 4.2: Measured parameters of the UCLARRCKIAE 2 m undulator.....79

Tab le 4.3: Summary of the experimental and simulation results and are

presented . .................................................................................................86

Tab le 4.4: Sum mary of the measured and pred icted fluctuations are presented.

....................................................................................................................89

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ACKNOWLEDGMENTS

The road leading to this thesis has been a long and often bumpy one and

would have been unbearable if not for the support of my many colleagues, my

wife, family members and friends. A number of people who assisted me and

positively affected my life are not listed here, but I thank them nonetheless.

My parents were a constant source of love, sup port an d encouragement in

my life and I only wish they had lived to read this.

Claudio Pellegrini is my ad visor, mentor and also my friend . He has always

been a patient and caring teacher as well as living proof that it is possible to

remain unjaded by the politics that often come along with cool projects. Jamie

Rosenzweig has also been my teacher and my friend. His quick wit and un relenting

intellect have been a constant reminder that there is so much more to learn.

Claudio and Jamie took me under their wing, when others may not have, and

afforded me great latitude in my research and extend ed m e all possible resources.

Professors David Cline and Harold Fetterman were on my committee.

They have been helpful and u nd erstanding, especially about last minu te dead lines.

Professor Cline has also been my teacher and collaborator.

About the only thing that can make the long days and nights in a small

room several floors below ground enjoyable is the company of your best friend.

During my years in graduate school, Gil Travish and I have shared almost every

aspect of our w ork. Gil kept the lab runn ing and contributed greatly to this work.

Gil brought me in to PBPL, showed me much of what I know about doing

experiments, and show ed m e how to make things that not only worked, but that

were cool.

PBPL was built and operated by students. Thanks to fellow graduate

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stud ents Scott Anderson, N ick Barov, Pepe Davis, Pedro Frigola, Spencer H artman ,

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Alex Murokh, Sven Reiche, Parviz Saghizadeh, Phong Tran, Aaron Tremaine,

and Renshan Zh ang. Kip Bishofberger came into the lab in its twilight bu t quickly

mad e himself useful. Thanks Kip for all the favors near th e end . My gratitude to

the undergraduates who made it possible to continually build and rebuild the

lab: Jesse Caulfied, Sonja Daffer, Mark Fauver, Parviz Ghavamian, Beth Gitter,

Mark Goertemiller, Dominic Gooden, Chris Hall, Rick Hedrick, Dan MacIntosh,

Patrick Kwok, Janki Patel, Katrin Shenk, Jordan Stevens, Soren Telfer, Cesar

Ternieden , Sedr ick Wells, Jason Wingo.

The experiment at Los Alamos was only possible because I was w elcomed

into another laboratory by people who w ere gracious with their time, know ledge

and resources. Richard Sheffield and Dinh Nguyen were the source of many

insightful discussions. Dinh is a skilled operator who spent many long hours in

the laboratory to ensure that a stud ent wou ld get his data. The MathCAD document

in Append ix C was originally entitled Cliff Rules! because Cliff Fortgan g was a

constant source of information and resources for the pulsed w ire measurements.

John KinrossWright, Scott Voltz and Mike Webber w ere instrum ental in keeping

the AFEL facility running smoothly.

Dick Cooper has been a great friend and a teacher as well as the source

of many, much n eeded Margaritas! Thanks Dick for all the great adv ice.

In add ition to the p eople at UCLA and Los Alamos, I owe m y gratitud e to

a number of colleagues around the world: Roger Carr, John Goldstein, Dennis

Palmer, Luca Serafini (for the climbing and being Extreme!), Bill Fawley, Ilan

BenZvi, and Glenn Westenskow. Working w ith our Russian collaborators at the

Kurchatov institute und er Alexand er Varfolomeev has been a p leasure.

My beloved wife Holly has been a daily source of strength and

encouragement. Thank you sweetie for putting up with the long hours, low pay

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and un certain schedules. Thank you Chris for being there when I needed you.

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Having spent m y academic career so close to Hollywood , it should not be

surp rising tha t I feel the need to thank Gene Rodd enberry and George Lucas for

their creative genius and the much n eeded escapism. The comic genius of Dennis

Miller, Denis Leary an d the creators of Bugs Bun ny h elped m e never take myself

or anything else too seriously.

I wou ld like to thank the su pp ort staff of the UCLA Depar tment of Physics

and Astronomy. The UCLA experiment could not have happened without the

machine shop personnel at UCLA who completed so many rush jobs that the

term almost lost its meaning; thank you Al Casillas, Harry Lockart (who even

made my titanium wedding ring!) and Frank Chase. Our building manager Tim

Smart did us many favors to keep the lab running smoothly. Thank you Penny

Lucky for making the d epartm ent a better place for grad uate studen ts. Jim Kolonko

and Christine Green kept the money flowing.

The US Departm ent of Energy, UCLA Dep artment of Physics and the Los

Alamos National Laboratory are thanked and acknowledged for providing

financial supp ort for the laboratories necessary for my livelihood .

Finally let me thank the coffee and banana growing regions of the world

for the two d ietary staples of my gradu ate career.

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VITA

August 6, 1967 Born in Stanford , CA.

December, 1989

Sep tem ber, 1990. Un dergrad u ate Stu d en t Research Assistan t

UCLA Departm ents of Physics.

September, 1993 B.S. in Physics at UCLA.

1993 1994 Graduate Division Scholorship UCLA.

Janu ary, 1994 US Particle Accelerator School UCLA.

Au gu st, 1994 International Particle Accelerator School Mau i,

Hawaii.

July, 1997

September, 1997 Visiting Scientist LAN L.

Presently Research Assistant, Particle Beam Physics

Laboratory UCLA.

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PUBLICATIONS

S.C. Hartman , et al., Initial measu rements of the UCLA RF ph otoinjector,

High Intensity Electron Sources (Legnaro, Italy: 1993).

S.C. Hartman, et al., Emittance measurements of the 4.5 MeV UCLA RF

photoinjector, Proceedings of the 1993 Particle Accelerator Conference

(Washington, DC, USA: 1993).

Baranov, G.; Barov, N.; Davis, P.; Fauver, M. et al., The UCLA IR FEL

Project, Nuclear Instruments & Methods in Physics Research, Section A ,1 July

1993, vol.A331, (no. 1-3):228-31.

Hogan, M.; Rosenzweig, J. Longitudinal Beam-Beam Effects in Circular

Colliders, Proceedings of the 1993 Particle Accelerator Conference, New York,

NY, USA: IEEE, 1993. p. 3494-6 vol. 5.

Rosenzweig, J.; Barov, N.; Hartman, S.; Hogan, M. et al. Initial

Measurements of the UCLA RF Photoinjector, Nuclear Instru ments & Methods

in Physics Research, Section A, 1 March 1994, vol. 341, (no. 1-3):379-85.

Travish, G.; Hogan, M.; Pellegrini, C.; Rosenzweig, J. The UCLA High

Gain Infrared FEL, Nuclear Instru men ts & Methods in Physics Research, Section

A, 11 April 1995, vol. 358, (no. 1-3).

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Hogan, M.; Pellegrini, C.; Rosenzweig, J.; Travish, G., et al., Status of the

UCLA High-Gain Infrared Free Electron Laser, Proceedings of the 1995 Particle

Accelerator Conference, N ew York, NY, USA: IEEE, 1995. p. 240-2 vol. 1.

Zhang, R.; Davis, P.; Hairapetian, G.; Hogan, M., et al. Initial Op eration of

the UCLA Plane Wave Transformer (PWT) Linac, Proceedings of the 1995 Particle

Accelerator Conference , N ew York, NY, USA: IEEE, 1995. p. 1102-4 vol. 2.

Davis, P.; Hairapetian, G.; Hogan , M.; Joshi, C. et al. The UCLA Compact

High Brightness Electron Accelerator, Proceedings of the 1995 Particle Accelerator

Conference, New York, NY, USA: IEEE, 1995. p. 1105-7 vol. 2.

Reiche, S.; Rosenzw eig, J.B. et al., Experimental Confirmation of Transverse

Focusing and Adiabatic Damp ing in a Standing Wave Linear Accelerator, Physical

Review E, Sep t. 1997, vol. 56, (no. 3): 3572-7.

Hogan, M; Pellegrini, C; Rosenzwig, J.; Travish, G. et al., Measurements

of High Gain an d Intensity Fluctuations in a SASE FreeElectron Laser, Physical

Review Letters, January 1998, vol. 80, p. 289292.

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ABSTRACT OF THE DISSERTATION

Observation of High Gain and Intensity Fluctuations in Self-Amp lified

Spontan eous Emission Free-Electron Lasers

by

Mark Jeffrey Hogan

Doctor of Philosoph y in Physics

University of California, Los Angeles, 1998

Professor Claud io Pellegrini, Chair

This thesis presents the results of two recent free electron laser (FEL)

experiments operating in the self amplified spontaneous emission (SASE) mode.

An Xray laser wou ld offer a u nique w ay to explore the structure of matter

at the atomic and molecular scale. Among the various schemes prop osed to reach

this wavelength region, the free electron laser, operating w ithout m irrors in a self

amp lified spontan eous emission mode offers a favorable scaling law. It has also

been show n th at u tilizing state of the art linear accelerators and electron sources

it is possible to build an Xray SASE FEL, and this has led to tw o major p roposals

to bu ild a SASE X-ray FEL, one at SLAC, the other at DESY.

The theory on which the SASE X-ray FEL is based, has been developed

over many years, but the experimental data to supp ort it are few an d incomplete.

Very large gain in SASE has so far been observed in the centimeter to millimeter

waves, and in the m edium infrared (IR) at Los Alamos; recently gain in the n ear

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IR has been observed at Orsay and at Brookhaven. The intensity distribution

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function has been previously measured only for spontaneou s und ulator radiation,

with no amplification, and long bunches. This thesis analyzes two recent

experiments d esigned to verify the models of high gain FELs.

High gain FEL theory is reviewed with a emphasis on the characteristics

of SASE measu rable by these exper iments. The accelerator, beam line comp onen ts

and diagnostics are described with an emphasis on the measurements. The FEL

un du lators and op tical diagnostics are also described, again with an emp hasis on

the m easurements.

The experimental data are comp ared to analytic mod els, where ap plicable,

and to comp uter simulation codes.

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Chapter 1Introduction and

Motivation

The theoretical and experimental developments which led to the selfamplified

spontaneous emission freeelectron laser (SASE FEL) experiments discussed in

Chapters 3 an d 4 are reviewed. The philosophy and objectives of the two high

gain SASE experim ents d iscussed in Chap ters 3 an d 4 are presented.

Chapter Contents1.1: Motivation For These Experim ents ..........................................2

1.2: Organization ................................................................................5

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develop in the FEL producing exponentially growing radiation intensity along

the undulator [2] [3] [4] [5] [6] [7] [8]. Soon thereafter, it was shown that this

instability could amp lify a portion of the spontaneous emission from the electron

beam, mitigating the need for an input radiation source [9]. The prospect of

creating an FEL that required both no input source and no mirrors to make an

optical cavity led to the consideration of FELs as sources of short wavelength

radiation (VUV and soft x-rays). At the time however, it was concluded that

electron beam s of sufficient quality to reach short w avelength s, were not available

[9]. The electron beam quality was sufficient for operation at longer wavelengths

however, and data showing exponential growth of 8 mm radiation as a function

of und ulator length was pu blished in 1985 [10].

As the theoretical understanding of SASE FELs continued to evolve, so

did accelerator technology. The development of the photoinjector at Los Alamos

National Laboratory and Brookhaven National Laboratory [11] [12] [13] [14] [15]

opened the door for short wavelength FELs by offering beams with high peak

currents, low normalized emittances and small energy spreads [16] [17] [18].

Photoinjectors use short pulses of laser light to generate the electron beam, via

the photoelectric effect, from a cathode located inside an accelerating cavity.

Since the electron emission is proportional to the number of incident photons

(neglecting space charge forces in the electron beam), the electron beam profile

(transverse and temp oral) can be controlled at least to the extent th at the laser

beam p rofile can be controlled.

Undulator design, construction and characterization techniques were

enhanced by the ongoing efforts at third generation synchrotron light sources

3

and other institut ions [19].

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The development of electron beam sources capable of generating high

brightness electron beams led people to consider the possibility of using these

high quality beams in conjunction with linear accelerators to produce high

lum inosities in a Next Linear Collider (NLC) [20]. The Stanford Linear Accelerator

Center (SLAC) Linear Collider Project and others have developed models for

preserving and even enhan cing the beam brightness du ring the acceleration process

via longitud inal bunch compression.

In 1992, an x-ray Free Electron Laser (FEL) operating in the SelfAmplified

Spontaneous Emission (SASE) mode, utilizing a photoinjector and a section of

the SLAC linac, was proposed [21]. Installing a photoinjector on a section of the

SLAC linac, accelerating to 14 GeV and compressing the beam to several kilo-amps

of peak current, and then sending it through a long 100 m u nd ulator may p rodu ce

coherent x-rays with a brightness roughly ten orders of magnitude greater than

current third generation synchrotron sources. A design group was formed and

has since explored the issues associated with constructing the Linac Coherent

Light Source (LCLS) [22] [23] [24] [25] [26] [27] [28] [29]. The recently published

LCLS Design Study Report [30] concludes that if the SASE FEL theory is correct,

the LCLS is feasible. In fact, research into the LCLS project has inspired other

projects at The Advanced Photon Source (APS) at Argonne National Lab (ANL)

[31] and DESY in Hamburg, Germany [32]. Experimental data to compare with

SASE FEL theory are however, few and incomplete. Until recently, the only

experiment to show the exponential growth in radiation intensity from SASE

operated in the microwaves (8 mm) [10] almost eight orders of magnitude

away from the wavelength p roposed for the LCLS.

More recently, experimental resu lts have been obtained by several group s

4

in the infrared [33] [34] [35] and visible [36] with gains of about one order of

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magnitude or less and another with a gain of about 300 [37]. The intensity

distribution function of the output radiation has been previously measured only

for spontaneous undulator radiation, with no amplification, and long bunches

[38].

1.2 ORGANIZATION

This thesis is divided into two parts theory and experiment. In the first

part, Chap ter 2, the spon taneous emission from a single electron in an u nd ulator

is discussed, and relevant prop erties of the rad iation are d efined. The interactions

of many electrons is taken into account and the concept of bunching is introdu ced.

The production of stimulated emission and the FEL instability are introduced.

Limiting conditions on the instability and fluctuations in the output radiation

intensity are discussed. The need for simu lation codes is p resented. The theoretical

framework put forth in Chapter 2 constitutes the basis for analyzing the

experimental data in Chap ters 3 and 4.

In Chapter 3 this thesis reports the results of measurements, at 16 m, of

large gain and of the intensity distribution function for amplified radiation, and

for a short bunch length [33]. Chapter 4 reports additional experimental data

showing a gain of 3x105 at 12 m [39]. This is the largest gain to d ate at an op tical

wavelength for a SASE FEL. The fluctuations of the output intensity from pulse

to pu lse were also measured and analyzed.

The UCLA experiment discussed in Chapter 3 chose to utilize a state of

the art electron beam w ith a high qu ality un du lator to explore the start-up p rocess

in a h igh-gain SASE FEL. The m oderate energy electron beam and short u nd ulator

5

produce radiation at an optical wavelength, avoiding complications in the

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interpretation of data resulting from the use of a waveguide and operating at a

wavelength close to noise in the RF and electron beam. In addition to a high

quality beam, a heavily instrum ented beamline was bu ilt to fully characterize the

param eters that an FEL is critically dep endent u pon . The straight beam line coup led

the beam into the undulator with no bends or dispersive elements that could

dilute the phase space. Single bunch operation with a phase stability of better

than 1 ps and a high speed infrared detector allowed shot-to-shot measurements

of both the electron beam as well as the FEL output. Because the undulator

allowed no side access for m easuring the outp ut intensity as a function of position

in the un du lator, the FEL outp ut w as stud ied for different electron beam charges

with an u nd ulator of fixed length. By characterizing the electron beam prop erties

as a function of charge and then characterizing the FEL output as a function of

charge, we can then interpret the FEL output as a function of the electron beam

properties.

Building on the success of both the UCLA experiment as well as ongoing

efforts at Los Alamos, a collaboration was formed to extend these measurem ents

from the start-up regime to well into the high-gain process. The experiment

discussed in Chapter 4 utilized the brighter beam produced by the Advanced

Free Electron Laser (AFEL) facility at Los Alamos and a longer undulator

constructed at UCLA to push well into the high gain regime with gains many

orders of magnitude above the spontaneous level. The measured gain of 3 x 105

(or 27.5 db/ m) is the highest gain to date for a SASE FEL operating a t an op tical

wavelength an d very near the 30 db/ m record for any wavelength. The AFEL

accelerator produces trains of several hundred electron bunches within a single

macropu lse operating at 1 Hz. Measurements of the electron beam are thu s average

6

values as opposed to single shot measurements. However, the high average electron

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beam pow er produces correspond ingly higher average FEL outp ut powers which

allows ad ditional diagnostic tools to be used on the outp ut rad iation.

Appendicies A and B are MathCAD worksheets which calculate many of

the interesting parameters in the experiments discussed in Chapters 3 and 4

respectively; pulse length; peak current; emittance; transverrse spot size; bunch

length; FEL parameter; cooperation length; Rayleigh range; and gain length to

name a few. They are intended as a resource for the reader to consult periodically,

wh enever the qu estion w hat is the ______ comes to mind . Appendix C comp utes

the focusing properties of the UCLARRCKIAE und ulator discussed in Chap ter

7

4 based on measurements made with the p ulsed wire technique.

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Chapter 2

SASE-FEL Theory

The spontaneous emission from a single electron in an undulator is discussed,

and relevant properties of the radiation are defined. The interactions of many

electrons is taken into account and the concept of bunching is introduced. The

pr odu ction of stimulated emission and the FEL instability are introd uced. Limiting

conditions on the instability and fluctuations in the output radiation intensity are

discussed. The need for simulation codes is presented.

Chapter Contents2.1: Overview ......................................................................................9

2.2: Spontaneous Emission ..............................................................13

2.3: Bunching.....................................................................................152.4: The FEL Instability ....................................................................17

2.5: 1-D Model...................................................................................18

2.6: Slippage ......................................................................................202.7: Fluctuations................................................................................20

2.8: 3-D Models.................................................................................22

2.9: Ginger .........................................................................................24

8

2.10: Conclusion................................................................................25

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2.1 OVERVIEW

A free electron laser (FEL) is a device that converts the energy in a relativistic

electron beam into electromagnetic radiation v ia emission ind uced by the periodic

magnetic field of an undulator. Here the term free means the electron is not

bound to any atom. The electron beam oscillates (or und ulates) in the transverse

direction, as it propagates colinearly with its own synchrotron radiation down

the axis of the un du lator. The tran sverse comp onent of the electron beam velocity

vector is parallel to the electric field component of the electromagnetic field,

resulting in an energy exchange between the electron beam and the radiation

field. The kinetic energy of the electron beam is thu s converted to electrom agnetic

radiation. The wavelength of the output radiation is dependent on the energy of

the electron beam and the strength and periodicity of the magnetic field in the

undulator.

FELs operate in m any different configurations an d regimes. In this chapter

we limit our d iscussion to single pass amp lifiers operating in the high gain regime,

starting from the spontaneous emission or noise in the electron beam the so

called self amp lified spontaneou s emission (SASE) mode.

9

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N

S N

S N

S N

S N

S N

S N

S N

S

Electron Beam

Lu

Output RadiationField

uPlanar Undulator

Figure 2.1: Schem atic diagram of basic FEL comp onents: an u nd ulator of magnetic

period u and length Lu , an electron beam, and the output radiation field ofradiation wav elength .

The spon taneou s emission from a single electron , as well as the FEL collective

instability, have been described in great detail elsewhere [40] [48]. This chapter

will present a review of the relevant equations and scalings necessary for analyzing

the experimental data in Chapters 3 and 4. After pointing out the more salient

features of the spontaneous emission from a single electron passing through an

undulator, we discuss how the undulator provides a medium for stimulated

emission from the electron beam via the FEL collective instability. The notation

and Equations given in Sections 2.22.6 are based on the work of Murphy and

Pellegrini[41]. Finally, the theoretical predictions regarding the statistical nature

of the output radiation intensity are presented. The notation and equations used

in Section 2.7 is taken from [38] and [41]. A table of the notation u sed throughou t

10

this th esis is given in Table 2.1.

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Tab le 2.1: A list of notation u sed in this docum ent.

Description Symbol or Notation

Effective optical beam radius aBun ching parameter B

Initial bu nching B0

Normalized undulator field K

Normalized undulator field K=(e/mc2)Bu

Focusing betafunction =2/Und ulator m agnetic field Bu

Longitudinal electron velocity [c] |Speed of light c

Electron charge e

Electric field from a single electron E0

Beam Emittance (norm alized, RMS) n

Electron Beam Energy [mc2]

Start-up intensity i0

Radiated intensity i

Beam current I

Bessel function factor Fn(K)

Radiation wavenu mber kr

Radiation wavenu mber kr=2/

r

Undulator wavenumber ku

Undulator wavenumber ku=2/u

Radiation w avelength

Betatron wavelength Cooperation length Lc

11

1D Gain length L1D

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Und ulator period u

Und ulator length Lu

Electron mass m

Nu mber of transverse modes MT

Nu mber of longitud inal modes ML

Total nu mber of modes M

Electron density n or nb

Num ber of electrons Nb

Nu mber of photons per nC Nph

Nu mber of und ulator periods Nu

Collected solid angle

Coherent solid angle c

Beam plasma frequency p

Ratio of the circumference to the d iameter of a circle

FEL Param eter

Beam sp ot size (one stand ard deviation) , b, rSlipp age param eter S

Coherent angle c

Radiation an gular frequency

Radiation an gular frequency 2c

Longitudinal undulator axis z

12

Rayleigh ran ge ZR

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2.2 SPONTANEOUS EMISSION

We begin by considering the radiation from a single electron. A single

electron traversing a planar u nd ulator emits radiation at a wavelength

=u

221+

K2

2+ 22

, 2.1

and at corresponding odd higher harmonics. The radiation wave train will have

a finite num ber of periods,Nu , and thu s the frequency will be imperfectly defined :

the band width w ill have a full width at half maximum (FWHM) of

~1

Nu. 2.2

The undulator is an extended linear source, but the coherent fraction of the

radiation, within the bandwidth given by Equation 2.2, can be described as a

source at the center of the und ulator, with an angu lar aperture

c 2uNu

12

, 2.3

and an effective source radius

a 1

4uNu

2. 2.4

The angle given in Equation 2.3 is only valid for values greater than the d iffraction

limited m innimu m angle

RMS =

4b. 2.5

For short undulators, the angular distribution will be bandwidth limited, but for

13

longer undulators, when the angle given in Equation 2.3 is smaller than the

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diffraction limited value, the radiation will still be limited by Equation 2.5. The

product of Equation 2.3 and Equation 2.4 is analogous to an optical emittance,

and gives the minimu m p hase space of the rad iation pu lse:

ac = 4

. 2.6

A rad iation pulse satisfying Equation 2.6 is said to be diffraction limited .

The intensity spectrum of the radiation emitted on axis ( = 0 ) at wavelength

, per electron, per un it frequency (d ) and u nit solid angle (d ) is approximately

d2In

dd = 0=

Nu2e22K2

c 1 + K2

2( )2 Fn K( )

sin2 xn 2( )

xn 2( )2 2.7

where

Fn K( ) = Jn +1( ) 2nK2

4 1+ K2 2( )

Jn 1( ) 2

nK2

4 1+ K2 2( )

2

n2

2.8

an d

xn =2Nun n( )

n2.9

with

n =2ncku

2

1 + K2 2, 2.10

wh ere we have introdu ced the harmonic number n = 1,3,5K( ) .

The coherent intensity is obtained by multiplying Equation 2.7 by the

band wid th of Equa tion 2.2 and a solid angle

c = c2

. 2.11

To calculate the number of photons we would expect to measure from just

14

spontan eous emission, we d ivide the coherent intensity by the energy per photon

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at the fund amental w avelength (see Equa tion 2.1)

Eph = h =hc

. 2.12

The num ber of coherent p hotons p er electron is then

Nph = K2

1+ K2F1 K( ) , 2.13

where is the fine structure constant. For a typical value of K~ 1, Nph 0.01 .

Thus, for any beam of electrons passing through an u nd ulator, only about 1% of

the electrons will radiate a photon within the bandwidth of Equation 2.2 and the

coherent solid angle, Equation 2.11. By comparing the number of photons given

by Equation 2.13, with the measured num ber for electron beam p arameters where

we expect no FEL gain, we can verify the calibration of our detectors. By then

comparing the calculated value to the measured value, for electron beam

parameters where we do expect gain, we can quantify the FELs performance as

an increase over the spon taneous em ission level.

2.3 BUNCHING

Since any p ractical FEL operates w ith a beam of many relativistic electrons,

the sp atial characteristics of the electron beam, both longitudinal an d transverse,

mu st be considered . To describe the rad iation field from man y electrons, a ph ase

factor must be introduced to account for the superposition of the individual

fields from m any electrons. The field from th ejth electron m ay then be w ritten as

E= E0 exp it0 j( ) , 2.14

where the time t0j denotes the time the j th electron enters the undulator. This

15

time, t0j , is equivalent to a displacement z0 j = czt0 j . Thus the intensity (which is

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of electrons and will fluctu ate from shottoshot.

The total number of photons given in Equation 2.13 can be increased by

either increasing the nu mber of electrons in the beam or increasing the number of

emitted photons per electron. One way to increase the number of photons per

electron is to distribute the electrons at spacing intervals of (as with phased

arrays of antennae) or to bunch the electrons all within a small fraction of a

wavelength . In either case, the fields of individu al electrons add in phase, the

bun ching factor B ( ) 1, and the intensity scaling ap proaches Ne2. A free electron

laser works towards both of these ends by creating an instability in which the

electrons organize themselves, or bunch, in a collective way, to increase the

radiation intensity. With typical values for Ne between 1081010, the potential for

enhancing the number of photons is enormou s.

2.4 TH E FEL IN STABILITY

Return ing to the simple picture in Figure 2.1, we can d escribe the FEL

process. Again, an FEL is a device that couples energy stored in a relativistic

electron beam into an optical field via an un du lator. The planar un du lator provides

a sinusoidal m agnetic field perp end icular to the axis of propagation of the electron

beam. The electron beam then experiences a Lorentz force causing it to w iggle (or

undulate) transversely. Some of the electrons in the beam will do work against

the electric field component of the radiation field thus loosing energy, others will

be worked on by the electric field component thus gaining energy, while yet

others neither loose nor gain energy. The result is an energy modulation in the

electron beam on the scale of the rad iation w avelength . The wiggle amplitude

17

of the electrons is

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i =i0

9exp

2z

L1D

2.20

where i0 is the effective start-up pow er and z is the position along the un du lator.

When operating in SASE mode, the effective start-up power is given by

the spontaneous emission in the first field gain length, or equivalently the first

two power gain lengths. Since SASE is a transition from a linear process,

spontan eous emission, to an exponentially grow ing p rocess, it is natu ral to consider

the rad iated pow er prior to the first e-folding as the startup pow er. Additionally,

we can define the total gain, G , at the end of the undulator, as the increase in

emission over i0 :

G =1

9exp

2Lu

L1D

. 2.21

This nu mber will serve as the benchmark for FEL performance in Chapters 3 and

4.

The satura tion power is

Psat = Imec2

e. 2.22

Saturation occurs a fter abou t tw enty field gain lengths. As mentioned in Chap ter

1, a high-gain SASE FEL requires an electron beam with a high sixdimensional

phase space density and a long undulator (Lu > L1D ). If we take typical order of

magnitude estimates I~100 A, ~10 mm -mrad and u ~1 cm, the FEL parameter

~0.01, giving L1D ~10 cm. This would require an undulator on the order of a

couple meters to saturate.

19

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2.6 SLIPPAGE

Radiation p ropagates faster than the electrons, whose longitud inal velocity

is less than c, and thus provides a mechanism for electrons in the tail of the

bunch to communicate with electrons in the front of the bunch. The radiation

slips past the electrons at a rate of one radiation wavelength p er und ulator period,

and so we may d efine the slippage (S) for the full und ulator as

S = Nu . 2.23

A more interesting quantity is the slippage in one gain length, defined as the

cooperation length:

Lc =Lu

Lg

6 2

. 2.24

The cooperation length plays a m ajor role in d etermining the statistical natu re of

the outp ut rad iation, as we sha ll see in the next section.

2.7 FLUCTUATIO NS

While each electron radiates independently from the other electrons, the

fields from the many electrons within one cooperation length coalesce, in effect

redu cing the number of indep endent radiators in the beam from Ne to

ML =Lb

Lc. 2.25

The intensity from ML independent radiators fluctuates with a distribution of

RMS width (for

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If the rad iation is observed (detected) with an angle greater than th e coherent

angle given in Equation 2.3 there are additional contributions to th e total M value

and smaller fluctuations. The additional contributions are given by the ratio of

the observed solid angle to the coherent one:

MT =c

2.27

where c = c2

(see Equation 2.3). The total number of degrees of freedom is

now

M= MLMT 2.28

with fluctuations given by

M =1

M. 2.29

The shape of the output intensity distribution function is a Gamma Probability

Distribution Function p W( ) :

p W( ) =MM

M( )

W

W

M1

1

Wexp M

W

W

2.30

where Wis the single shot outp ut intensity, W is the mean value of a distribution

of measured shots,M is given by Equation 2.28, and M( ) is the Gamma function

of argument M. As M tends to unity, p W( ) tends to the negative exponential

distribution with the highest probability W= 0 ; when M>> 1, p W( ) tends to a

Gaussian d istribution. In Chapters 3 and 4, the fluctuations in the outp ut rad iation

and the shape of the intensity distribution fun ction have been measured, and will

be compared to the theoretical estimates of the SASE FEL theory.

21

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2.8 3D MODELS

The app roximations u sed in the calculation of the 1-D gain length given in

Equation 2.19 are only valid when the electron beam satisfies the following four

conditions:

< 2.31

1 2.33

an d

S uNu

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with the spontaneous emission from a single electron. For example, for a

one Angstrom FEL from a beam in the 10 20 GeV range, the normalized

emittance required is on the ord er of 1 mm mrad. Currently, only electron

beams from RF photoinjectors (as opposed to storage rings) have an

emittance low enough for use in SASE FELs in the x-ray region. This

requirement is well satisfied by th e experiments in Chapters 3 and 4 (see

also Appendix A and B).

Equation 2.33 requires the radiation Rayleigh range to be longer than the

FEL gain length. If the Rayleigh range becomes too shor t, rad iation diffracts

away on the same length scale that the FEL process adds to it again

increasing the gain length over the 1-D value. Indeed, this requirement is

not satisfied in either of the experiments discussed in Chapters 3 and 4

(see also Appen dix A and B).

Equation 2.34 requires that the rad iation not slip past a majority of the

bunch length. The concept of slippage is discussed further in the next

section. Once the radiation has slipped past the electron bunch, there is no

longer a m echanism for energy exchange. Hence the feedback mechanism

is reduced and the gain length is increased beyond the 1D steady state

model. This requirement is neither grossly violated nor well satisfied in

the experiments discussed in Chapters 3 and 4 (see also Appendix A and

B).

Equations 2.33 and 2.34 indicate that several effects relevant to the

interpretation of the data and comparison to theory are not handled well by the

1D analytic models. A 3D model of an FEL can naturally include important

23

effects such as diffraction by incorporating the additional transverse degrees of

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3.1 EXPERIM ENTALISTS VIEW OF AN FEL

The FELs discussed in this thesis as well as the measurements made to

characterize them, may be understood by considering the several individual

components or elements involved: electron beams; electron beam optics; electron

beam diagnostics; un du lators; outp ut rad iation; outp ut rad iation optics and ou tpu t

rad iation diagnostics.

The electron beams under consideration are produced by radio frequency(RF) photocathode systems (a photoinjector plus add itional accelerating stru ctures)

that u tilize laser pu lses on the order of a few ps to create electron bu nches wh ich

are then accelerated to relativistic energies with high density six dimensional (x,

px , y, py, , ) phase spaces. Electron beam optics employ several types of

magn ets: solenoids for focusing; dipole bends for measuring the beam mom entum ,

momentum spread and disposing of the beam; quadrupole magnets for

focusing/ defocusing the beam in a single transverse dimension; and steering

magnets for correcting the beam trajectory. Electron beam diagnostics include

phosphor and optical transition radiation (OTR) screens for measuring the

transverse profile; slits for measuring the emittance; Faraday cups, integrating

current transformers (ICTs) and beam position monitors (BPMs) for measuring

the charge; dipole spectrometers for measuring the beam momentum and

momentum spread; and streak cameras to determine the bunch length and

longitudinal profile.

The und ulators provide a strong, uniform, periodic magn etic field transverse

to the electron beam s d irection of prop agation. Both of the u nd ulators d iscussed

27

in this dissertation are m ade entirely of perm anent m agnets no electromagn ets.

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They provide no or limited side access necessitating measuring the FEL outpu t as

a function of electron beam p arameters for a fixed un du lator length.

The spontaneous and stimulated emission exiting the undulator must be

transported and characterized. The radiation optics are made from materials

designed to reflect or transm it radiation in the infrared with m inimal attenuation.

The radiation d iagnostics includ e optical filters and monochromators to m easure

the w avelength; sensitive high speed infrared detectors cooled to liquid Nitrogen

and Helium temperatures; apertures to measure information on the transverse

profile of the radiation; and energy meters to provide an absolute calibration of

the output. We now present an overview of the entire system used in the first

FEL experiment, and then d iscuss the individu al measurements made, in roughly

the order m entioned above.

3.2 TH E PBPL FACILITY

The Particle Beam Physics Lab (PBPL) has been d escribed in great d etail in

a dissertat ion [47] elsewhere [33]. The laboratory w as constru cted for the p urpose

of educating students, generating and characterizing high brightness electron

beams, and conducting experiments on beam plasma and beam radiation

28

interactions. The PBPL linac is shown in Figure 3.1:

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Quadrupole

Steering magnet

6-way diagnostic cross

Beam Position Monitor

Gate Valve

Bellows

LEGEND

ICT

Steering Magnet #1

Solenoid

Gun Pneumatic Valve

PS #2 (Emittance Slits)FC #1 (Pneumatic)

PS#3 (After Linac)FC #2 (Manual)

Quad Doublets (2)Quads #1-4

PS #4 (After Doublets)

FC #3(Manual)

FC #5

Dipole #1

30 l/s

30 l/s

140 l/s

20l/s

20 l/s

Steering Magnet #3

Steering Magnet #4

Steering Magnet #2

PS #6(First Beam Dump)

PS #5 (Before Triplet)FC #4

Quad TripletQuads #5-7

Pulse LengthMonitor

20 l/s

20l/s

Steering Magnet #5

Steering Magnet #6

Slits

PS #7 (After Triplets)

After Linac Pneumatic Valve

Before Linac Pneumatic Valve

Steering Magnet #7

Steering Magnet #8

Steering Magnet #9

Slits

Figure 3.1: The PBPL linac showing all of the components necessary for the

production, acceleration, transport, characterization and disposal of the electron

29

beam.

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3.2.1: Th e PBPL Lin ac

The electron beam is generated in a Brookhaven S-band 1.5 cell photocathod e

RF gun [48] [49]. The low quantum efficiency (10-5) copper (Cu) cathode means

that in order to produce the desired charges (~1 nC or ~1010 electrons) with the

low energy sp read requ ired by the FEL (see Equation 2.31), the dr ive laser system

must deliver on the order of 200 J (~1015 photons) of light with a photon energy

greater than the w ork function of the copp er photo-cathod e (4.65 eV or 266 nm)

within a pu lse of a few p icoseconds.

3.2.1.1 The PBPL Drive Laser System

The laser system w hich m eets all the requirements d escribed in the p revious

section is show n in Figure 3.2. A Nd:YAG laser p rod uces a train of 80 ps (FWHM)

pulses at 1064 nm with a repetition frequency of 76.16 MHz. These pulses are

coup led into a 500 m single mode fiber w ith a 8 m d iameter core. Although the

Nd:YAG produces 25 Watts of average power, only enough to produce the

app ropr iate chirp (time-wavelength correlation) on the emergent p ulses is coup led

into the fiber, typically 1.2 Watts. Individual chirped pulses are switched into a

Nd :glass regenerative amplifier (Regen) at a rate of 5 Hz. The Nd :glass supp orts

the larger bandwidth of the chirped pulses which have been lengthened in the

fiber by group velocity dispersion. The Regen amp lifies the ind ividu al pu lses to

an energy of 5 mJ/ pu lse. The amp lified p ulses are then p assed twice throu gh a

pair of diffraction gratings to compress the chirped pulse down to 3 ps FWHM

(measured a t the scanning autocorrelator). The high intensity 1064 nm (IR) pu lses

30

are sent through a set of KD*P frequencydoubling crystals, bringing the

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P

hotodiode

E

nergyMonitor

Grating

Pair

CoherentAntaresYAG

Oscillator

Fast

Photodiode

2x

4x

ToPhotocathode

ContinuumN

d:Glass

RegenerativeAmplifier

500m

Fiber

KD*PCrystals

Autocorrelator

1/4Meter

Spectrom

eter

Figure 3.2: The PBPL drive laser system produces the roughly 200 J of UV laser

light ,in pulses a few ps wide at a rep rate of 5 Hz, necessary for generating the

32

beam from the copper p hotocathode in th e RF gun..

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is measured at many locations along the beamline with phosphor screens. The

emittance of the space charge dominated beam is measured using slits [58] [59]

[60] (a one dimensional pepper-pot) at full charge not possible using the

quadrupole scanning techniqu e (see Table 3.2).

3.2.1.5 Magnetic Optics

In addition to the focusing solenoid and bucking coil around the gun,

there are also several quadrupole magnets along the beamline. The quadrupoles

adjust the electron beam size and angle at the entrance of the un du lator to provide

the p roper matching cond ition (see Equations 2.3 and 2.4). Although four m agnets

are in principal sufficient for adjusting the four parameters (x, px , y, py) into the

undulator, simulations using the code TRACE3D [61] found an easier and more

robust control wh en using a dou blet and trip let as shown in Figure 3.1.

3.3 TH E ELECTRO N BEAM

The same w ealth of diagnostics w hich were necessary to characterize and

commission the accelerator were necessary for the SASE-FEL experiment. The

performance of the FEL is critically dependent on nearly every aspect of the

electron beam; spot size and emittan ce (see Equations 2.18 and 2.19), energy (see

Equation 2.1), energy spread (see Equation 2.31) and peak current (see Equation

2.18).

3.3.1 Spot Size

Phosphor screens measure the electron beam spot size. The screens are

34

created by precipitating a layer of phosphor Gd 2O 2S:Tb onto a thin piece of

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stainless steel typically one inch square [62]. When the electron beam imp acts the

phosphor, the screen fluoresces then decays on a time scale short compared to

the interbunch spacing [48]. The light is collected by a camera, digitized by a

computer and fit to a distribution to obtain the spot size. By comparing the

measured spot size to the corresponding size of a known fiducial mark on the

surface of the ph osphor, an absolute size of the electron beam can be d etermined.

The high accelerating fields on the cathode result in a continuous stream

of electrons leaving the gun during the majority of the RF pulse. Since these

electrons are being emitted in the absence of a laser p ulse, they are referred to as

dark current. Imp erfections or damage to the su rface of the cathode, i.e. areas

that are not smooth, give rise to sharp gradients in electric potential and thus

localized h igh p eak electric fields. These localized areas of large electric field em it

large amounts of dark current which can obscure the photoelectrons and make

characterization of the electron beam difficult.

The Brookhaven gun used for this experiment suffered laser damage to

the cathode region of the fixed backplane prior to its installation at UCLA. The

backplane of the gun showing the damaged region (prior to installation) is show n

in Figure 3.3. The damaged region shown in Figure 3.3 emits large amounts of

dark current, which at charges in the photoelectron bunch of < 2 nC, obscures a

portion or all of the photoelectrons on the phosphors. At low charge, where the

signal from th e dark current is comp arable to the signal from th e ph otoelectrons,

the dark curren t backgroun d can prod uce erroneously large measured spot sizes.

In fact, the large transverse spot size at phosphor screen 8 (PS 8) in Figure 3.4 is

probably an ar tifact of a poor signal to noise ratio.

35

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0.2

0.4

0.6

0.8

1

1.2

1.4

1.61.8

0.3 0.4 0.5 0.6 0.7 0.8

Average PS8

Average PS9

SpotSize(sigma)[mm]

ICT [pC]

Before Undulator Entrance

After Undulator Exit

Figure 3.4: PBPL electron beam spot size versus charge at the phosphor screens

before (PS8) and a fter (PS9) the undu lator.

Figure 3.5: Composite image of dark current an d photoelectron beams at p hosphor

screens 8 (PS8) and 9 (PS9), before and after the undulator respectively. At PS8,

the p hotoelectrons are difficult to d istinguish against the d ark current background .

At PS 9 (after the und ulator) the .dark curr ent is all but gone and the ph otoelectrons

are clearly visible. The large dark current background makes the spot size

37

measu remen ts inFigu re 3.4 difficult.

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3.3.2 Emittance

The Equation governing the transverse size of an electron beam of given

normalized em ittance (n ) and p eak current I, and in a focusing channel with k

is given by

=n

2

23+

2I

3IA k

2 . 3.1

Of the three terms on the right hand side (emittance, space charge, and focussing

respectively), the space charge term is of the same order or greater than the

emittan ce term for the high brightn ess beams need ed for SASE-FELs (see App end ix

A and B). Thus, to measure the beam emittance using the traditional quadrupole

scan method requires lowering the charge (and thus the peak current) to levels

uninteresting for the FEL and extrapolating upwards by making assumptions

about the effects of the space charge forces on the measurement [63]. The PBPL

undulator allows no side access to measure the electron beam size inside the

un du lator. For the small spot sizes inside th e focusing chann el of the und ulator,

the ratio of the space charge term to the emittance term is of the order of 25%, so

we m ay estimate the beam d ensity within the und ulator based on the measured

emittance. Given that the FEL performance depend s on the beam density, having

an accurate estimate of the emittance is pa ram oun t (see Equation 3.1).

To avoid the inherent uncertainties associated with the quadrupole scan

techniqu e, the emittance of the PBPL beam w as measured using a set of extremely

thin slits [59] [60] [61]. The slits break th e beam up into m any ind ividu al beamlets

with low enough individual charge that the space charge term in the envelope

equation can be neglected. By propagating the beamlets a known distance to a

phosphor screen, measuring their centroid p osition (x ) and subsequent translation

38

and growth in size (du e to x ), it is possible to work backward s and calculate the

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emittan ce of each beamlet directly:

rmsx x2 x 2 x x 2 3.2

where x is one transverse dimension and x is the particle divergence. The

emittance of the w hole beam is a ph ase space sum of the individual beamlets. A

schematic of the slit based emittance measu rement system is show n in Figure 3.6.

Figure 3.6: The PBPL slit based emittance measurement system. The beam is

broken up into a series of individual beamlets in which the emittance term of the

envelope equation is the dominant effect. The image of the beamlets is analyzed

to determine the peak p ositions and w idths. Based on the kn own geometry of the

slits that created the beamlets and the distance propagated to the phosphor, the

ph ase space area is calculated.

Because the slits in the PBPL system could not be rotated, there is an

inherent assumption that the beam emittance is the same in both planes. The

39

measured emittance as a function of charge is shown in Figure 3.7.

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7

8

9

1 0

1 1

1 2

1 3

1 4

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Emittance(norm.rms)[mm-mra

d]

Charge [nC]

Emittance = [7.12+(14*Q) 2]1 / 2

Figure 3.7: Normalized emittance of the PBPL electron beam versus charge as

measured in the horizontal transverse plane with the emittance slits. The data arefit to the expected form corresponding to a charge independent term adding in

squares w ith another term growing linearly w ith charge. The horizontal bars are

the width of the charge bins used to compute the mean (data point) and spread

(vertical bar).

3.3.3 Energy an d Energy Sp read

Electrons w ithin a m icropu lse are created by a laser pu lse that has a finite

pu lse length, . Because the fields in the accelerating cavity are oscillating w ith aperiod T=

1

fRF, electrons created at the cathode experience an overall variance in

electric field given by

40

EaccEacc

fRF 3.3

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Tab le 3.1: Characteristics of the PBPL dipole spectrometer used for measuring

the beam energy and energy spread. The energy spread is used to calculate the

electron beam bunch length.

Parameter Value

Design rad ius of curvatu re 67 cm

Bend angle 45

Physical pa th length 52 cm

Effective path length 57 cm

Maximum available field 0.14 T

Average field excitation 0.014 T/ Amp

Resolution - Energy ~ 0.1%

Resolution - Energy Spread ~0.01%

Using the spectrometer d escribed in Table 3.1, the mean energy was measured to

be 13.5 MeV. The measured energy spread grows as the sum of a charge ind epend ant

term an d another term growing linearly w ith charge [5052] The d ata are fit to a

function of this form and p lotted in Figure 3.8.

42

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0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.1 0.2 0.3 0.4 0.5 0.6UncorrelatedEnergySpread[%

]

Charge [nC]

E/E = 0.272 + (0.44*Q)2

Figure 3.8: Measured uncorrelated energy spread versus charge for the PBPL

electron beam. The horizontal bars are the width of the charge bins used tocompute the m ean (data point) and spread (vertical bar). The pu lse length grows

linearly with charge, and the energy spread scales as the pulse length squared,

therefor the energy spread data are fit corresponding to a charge independent

term ad ding linearly w ith another term grow ing quad ratically w ith charge.

3.3.4 Pulse Length and Peak Cu rrent

The charge was measured non-destructively via an Integrating Current

Transformer (ICT) [57]. The energy spread given by Equation 3.3 does not take

into account the fact that the accelerating fields in the cavity have a sinusoidal

dependence. By creating the electrons near a crest ( =2

) of the accelerating

field, for durations short compared to the RF period, the contributions to the

43

energy sp read from finite pulse length effects are, to first ord er, negligible. However,

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the electron beam bun ch length (b ), and thus the peak current (IQ

2b), can

still be inferred from the measured energy spread

EE

12

2bRF

2

. 3.6

Based on Equation 3.6 and Figure 3.8, we can estimate th e peak current as a

function of charge:

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

0.1 0.2 0.3 0.4 0.5 0.6

P

eakCurrent[A]

Charge [nC]

I = Q*1000/[5.12+(8.1*Q)2]1 / 2

Figure 3.9: Peak current as a function of charge, calculated from the measured

uncorrelated energy spread . The bun ch length w ith a term grow ing linearly with

charge , causes the pulse length to increase, and thus the peak current to roll offwith increasing charge. The horizontal bins are the size of the charge bin used to

compute the mean (point) and standard deviation (vertical bar).

A summary of the measured electron beam parameters for the PBPL linac is

given in Table 3.2.

44

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Figu re 3.10: An internal crosssection of the PBPL undulator. The markers refer

to 1) VanadiumPermandur Cshaped yokes, 2) NeodyniumIronBoron pole

tip magnets, 3) SamariumCobalt booster magnets, 4) Halldetectors support

plate, 5) Translation stage for supp ort plate.

The undulator was characterized using Hall Probes and the pulsed wire

technique [67] and was found to have excellent field uniformity. The main

characteristics are listed in Table 3.3. The PBPL/ Kurchatov un dulator h as a peak

field deviation of 0.25% corresponding to an RMS error of ~0.04%. Measured

errors in the second integral of the magnetic field ind icate the resulting d eviations

in the electron beam trajectory are less that one w iggle amplitud e of ~72 m, so

46

we can neglect und ulator field errors in the analysis.

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Tab le 3.3: The characteristics of the UCLAKIAE Und ulator.

Parameter Value

Period u 1.5 cm

Total length Lu 60 cm

Fixed Gap g 5 mm

Pole tip field Bu 7.5 kG

Undu lator Parameter K 1.05

Focusing 12 cm

Beam pipe ID 4 mm

The undulator support structure was originally designed to allow adjustment of

the undulator magnetic axis (pitch, yaw, roll) with respect to the mechanical

center of the linac. In order to maintain access to these controls, the undulator

could not be encased in a vacuum box. The electron beam propagates in a thin

non-magnetic vacuum pipe (4 mm inner diameter) that runs down th e mechan ical

center of the undulator. A 70 cm long pipe with sub-millimeter wall thickness

can easily flex on the order of several millimeters over its entire length. Since the

same u nique construction w hich allows for su ch strong on axis fields allows for

no side access to align the pipe it was necessary to align it optically. After

removing the downstream IR-vacuum window, a target of known dimensions

(~4 mm wide) was p laced on the up stream side of the und ulator, and the vacuu m

pipe was aligned until all 4 mm of the target were visible. A target imaged

47

throu gh the u nd ulator vacuum p ipe is shown in Figure 3.11.

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Figu re 3.11: Target of the letters UCLA in 4 point font, imaged from the end of

the beamline through the 4 mm inner d iameter vacuu m p ipe of the PBPL und ulator.

The visibility of all four letters indicates the beam pipe inside the undulator is

prop erly aligned.

3.5 IR DIAG NOSTIC BEAMLINE

The PBPL Infrared (IR) diagnostic beamline is responsible for propagating

the FEL output radiation to the appropriate diagnostics, determining the

wavelength of the FEL, selecting the coherent fraction of the radiation, and

determining the contributions to the detector signal from background s and detector

48

noise. The layou t of the IR diagn ostic beamline is show n in Figure 3.12.

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Liquid He Cooled Ge:Cu Detector

Focussing IR Mirror

(f~0.3m)Amplifier

Scope

Lead Shielding

Faraday Cup Beam Dump

IR Block

Focussing IR Mirror(f~1m)

Iris

CaF2 filter

Figu re 3.12: The PBPL IR diagnostic beamline showing all of the components

necessary for transporting the FEL output from the exit of the beamline to the

Cu:Ge detector. An iris used to quantify contributions from outside the coherent

solid angle is shown along with the filter materials used to determine the

contributions from higher h armonics or CSE at a w avelength on th e order of theelectron beam bunch length..

3.5.1 IR Tran sport Line

Since the PBPL accelerator was experimental in nature, the final electron

beam energy (and thus the FEL wavelength) was not known until immediately

before the experiment. This uncertainty, as well as the stock of equipment on