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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
x
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
1
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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.
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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